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CHAPTER16 ManagingBondPortfolios InverserelationshipbetweenpriceandyieldAnincreaseinabond syieldtomaturityresultsinasmallerpricedeclinethanthegainassociatedwithadecreaseinyieldLong termbondstendtobemorepricesensitivethanshort termbonds BondPricingRelationships Figure16 1ChangeinBondPriceasaFunctionofChangeinYieldtoMaturity Asmaturityincreases pricesensitivityincreasesatadecreasingratePricesensitivityisinverselyrelatedtoabond scouponratePricesensitivityisinverselyrelatedtotheyieldtomaturityatwhichthebondisselling BondPricingRelationshipsContinued Table16 1Pricesof8 CouponBond CouponsPaidSemiannually Table16 2PricesofZero CouponBond SemiannuallyCompounding AmeasureoftheeffectivematurityofabondTheweightedaverageofthetimesuntileachpaymentisreceived withtheweightsproportionaltothepresentvalueofthepaymentDurationisshorterthanmaturityforallbondsexceptzerocouponbondsDurationisequaltomaturityforzerocouponbonds Duration Duration Calculation Spreadsheet16 1CalculatingtheDurationofTwoBonds PricechangeisproportionaltodurationandnottomaturityD modifiedduration Duration PriceRelationship RulesforDuration Rule1Thedurationofazero couponbondequalsitstimetomaturityRule2Holdingmaturityconstant abond sdurationishigherwhenthecouponrateislowerRule3Holdingthecouponrateconstant abond sdurationgenerallyincreaseswithitstimetomaturityRule4Holdingotherfactorsconstant thedurationofacouponbondishigherwhenthebond syieldtomaturityislowerRules5Thedurationofalevelperpetuityisequalto 1 y y Figure16 2BondDurationversusBondMaturity Table16 3BondDurations YieldtoMaturity 8 APR SemiannualCoupons Convexity TherelationshipbetweenbondpricesandyieldsisnotlinearDurationruleisagoodapproximationforonlysmallchangesinbondyields Figure16 3BondPriceConvexity 30 YearMaturity 8 Coupon InitialYieldtoMaturity 8 CorrectionforConvexity CorrectionforConvexity Figure16 4ConvexityofTwoBonds CallableBonds Asratesfall thereisaceilingonpossiblepricesThebondcannotbeworthmorethanitscallpriceNegativeconvexityUseeffectiveduration Figure16 5Price YieldCurveforaCallableBond Mortgage BackedSecurities AmongthemostsuccessfulexamplesoffinancialengineeringSubjecttonegativeconvexityOftensellformorethantheirprincipalbalanceHomeownersdonotrefinancetheirloansassoonasinterestratesdrop Figure16 6Price YieldCurveforaMortgage BackedSecurity Mortgage BackedSecuritiesContinued TheyhavegivenrisetomanyderivativesincludingtheCMO collateralizedmortgageobligation Useoftranches Figure16 7PanelA CashFlowstoWholeMortgagePool PanelsB DCashFlowstoThreeTranches Bond IndexFundsImmunizationofinterestraterisk NetworthimmunizationDurationofassets DurationofliabilitiesTargetdateimmunizationHoldingPeriodmatchesDuration PassiveManagement Figure16 8StratificationofBondsintoCells Table16 4TerminalvalueofaBondPortfolioAfter5Years AllProceedsReinvested Figure16 9GrowthofInvestedFunds Figure16 10Immunization Table16 5MarketValueBalanceSheet CashFlowMatchingandDedication AutomaticallyimmunizetheportfoliofrominterestratemovementCashflowandobligationexactlyoffseteachotheri e Zero couponbondNotwidelyusedbecauseofconstraintsassociatedwithbondchoicesSometimesitsimplyisnotpossibletodo SubstitutionswapIntermarketswapRateanticipationswapPureyieldpickupTaxswap ActiveManagement SStrategies HorizonAnalysis SelectaparticularholdingperiodandpredicttheyieldcurveatendofperiodGivenabond stimetomaturityattheendoftheholdingperiodItsyieldcanbereadfromthepredictedyieldcurveandtheend of periodpricecanbecalculated ContingentImmunization AcombinationofactiveandpassivemanagementThestrategyinvolvesactivemanagementwithafloorrateofreturnAslonga
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