CFA一级百题进阶：固收

7.FixedIncome

Q-1.

A5-year,5%semiannualcouponpaymentcorporatebondispricedat104.967per100

ofparvalue.Thebond'syield-to-maturity,quotedonasemiannualbondbasis,is

3.897%.Ananalysthasbeenaskedtoconverttoamonthlyperiodicity.Underthis

conversion,theyield-to-maturityisclosestto:

A.3.87%.

B.4.95%.

C.7.67%.

Solution:A.

0.03897

YTM

(1

)2(1

12)12

2

12

YTM0.00322*120.0387

12

1-15

Q-2.

A10%couponbondwithannualpayments,maturingin3years,ispricedat105.The

bondiscallableinoneyearatacallpriceof104ortwoyearsatacallpriceof102.The

bondsyieldtoworstmostlikelyoccurswhenthebondis:

A.Calledinyear1.

B.Calledinyear2.

C.Helduntilmaturity.

Solution:C.

Theyieldtoworstforacallablebondisthelowestoftheyieldstocallforeachpossiblecalldate

andtheyieldtomaturity.Theyieldtocalloryieldtomaturitysolvesthefollowingequation:

T

PCF/(1i)

t

t

,whereiistheyieldtocall,oryieldtomaturityCFisthecashflowatdatet,

t1

andTisthematurityorcalldate.

10104

Theyieldtocallifthebondiscalledinoneyearis8.57%,because105=

1.0857

10

1.0815

1

10102

Theyieldtocallifthebondiscalledintwoyearsis8.15%,because105=

.

1

1.0815

2

10

10

10100

Theyieldtomaturityofthebondis8.06%,because105

.The

1.080611.080621.08063

yieldtoworstisthelowestoftheseandoccurswhenthebondishelduntilmaturity(i.e.,itisthe

yieldtomaturity).

2-15

Q-3.

AssumetheUSTreasuryforwardratesasfollows,thevalueofa2year$1000parvalue

semi-annuallyTreasurybondwitha6%couponrateisclosestto:

Period

ForwardRate

1

2

3

4

1.40%

2.00%

2.50%

2.90%

A.$1076.82

B.$1074.33

C.$1072.46

Solution:B.

Thevalueofthebondis

30

30

30

(10.014/2)(10.014/2)(10.02/2)(10.014/2)(10.02/2)(10.025/2)

1030

(10.014/2)(10.02/2)(10.025/2)(10.029/2)

$1074.33

3-15

Q-4.

Whichofthefollowing90-daymoneymarketinstrumentsmostlikelyoffersthe

investorthehighestrateofreturn?

MoneyMarket

QuotedRate

QuotationBasis

DayConvention

Instrument

InstrumentA

InstrumentB

InstrumentC

5.80%

5.65%

5.88%

360

365

365

Discountrate

Discountrate

Add-onrate

A.InstrumentC

B.InstrumentA

C.InstrumentB

Solution:B.

InstrumentCprovidesabondequivalentyieldof5.88%,comparedwith5.97%forInstrumentA

and5.73%forInstrumentB.

ForInstrumentA:assumeFV=100,

100−푃푉

100

360

90

×

=0.058,PV=98.55.

100−98.55365

AOR=

×

=0.0597

98.55

90

ForInstrumentB:assumeFV=100,

100−푃푉

100

365

90

×

=0.0565,PV=98.6068.

100−98.6068365

AOR=

×

=0.0573

98.6068

90

ForInstrumentC=5.88%

4-15

Q-5.

Anoption-adjusted-spread(OAS)onacallablebondistheZ-spread:

A.Overthebenchmarkspotcurve.

B.Minusthestandardswaprateinthatcurrencyofthesametenor.

C.Minusthevalueoftheembeddedcalloptionexpressedinbasispointsperyear.

Solution:C.

TheoptionvalueinbasispointsperyearissubtractedfromtheZ-spreadtocalculatethe

option-adjustedspread(OAS).TheZ-spreadistheconstantyieldspreadoverthebenchmarkspot

curve.TheI-spreadistheyieldspreadofaspecificbondoverthestandardswaprateinthat

currencyofthesametenor.

