sapm final (3)
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SAPMTHERE'S NO SUCH THING AS A SURE
THING, EVEN IN THE BOND WORLD
Prepared By:DEVESHREE RAUT
DEBJANI SINGHA
JAGRUTI CHAUHAN
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EXAMPLE
5 Year Bond, Coupon Rate5%, FV Rs. 1000
1st Year 2nd Year 3rd Year 4th year 5thyear
(Interest) (Interest) (Interest) (Interest)
(Interest + Face Value)
Howtocalculate Duration:
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FACTORS AFFECTING BOND
DURATION1). TIME TOMATURITY:Consider 2 Bonds
A B
Face Value 1000 1000Interest Rate 5% 5%
Maturity 1 year10 year
Therefore, everyone would prefer BondA as itwillrepayits true cost quicklythan Bond B.
Hence, shorter duration maturity bond
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FACTORS AFFECTING BOND
DURATION
2).COUPON RATE
A Bonds paymentis the key factorin
calculating duration. Bonds withhigher
couponwillpaybackits originalcost
quickerthanthe loweryielding bonds.
Therefore, higher the coupon, the
lowerwill be the duration.
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UNDERSTANDING BOND DURATION
You may think a 30 year treasury is your
safest investment, but if you dont
understand the dynamics of Bond
duration you could be taking a big risk.
ONE RISK IN BOND MARKET= Interest Rate
Riskwhich is easy to determine through
the concept ofMODIFIEDDURATION.(1966, LarryFisher)
It is defined as the percentage change in
price for a 100 basis point change in
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MODIFIED DURATION
Itis the modified versionof theMacaulay Modelthataccounts forchange ininterestrates.
Fluctuatinginterestrates willaffect duration.
MODIFIED DURATIONFORMULA
MD = Macaulay Duration1 + YTM
no.of couponperyear
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EXAMPLE OFMACAULAY AND MODIFIED
Bettyhold a5year bond withaparvalue of 1000 and couponrate 5%.(Macaulay Duration).
Solution
1(50/1250)+2(50/1250)+3(50/1250)+4(50/1250)+5(50/1250)+5(1000/1250)= 4.6
years.
Continue with same Eg for ModifiedDuration.
Md=(4.55/ (1+0.05/1))= 4.33.
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EXAMPLE
2 bonds with similar maturity butwith differentcouponrates and
cash flowpatterns willhave
different duration.
1st Bond =5year maturity, 8.5%rate
,1000 face value , YTM=10%
2nd Bond =5year maturity,11.5%
rate,1000FV, YTM=10.6%.
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Duration of 8.5% Bond
YEAR CASH FLOW PV @ 10% BOND PRICE
PROPORTION
BOND
PRICE* TIME
1 85 77.27 0.082 0.082
2 85 70.25 0.074 0.149
3 85 63.86 0.068 0.203
4 85 58.06 0.062 0.246
5 1085 673.70 0.0714 3.572
943.14 1.000 4.252
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Duration of 11.5%Bond
YEAR CASH FLOW PV @ 10.6% BONDPRICE
PROPORTION
BOND
PRICE* TIME
1 115 103.98 0.101 0.101
2 115 94.01 0.091 0.182
3 115 85.00 0.082 0.247
4 115 76.86 0.074 0.297
5 1115 673.75 0.652 3.259
1033.60 1.0000 4.086
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COMPARISION OFBOTH THEBONDS
Durationof 1
st
bond=4.25
2 years Durationof 2nd bond=4.086years
Now, if we calculate the volatilityof boththe
bonds i.e. Modified Duration
Volatilityof 8.5% bond = 4.252/(1.100)= 3.87
Volatilityof 11.5% bond= 4.086/(1.106)= 3.69
Whichindicates that 8.5% bond has highervolatility.
If YTMincrease by 1%, this willresultin 3.87%
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PRESENT VALUE(IN RUPEES)
DISCOUNT RATE(In%)
5 YEAR BOND 10YEAR BOND PERPETUALBOND
5 1216 1386 2000
10 1000 1000 1000
15 832 749 667
20 701 581 500
25 597 464 400
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WHATCOULDBE THE REASON?
The reason forthis differential
responsiveness is not difficultto
understand.
Incase of 10 year bond, one would
get just Rs.100 evenif interestrate
rises to say 15percent.Incase of 5
year bond, one canatleast sellthe
bond after5years and reinvest
moneytoreceive Rs.150 forthe next
five years.
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WHAT IS PORTFOLIO DURATION?
A portfolio's durationis equal
tothe weighted average of
the durations of the bonds in
the portfolio. The weightis
proportionaltohow muchofthe portfolioconsists of a
certain bond.
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EXAMPLEPortfolio Duration =w1D1 + w2D2 ...+ wkDk
Let's take 3 bonds:
6,000 market value of ABC ltd 7%of 10 with durationof
5.5
3,400 market value of XYZ 5%or 15with durationof 7.8
1,535,market value of CDS 9%or 20 with durationof 12
Total market valve of 10,935.
Solution:
Firstlet's find the weighted average of each bond:
ABC LTDweighted average is 6,000/ 10,935=.548
XYZ LTDweighted average is 3,400 / 10,935 =.311
CDS LTDweighted average is 1,535/ 10935, =.14
Sothe PortfolioDuration =.548(5.5) + .311(7.8) + .14 (12)=
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LIMITATION OFTHE PORTFOLIO
DURATION ME
ASURE
Eachof the bonds inthe
portfolio mustchange bythe100 or50bps, orthere must be
aparallel shiftinthe yield
curve forthe durationmeasure to be useful.
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EFFECTIVE DURATION
The modified duration formula discussed aboveassumes thatthe expected cash flows willremainconstant, evenif prevailinginterestrates change; this is alsothe case foroptionfree fixedincome securities.
Onthe otherhand, cash flows from securitieswith embedded options orredemption featureswillchange wheninterestrates change.
Forcalculatingthe durationof these types ofbonds, Effective Durationis the mostappropriate.
EG CALLABLE BONDS.
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WHAT ISCONVEXITY?
Why durationis inaccurate in measuringthe effectofyield changes onprice?
Durationand YTMare inverselyrelated.
As yields rise, duration falls. Thus, the nextyield
increase has less of anegative effectonprice since
durationis lower.
As yields fall, durationrises. Thus, the nextyield
decline has more of apositive effectonprice sincedurationis higher.
Usingthe duration method tocalculate the new
price of a bond followingayield change negative
orpositive will, therefore, be inaccurate (and
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The more Convex a Bond, the
more attractive. Bond A has a higher convexity than Bond B,
which means that all else being equal,Bond A
will always have a higherprice than Bond B as
interest rates rise or fall.
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WHAT IS NEGATIVECONVEXITY?
Foranoncallable bond, there is aninverserelationship between durationand yield.
Negative convexity means thatas marketyieldsdecrease, duration decreases as well.
Since this is anunfavorable characteristicof a bond,investors demand ahigheryield.
Negativelyconvex bonds (suchas callable corporate
and mortgages)thus yield more thanotherwiseequivalentnoncallable, orpositivelyconvex, bonds.
Investors expecting stabilityinyields are attractedto such bonds.
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THANK YOU
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