投资学10版习题答案16文档格式.docx

投资学10版习题答案16文档格式.docx

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（5）

TimeuntilPayment（Years）

CashFlow

PVofCF（DiscountRate=6%）

Weight

Column

（1）Column（4）

1

$60.00

$56.60

0.0566

2

60.00

53.40

0.0534

0.1068

3

1,060.00

890.00

0.8900

2.6700

Columnsums

$1,000.00

1.0000

2.8334

Duration=2.833years

b.YTM=10%

PVofCF（DiscountRate=10%）

$54.55

0.0606

49.59

0.0551

0.1102

796.39

0.8844

2.6532

$900.53

2.8240

Duration=2.824years,whichislessthanthedurationattheYTMof6%.

5.Forasemiannual6%couponbondsellingatpar,weusethefollowingparameters:

coupon=3%perhalf-yearperiod,y=3%,T=6semiannualperiods.

PVofCF（DiscountRate=3%）

$3.00

$2.913

0.02913

3.00

2.828

0.02828

0.05656

2.745

0.02745

0.08236

4

2.665

0.02665

0.10662

5

2.588

0.02588

0.12939

6

103.00

86.261

0.86261

5.17565

$100.000

1.00000

5.57971

D=5.5797half-yearperiods=2.7899years

Ifthebond’syieldis10%,useasemiannualyieldof5%andsemiannualcouponof3%:

PVofCF（DiscountRate=5%）

$2.857

0.03180

2.721

0.03029

0.06057

2.592

0.02884

0.08653

2.468

0.02747

0.10988

2.351

0.02616

0.13081

76.860

0.85544

5.13265

$89.849

5.55223

D=5.5522half-yearperiods=2.7761years

6.IfthecurrentyieldspreadbetweenAAAbondsandTreasurybondsistoowidecomparedtohistoricalyieldspreadsandisexpectedtonarrow,youshouldshiftfromTreasurybondsintoAAAbonds.Asthespreadnarrows,theAAAbondswilloutperformtheTreasurybonds.Thisisanexampleofanintermarketspreadswap.

7.D.Investorstendtopurchaselongertermbondswhentheyexpectyieldstofallsotheycancapturesignificantcapitalgains,andthelackofacouponpaymentensuresthecapitalgainwillbeevengreater.

8.a.BondBhasahigheryieldtomaturitythanbondAsinceitscouponpaymentsandmaturityareequaltothoseofA,whileitspriceislower.（Perhapstheyieldishigherbecauseofdifferencesincreditrisk.）Therefore,thedurationofBondBmustbeshorter.

b.BondAhasaloweryieldandalowercoupon,bothofwhichcauseBondAtohavealongerdurationthanBondB.Moreover,Acannotbecalled,sothatitsmaturityisatleastaslongasthatofB,whichgenerallyincreasesduration.

9.a.

$10million

$9.09million

0.7857

4million

2.48million

0.2143

1.0715

$11.57million

1.8572

D=1.8572years=requiredmaturityofzerocouponbond.

b.Themarketvalueofthezeromustbe$11.57million,thesameasthemarketvalueoftheobligations.Therefore,thefacevaluemustbe:

$11.57million（1.10）1.8572=$13.81million

10Ineachcase,choosethelonger-durationbondinordertobenefitfromaratedecrease.

a.ii.TheAaa-ratedbondhastheloweryieldtomaturityandthereforethelongerduration.

b.i.Thelower-couponbondhasthelongerdurationandgreaterdefactocallprotection.

c.i.Thelowercouponbondhasthelongerduration.

11.Thetablebelowshowstheholdingperiodreturnsforeachofthethreebonds:

Maturity

1Year

2Years

3Years

YTMatbeginningofyear

7.00%

8.00%

9.00%

Beginningofyearprices

$1,009.35

$974.69

Pricesatyear-end（at9%YTM）

$990.83

$982.41

Capitalgain

–$9.35

–$9.17

$7.7