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8/13/2019 CC-Fixed Income

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Crash Course forFixed Income

CFA Level-I Exam

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Fixed Income



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Debt Investment

Basics of BondBonds & RiskManagement

Advanced Features ofBonds

Bond Pricing

Basic Features ofBond Structures

Basics of FloatingRate Bonds

Repayment / Pre-payment Provisions

Yield Calculation

Indenture: Agreement containing the termsunder which money is borrowed.

Par value: Amount borrower promises to payon or before maturity date of the issue

Term to maturity: Length of time until loancontract or agreement expires.

Coupon rate when multiplied by par value,gives amt of interest to be paid each period

Zero-coupon bonds: No interest; bonds aresold at a deep discount to their par values

To derive a bond's valueusing spot rates, discount theindividual cash flows bybenchmark rate for eachflow's time horizon. Sum ofPV of the cash flow is bond'scurrent value. This value isthe arbitrage free value.

Q. Given the following spot rates calculatethe value of 3 year, 6% treasury bond?1 year5% 2 year5.5% 3 year6%Ans.

1046.100

%)61(

106

%)5.51(

6

%51

632



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Debt Investment



Bond Pricing



Yield Calculation

Bullet bonds: Lump sum at maturity, pays entire principal.

Amortizing securities: periodic principal & interest payments.

Serial bonds: Pay- off principal through series of payments overtime.

Sinking fund provisions for bond retirement through pre-definedprincipal payments over life of the issue.

Call provisions: Issuer has right (but not obligation) to retire all orpart of issue prior to maturity. Issuer owns option to call the bondsaway from investor.

Non-refundable bonds prohibit premature retirement of an issuefrom proceeds of a lower coupon bond. Bonds that carry theseprovisions can be freely callable but nonrefundable

Basics of FloatingRate Bonds



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Basics of Floating Rate

Bonds


These securities payvariable rate of interest.Common procedure for

setting coupon rates onfloating rate bonds starts withreference rate; then adds/subtracts a stated spread.

Debt Investment



Bond Pricing Yield Calculation



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Interest Rate Risk

Credit Risk

ReinvestmentRisk

Inverse Relationship b/wInterest Rates & Bond Prices.

Floating Rate Securities havevery low level of price volatility

Longer maturity bonds. Higher interest raterisk (all else same).Smaller coupon bonds. Higher interest raterisk (all else same).If market interest rates are high, pricevolatility will be lower than if market interestrates are low If call/put option is embedded, then interestrate risk will be lower

If coupon rate > required market yieldbond price > par value : premium bondIf coupon rate < required market yieldbond price < par value : discount bondIf coupon rate = required market yieldbond price = par value : par bond

CallPrice

Calloption

value

Option free bond

Price

Yield

Put optionvalue

Callablebond

Putable bond

Sovereign Risk

Event Risk

Debt Investment






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Interest Rate Risk

Credit Risk

Reinvestment Risk

If interest rates decline, investors areforced to reinvest at lower yields. Bonds with high coupons have greaterrisk.Greatest risk is with callable bonds,where all or part of principal can be repaidin low interest rate environment.Zero Coupon Bonds eliminatereinvestment risk

Credit spread risk: credit spread isdifference in bond's yield and yield on

risk-free security. All else equal,riskier the bond, higher the spreadDowngrade risk: Bond may bereclassified as riskier security by amajor rating agency.Default risk: Issuer might not makepayments.

