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债券

航海_
2014-03-29 0人阅读 举报 0 0 暂无简介

简介:本文档为《债券pdf》,可适用于经济金融领域

Bond徐建国北京大学OutlineValuationofCashflowBondcharacteristicsandvaluationInterestratesValuingaStreamofCashFlows()()NNnnnnnCPVPVCrValuingaStreamofCashFlows(cont’d)Example(Berk,Chapter)YouhavejustgraduatedandneedmoneytobuyanewcarYourrichUncleHenrywilllendyouthemoneysolongasyouagreetopayhimbackwithinfouryears,andyouoffertopayhimtherateofinterestthathewouldotherwisegetbyputtinghismoneyinasavingsaccountBasedonyourearningsandlivingexpenses,youthinkyouwillbeabletopayhim$inoneyear,andthen$eachyearforthenextthreeyearsIfUncleHenrywouldotherwiseearnperyearonhissavings,howmuchcanyouborrowfromhimSolution:PVPerpetuities,Annuities,andOtherSpecialCasesPerpetuitiesAnnuities𝑃𝑉𝑎𝑛𝑛𝑢𝑖𝑡𝑦𝑜𝑓𝐶𝑓𝑜𝑟𝑁𝑝𝑒𝑟𝑖𝑜𝑑𝑠=𝑃𝑉𝐶𝑖𝑛𝑎𝑛𝑛𝑢𝑖𝑡𝑦−𝑃𝑉𝐶𝑖𝑛𝑎𝑛𝑛𝑢𝑖𝑡𝑦𝑖𝑛𝑝𝑒𝑟𝑖𝑜𝑑𝑁=𝐶𝑟(−(𝑟)𝑁)Growingannuities(inperpetuity)CPVCr()NgPVCrgrPerpetuities,Annuities,andOtherSpecialCasesExample(Berk,Chapter)Ellenconsideredsaving$,peryearforherretirementAlthough$,isthemostshecansaveinthefirstyear,sheexpectshersalarytoincreaseeachyearsothatshewillbeabletoincreasehersavingsbyperyearWiththisplan,ifsheearnsperyearonhersavings,howmuchwillEllenhavesavedatageSolution:$(())$,PV$,$FVmillionSolvingforVariablesOtherThanPVorFVSometimesweknowthepresentvalueorfuturevalue,butdonotknowoneoftheinputsAnnualpaymentInternalrateofreturnAccumulationtimeSolvingforVariablesOtherThanPVorFVAnnualpayment(Example,Berk,Chapter)YourbiotechfirmplanstobuyanewDNAsequencerfor$,Thesellerrequiresthatyoupayofthepurchasepriceasadownpayment,butiswillingtofinancetheremainderbyofferingamonthloanwithequalmonthlypaymentsandaninterestrateofpermonthWhatisthemonthlyloanpaymentSolution:$()()()()NPCrrSolvingforVariablesOtherThanPVorFVInternalrateofreturn(Example,Berk,Chapter)JessicahasjustgraduatedwithherMBARatherthantakethejobofaprestigiousinvestmentbank,shehasdecidedtogointobusinessforherselfShebelievesthatherbusinesswillrequireaninitialinvestmentof$millionThebankhasdecidedtofundherbusinessInreturnforprovidingtheinitialcapitalof$million,Jessicahasagreedtopaythem$,attheendofeachyearforthenextyearsWhatistheinternalrateofreturnonbank’sinvestmentinJessica’scompany,assumingshefulfillshercommitmentSolution:,,,()()rrSolvingforVariablesOtherThanPVorFVAccumulationtime(Example,Berk,ndedition,Chapter)YouaresavingforadownpaymentonahouseYouhave$,savedalready,andyoucanaffordtosaveanadditional$,peryearattheendofeachyearIfyouearnperyearonyoursaving,howlongwillittakeyoutosave$,Solution:(),NN,,Nln()Nln()yearsEffectiveAnnualRateversusAnnualPercentageRateEffectiveAnnualRate(EAR):有效年利率ConsiderscompoundingAlsoreferredtoastheeffectiveannualyield(EAY)orannualpercentageyield(APY)Annualpercentagerate(APR):年度百分比利率SimpleinterestearnedwithoutcompoundingTypicallylessthanEAR“TheAPRwithkcompoundingperiods”EquivalentPeriodDiscountRate()nnrAPRInterestRateperCompoundingPeriodperiodsyearkEffectiveAnnualRateandAnnualPercentageRate(cont'd)TheAPRitselfcannotbeusedasadiscountrateConvertinganAPRtoanEARTheEARincreaseswiththefrequencyofcompoundingContinuouscompoundingiscompoundingeveryinstantkAPREARk()APREAReEffectiveAnnualRateandAnnualPercentageRate(cont'd)AAPRwithcontinuouscompoundingresultsinanEARofapproximatelyTableEffectiveAnnualRatesforaAPRwithDifferentCompoundingPeriodsEffectiveAnnualRateandAnnualPercentageRate(cont'd)Amortizingloans(Chapter,Berk)Typicaltermsforanewcarloanmightbe“APRformonths”Whatisthemonthlypaymentfor$,carSolution:=(),C,$()CBondCharacteristicsBondTerminologyMaturityDate,Term,FaceParValue,Coupon,CouponRateCouponPayment:Zerocoupon(purediscount)ReceivefacevalueatmaturitydatebutnointerestpaymentExample:TreasuryBillsCouponRateFaceValueNumberofCouponPaymentsperYearCPNTNotes:中期国债()TBonds:长期国债(>)Maturity:到期日Coupon:息票率Bid:出价Ask:要价Chg:Askedyield:YTMbasedonaskpriceAccruedInterest:应计利息yBondCharacteristicsCorporateBondsBondsafetyisratedbythreemajorbondratingagenciesCallProvisiononCorporateBondsAllowfirmtobuybackthebondsandrefinanceatlowerinterestrateswhenmarketratesfallPuttableBondsConvertiblebondsBondholdershaveoptiontoexchangebondsforsharesofcommonstockFloatingRateBondsPreferredStockInternationalBonds:foreignbondsandEurobondsBondCharacteristicsYieldtoMaturityofabondisthediscountratethatsetsthepresentvalueofthepromisedbondpaymentsequaltothecurrentmarketpriceofthebondInternalrateofreturn(IRR)YieldtoMaturity𝑃=𝐶𝑃𝑁×𝑟(−𝑟𝑁)𝐹𝑉𝑟𝑁YieldtoMaturityofannYearZeroCouponBondnnFVYTMPBondCharacteristicsProblem:YieldtoMaturityofCouponBondsConsiderthefiveyear,$bondwithacouponrateandsemiannualcouponsIfthisbondiscurrentlytradingforapriceof$,whatisthebond’syieldtomaturitySolution:Becausethebondhasremainingcouponpayments,wecomputeitsyieldrbysolving:=×𝑟(−𝑟)𝑟Wecangetr=ThusthebondhasayieldtomaturityequaltoaAPRwithsemiannualcompoundingBondPricingExample(Berk,Chapter)TheUSTreasuryhasjustissuedafiveyear,$bondwithacouponrateandsemiannualcouponsSupposeyouaretoldthatitsyieldtomaturityhasincreasedto(expressedasanAPRwithsemiannualcompounding)WhatpriceisthebondtradingfornowSolution:CPN=$*=$()()TtttCouponParvaluerrBondValue=()$PDynamicBehaviorofBondPricesAbondcanbesoldAtadiscount(YTM>couponrate)Atpar(YTM=couponrate)Atapremium(YTM<couponrate)Example(Berk,Chapter)ConsiderthreeyearbondswithannualcouponpaymentsOnebondhasacouponrate,onehasacouponrate,andonehasacouponrateIftheyieldtomaturityofeachbondis,whatisthepriceofeachbondper$facevalueSolution:P(coupon)=()$()tradesatapremiumP(coupon)=()$()tradesatparP(coupon)=()$()tradesatadiscountDynamicBehaviorofBondPricesTheEffectofTimeonthePriceofaCouponBondAssumeYTM=DynamicBehaviorofBondPricesBondpricefluctuateswithinterestrateInverselyandhighlysensitiveDurationPriceofancouponbondwithyearmaturitymakingsemiannualpaymentsDynamicBehaviorofBondPricesDurationDynamicBehaviorofBondPricesBondpricesandyieldsareinverselyrelatedAnincreaseinabond’syieldtomaturityresultsinasmallerpricechangethanadecreaseinyieldofequalmagnitudePricesoflongtermbondstendtobemoresensitivetointerestratechangesthanpricesofshorttermbondsThesensitivityofbondpricestochangesinyieldsincreasesatadecreasingrateasmaturityincreasesInotherwords,interestrateriskislessthanproportionaltobondmaturityInterestrateriskisinverselyrelatedtothebond’scouponratePricesoflowcouponbondsaremoresensitivetochangesininterestratesthanpricesofhighcouponbondsThesensitivityofabond’spricetoachangeinitsyieldisinverselyrelatedtotheyieldtomaturityatwhichthebondcurrentlyissellingDynamicBehaviorofBondPricesDurationmeasuresthesensitivityofbondpricetoyieldtomaturity𝑑𝑃𝑃𝑑𝑟=−𝑡×𝐶𝐹𝑡𝑟𝑡𝑃=𝑇𝑡=−𝑟𝑡×𝐶𝐹𝑡𝑟𝑡𝑃𝑇𝑡=Macaulay’sdurationequalstheweightedaverageofthetimestoeachcouponorprincipalpaymentmadebythebond𝐷=𝑡×𝑤𝑡,𝑇𝑡=𝑤𝑡=𝐶𝐹𝑡𝑟𝑡𝐵𝑜𝑛𝑑Pr𝑖𝑐𝑒𝑑𝑃𝑃𝑑𝑟=−𝑟×𝐷Modifiedduration:𝐷=𝐷∗(𝑟)DynamicBehaviorofBondPricesExampletocalculateduration:FindthedurationofacouponbondmakingsemiannualcouponpaymentsifithasyearsuntilmaturityandhasayieldtomaturityofWhatisthedurationiftheyieldtomaturityisSolution:DynamicBehaviorofBondPricesExample:Considertheyearmaturity,couponbondmakingsemiannualcouponpaymentsandsellingatapriceof$,forayieldtomaturityofThedurationofthisbondisyearsSupposethesemiannualinterestrateincreasesfromtoWhat’sthepricechangeofthiscouponbondSolution:TreatoneperiodasahalfyearDurationofeachbondis*=periods,withaperperiodinterestrateofModifieddurationofeachbondis=periodsThebondpricesfallby*=DynamicBehaviorofBondPricesExample:Aninsurancecompanythatissuesaguaranteedinvestmentcontract,orGIC,for$,(Essentially,GICsarezerocouponbondsissuedbytheinsurancecompanytoitscustomersTheyarepopularproductsforindividuals’retirementsavingsaccounts)IftheGIChasayearmaturityandaguaranteedinterestrateof,theinsurancecompanyisobligatedtopay$,*()^=$,inyearsSupposethattheinsurancecompanychoosestofunditsobligationwith$,ofannualcouponbonds,sellingatparvalue,withyearstomaturityThedurationoftheannualcouponbondsisyearsDynamicBehaviorofBondPricesAsinterestrateschange,thechangeinvalueofboththeassetandtheobligationisequal,sotheobligationremainsfullyfundedRealVersusNominalInterestRatesInflationandRealVersusNominalRatesQuotedinterestratesarenominalinterestrates,whichindicatetherateofgrowthofthemoneyinvestedTherealinterestrateindicatestherateofgrowthofone’spurchasingpowerafteradjustingforinflationGrowthofMoneyGrowthinPurchasingPowerGrowthofPricesrrrirrirriiRealVersusNominalInterestRatesRealVersusNominalInterestRatesRiskfreeinterestrateandriskpremiumRiskFreeInterestRatesAdefaultfreezerocouponbondthatmaturesondatenprovidesariskfreereturnoverthesameperiodTheLawofOnePriceguaranteesthattheriskfreeinterestrateequalstheyieldtomaturityonsuchabondZeroCouponYieldCurveAplotoftheyieldofriskfreezerocouponbondsasafunctionofthebond’smaturitydateProvidessufficientinformationtoevaluateallriskfreebondsTreasuryCouponPayingYieldCurveOftenreferredtoas“theyieldcurve”OntheRunBonds(新券)nnrYTMTheYieldCurveTermStructure:TherelationshipbetweentheinvestmenttermandtheinterestrateYieldCurve:thetermstructureofriskfreeinterestrateTheYieldCurve(cont'd)ThetermstructurecanbeusedtocomputethepresentandfuturevaluesofariskfreecashflowoverdifferentinvestmenthorizonsYieldcurvecanbeusedtovaluecouponbondsPVusingaTermStructureofDiscountRate()()()NNNNnnNnCCCCPPVrrrrTheYieldCurve(cont'd)ForcouponbondTosummarize$()()rrr$PRiskfreeinterestrateandriskpremiumRiskfreeinterestrateandriskpremiumExpectedreturnforMarketindexiswhilereturnforriskfreebondisThedifferenceiscalledRiskPremiumExpectedreturnofA=RiskpremiumofA==ExpectedreturnofB=RiskpremiumofB==ForwardInterestRatesAforwardinterestrate(orforwardrate)isaninterestratethatwecanguaranteetodayforaloanorinvestmentthatwilloccurinthefutureSotheforwardrateforyearmeanstherateavailabletodayonaoneyearinvestmentthatbeginsfouryearsfromtodayBytheLawofoneprice,theforwardrateforyearisequivalenttoaninvestmentinaoneyear,zerocouponbondfYTMComputingForwardRatesAtwoyearforwardratecanbederivedfromoneyearzerocouponyieldandtwoyearzerocouponyield𝑓=,YTM=,𝑡ℎ𝑒𝑛𝑓=Ingeneral:nnnnn(YTM)f=(YTM)TextbookExampleAExample(Solution:fYTM()()YTMfYTM()()YTMfYTM()()YTMfYTMAForwardRatesandFutureInterestRatesHowdoestheforwardratecomparetotheinterestratethatwillactuallyprevailinthefutureItisagoodpredictoronlywheninvestorsdonotcareaboutriskConsidertheforwardrateasabreakevenrate(收支相抵的利率)Ifmostindividualsareshortterminvestors,theyshouldbecompensatedfortheuncertaintyaboutthepriceatwhichtheywillbeabletoselltheirlongtermbondsattheendoftheyearIfallinvestorswerelongterminvestors,noonewouldbewillingtoholdshorttermbondsunlessthosebondsofferedarewardforbearinginterestrateriskTheoriesoftheTermStructuresTheExpectationsHypothesis(预期理论)Theforwardrateequalsthemarketconsensusexpectationofthefutureshortinterestratethatis,f=E(r)andliquiditypremiumsarezeroLiquidityPreferenceTheory(流动性偏好理论)Shortterminvestorswillbeunwillingtoholdlongtermbondsunlesstheforwardrateexceedstheexpectedshortinterestrate,f>E(r)ShortterminvestorsdominatethemarketMarketSegmentationTheory(市场分割理论)PreferredHabitatTheory(期限偏好理论优先置产理论)()nnfErLiquiditypremiumTheYieldCurveandtheEconomyInterestDeterminationTheFederalReservedeterminesveryshortterminterestratesthroughitsinfluenceonthefederalfundsrate,whichistherateatwhichbankscanborrowcashreservesonanovernightbasisAllotherinterestratesontheyieldcurvearesetinthemarketandareadjusteduntilthesupplyoflendingmatchesthedemandforborrowingateachloantermTheYieldCurveandtheEconomyYieldcurveisagoodpredictorofthebusinesscycleVerysteepyieldcurvesareinterpretedbymanymarketprofessionalsaswarningsignsofimpendingrateincreasesTheyieldcurvetendstobesharplyincreasingastheeconomycomesoutofarecessionandinterestratesareexpectedtoriseAninvertedyieldcurveindicatesthatinterestratesareexpectedtodeclineinthefuture,suchaswhenexpectingeconomicslowdownEachofthelastsevenrecessionsintheUnitedStateswasprecededbyaperiodofinvertedyieldcurvewasinvertedTheYieldCurveandtheEconomyRelatedreadingsBerkandDemarzoChapTheTimeValueofMoneyChapInterestRateChapValuingBondsBodie,KaneandMarcusChapBondPricesandYieldsChapTheTermStructureofInterestRates

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