固定收益证券的复习计算题.docx

固定收益证券的复习计算题.docx

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固定收益证券的复习计算题

Fixed-incometreasury

Ppt3

1、公式：

PracticeQuestion3.1

Supposecurrently,1-yearspotrateis1%andmarketexpectsthat1-yearspotratenextyearwouldbe2%and1-yearspotratein2yearswouldbe3%.Computetoday’s2-yearspotrateand3-year

spotrate.（已做答案）

2、CurrentYield

Computethecurrentyieldfora7%8-yearbondwhosepriceis$94.17.Howaboutthecurrentyieldifpriceis$100,$106,respectively?

3Case3.1

Considera7%8-yearbondpayingcouponsemiannuallywhichissoldfor$94.17.Thepresentvalueusingvariousdiscountrateis:

A.WhatistheYTMforthisbond?

B.Howmuchisthetotaldollarreturnonthisbond?

C.Howmuchisthetotaldollarreturnifyouputthesameamountofdollarsintoadepositaccountwiththesameannualyield?

4、ForwardRates

注：

6-monthbillspotrateis3%是年化利率（3%要除以2）

1-yearbillspotrateis3.3%是年化利率（3.3%要除以2）

Ppt4

1、Fixed‐CouponBonds

PracticeQuestion4.2

A.Whatisthevalueofa4-year10%couponbondthatpaysinterestsemiannuallyassumingthattheannualdiscountrateis8%?

Whatisthevalueofasimilar10%couponbondwithaninfinitematurity（无期限）?

B.Whatisthevalueofa5-yearzero-couponbondwithamaturityvalueof$100discountedatan8%interestrate?

C.Computethevaluepar$100ofparvalueofa4-year10%couponbond,assumingthepaymentsareannualandthediscountrateforeachyearis6.8%,7.2%,7.6%and8.0%,respectively.

Infinitematurity

Pv=（$100*10%/2）/（8%/2）

（半年付息）

PresentValueProperties

PracticeQuestion4.4

A.Supposethediscountrateforthe4-year10%couponbondwithaparvalueof$100is8%.Computeitspresentvalue.

B.Oneyearlater,supposethatthediscountrateappropriatefora3-year10%couponbondincreasesfrom8%to9%.RedoyourcalculationinpartAanddecomposethepricechangeattributabletomovingtomaturityandtotheincreaseinthediscountrate.

（期限与贴现率变化）

3、PricingaBondbetweenCouponPayments

PracticeQuestion4.6

Supposethattherearefivesemiannualcouponpaymentsremainingfora10%couponbond.Alsoassumethefollowing:

①Annualdiscountrateis8%

②78daysbetweenthesettlementdateandthenextcouponpaymentdate

③182daysinthecouponperiod

Computethefullpriceofthiscouponbond.Whatisthecleanpriceofthisbond?

4、ValuationApproach

Case4.1

A.Considera8%10-yearTreasurycouponbond.Whatisitsfairvalueiftraditionalapproachisused,givenyieldforthe10-yearon-the-runTreasuryissueis8%?

B.WhatisthefairvalueofaboveTreasurycouponbondifarbitrage-freeapproachisused,giventhefollowingannualspotrates?

C.Whichapproachismoreaccurate（准确）?

C、Arbitrage-FreeApproachismoreaccurate

Ppt5

2、Convexity

Considera9%20-yearbondsellingat$134.6722toyield6%.Fora20bpchangeinyield,itspricewouldeitherincreaseto$137.5888ordecreaseto$131.8439.

A.Computetheconvexityforthisbond.

B.Whatistheconvexityadjustmentforachangeinyieldof200bps?

C.Ifweknowthatthedurationforthisbondis10.66,whatshouldthetotalestimatedpercentagepricechangebefora200bpincreaseintheyield?

Howabouta200bpdecreaseintheyield?

Ppt6

1、MeasuringYieldCurveRisk

Case6.1:

PanelA

Considerthefollowingtwo$100portfolios

composedof

2-year,16-year,and30-year

issues,allofwhicharezero-couponbonds:

Forsimplicity,assumethereareonlythreekeyrates—2years,16yearsand30years.Calculatetheportfolio’skeyratedurationsatthesethreepointsanditseffectiveduration.

Case6.1:

PanelB

Considerthefollowingthreescenarios:

Scenario1:

Allspotratesshiftdown10basispoints.

Scenario2:

The2-yearkeyrateshiftsup10basispointsanthe30-yearrateshiftsdown10basispoints.

Scenario3:

The2-yearkeyrateshiftsdown10basispointsandthe30-yearrateshiftsup10basispoints.

Howwouldtheportfoliovaluechangeineachscenario?

Ppt7

Considera6.5%option-freebondwith4yearsremainingtomaturity.Iftheappropriatebinomialinterestratetreeisshownasbelow,calculatethefairpriceofthisbond.

Ppt8

1、ValuingCallableandPutableBonds

Case8.1:

Valuingacallablebondwithsingle

callprice

Considera6.5%callablebondwith4yearsremainingtomaturity,callable

inoneyearat$100.Assumetheyieldvolatilityis10%andtheappropriate

binomialinterestratetreeissameasCase6.4.Calculatethefairprice

ofthiscallablebond.

2、Case8.2:

ValuingacallablebondwithcallscheduleConsidera6.5%callablebondwith4yearsremainingtomaturity,callableinoneyearatacallscheduleasbelow:

Assumetheyieldvolatilityis10%andtheappropriatebinomialinterest

ratetreeissameasCase6.4.Calculatethefairpriceofthiscallablebond.

