(45)-CFA固定收益證券

CFA固定收益證券Chapter5.5DurationofBondPortfolio第五章第五節(jié)：債券投資組合的久期DurationofBondPortfolioThedurationofabondportfoliocanbecalculatedusingtwomethods:Theweightedaverageoftimetoreceiptoftheaggregatecashflows:Inthisapproach,theMacaulaydurationoftheportfolioiscalculatedastheweightedaverageoftimetoreceiptofaggregatedcashflow.Thecashflowyieldisusedtoobtaintheweights.Inthisapproach,theportfolioisviewedasaseriesofaggregatedcashflows.Itisthetheoreticallycorrectapproach,butpractically,itisdifficulttouse.9/13/2023Page1DurationofBondPortfolioThismethodisdifficulttouseinpracticeduetothefollowingreasons:Thecashflowyieldisnotcommonlycalculatedforbondportfolios.Iftheportfoliocontainscallableorputablebondsorfloatingratenotes,theamountandtimingoffuturecouponandprincipalpaymentsareuncertain.Interestrateriskisusuallyexpressedasachangeinbenchmarkinterestratesratherthanasachangeinthecashflowyield.Forindividualbonds,thechangeinthecashflowyieldisnotnecessarilythesameamountasthechangeintheyields-to-maturity.9/13/2023Page2DurationofBondPortfolioExample1:Firstyearcashflow:10,000,000,cashflowin30thyear:100,000,000Financialcalculatorinputs:CF0=-19,600,000,CF1=10,000,000,F01=1,CF2=0,F02=28,CF3=100,000,000,F3=1,IRRCPT,I=7.8611Ifthecashflowyieldincreasesordecreasesby100bps,themarketvalueoftheportfolioisexpectedtoincreaseordecreasebyabout15.0958%.9/13/2023Page3DurationofBondPortfolioTheweightedaverageoftheindividualbonddurationsthatcomprisetheportfolio:Inthismethod,theMacaulayandmodifieddurationsfortheportfolioarecalculatedastheweightedaverageofthestatisticsfortheindividualbonds.Thisweightedaverageisanapproximationofthe1stapproach.Whentheyieldcurveisflatanddifferencesintheyields-to-maturityonthebondsintheportfolioaresmaller,thetwoapproachesproducethesameportfolioduration.AdvantagesofSecondMethod:Inthesecondmethod,callablebonds,putablebonds,andfloating-ratenotescanbeincludedintheweightedaverageusingtheeffectivedurationsforthesesecurities.Thesecondmethodcanbeeasilyusedasameasureofinterestraterisk.LimitationsofSecondMethod:Thismethodassumesaparallelshiftintheyieldcurve.9/13/2023Page4Example2:Aninvestmentfundownsthefollowingportfolioofthreefixed-rategovernmentbonds:ThetotalmarketvalueoftheportfolioisEUR96,437,017.Eachbondisonacoupondatesothatthereisnoaccruedinterest.Themarketvaluesarethefullpricesgiventheparvalue.Couponsarepaidsemiannually.Theyields-to-maturityarestatedonasemiannualbondbasis,meaninganannualrateforaperiodicityof2.TheMacaulaydurationsareannualized.DurationofBondPortfolio9/13/2023Page5Q1:Calculatetheaverage(annual)modifieddurationfortheportfoliousingthesharesofmarketvalueastheweights.Q2:Estimatethepercentagelossintheportfolio’smarketvalueifthe(annual)yield-to-maturityoneachbondgoesupby20bp