5-15

Q-6.

Whichofthefollowingsourcesofreturnismostlikelyexposedtointerestrateriskfor

aninvestorofafixed-ratebondwhoholdsthebonduntilmaturity?

A.Capitalgainorloss

B.Redemptionofprincipal

C.Reinvestmentofcouponpayments

Solution:C.

Becausethefixed-ratebondisheldtomaturity(a"buy-and-hold"investor),interestraterisk

arisesentirelyfromchangesincouponreinvestmentrates.Higherinterestratesincreaseincome

fromreinvestmentofcouponpayments,andlowerratesdecreaseincomefromcoupon

reinvestment.Therewillnotbeacapitalgainorlossbecausethebondisheldtomaturity.The

carryingvalueatthematuritydateisparvalue,thesameastheredemptionamount.The

redemptionofprincipaldoesnotexposetheinvestortointerestraterisk.Therisktoabond's

principaliscreditrisk.

6-15

Q-7.

Aninvestorbuysathree-yearbondwitha5%couponratepaidannually.Thebond,

withayield-to-maturityof3%,ispurchasedatapriceof105.657223per100ofpar

value.Assuminga5-basispointchangeinyield-to-maturity,thebond'sapproximate

modifieddurationisclosestto:

A.2.78.

B.2.86.

C.5.56.

Solution:A.

loweryieldtomaturityby5bpsto2.95%

5

5

105

PV

105.804232

105.510494

(10.0295)1(10.0295)2(10.0295)3

higheryieldtomaturityby5bpsto3.05%

105

5

5

PV

(10.0305)1(10.0305)2(10.0305)3

105.804232105.510494

approximatemodifiedduration

2.78

2*0.0005*105.657223

7-15

Q-8.

Inarecentpresentation,TerrymadetwostatementsaboutMacaulayduration:

Statement1:"Macaulaydurationwilldecreaseastimepassesandimmediately

increaseaftercouponpayment."

Statement2:"Macaulaydurationwillincreaseastimepassesandimmediately

decreaseaftercouponpayment."

AreTerry'stwostatementscorrect?

A.YesforStatement1andnoforStatement2

B.NoforStatement1andyesforStatement2

C.Noforbothstatements

Solution:A.

Astimepassesduringthecouponperiod,theMacaulaydurationdeclinessmoothlyandthen

jumpsupwardafterthecouponispaid.

8-15

Q-9.

Abondwithexactlynineyearsremaininguntilmaturityoffersa3%couponratewith

annualcoupons.Thebond,withayield-to-maturityof5%,ispricedat85.784357per

100ofparvalue.Theestimatedpricevalueofabasispointforthebondisclosestto:

A.0.0086.

B.0.0648.

C.0.1295.

Solution:B.

Loweringtheyield-to-maturitybyonebasispointto4.99%resultsinabondpriceof85.849134:

3

103

PV

...

85.849134

9

(10.0499)

1

(10.0499)

Increasingtheyield-to-maturitybyonebasispointto5.01%resultsinabondpriceof85.719638:

3

103

(10.0501)9

PV

...

85.719638

(10.0501)1

85.84913485.719638

PVBP

0.06475

2

9-15

Q-10.

Abondiscurrentlytradingfor98.722per100ofparvalue.Ifthebond’s

yield-to-maturity(YTM)risesby10basispoints,thebond’sfullpriceisexpectedtofall

to98.669.ifthebond’sYTMdecreasesby10basispoints,thebond’sfullpriceis

expectedtoincreaseto98.782.Thebond’sapproximateconvexityisclosestto:

A.0.0071.

B.70.906.

C.1144.628.

Solution:B.

VV2V

0

approximateconvexity

(YTM)V0

2

approximateconvexity[98.78298.669(2*98.722)]/(0.001*98.722)70.906

2

10-15

Q-11.

Thedurationofanoption-freebondpricedat$900is8.5.Ifyieldsdecreaseby150

basispoints,themostaccuratestatementabouttheactualpriceofthebondafterthe

decreaseinyieldsisthattheactualpricewillbe:

A.Equalto$1,014.75.

B.Greaterthan1,014.75.

C.Lessthan1,014.75becausethelowerlevelofyieldsincreasesthebond'sinterestraterisk.

Solution:B.

Thepriceadjustmentfordurationcanbecalculatedasfollows:

8.5×(0.015)×100=12.75%.

$900(1.1275)=$1,014.75

Thisadjuststhepricefordurationonly.Becausethebondisoption-freeandthechangeinyieldis

large,usingdurationaloneunderestimatestheactualpriceofthebondbecauseoftheeffectof

convexity.Onceanadjustmentismadeforconvexity,thepricewouldbegreaterthan$1,014.75.

11-15

Q-12.

Aninvestorpurchasesanannualcouponbondwitha8%couponrateandexactly20

yearsremaininguntilmaturityatapriceequaltoparvalue.Theinvestor'sinvestment

horizoniseightyears.Themodifieddurationofthebondis12.480years.Theduration

gapatthetimeofpurchaseisclosestto:

A.-6.842.

B.4.480.

C.5.478.

Solution:C.

Thedurationgapisclosestto4.158.Thedurationgapisabond'sMacaulaydurationminusthe

investmenthorizon.TheapproximateMacaulaydurationistheapproximatemodifiedduration

timesoneplustheyield-to-maturity.Itis13.478(=12.480×1.08).

Givenaninvestmenthorizonofeightyears,thedurationgapforthisbondatpurchaseispositive:

13.478-8=5.478.WhentheinvestmenthorizonislessthantheMacaulaydurationofthebond,

thedurationgapispositive,andpriceriskdominatescouponreinvestmentrisk.

12-15

Q-13.

AcreditanalystobservesthefollowinginformationforAlphaCo.atfiscalyearsending

20X7and20X8.ExcerptfromtheConsolidatedIncomeStatementofAlphaCo.forthe

fiscalyearsending31December20X7and20X8(inmillions)

20X7

$549.0

451.0

98.0

20X8

$506.0

372.0

134.0

35.0

Grossprofit

Operatingexpenses

Operatingprofit

Interestexpense

29.0

Incomebeforetaxes

Incometaxes(at30%)

Netincome

69.0

99.0

22.0

31.0

47.0

68.0

Additionalinformation

Depreciationandamortization26.0

34.0

Basedonthisinformation,overthisperiodAlpha'sinterestcoverageratiohas:

A.Remainedunchanged.

B.Improved.

C.Deteriorated.

Solution:B.

Thecompany'sinterestcoverageratiocanbecomputedas:EBITDA/Interestexpense.Thatis:

20X7

124.0

29.0

20X8

168.0

35.0

4.8

EBITDA

Interestexpense

EBITDA/Interestexpense

4.28

EBITDA=Operatingprofit+Depreciationandamortization

Thecompany'sEBITDAinterestcoverageratiohasimprovedoverthisperiod.IfEBITisusedto

calculatethecoverageratiosyoureachthesameconclusion,for20X7theratiois3.38andfor

20X8itis3.83.

13-15

Q-14.

Thefundmanagerisconcernaboutthefactthatmarketinterestrateswillgoup

unexpectedlyandleadtoprepaymentratesthataremuchlowerthanprevious

expectation.Healsoexpresseshisexpectationforarelativelylong-terminvestment

(averagelifeofgreaterthanfiveyears)anddoesnotwanttoreceiveanycashflow

fromcomingyears.Theendowmentfundmanager'sconcernabouttheimpactof

movementsinmarketinterestratesisbestdescribedasaconcernabout:

A.Extensionrisk.

B.Prepaymentrisk.

C.Contractionrisk.

Solution:A.

Iftheprepaymentratefalls,itusuallyresultinalengtheningofthesecurity'slifewhichiscalled

extensionriskandisalsofundmanager’sconcern.

14-15

Q-15.

Twodifferentstructuresofcollateralizedmortgageobligations(CMO)arebeing

consideredforissuance:

Structure1:$400millionofpass-throughwillbeusedascollateralfortwosequential

paytranches:$325millionworthofbondsofTrancheXand$75millionofbondsof

TrancheY.The