Q. How much reinvestment incomeneeds to be generated to get a CAGR of7% from 6%, 10 year treasury bond?Ans. =100*(1.035)20= 198.98Required reinvestment income =198.98100(3*20) = 38.98

Sovereign RiskEvent Risk

Debt Investment







Interest Rate Risk

Credit Risk

Reinvestment RiskRisks in investing in aforeign bond:Adverse Price Change

Credit Spread RiskDowngrade Risk

DefaultUnwillingness offoreign governmentto payInability to pay dueto unfavorableeconomicconditions

The ability of an issuer to makeinterest and principal paymentchanges drastically and unexpectedly

because of one of the followingfactors:A natural disasterAn industrial accidentA takeoverCorporate restructuringA regulatory change

Sovereign RiskEvent Risk

Debt Investment







Accrued Interest &Clean Prices

Full price/Dirty Price includes accruedinterest. Bond price without accruedinterest is clean price.Full price = Clean price + Accrued interest

Basic Bond Pricing

Treat each cash flow as a single zero-coupon bond & find PV of each bondusing appropriate spot rates for eachcash flow. Prices must be the same toprevent arbitrage.

Discount at constant rate applied to allcash flows (YTM) to find all future cash

flows' PV

Q.What is the market price of a ten year, $1,000bond with a 5% coupon paid annually, if thebondsyield-to-maturity is 6%?Ans.= 50/1.061+ 50/1.062+.+1050/1.0610

= 926.40

Q. If you want to purchase a $1,000 bondwith a 5% coupon, paid semiannually.Today is July 15th. The last coupon waspaid June 30th. If the quoted price is $902,how much is the cash or full priceAns. Cash Price = Quoted Price + AccruedInterest = 902 + (1,000)(0.05)(15/365)

= 902 + 2.05 = $904.05

..

YTM1

CF

YTM1

CF

YTM1

CFpriceMarket

3

3

2

2

1

1

...

S1

CF

S1

CF

S1

CFpriceMarket

3

3

2

21

Using Calculator:Y=6%, T=10, PMT=50, FV=1000CMP PV -> -926.40

Debt Investment







Current yield = annualcoupon payment / bond

priceConverting a bondequivalent yield (BEY) to anequivalent annual yield(EAY) or vice versa:BEY of an annual pay bond

Annual equivalent Yield=(1+(BEY/2))2-1

Q.If a bond has a 5.5% annualpay coupon and the currentmarket price of the bond is

$1,050, the current yield isAns. = 55/1050 = 5.24%

YTM is a IRR based on bond price& its future cash flow

..YTM)(1

CF

YTM)(1

CFPriceBond

2

2

1

1

Forward rate is a lending rate fora future loan(1+S2)

2= (1+S1)*(1+1f1)Q. Calculate the 1yr fwd rate twoyears from now, if S1=4% S2=5%& S3=6%Ans.(1+S3)

3= (1+S2)2*(1+1f2)

1f2 = 8.03%

1YTM1*2 1/2PayAnnual

Nominal Spread

Z-SpreadSolve for ZS where price =

OAS

Option Adjusted Spread = Z-Spread Option Cost

Yield Volatility

When the yield level ishigh, a change in interestrates does not produce alarge change in price.

However, when yields

are low, changes in interestrates produces a largechange in price.

TreasuryBond YTMYTMSpreadNominal

2121

Coupon

ZSrateSpot1yr1

Coupon

ZSrateSpotyr

Debt Investment







Expectations Hypothesis:Yield curve shape reflectsinvestor expectations aboutfuture behavior of short-terminterest rates. Fwd ratescomputed using today's spotrates are best guess of futureinterest rates.

Term Structure Theories

Liquidity PreferenceTheory: Investorsprefer greater liquidityand will demandpremium forilliquidity(higher yieldsto invest in longer-termissues).

Market SegmentationTheory: Market for debtsecurities is segmented onbasis of investors maturitypreference. Each segment'sinterest rate level isdetermined bysupply/demand

Duration & ConvexityOther Duration Measures

Debt Investment







Term Structure TheoriesDuration & Convexity

Convexity is a measure of degree of

curvature or convexity in the price/yieldrelationship. Convexity accounts for amt oferror in estimated price (based on duration)

Duration is the slope of a bond's price-yieldfunction. It is steeper at low interest rates,

flatter at high interest rates. So, duration(interest rate sensitivity) is high at low ratesand low at higher rates, this holds for noncallable bonds.

A callable bond is likely to be called as

yields fall, so no one will pay a pricehigher than the call price. The price won'trise significantly as yield falls & you'll seenegative convexity at work as yields fall,prices rise at a decreasing rate. For apositively convex bond, as yields fall,prices rise at an increasing rateEffective duration (D) =(V--V+)/(2V0(y))

Convexity measures curvature of the price yieldfunction

Note:y is in decimal form

Q. Calculate the new price of a bondcurrently trading at 105.5 having a durationof 7.5, if its yield rises to 6.5% from 6.2%?Ans. % change in price =-0.3%*7.5=-2.25%

= (1 - 2.25%)*105.5 = 103.1263

Modified duration assumes that bond is a noncallable bond, due to which cash flows of the

bond will not change in calculation of duration

YTM1DurationMacaulay

DurationModified

100*])(**[% 2yConvexityyDurationP

Other Duration Measures

Debt Investment







DV01/PVBPIt is the absolute value of the changein the price of a bond for a 1 basispoint change in yield

Term Structure Theories

Dollar DurationThe approximate dollar pricechange for a 100bps changein yield

Duration & Convexity Other Duration Measures

ValueBond*0.01%*DurationPVBP

Debt Investment






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Question 1

A floating rate issue has the following provision in which the coupon rate is calculated

as 6- month LIBOR80 basis points. The issue has a floor at 5.5%. If the 6-monthLIBOR on the reset date is 5.8%, the coupon rate is closest to

A. 4.5%

B. 5.5%

C.5.0%




Answer 1

B.

Coupon rate = ref rate + quoted margin = 5.8% - 80 basis points = 5.0%. Since thefloater has a floor at 5.5%. The coupon is set to 5.5% on the reset date.




Question 2

A buyer of a bond pays the seller $105 2/5 for a at par bond. The bond is cum-coupon.

The full price and the clean price is closest toFull Price Clean Price

A 5 2/5 $100

B 3 3/8 $105

C 2 1/2 $100




Answer 2

A.

The full price = bond price + accrued interest. Since the bond is at par the bond price is$100 (clean price) and the accrued interest is 5 2/5.




Question 3

For a 100 basis points downward shift in the yield curve which of the following bonds

will have the lowest percentage price changeA. An option-free bond

B. A callable bond

C.A putable bond




Answer 3

B.

The value of a callable bond does not rise as much as a comparable option-free bond.Price of a putable bond = price of an option-free bond + price of the embedded put. Sowhen the yield curve is shifted downwards the price of a putable bond will changemore than a comparable option-free bond.




Question 4

Carl and Karen are CFA Level I candidates. Carl says that a zero coupon bond has

higher interest rate risk than a coupon bond of the same maturity. While Karen saysthat a callable bond has higher volatility risk than an option-free bond. Which of the twostatements are most likely correct

Carl Karen

A. No Yes

B Yes No

C. Yes YesThis files has expired at 30-Jun-13



Answer 4

B.

Callable options have lower volatility risk than option-free bond because of theembedded call option in the bond. Zero-coupon bonds have a higher interest rate riskand their prices can change significantly if the yields change.




Question 5

GNB has a portfolio of mortgage loans. These amortizing loans have three distinct

cash flows. Which of the following is least likely to be considered as a cash flow for themortgages

A. Interest payments

B. Servicer costs

C.Scheduled principal payments



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Answer 5

B.

Servicer costs are not one of the cash flows from a mortgage



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Question 6

Sally makes the following statement regarding corporate debts, CPs is a long term

note that can have maturity of up to 15 years or more. In an IAN (Index AmortizingNote) the maturity increases when interest rate increases. Sally is most likely correctregarding

Commercial Papers IAN

A Correct Incorrect

B Incorrect Correct

C Incorrect IncorrectThis files has expired at 30-Jun-13


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Answer 6

B.

CPs is a short term note. Maturity of IANs increases when the rates rise. An IAN issimilar to a CMO and the maturity lengthens as interest rates go up.



