固定收益證券的復(fù)習(xí)計算題

載Fixed-incometreasury1、公式：PracticeQuestion3.1Supposecurrently,1-yearspotrateis1%andmarketexpectsthat1-yearspotratenextyearwouldbe2%and1-yearspotratein2yearswouldbe3%.Computetoday’s2-yearspotrateand3-yearspotrate.(已做答案)2、CurrentYieldComputethecurrentyieldfora7%8-yearbondwhosepriceis$94.17.Howaboutthecurrentyieldifpriceis$100,$106,respectively?Considera7%8-yearbondpayingcouponsemiannuallywhichissoldfor$94.17.Thepresentvalueusingvariousdiscountrateis:A.WhatistheYTMforthisbond?B.Howmuchisthetotaldollarreturnonthisbond?C.Howmuchisthetotaldollarreturnifyouputthesameamountofdollarsintoadepositaccountwiththesameannualyield?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)PracticeQuestion4.2A.Whatisthevalueofa4-year10%couponbondthatpaysinterestsemiannuallyassumingthattheannualdiscountrateis8%?Whatisthevalueofasimilar10%couponbondwithaninfinitematurity(無期限)?B.Whatisthevalueofa5-yearzero-couponbondwithamaturityvalueof$100discountedatan8%interestrate?C.Computethevaluepar$100ofparvalueofa4-year10%couponbond,assumingthepaymentsareannualandthediscountrateforeachyearis6.8%,7.2%,7.6%and8.0%,respectively.nfinitematurityPv=($100*10%/2)/(8%/2)(半年付息)PresentValuePropertiestionA.Supposethediscountrateforthe4-year10%couponbondwithaparvalueof$100is8%.Computeitspresentvalue.B.Oneyearlater,supposethatthediscountrateappropriateforacouponbondincreasesfrom8%to9%.Redoyourcalculationindecomposethepricechangeattributabletomovingtomaturityincreaseinthediscountrate. (期限與貼現(xiàn)率變化)3-year10%partAandandtothePracticeQuestion4.6Supposethattherearefivesemiannualcouponpaymentsremainingfora10%couponbond.Alsoassumethefollowing:①Annualdiscountrateis8%②78daysbetweenthesettlementdateandthenextcouponpaymentdate③182daysinthecouponperiodComputethefullpriceofthiscouponbond.Whatisthecleanpriceofthisbond?4、ValuationApproachCase4.1A.Considera8%10-yearTreasurycouponbond.Whatisitsfairvalueiftraditionalapproachisused,givenyieldforthe10-yearon-the-runTreasuryissueis8%?B.WhatisthefairvalueofaboveTreasurycouponbondifarbitrage-freeapproachsedgiventhefollowingannualspotrates?C.Whichapproachismoreaccurate(準(zhǔn)確)?2、ConvexityConsidera9%20-yearbondsellingat$134.6722toyield6%.Fora20bpchangeinyield,itspricewouldeitherincreaseto$137.5888ordecreaseto$131.8439.A.Computetheconvexityforthisbond.B.Whatistheconvexityadjustmentforachangeinyieldof200bps?C.Ifweknowthatthedurationforthisbondis10.66,whatshouldthetotalestimatedpercentagepricechangebefora200bpincreaseintheyield?Howabouta200bpdecreaseintheyield?1、MeasuringYieldCurveRiskelAConsiderthefollowingtwo$100portfolioscomposedof2-year,16-year,and30-yearissues,allofwhicharezero-couponbonds:Forsimplicity,assumethereareonlythreekeyrates—2years,16yearsand30years.Calculatetheportfolio’skeyratedurationsatthesethreepointsanditseffectiveduration.Case6.1:PanelBariosearrateshiftsdownbasispointsdthe30-yearrateshiftsup10basispoints.cenarioConsidera6.5%option-freebondwith4yearsremainingtomaturity.Iftheappropriatebinomialinterestratetreeisshownasbelow,calculatethefairpriceofthisbond.1、ValuingCallableandPutableBondsleConsidera6.5%callablebondwith4yearsremainingtomaturity,callableinoneyearat$100.Assumetheyieldvolatilityis10%andtheappropriatebinomialinterestratetreeissameasCase6.4.Calculatethefairpriceofthiscallablebond.Assumetheyieldvolatilityis10%andtheappropriatebinomialinterestyearsremainingtomaturity,putableinoneyearat$100.Assumethes載ValueofappppCapppppppConvertibleBondsCase9.1:Supposethatthestraightvalueofa5.75%ADCconvertiblebondis$981.9per$1,000ofparvalueanditsmarketpriceis$1,065.Themarketpricepershareofcommonstockis$33andtheconversionratiois25.32sharesper$1,000ofparvalue.Alsoassumethatthecommonstockdividendis$0.90pershare.ption載公式：MinimumValue:thegreaterofitsconversionpriceanditsstraightvalue.ConversionPrice=Marketpriceofcommonstock×ConversionratioStraightValue/InvestmentValue:presentvalueofthebond’scashflowsdiscountedattherequiredreturnonacomparableoption-freeissue.MarketConversionPrice/ConversionParityPrick=Marketpriceofconvertiblesecurity÷ConversionratioMarketConversionPremiumPerShare=Marketconversionprice–MarketpriceofcommonstockMarketConversionPremiumRatio=Marketconversionpremiumpershare÷MarketpriceofcommonstockPremiumoverstraightvalue=(Marketpriceofconvertiblebond/Straightvalue)–1Thehigherthisratio,thegreaterdownsideriskandthelessattractivetheconvertiblebond.載PremiumPaybackPeriod=Marketconversionpremiumpershare÷FavorableincomedifferentialpershareFavorableIncomeDifferentialPerShare=[Couponinterest–(Conversionratio×Commonstockdividendpershare)]÷ConversionratioA.Whatistheminimumvalueofthisconvertiblebond?B.Calculateitsmarketconversionprice,marketconversionpremiumpershareandmarketconversionpremiumratio.C.Whatisitspremiumpaybackperiod?D.Calculateitspremiumoverstraightvalue.ppMarketpriceofcommonstock=$33,conversionratio=25.32StraightValue=$981.9，marketpriceofconversiblebond=$1,065commonstockdividend=$0.90A、ConversionPrice=Marketpriceofcommonstock×Conversionratiotheminimumvalueofthisconvertiblebond=max{$835.56,$981.9}=$981.9B、MarketConversionPrice/ConversionParityPrick=Marketpriceofconvertiblesecurity÷ConversionratioMarketConversionPremiumPerShare=Marketconversionprice–MarketpriceofcommonstockMarketConversionPremiumRatio=Marketconversionpremiumpershare÷MarketpriceofcommonstockPremiumPaybackPeriod=Marketconversionpremiumpershare÷FavorableincomedifferentialpershareFavorableIncomeDifferentialPerShare=[Couponinterest–(Conversionratio×Commonstockdividendpershare)]÷ConversionratioCouponinterestfrombond000=$57.50D、Premiumoverstraightvalue=(Marketpriceofconvertiblebond/Straightvalue)–1載No-ArbitragePrinciple:norisklessprofitsgainedfromholdingacombinationofaforwardcontractpositionaswellaspositionsinotherassets.FP=PricethatwouldnotpermitprofitablerisklessarbitrageinssmarketsthatisCase10.1Considera3-monthforwardcontractonazero-couponbondwithafacevalueof$1,000thatiscurrentlyquotedat$500,andassumearisk-freeannualinterestrateof6%.Determinethepriceoftheforwardcontractunderthenoarbitrageprinciple.Solutions.Supposetheforwardcontractdescribedincase10.1isactuallytradingat$510,whichisgreaterthanthenoarbitrageprice.Demonstratehowanarbitrageurcanobtainrisklessarbitrageprofitfromthisoverpricedforwardcontractandhowmuchthearbitrageprofitwouldbe.Case10.3Iftheforwardcontractdescribedincase10.1isactuallytradingat$502,whichissmallerthantheno-arbitrageprice.Demonstratehowanarbitrageurcanobtainrisklessarbitrageprofitfromthisunderpricedforwardcontractandhowmuchthearbitrageprofitwouldbe.Case10.4:Calculatethepriceofa250-dayforwardcontractona7%U.S.Treasurypaidacouponandwillmakeanothercouponpaymentin182days.TheSolutions.RememberthatT-bondsmakesemiannualcouponpayments,Case10.6Solutions.Thesemiannualcoupononasingle,$1,000face-value7%bondis$35.Abondholderwillreceiveonepayment0.5yearsfromnow(0.7yearsleftentyearfromnowyearshusandProfitseefortheunderlyingbondis$1,000,whatisthecalloption’spayoffaswellasitsgain/loss?Isthisoption