Bodie2eChapter08-Valuation-of-Known-Cash-Flows-Bonds-英文版PPT金融学(第二版)-教学课件

Chapter8:

ValuationofKnown CashFlows:BondsObjectiveValuationoffixedincomesecuritiesExplainwhybondpriceschange1Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallChapter8Contents8.1UsingPresentValueFormulastoValueKnownFlows8.2TheBasicBuildingBlocks:PureDiscountBonds8.3CouponBonds,CurrentYield,andYield-to-Maturity8.4ReadingBondListings8.5WhyYieldsforthesameMaturityDiffer8.6TheBehaviorofBondPricesOverTime2Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.1UsingPresentValueFormulastoValueKnownFlowsYouhavebeenofferedtheopportunitytopurchaseamortgage.ItwasoriginallypartofacreativefinancingpackagewheretheoriginalownerfinancedthebuyerTheremaininglifeofthemortgageis60months,withpaymentof$400.Yourrequiredrateofreturnis1.5%/month3Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallCalculationUsingthepresentvalueofanannuityformuladiscussedinchapter4,youwillpaynomorethan4Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallFinancialCalculatorAlternatively,usingyourfinancialcalculator(remembertosetthecorrectdefaults)youobtain5Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallChangeinRequiredRateIfyourrequiredrateofreturnincreasedto1.6%/month6Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallUsingPresentValueFormulastoValueKnownFlowsObservethatthemaximumyouwouldpayforthebondhasdecreasedAnincreaseintherequiredrateofreturnalwaysleadstoadecreaseinthevalueofafixedincomesecurityTheproofisveryeasy7Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPricesRiseastheInterestRatesFallWritethePVofthefixedincomesecurityasthesumterms8Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPricesRiseastheInterestRatesFallIfigoesup,1+igoesup,1/(1+i)goesdownfori>-1,(1/(1+i))jgoesdownfori>0.Soifthepaymentsarepositive,thenthesummustalsogodownSimilarly,idown->PVup9Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPricesRiseastheInterestRatesFallBasicprincipleinevaluatingknownflowsAchangeinmarketinterestratescausesachangeintheoppositedirectioninthemarketvaluesofallexistingcontractspromisingfixedpaymentsinthefuture10Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallNoteVolatilemarketratesimplyvolatilemarketvalues11Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallFindingtheCorrectDiscountRateBondanalysisisnotaseasyasthisanalysisappearstoimplyWeneedaninterestratetouseintheformulaWesawinChapter2thatinterestratesareafunctionoftime-to-maturityTwodefault-freebondswithidenticalmaturitiesmayhavedifferentYTMs12Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallYieldCurveAtypicalyieldcurve:13Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.2TheBasicsBuildingBlocks:PureDiscountBondsWecanalwaysanalyzeanyfixedincomecontractintoasumofpurediscountbondsApurediscountbondisasecuritythatpromisestopayaspecifiedsinglecashpayment(facevalueorparvalue)ataspecifieddatecalleditsmaturitydate14Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPureDiscountBondsNoteThereisnocashflowassociatedwithinterestPurediscountbondsarepurchasedatadiscountfromtheirfaceorparvalue15Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPureDiscountBondsThepurediscountbondisanexampleofthepresentvalueofalumpsumequationweanalyzedinChapter4Solvingthis,theyield-to-maturityonapurediscountbondisgivenbytherelationship:16Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPureDiscountBondsInthisequation,PisthepresentvalueorpriceofthebondFisthefaceorfuturevaluenistheinvestmentperiodiistheyield-to-maturity17Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPureDiscountBondsExampleYoucanpurchaseapurediscountbondfor$9,000,anditmaturesintwoyearswithafacevalueof$10,000Whatistheytm?18Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPureDiscountBonds19Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.3CouponBonds,CurrentYield,andYieldtoMaturityAcouponbondobligatestheissuertomakeperiodicpaymentsofinterest(calledcouponpayments)tothebondholderuntilthebondmaturesatwhichtimethefacevalueofthebondisalsopaidtothebondholderandthecontractissatisfied20Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallCouponRateThecouponrateistheinterestrateappliedtothefacevaluetocomputethecouponpaymentAbondwithafacevalueof$1,000andacouponrateof10%paysanannualcouponof$100Atmaturity,thepaymentis$1,000+$10021Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallCashFlowsfor10%$1,000CouponBond22Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallPar,premium,andDiscountBondsAcouponbondwithitscurrentpriceequaltoitsparvalueisaparbondIfitistradingbelowparitisadiscountbondIfitistradingaboveparitisapremiumbond(nottobeconfusedwiththeU.K.lotterybondofthesamename!)23Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondsTradingatParBondPricingPrinciple#1:(ParBonds)Ifabond’spriceequalsitsfacevalue,thenitsyield-to-maturity=currentyield=couponrate. Proof:24Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallCouponBonds,CurrentYield,andYield-to-MaturityTheyield-to-maturityisthediscountratethatmakesthepresentvalueofthecashflowsfromthebondequaltothecurrentpriceofthebondAnexcellentwaytocomputetheytmisgiveninChapter425Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallUsingPureDiscountBondstoValueotherBondsValueabondthatpaysits$100couponattheendofeachyearfor3-years,anditsparvalueof$1,000in3-yearsYouhavediscoveredthreepurediscountbonds(eachwitha$1,000parvalue)thatmaturein1,2,and3years,andthataretradingat$960,$890,and$810respectively26Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallFirstSolutionMethod27Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallSecondSolutionMethod28Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallConclusionThefirstmethodusesthefactthatacouponbondisthesumofpurediscountbondsitisfastanddirectThesecondmethodfirstdeterminestheyields-to-maturityofeachdiscountbondcashflowsarethenevaluatedusingthem29Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallTheYTMoftheCouponBondWehavethepriceofthecouponbond,andthetimingandmagnitudeofitsfuturecashflows,sowecandetermineitsYTMWeusethefinancialcalculator,butanumericalmethodwasprovidedinchapter4forthisclassofproblems30Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallTheYTMoftheCouponBond31Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallObservationTheyieldtomaturityonthe3-yearpurediscountbondwas7.28%andtheyield-to-maturityonthe3-yearcouponbondwas7.10%Theyield-curvefordefault-freebondsisnotauniquevalue32Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPricingPrinciple#2&3BondPrinciple#2:PremiumBonds bondprice>facevalueÞytm<currentyield<couponrateBondPrinciple#3:DiscountBonds bondprice<facevalueÞytm>currentyield>couponrate33Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallProofofRelationshipbetweenYTMandCurrentYieldForcouponbonds,wehavethefollowingrelationshipsNotethe(sensible)restrictionsonthevariablerangesNotethat1/((1+i)^n-1)isalwayspositive34Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall35Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallProofofRelationshipbetweenCurrentandCouponYieldsForcouponbonds,wehavethefollowingrelationshipderivedfromthebondformulaNotethatthedifferencesbetweenthereciprocalshavethesamesign,sotheactualdifferencesalsohavethesamesignNotethatsizerelationshipisdeterminedbythediscountfactorwhichisalways<136Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall37Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallHowtoRememberPrinciplesImaginethatthebondwasissuedatpartheyield-to-maturitymovesfromthecouponyieldintheoppositedirectiontopricethecouponrateisunchangingThisdiagrammayhelp:38Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall39Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallHighYieldT-BondFundsYieldcurveswithlargepositiveslopesmakelonger-termT-bondstemptingbecause,likeT-bills,theyaredefault-freeTheabovediagramwasbasedon:par=$1000,coupon=$100,n=10-years,flatObservethelargeeffectofmodestchangesininterestoncapitalAcloseupisgivenbelow40Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall41Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallClarificationThelastexampleusedaflatyieldcurveLetuslookatanexamplewithshort-termratesremainingfixedlonger-termratesrisingonincreasedexpectationofageneralriseininterestrates42Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall43Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallInvestmentImplicationsAssumea20-yearbondwithacouponrateof6%Purchasefor$1016.54whenthelowercurveprevailsWhenyieldcurverises,thebondisworthonly$814.05ThisisamassivecapitalriskAdditionally,long-termratesaremorevolatilethanshort-termrates44Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.4ReadingBondListings

