投资学第16章债券资产组合管理

Investments,8theditionBodie,KaneandMarcusSlidesbySusanHineMcGraw-Hill/IrwinCopyright©2009byTheMcGraw-HillCompanies,Inc.Allrightsreserved.CHAPTER16ManagingBondPortfolios16-2•Inverserelationshipbetweenpriceandyield•Anincreaseinabond’syieldtomaturityresultsinasmallerpricedeclinethanthegainassociatedwithadecreaseinyield•Long-termbondstendtobemorepricesensitivethanshort-termbondsBondPricingRelationships16-3Figure16.1ChangeinBondPriceasaFunctionofChangeinYieldtoMaturity16-4•Asmaturityincreases,pricesensitivityincreasesatadecreasingrate•Pricesensitivityisinverselyrelatedtoabond’scouponrate•PricesensitivityisinverselyrelatedtotheyieldtomaturityatwhichthebondissellingBondPricingRelationshipsContinued16-5Table16.1Pricesof8%CouponBond(CouponsPaidSemiannually)16-6Table16.2PricesofZero-CouponBond(SemiannuallyCompounding)16-7•Ameasureoftheeffectivematurityofabond•Theweightedaverageofthetimesuntileachpaymentisreceived,withtheweightsproportionaltothepresentvalueofthepayment•Durationisshorterthanmaturityforallbondsexceptzerocouponbonds•DurationisequaltomaturityforzerocouponbondsDuration16-8tttwCFyice()1PrtwtDTt1CFCashFlowforperiodttDuration:Calculation16-9Spreadsheet16.1CalculatingtheDurationofTwoBonds16-10PricechangeisproportionaltodurationandnottomaturityD*=modifieddurationDuration/PriceRelationship(1)1PyDxPy*PDyP16-11RulesforDurationRule1Thedurationofazero-couponbondequalsitstimetomaturityRule2Holdingmaturityconstant,abond’sdurationishigherwhenthecouponrateislowerRule3Holdingthecouponrateconstant,abond’sdurationgenerallyincreaseswithitstimetomaturityRule4Holdingotherfactorsconstant,thedurationofacouponbondishigherwhenthebond’syieldtomaturityislowerRules5Thedurationofalevelperpetuityisequalto:(1+y)/y16-12Figure16.2BondDurationversusBondMaturity16-13Table16.3BondDurations(YieldtoMaturity=8%APR;SemiannualCoupons)16-14Convexity•Therelationshipbetweenbondpricesandyieldsisnotlinear•Durationruleisagoodapproximationforonlysmallchangesinbondyields16-15Figure16.3BondPriceConvexity:30-YearMaturity,8%Coupon;InitialYieldtoMaturity=8%16-16CorrectionforConvexityntttttyCFyPConvexity122)()1()1(1CorrectionforConvexity:21[()]2PDyConvexityyP16-17Figure16.4ConvexityofTwoBonds16-18CallableBonds•Asratesfall,thereisaceilingonpossibleprices–Thebondcannotbeworthmorethanitscallprice•Negativeconvexity•Useeffectiveduration:/EffectiveDuration=PPr16-19Figure16.5Price–YieldCurveforaCallableBond16-20Mortgage-BackedSecurities•Amongthemostsuccessfulexamplesoffinancialengineering•Subjecttonegativeconvexity•Oftensellformorethantheirprincipalbalance–Homeownersdonotrefinancetheirloansassoonasinterestratesdrop16-21Figure16.6Price-YieldCurveforaMortgage-BackedSecurity16-22Mortgage-BackedSecuritiesContinued•TheyhavegivenrisetomanyderivativesincludingtheCMO(collateralizedmortgageobligation)–Useoftranches16-23Figure16.7PanelA:CashFlowstoWholeMortgagePool;PanelsB–DCashFlowstoThreeTranches16-24•Bond-IndexFunds•Immunizationofinterestraterisk:–NetworthimmunizationDurationofassets=Durationofliabilities–TargetdateimmunizationHoldingPeriodmatchesDurationPassiveManagement16-25Figure16.8StratificationofBondsintoCells16-26Table16.4TerminalvalueofaBondPortfolioAfter5Years(AllProceedsReinvested)16-27Figure16.9GrowthofInvestedFunds16-28Figure16.10Immunization16-29Table16.5MarketValueBalanceSheet16-30CashFlowMatchingandDedication•Automaticallyimmunizetheportfoliofrominterestratemovement–Cashflowandobligationexactlyoffseteachother•i.e.Zero-couponbond•Notwidelyusedbecauseofconstraintsassociatedwithbondchoices•Sometimesitsimplyisnotpossibletodo16-31•Substitutionswap•Intermarketswap•Rateanticipationswap•Pureyieldpickup•TaxswapActiveManagement:SwappingStrategies16-32HorizonAnalysis•Selectaparticularholdingperiodandpredicttheyieldcurveatendofperiod•Givenabond’stimetomaturityattheendoftheholdingperiod–Itsyieldcanbereadfromthepredictedyieldcurveandtheend-of-periodpricecanbecalculated16-33ContingentImmunization•Acombinationofactiveandpassivemanagement•Thestrategyinvolvesactivemanagementwithafloorrateofreturn•Aslongastherateearnedexceedsthefloor,theportfolioisactivelymanaged•Oncethefloorrateortriggerrateisreached,theportfolioisimmunized16-34Figure16.11ContingentImmunization