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Question 7

Smith is comparing the yields that he gets from investing in two securities. The first one

is a taxable issue A with a yield of 8.75%, the other is a tax-exempt issue B with a yieldof 6.25%. Smith is in the 40% marginal tax bracket. In which of the securities is Smithmost likely to invest

A. Security A; since the yield is higher

B. Security B; since the tax-equivalent yield is higher

C. Both the securities provide the same yield



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Answer 7

B.

Tax-equivalent yield for security B is 6.25 %/( 1-0.4) = 10.42% which is significantlyhigher than the yield for security A.



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Question 8

Carl says that treasury strips offered by his bank are guaranteed by the full faith and

credit of the US Government. He also says that strips provide better yield as comparedto an on-the-run Treasury security of the same maturity. Carl is most likely

A. Correct regarding both the statements

B. Incorrect regarding one of the statements and Correct regarding the other

C. Incorrect regarding both the statements



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Answer 8

A.

Treasury strips are created by stripping securities issued by the US Government,hence they are effectively guaranteed by the full faith and credit of the US government.Since they are zero coupon securities they provide a better relationship between yieldand maturity as compared to a comparable on-the-run Treasury security of the samematurity. Strips do not face any reinvestment risk as they do not pay any coupons.



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Question 9

A callable bond will have a higher yield spread than a comparable putable bond. The

statement is most likelyA. Correct; the call option is favorable to the issuer hence the bond should have a

higher yield

B. Correct; the put option is favorable to the issuer hence the bond can have a loweryield

C. Incorrect; the call option embedded in the bond is favorable to the investor hence

the yield should be lowerThis files has expired at 30-Jun-13


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Answer 9

A.

A call option is favorable to the issuer hence the yield spread relative to a Treasurysecurity should be larger than that of a comparable putable bond.



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Question 10

For an 8% 10-year semi-annual coupon bond the discount rate is 6.5% p.a. The fair

value is closest toA. 110.9

B. 112.9

C.102.9



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Answer 10

A.

For the 10-year 8% semi-annual coupon bond. The cash flows include 20 couponpayments and one principal payment. Using the cash flow function in your calculatorthe NPV= 110.9



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Question 11

For a 7% 3-year semi-annual option-free bond. The Treasury spot rates are

6 month 5.2%

12 month 5.5%

18 month 5.8%

24 month 6.0%

30 month 6.2%36 month 6.5%

The bond is at par. Calculate the no-arbitrage price for the bond. If the market price is$104.5 the BEY is closest to

No-arbitragePrice BEY

A 102.34 5.45%

B 101.48 5.36%

C 104.5 5.25%



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Answer 11

B.

No-arbitrage price is calculated by discounting all the cash flows by the spot ratesCash Flow PV Factor PV of Cash Flow

3.5 0.9747 3.41

3.5 0.9472 3.32

3.5 0.9178 3.21

3.5 0.8885 3.113.5 0.8584 3.00

103.5 0.8254 85.43

Total PV of Cash Flows 101.48

The bond equivalent yield can be calculated by using the CF function

Input 6 cash flows for coupon payment and one principal payment cash flow. CF0 =104.5 CPT IRR. IRR = 2.68%

BEY = 2* IRR = 5.36%



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Question 12

A fixed income analyst makes the following two statements

Statement 1: YTM assumes that coupon payments are reinvested at the rate equalto the cash flow yield.

Statement 2: The bond is assumed to be held till maturity.

Statement 1 Statement 2

A Correct Correct

B Correct Incorrect

C Incorrect CorrectThis files has expired at 30-Jun-13


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Answer 12

A.

Both the statements are true.



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Question 13

An option-free bond has duration of 5.25 and convexity of 94.6. The change in the

value for a 100 bps upward shift in the yield curve is closest toA. - 5.2405%

B. - 5.273%

C.- 5.354%



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Answer 13

A.

Duration effect = -5.25*0.01*100 = -5.25Convexity effect = 94.6 * (0.01)2 = 0.0095

Total effect = -5.2405%



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Question 14

A bond is likely to get matured in next three years has a par value of $500 and a

coupon rate of 7.75% payable semiannually. Which of the following is closest amountof semiannual coupon payment?

a. Rs 38.75

b. Rs 19.375

c. Rs 19.75



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Answer 14

B.

The correct answer is Rs 19.375=500*7.75%/2 =19.375



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Question 15

Institutional users use a number of methods for borrowing money for the purchase ofbonds, the least likely method of borrowing is

A. Margin buying

B. Repurchase agreement

C. Loan against property



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Answer 15

C.

Institutional users generally borrow margin money through collateralized securities orthrough a repurchase agreement. Loan against property is generally not permitted fortrading activities.



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Question 16

A $100 par value bond has duration of 12.7 If the price rises to 104.57 when the yielddeclines by 50 basis points, the price when the yield rises by 50 basis points is closestto

A. 95.7

B. 91.8

C.92.5



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Answer 16

B.

Duration = Price if yield declinesprice if yield rises /( 2 * (initial price) * (change inyield in decimals))

Price if yield rises = 104.5712.7*(2*100*0.005)= 91.8



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Question 17

Carl an analyst with a fixed income hedge fund states that investments in high yieldsecurities from emerging economies carries a number of risk factors. Which of thefollowing is least likely to be listed as a risk when investing in high yield securities fromemerging markets

A. Sovereign risk

B. Exchange rate risk

C.Downgrade risk



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Answer 17

C.

A high yield bond has generally a low-credit and is of speculative nature. Investmentsin foreign currency bonds carry exchange rate risks. The bonds also have sovereignrisk due to the risk of actions of the foreign government in case of default.



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Question 18

Carl a fixed income analyst is discussing investment strategies with Karen. He saysthat a $ 100mn 8% 10-year semi-annual T-note issued by the US government can bestripped into 20 Treasury strips. The 20th treasury strip is the final coupon and principalstrip and has a maturity value of $104mn. Karen disagrees with both the points. She ismost likely correct regarding

Number of Treasury Strip Maturity value

A Incorrect IncorrectB Correct Correct

C Incorrect Correct



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Answer 18

B.

The Treasury note can be stripped into 20 coupon strips and one principal strip. The21st strip is the principal strip of $100mn. When Karen disagrees with Carl she iscorrect regarding both the point



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Question 19

Bart wants to invest in a municipal bond. Which of the following is he least likely toinvest in

A. Tax backed bonds

B. Revenue bonds

C. Bankruptcy bonds



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Answer 19

C.

The types of municipal bonds are a) tax backed bonds b) revenue bonds c) specialbond structures



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Question 20

Ted makes the following statements:

Statement 1: In a bought deal the underwriting firm offers the issuer to buy a specifiedamount of securities with a certain coupon rate and maturity.

Statement 2: In a bought deal the underwriting firm usually has presold most of thesecurities and has hedged its interest rate risk.

Which of the above statements is most likely to be correct?

Statement 1 Statement 2

A Correct Incorrect

B Correct Correct

C Incorrect Incorrect



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Answer 20

B.

Both the statements are true for bought deals



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Question 21

The pure expectation theory suggests that an upwardly sloping curve means that therates are expected to rise. However the liquidity preference theory an upwardly slopingcurve least likely suggests

A. The future interest rates are likely to rise

B. The rates will be unchanged or may even fall; but yield premium will change

C. The rates will be unchanged or may even fall; but yield premium will remain thesame



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Answer 21

C.

Liquidity preference theory says that an upward sloping yield curve may indicate thatthe rates are likely to rise or remain unchanged or even fall with a change in the yieldpremiums



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Question 22

A 10-year Treasury security has a yield of 5.2%. A 10-year corporate bond issued byMotorola has a yield of 5.65%. The absolute spread, relative spread and the yield ratiois closest to

A. 45 bps; 9%; 1.09

B. 40 bps; 9%; 1.10

C. 45 bps; 8%; 1.09



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Answer 22

A.