3、Case8.3:

ValuingaputablebondConsidera6.5%putablebondwith4

yearsremainingtomaturity,putableinoneyearat$100.Assumetheyieldvolatilityis10%andtheappropriatebinomialinterestratetreeissameasCase6.4.Calculatethefairpriceofthisputablebond.

Vapppplueofa

Cappppppp

ConvertibleBonds

Case9.1:

Supposethatthestraightvalueofa5.75%ADCconvertiblebondis$981.9

per$1,000ofparvalueanditsmarketpriceis$1,065.Themarketprice

pershareofcommonstockis$33andtheconversionratiois25.32shares

per$1,000ofparvalue.Alsoassumethatthecommonstockdividendis$0.90pershare.ption

公式：

MinimumValue:

thegreaterofitsconversionpriceanditsstraightvalue.

ConversionPrice=Marketpriceofcommonstock×Conversionratio

StraightValue/InvestmentValue:

presentvalueofthebond’scashflowsdiscountedattherequiredreturnonacomparableoption-freeissue.

MarketConversionPrice/ConversionParityPrick

=Marketpriceofconvertiblesecurity÷Conversionratio

MarketConversionPremiumPerShare

=Marketconversionprice–Marketpriceofcommonstock

MarketConversionPremiumRatio

=Marketconversionpremiumpershare÷Marketpriceofcommonstock

Premiumoverstraightvalue

=（Marketpriceofconvertiblebond/Straightvalue）–1

Thehigherthisratio,thegreaterdownsideriskandthelessattractivetheconvertiblebond.

PremiumPaybackPeriod

=Marketconversionpremiumpershare÷Favorableincomedifferentialper

share

FavorableIncomeDifferentialPerShare

=[Couponinterest–（ConversionratioCommon×stockdividendpershare）]÷

Conversionratio

A.Whatistheminimumvalueofthisconvertiblebond?

B.Calculateitsmarketconversionprice,marketconversionpremium

shareandmarketconversionpremiumratio.

C.Whatisitspremiumpaybackperiod?

D.Calculateitspremiumoverstraightvalue.pp

per

Marketpriceofcommonstock=$33,

conversionratio=25.32

StraightValue=$981.9，

marketpriceofconversiblebond=$1,065

commonstockdividend=$0.90

Couponrate=5.75%

A、ConversionPrice=Marketpriceofcommonstock×Conversionratio

=$33*25.32=$835.56

theminimumvalueofthisconvertiblebond=max{

$835.56,$981.9}=$981.9

B、MarketConversionPrice/ConversionParityPrick

=Marketpriceofconvertiblesecurity÷Conversionratio

=$1065/25.32

=$42.06

MarketConversionPremiumPerShare

=Marketconversionprice–Marketpriceofcommonstock

=$42.06-$33

=$9.06

MarketConversionPremiumRatio

=Marketconversionpremiumpershare÷Marketpriceofcommonstock

=$9.06/$33

=27.5%

C、

PremiumPaybackPeriod

=Marketconversionpremiumpershare÷Favorableincomedifferentialper

share

FavorableIncomeDifferentialPerShare

=[Couponinterest–（Conversionratio

Common×stockdividendpershare）]

÷

Conversionratio

Couponinterestfrombond=5.75%×$1,000=$57.50

Favorableincomedifferentialpershare=（$57.50–25.32×$0.90）÷25.32=$1.37Premiumpaybackperiod=$9.06/$1.37=6.6years

D、Premiumoverstraightvalue

=（Marketpriceofconvertiblebond/Straightvalue）–1=$1,065/$981.5–1=8.5%

Ppt10

No-ArbitragePrinciple

:

noriskless

profits

gained

fromholdinga

combination

ofaforward

contractposition

aswellas

positionsinotherassets

.

FP=Price

that

wouldnot

permitprofitable

riskless

arbitragein

frictionlessmarkets,thatis:

Case10.1

Considera3-monthforward

contractonazero-couponbondwithaface

value

of$1,000thatiscurrently

quotedat$500,andassumearisk-free

annual

interestrateof6%.Determine

thepriceoftheforwardcontract

under

theno-arbitrageprinciple.

Solutions.

Case10.2

Supposetheforwardcontractdescribedincase10.1isactuallytradingat$510,whichisgreaterthanthenoarbitrageprice.Demonstratehowanarbitrageurcan

obtainrisklessarbitrageprofitfromthisoverpricedforwardcontractandhowmuchthearbitrageprofitwouldbe.

Case10.3

Iftheforwardcontractdescribedincase10.1isactuallytradingat$502,whichissmallerthantheno-arbitrageprice.Demonstratehowanarbitrageurcanobtainrisklessarbitrageprofitfromthisunderpricedforwardcontractandhowmuchthearbitrageprofitwouldbe.

Case10.4:

Calculatethepriceofa250-dayforwardcontractona7%U.S.Treasurybondwithaspotpriceof$1,050（includingaccruedinterest）thathas

justpaidacouponandwillmakeanothercouponpaymentin182days.Theannualrisk-freerateis6%.

Solutions.RememberthatT-bondsmakesemiannualcouponpayments,so

Case10.6

Solutions.

Thesemiannualcoupononasingle,$1,000face-value7%bondis$35.A

bondholderwillreceiveonepayment0.5yearsfromnow（0.7yearslefttoexpirationoffutures）andonepayment1