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-yearspotrate.（已做答案）

2、CurrentYield

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

3、Case3.1

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.Whatisitsfairvalueiftraditionalapproachis

used,givenyieldforthe10-yearon-the-runTreasuryissueis8%?

B.WhatisthefairvalueofaboveTreasurycouponbondifarbitrage-freeapproachisused,

giventhefollowingannualspotrates?

C.Whichapproachismoreaccurate（准确）?

C、Arbitrage-FreeApproachismoreaccurate

Ppt5

2、Convexity

Considera9%20-yearbondsellingat$134.6722toyield6%.Fora20bpchangeinyield,itspricewould

eitherincreaseto$137.5888ordecreaseto$131.8439.

A.Computetheconvexityforthisbond.

B.Whatistheconvexityadjustmentforachangeinyieldof200bps?

C.Ifweknowthatthedurationforthisbondis10.66,whatshouldthetotalestimatedpercentagepricechangebefora200bpincreaseintheyield?

Howabouta200bpdecreaseintheyield?

Ppt6

1、MeasuringYieldCurveRisk

Case6.1:

PanelA

Considerthefollowingtwo$100portfolioscomposedof2-year,16-year,and30-yearissues,allofwhicharezero-couponbonds:

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

Case6.1:

PanelB

Considerthefollowingthreescenarios:

Scenario1:

Allspotratesshiftdown10basispoints.

Scenario2:

The2-yearkeyrateshiftsup10basispointsanthe

30-yearrateshiftsdown10basispoints.

Scenario3:

The2-yearkeyrateshiftsdown10basispointsand

the30-yearrateshiftsup10basispoints.

Howwouldtheportfoliovaluechangeineachscenario?

Ppt7

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

Ppt8

1、ValuingCallableandPutableBonds

Case8.1:

Valuingacallablebondwithsingle

callprice

Considera6.5%callablebondwith4yearsremainingtomaturity,callableinoneyearat$100.Assumetheyieldvolatilityis10%andtheappropriatebinomialinterestratetreeissameasCase6.4.Calculatethefairpriceofthiscallablebond.

2、Case8.2:

Valuingacallablebondwithcallschedule

Considera6.5%callablebondwith4yearsremainingto

maturity,callableinoneyearatacallscheduleasbelow:

Assumetheyieldvolatilityis10%andtheappropriatebinomialinterestratetreeissameasCase6.4.Calculatethefairpriceofthiscallablebond.

3、Case8.3:

ValuingaputablebondConsidera6.5%putablebondwith4yearsremainingtomaturity,putableinoneyearat$100.Assumetheyield

volatilityis10%andtheappropriatebinomialinterestratetreeissameasCase6.4.Calculatethefairpriceofthisputablebond.

ConvertibleBonds

Case9.1:

Supposethatthestraightvalueofa5.75%ADCconvertiblebondis$981.9per$1,000ofparvalueanditsmarketpriceis$1,065.Themarketpricepershareofcommonstockis$33andtheconversionratiois25.32sharesper$1,000ofparvalue.Alsoassumethatthecommonstockdividendis$0.90pershare.

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,thegreaterdownsideriskandthe

lessattractivetheconvertiblebond.

PremiumPaybackPeriod

=Marketconversionpremiumpershare÷Favorableincomedifferentialpershare

FavorableIncomeDifferentialPerShare

=[Couponinterest–（Conversionratio×Commonstockdividendpershare）]÷Conversionratio

A.Whatistheminimumvalueofthisconvertiblebond?

B.Calculateitsmarketconversionprice,marketconversionpremiumpershareandmarketconversionpremiumratio.

C.Whatisitspremiumpaybackperiod?

D.Calculateitspremiumoverstraightvalue.

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÷Favorableincomedifferentialpershare

FavorableIncomeDifferentialPerShare

=[Couponinterest–（Conversionratio×Commonstockdividendpershare）]÷Conversionratio

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

Favorableincomedifferentialpershare=（$57.50–25.32×$0.90）÷25.32=$1.37

Premiumpaybackperiod=$9.06/$1.37=6.6years

D、Premiumoverstraightvalue

=（Marketpriceofconvertiblebond/Straightvalue）–1

=$1,065/$981.5–1=8.5%

Ppt10

No-ArbitragePrinciple:

norisklessprofitsgainedfromholdingacombinationofaforwardcontractpositionaswellaspositionsinotherassets.

FP=Pricethatwouldnotpermitprofitablerisklessarbitrageinfrictionlessmarkets,thatis:

Case10.1

Considera3-monthforwardcontractonazero-couponbondwithafacevalueof$1,000thatiscurrentlyquotedat$500,andassumearisk-freeannualinterestrateof6%.Determinethepriceoftheforwardcontractunder

theno-arbitrageprinciple.

Solutions.

Case10.2

Supposetheforwardcontractdescribedincase10.1isactuallytradingat$510,whichisgreaterthanthenoarbitrageprice.Demonstratehowanarbitrageurcanobtainrisklessarbitrageprofitfromthisoverpricedforwardcontractandhowmuchthearbitrageprofitwouldbe.

Case10.3

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

Case10.4:

Calculatethepriceofa250-dayforwardcontractona7%U.S.Treasurybondwithaspotpriceof$1,050（includingaccruedinterest）thathasjustpaidacouponandwillmakeanothercouponpaymentin182days.Theannualrisk-freerateis6%.

Solutions.RememberthatT-bondsmakesemiannualcouponpayments,so

Case10.6

Solutions.

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

0.5yearsfromnow（0.7yearslefttoexpirationoffutures）andonepayment1yearfromnow（0.2years

untilexpiration）.Thus,

Ppt11

PayoffsandProfits

Case11.1

ConsideraEuropeanbondcalloptionwithanexercisepriceof$900.Thecallpremiumforthisoptionis$50.Atexpira