TherearetraditionsforreportingyieldsandcomputingearnedinterestthatneedtobeunderstoodbeforetradingCouponbondsareoftenquotedintermsoftheannualratecompoundedsemi-annuallyT-billsareoftenquotedonadiscountbasise.g.,a1yearT-billhas364daysoutstanding,butayearhasonly360days…(itgetsnasty)45Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallReadingBondListings

TakecarethatthefractionalpartofanumberisunderstoodIsit16ths,32nds,64ths,100thsorsomeotherconvention?Askprice:dealer’ssellingpriceBidprice:dealer’sbuyingprice46Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.5WhyYieldsforthesameMaturityDiffer

Thefundamentalbuildingblockofbondsisthepurediscountbond:CouponbondsmaybeviewedasaportfolioofdiscountbondsTheruleofonepriceappliestobondsthroughpurediscountbondsItisamistaketoassumethatcouponbondswiththesamelifehavethesameyield--theircouponratesdiffer,leadingtoadifferent%mixofdiscountbonds47Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallMovementofaPureDiscountBond’sPriceoverTime48Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall8.6TheBehaviorofBondPricesOverTimeTheexpectedpriceofpurediscountbondsrisesexponentiallytothefacevaluewithtime,andtheactualpriceneverexceedsparCouponbondsaremorecomplex,andtheirpricemayexceedtheirparvalue,butatmaturitytheyreachtheirparvalue49Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPricesatAlternativeYields50Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHallBondPriceSens