IELD CURVES AND INTEREST FORECASTS - Madison · Yield Curves and Interest Forecasts. ... Fed sold T -bills from its portfolio. ... “subsidiaries” Maiden Lane II and III to purchase,
38
Lecture Materials TOPIC 3: YIELD CURVES AND INTEREST FORECASTS ECONOMICS, MONEY MARKETS AND BANKING James M. Johannes Interim Associate Dean for Executive and Evening MBA Programs Aschenbrener Chair of Banking & Finance Graduate School of Banking-Prochnow Professor of Banking Director, Puelicher Center for Banking Education Director, Officer Education Program University of Wisconsin-Madison Madison, Wisconsin [email protected]608-265-2323 August 2-5, 2016
James M Johannes Interim Associate Dean for Executive and Evening MBA Programs
Aschenbrener Chair of Banking amp Finance Graduate School of Banking-Prochnow Professor of Banking
Director Puelicher Center for Banking Education Director Officer Education Program
University of Wisconsin-Madison Madison Wisconsin
jjohannesbuswiscedu 608-265-2323
August 2-5 2016
Topic 3
Yield Curves and Interest Forecasts
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Topic 3
Yield Curves and Interest Forecasts
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Chart1
Maturity (years)
Interest Rate
Government Yield Curve
2
3
4
5
6
7
8
9
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
1
2
3
4
5
6
7
8
Sheet1
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
Sheet2
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Sheet3
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Chart1
Forward Rate - Actual Rate
00140273751
00000020816
00065300388
00163140265
0017161465
00136189731
00082271281
00066057817
002337434
00111413793
00094226916
00027011479
00071090515
00182610665
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
061976
00150397834
00142374434
00150317838
00117218389
00144256815
00058228906
00104353405
00121364464
00124329953
00064256449
00086158825
0005210293
00023102794
00032054151
-00007969586
00030018323
00037033754
00012045251
00036041107
00049049283
00040067934
00021078269
00011033482
061978
00028009226
-00020996676
-0006399549
-00144922943
-00146683574
-00126695014
-00092726021
-00104754717
-00078808073
-00067895024
-00012895024
-00076888199
-00133771981
-00189754137
-00315451101
-0018419735
-00074700685
-00125689141
-0029772015
-00289780548
00064762908
00231564872
00135003291
061980
-00082867096
-00069923712
-00086997758
-00245857765
-00200641174
-00079442897
-00212410589
-0004363123
-00088982763
-0022197472
-00013528744
-00155893348
-00173881697
-00067834133
0010200309
00329022188
00050196513
-00058828445
00009054671
0009600706
00045050548
00108042464
00015170813
061982
00293276934
0023671085
00339780244
00190692371
00153375229
00179516481
00112464095
00132475946
00130352531
00126319416
00042319651
0005024658
00065217877
0014526382
00161360294
00139525999
0012747153
00167483971
00134498271
00095511178
00113468758
00082562759
00120587587
061984
00191644917
00146332767
00192344506
00248441839
00215627299
00201660843
00155759585
00119708574
00242657655
0025882692
00252797437
00172734787
00163767754
00176733087
00188766263
0018366892
00161454208
00090213987
00094156038
00130120435
00095030272
0003106351
00076165401
061986
0011415056
00096151043
00121318049
00104296633
00089217769
00089151129
00072191435
0008118271
0003114345
00054253897
00172539813
0016655515
00117541432
0008048435
00142416922
00225609815
00125498224
00156444247
0016338284
00101273443
00082293881
00077314363
00111335196
061988
00064260696
00100195618
00072126654
00011053279
-00012966722
00014009175
00006015497
-00007986819
00043011043
00056007407
00062001468
0004900083
-00042995458
-00011998521
00035003327
00020000093
00011000835
-00007996658
00015026779
00028062529
00051072358
00072094465
00086094535
061990
0006004484
00058072741
00085095026
00090101255
00084078371
00093063148
0013522515
0010733876
00156460526
00153474492
00107398097
00125338473
00175350014
00151399414
00146352468
00160319377
00185427972
00153404771
00148629957
00150811583
00246073879
00220037009
00211038103
061992
00165557529
00173501015
00130488564
00118588964
0017778125
00213888632
00189765314
00148487571
00133372012
00108348702
00106371904
00131371257
00123347927
00120303171
00095232295
00077222846
00113324773
00127347457
00087347692
00075346587
00086443252
00097508395
00136413636
061994
0012240055
00104364153
00091375284
00081362266
00062349258
00099189005
00127197665
00109157545
00086115099
0008708469
00070027264
00021006058
00022034189
00059050024
00041034179
00038011459
00022002371
00024000095
00019000381
-00021992281
00044097209
0007416714
00075200303
061996
00102166651
00056122646
00108151186
00085122785
00051074369
00048091116
00088151501
00047129726
0006516673
00104199641
0010015878
00095151386
0006811607
00080136794
0007812282
00062091125
00043059264
00067034208
00017013683
0001401149
00035027422
00030030746
00033021339
061998
00035009491
00062003422
00051001528
-00046999136
00003000096
-00000999904
00003011578
00028030946
00063069574
00042080332
00055152599
00111257279
0008725745
00091219011
00064159715
00074175377
00033091047
0002406387
00054096495
00078143193
00069090473
00032058879
00112216684
062000
00042063725
00015002354
00002002356
-00027990567
00007041568
00029059186
00003002385
00034000382
00040001534
00070060108
00116222008
00096241359
00099170237
0012308128
00109087532
00095156357
00116352319
00184774897
00167740897
00124610486
00207955543
00201862217
00197809086
062002
0014035308
00078134532
00063077074
00068066503
00090182185
00087149926
00082142463
00072107502
00063107566
Sheet2
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
1 yr T- notes - mat constants
2yr T- notes - mat constants
Source
httpwwwfederalreservegovreleasesh15datamtcm2ytxt
Date
Rate
Date
Rate
Implied one year forward rate
Forecast error
061976
652
061976
706
1076
62
071976
685
1075
14
6
081976
663
1073
15
584
091976
642
1070
14
55
101976
598
1065
15
529
111976
581
1063
12
489
121976
538
1059
14
529
011977
59
1065
06
547
021977
609
1067
10
55
031977
609
1067
12
544
041977
596
1065
12
584
051977
625
1067
06
58
061977
613
1065
09
594
071977
627
1066
05
637
081977
661
1069
02
653
091977
671
1069
03
697
101977
711
1073
-01
695
111977
714
1073
03
696
121977
718
1074
04
728
011978
749
1077
01
734
021978
757
1078
04
731
031978
758
1079
05
745
041978
774
1080
04
782
051978
801
1082
02
061978
809
061978
824
1084
01
839
071978
849
1086
00
831
081978
837
1084
03
864
091978
857
1085
-02
914
101978
885
1086
-06
1001
111978
942
1088
-14
103
121978
972
1091
-15
1041
011979
986
1093
-13
1024
021979
972
1092
-09
1025
031979
979
1093
-10
1012
041979
978
1094
-08
1012
051979
978
1094
-07
957
061979
922
1089
-01
964
071979
914
1086
-08
998
081979
946
1089
-13
1084
091979
1006
1093
-19
1244
101979
1149
1105
-32
1239
111979
1181
1112
-18
1198
121979
1139
1108
-07
1206
011980
115
1109
-13
1392
021980
1342
1129
-30
1582
031980
1488
1139
-29
133
041980
125
1117
06
939
051980
945
1095
23
061980
816
061980
873
1093
14
865
071980
903
1094
07
1024
081980
1053
1108
-08
1152
091980
1157
1116
-07
1249
101980
1209
1117
-09
1415
111980
1351
1129
-25
1488
121980
1408
1133
-20
1408
011981
1326
1124
-08
1457
021981
1392
1133
-21
1371
031981
1357
1134
-04
1432
041981
1415
1140
-09
162
051981
1546
1147
-22
1486
061981
1451
1142
-01
1572
071981
1535
1150
-16
1672
081981
1628
1158
-17
1652
091981
1646
1164
-07
1538
101981
1554
1157
10
1241
111981
1288
1134
33
1285
121981
1329
1137
05
1432
011982
1457
1148
-06
1473
021982
1482
1149
01
1395
031982
1419
1144
10
1398
041982
142
1144
05
1334
051982
1378
1142
11
061982
1407
061982
1447
1149
02
1324
071982
138
1144
16
1143
081982
1232
1132
29
1085
091982
1178
1127
24
932
101982
1019
1111
34
916
111982
98
1104
19
891
121982
966
1104
15
862
011983
933
1100
18
892
021983
964
1104
11
904
031983
966
1103
13
898
041983
957
1102
13
89
051983
949
1101
13
966
061983
1018
1107
04
102
071983
1069
1112
05
1053
081983
1107
1116
07
1016
091983
1079
1114
15
981
101983
1057
1113
16
994
111983
1066
1114
14
1011
121983
1084
1116
13
99
011984
1064
1114
17
1004
021984
1079
1115
13
1059
031984
1131
1120
10
109
041984
1169
1125
11
1166
051984
1247
1133
08
061984
1208
061984
1291
1137
12
1203
071984
1288
1137
17
1182
081984
1243
1130
19
1158
091984
122
1128
15
109
101984
116
1123
19
982
111984
1065
1115
25
933
121984
1018
1110
22
902
011985
993
1108
20
929
021985
1017
1111
16
986
031985
1071
1116
12
914
041985
1009
1110
24
846
051985
939
1103
26
78
061985
869
1096
25
786
071985
877
1097
17
805
081985
894
1098
16
807
091985
898
1099
18
801
101985
886
1097
19
788
111985
858
1093
18
767
121985
815
1086
16
773
011986
814
1086
09
761
021986
797
1083
09
703
031986
721
1074
13
644
041986
67
1070
10
665
051986
707
1075
03
061986
673
061986
718
1076
08
627
071986
667
1071
14
593
081986
633
1067
11
577
091986
635
1069
10
572
101986
628
1068
12
58
111986
628
1068
10
587
121986
627
1067
09
578
011987
623
1067
09
596
021987
64
1068
07
603
031987
642
1068
08
65
041987
702
1075
03
7
051987
776
1085
05
68
061987
757
1083
17
668
071987
744
1082
17
703
081987
775
1085
12
767
091987
834
1090
08
759
101987
84
1092
14
696
111987
769
1084
23
717
121987
786
1086
13
699
011988
763
1083
16
664
021988
718
1077
16
671
031988
727
1078
10
701
041988
759
1082
08
74
051988
8
1086
08
061988
749
061988
803
1086
11
775
071988
828
1088
08
817
081988
863
1091
06
809
091988
846
1088
10
811
101988
835
1086
07
848
111988
867
1089
01
899
121988
909
1092
-01
905
011989
918
1093
01
925
021989
937
1095
01
957
031989
968
1098
-01
936
041989
945
1095
04
898
051989
902
1091
06
844
061989
841
1084
06
789
071989
782
1078
05
818
081989
814
1081
-04
822
091989
828
1083
-01
799
101989
798
1080
04
777
111989
78
1078
02
772
121989
778
1078
01
792
011990
809
1083
-01
811
021990
837
1086
02
835
031990
863
1089
03
84
041990
872
1090
05
832
051990
864
1090
07
061990
81
061990
835
1086
09
794
071990
816
1084
07
778
081990
806
1083
06
776
091990
808
1084
06
755
101990
788
1082
09
731
111990
76
1079
09
705
121990
731
1076
08
664
011991
713
1076
09
627
021991
687
1075
14
64
031991
71
1078
11
624
041991
695
1077
16
613
051991
678
1074
15
636
061991
696
1076
11
631
071991
692
1075
13
578
081991
643
1071
18
557
091991
618
1068
15
533
101991
591
1065
15
489
111991
556
1062
16
438
121991
503
1057
19
415
011992
496
1058
15
429
021992
521
1061
15
463
031992
569
1068
15
43
041992
534
1064
25
419
051992
523
1063
22
061992
417
061992
505
1059
21
36
071992
436
1051
23
347
081992
419
1049
17
318
091992
389
1046
17
33
101992
408
1049
13
368
111992
458
1055
12
371
121992
467
1056
18
35
011993
439
1053
21
339
021993
41
1048
19
333
031993
395
1046
15
324
041993
384
1044
13
336
051993
398
1046
11
354
061993
416
1048
11
347
071993
407
1047
13
344
081993
4
1046
12
336
091993
385
1043
12
339
101993
387
1044
10
358
111993
416
1047
08
361
121993
421
1048
11
354
011994
414
1047
13
387
021994
447
1051
09
432
031994
5
1057
08
482
041994
555
1063
09
531
051994
597
1066
10
061994
527
061994
593
1066
14
548
071994
613
1068
11
556
081994
618
1068
12
576
091994
639
1070
10
611
101994
673
1074
09
654
111994
715
1078
08
714
121994
759
1080
06
705
011995
751
1080
10
67
021995
711
1075
13
643
031995
678
1071
11
627
041995
657
1069
09
6
051995
617
1063
09
564
061995
572
1058
07
559
071995
578
1060
02
575
081995
598
1062
02
562
091995
581
1060
06
559
101995
57
1058
04
543
111995
548
1055
04
531
121995
532
1053
02
509
011996
511
1051
02
494
021996
503
1051
02
534
031996
566
1060
-02
554
041996
596
1064
04
564
051996
61
1066
07
061996
581
061996
63
1068
08
585
071996
627
1067
09
567
081996
603
1064
10
583
091996
623
1066
06
555
101996
591
1063
11
542
111996
57
1060
09
547
121996
578
1061
05
561
011997
601
1064
05
553
021997
59
1063
09
58
031997
622
1066
05
599
041997
645
1069
07
587
051997
628
1067
10
569
061997
609
1065
10
554
071997
589
1062
10
556
081997
594
1063
07
552
091997
588
1062
08
546
101997
577
1061
08
546
111997
571
1060
06
553
121997
572
1059
04
524
011998
536
1055
07
531
021998
542
1055
02
539
031998
556
1057
01
538
041998
556
1057
04
544
051998
559
1057
03
061998
541
061998
552
1056
03
536
071998
546
1056
03
521
081998
527
1053
04
471
091998
467
1046
06
412
101998
409
1041
05
453
111998
454
1046
-05
452
121998
451
1045
00
451
011999
462
1047
-00
47
021999
488
1051
00
478
031999
505
1053
03
469
041999
498
1053
06
485
051999
525
1057
04
51
061999
562
1061
06
503
071999
555
1061
11
52
081999
568
1062
09
525
091999
566
1061
09
543
101999
586
1063
06
555
111999
586
1062
07
584
121999
61
1064
03
612
012000
644
1068
02
622
022000
661
1070
05
622
032000
653
1068
08
615
042000
64
1067
07
633
052000
681
1073
03
062000
617
062000
648
1068
11
608
072000
634
1066
07
618
082000
623
1063
04
613
092000
608
1060
02
601
102000
591
1058
00
609
112000
588
1057
-03
56
122000
535
1051
01
481
012001
476
1047
03
468
022001
466
1046
00
43
032001
434
1044
03
398
042001
423
1045
04
378
052001
426
1047
07
358
062001
408
1046
12
362
072001
404
1045
10
347
082001
376
1041
10
282
092001
312
1034
12
233
102001
273
1031
11
218
112001
278
1034
10
222
122001
311
1040
12
216
012002
303
1039
18
223
022002
302
1038
17
257
032002
356
1046
12
248
042002
342
1044
21
235
052002
326
1042
20
062002
22
062002
299
1038
20
196
072002
256
1032
18
176
082002
213
1025
14
172
092002
2
1023
08
165
102002
191
1022
06
149
112002
192
1024
07
145
122002
184
1022
09
136
012003
174
1021
09
13
022003
163
1020
08
124
032003
157
1019
07
042003
127
042003
162
1020
06
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
Slide Number 20
Slide Number 21
Slide Number 22
Slide Number 23
Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
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Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
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Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
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Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
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Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
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Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13
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Slide Number 24
Slide Number 25
Slide Number 26
Slide Number 27
Slide Number 28
Slide Number 29
Slide Number 30
Slide Number 31
Slide Number 32
Slide Number 33
Slide Number 34
Slide Number 35
GAP Management
Slide Number 37
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