Absolute spread = 5.655.2 = 0.45Relative spread = 0.45/5.2 = 9%

Yield ratio = 5.65/5.2 = 1.09



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Question 23

Carl is discussing valuation models with Karen. Carl states that all valuation modelsare calibrated using on-the-run Treasury securities. Karen states that volatility ofinterest rates can vary from period to period; all models make some criticalassumptions regarding the volatility of short term interest rates. The two statements aremost likely

Carls Statement Karens Statement

A Incorrect Incorrect

B Correct CorrectC Correct Incorrect



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Answer 23

B.

Both the statements are true. Treasury securities are used for calibrating a model. Themodel should give a value equal to its market price. Also all the models make someassumptions regarding volatility.



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Question 24

Karen invests in an 8% 5-year semi-annual callable bond on 5th January 2010. TheZ-spread for the callable bond is 150bps. The option cost is 56 bps. The OAS is closestto

A. 100 bps

B. 94 bps

C. 206 bps



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Answer 24

B.

OAS = Z-spreadoption cost = 150 -56 = 94 bps



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Question 25

Sally states that there are a number of yield measures that are used traditionally in thebond market. The least likely yield measure that is used

A. Yield to call

B. Yield to worst

C. Yield to settlement



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Answer 25

C.

Yield to settlement is not a traditional measure of yield. The yield measures that aregenerally used are a) yield to maturity b) yield to call c) yield to put d) yield to worste)current yield f) cash flow yield.


Q ti 26


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Question 26

Carl manages the following portfolio

The value for the portfolio duration is closest to

A. 5.833

B. 4.351

C. 4.555

Coupon Maturity Par Value Market Value Duration

8% 5 years $ 5 mn $ 4 mn 4.87

11% 7 years $ 10mn $11.4mn 5.72

9.75% 10 years $ 15mn $14.5mn 8.50

10.25% 5 years $ 20mn $ 21.2 4.25


A 26


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Answer 26

A.

Issue Market Value MV % of Port Folio Value Duration MV% * Duration

A $ 4mn 7.83% 4.87 0.3813

B $ 11.4mn 22.31% 5.72 1.2761

C $14.5mn 28.38% 8.50 2.4123

D $ 21.2mn 41.49% 4.25 1.7633Total $ 51.1mmn 100% 5.8330


Q ti 27


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Question 27

Duration is not a good measure for large changes in yield. Duration also assumes thatthe yield curve will shift in a parallel fashion. The statements are most likely

A. Both statements are correct.

B. Only one statement is correct.

C. Both the statements are incorrect.


A 27


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Answer 27

A .

Both the statements are correct as the duration measure is not useful for measuringchanges in price when there are large changes in yield. The duration also assumesthat yields change is parallel across the entire yield curve.


Q ti 28


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Question 28

A straight 7% bond with two years to maturity is priced at $97.65. A putable bond whichis similar to straight bond in all aspects except for the put feature is priced at $98.45

and a callable bond that is same as the straight bond except for the call feature ispriced at $96.95. Which of the following will be the closest value of the call option andput option?

Call option value Put option value

A. $0.75 $0.75

B. $0.8 $0.7C. $0.7 $0.8


A 28


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Answer 28

C.

Call option value: $0.7, Put option value: $0.8

Call option value= 97.6596.95 =0.7

Put option value= 98.4597.65=0.8


Question 29


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Question 29

Which of the following is true:

A. When the yield level is high, a change in interest rates produces a large change inprice.

B. When yields are low, changes in interest rates produces a large change in price.

C. Change in Yields at any level will produce the same change in price


Answer 29


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Answer 29

B.

When the yield level is high, a change in interest rates does not produce a large changein price.

However, when yields are low, changes in interest rates produces a large change inprice.


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