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.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
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