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CHAPTER16ManagingBondPortfoliosCHAPTER16ManagingBondPortfoInverserelationshipbetweenpriceandyieldAnincreaseinabond’syieldtomaturityresultsinasmallerpricedeclinethanthegainassociatedwithadecreaseinyieldLong-termbondstendtobemorepricesensitivethanshort-termbondsBondPricingRelationshipsInverserelationshipbetweenpFigure16.1ChangeinBondPriceasaFunctionofChangeinYieldtoMaturityFigure16.1ChangeinBondPriAsmaturityincreases,pricesensitivityincreasesatadecreasingratePricesensitivityisinverselyrelatedtoabond’scouponratePricesensitivityisinverselyrelatedtotheyieldtomaturityatwhichthebondissellingBondPricingRelationshipsContinuedAsmaturityincreases,pricesTable16.1Pricesof8%CouponBond(CouponsPaidSemiannually)Table16.1Pricesof8%CouponTable16.2PricesofZero-CouponBond(SemiannuallyCompounding)Table16.2PricesofZero-CoupAmeasureoftheeffectivematurityofabondTheweightedaverageofthetimesuntileachpaymentisreceived,withtheweightsproportionaltothepresentvalueofthepaymentDurationisshorterthanmaturityforallbondsexceptzerocouponbondsDurationisequaltomaturityforzerocouponbondsDurationAmeasureoftheeffectivematDuration:CalculationDuration:CalculationSpreadsheet16.1CalculatingtheDurationofTwoBondsSpreadsheet16.1CalculatingtPricechangeisproportionaltodurationandnottomaturityD*

=modifieddurationDuration/PriceRelationshipPricechangeisproportionaltRulesforDurationRule1Thedurationofazero-couponbondequalsitstimetomaturityRule2Holdingmaturityconstant,abond’sdurationishigherwhenthecouponrateislowerRule3Holdingthecouponrateconstant,abond’sdurationgenerallyincreaseswithitstimetomaturityRule4Holdingotherfactorsconstant,thedurationofacouponbondishigherwhenthebond’syieldtomaturityislowerRules5Thedurationofalevelperpetuityisequalto:(1+y)/yRulesforDurationRule1ThedFigure16.2BondDurationversus

BondMaturityFigure16.2BondDurationversTable16.3BondDurations(YieldtoMaturity=8%APR;SemiannualCoupons)Table16.3BondDurations(YieConvexityTherelationshipbetweenbondpricesandyieldsisnotlinearDurationruleisagoodapproximationforonlysmallchangesinbondyieldsConvexityTherelationshipbetwFigure16.3BondPriceConvexity:30-YearMaturity,8%Coupon;InitialYieldtoMaturity=8%Figure16.3BondPriceConvexiCorrectionforConvexityCorrectionforConvexity:CorrectionforConvexityCorrecFigure16.4ConvexityofTwoBondsFigure16.4ConvexityofTwoBCallableBondsAsratesfall,thereisaceilingonpossiblepricesThebondcannotbeworthmorethanitscallpriceNegativeconvexityUseeffectiveduration:CallableBondsAsratesfall,tFigure16.5Price–YieldCurveforaCallableBondFigure16.5Price–YieldCurveMortgage-BackedSecuritiesAmongthemostsuccessfulexamplesoffinancialengineeringSubjecttonegativeconvexityOftensellformorethantheirprincipalbalanceHomeownersdonotrefinancetheirloansassoonasinterestratesdropMortgage-BackedSecuritiesAmonFigure16.6Price-YieldCurveforaMortgage-BackedSecurityFigure16.6Price-YieldCurveMortgage-BackedSecuritiesContinuedTheyhavegivenrisetomanyderivativesincludingtheCMO(collateralizedmortgageobligation)UseoftranchesMortgage-BackedSecuritiesConFigure16.7PanelA:CashFlowstoWholeMortgagePool;PanelsB–DCashFlowstoThreeTranchesFigure16.7PanelA:CashFlowBond-IndexFundsImmunizationofinterestraterisk:NetworthimmunizationDurationofassets=DurationofliabilitiesTargetdateimmunizationHoldingPeriodmatchesDurationPassiveManagementBond-IndexFundsPassiveManageFigure16.8StratificationofBondsintoCellsFigure16.8StratificationofTable16.4TerminalvalueofaBondPortfolioAfter5Years(AllProceedsReinvested)Table16.4TerminalvalueofaFigure16.9GrowthofInvestedFundsFigure16.9GrowthofInvestedFigure16.10ImmunizationFigure16.10ImmunizationTable16.5MarketValueBalanceSheetTable16.5MarketValueBalancCashFlowMatchingandDedicationAutomaticallyimmunizetheportfoliofrominterestratemovementCashflowandobligationexactlyoffseteachotheri.e.Zero-couponbondNotwidelyusedbecauseofconstraintsassociatedwithbondchoicesSometimesitsimplyisnotpossibletodoCashFlowMatchingandDedicatSubstitutionswapIntermarketswapRateanticipationswapPureyieldpickupTaxswapActiveManagement:SwappingStrategiesSubstitutionswapActiveManageHorizonAnalysisSelectaparticularholdingperiodandpredicttheyieldcurveatendofperiodGivenabond’stimetomaturityattheendoftheholdingperiodItsyieldcanbereadfromthepredictedyieldcurveandtheend-of-periodpricecanbecalculatedHorizonAnalysisSelectapartiContingentImmunizationAcombinationofactiveandpassivemanagementThestrategyinvolvesactivemanagementwithafloorrateofreturnAslongastherateearnedexceedsthefloor,theportfolioisactivelymanagedOncethefloorrateortriggerrateisreached,theportfolioisimmunizedContingentImmunizationAcombiFigure16.11ContingentImmunizationFigure16.11ContingentImmuniCHAPTER16ManagingBondPortfoliosCHAPTER16ManagingBondPortfoInverserelationshipbetweenpriceandyieldAnincreaseinabond’syieldtomaturityresultsinasmallerpricedeclinethanthegainassociatedwithadecreaseinyieldLong-termbondstendtobemorepricesensitivethanshort-termbondsBondPricingRelationshipsInverserelationshipbetweenpFigure16.1ChangeinBondPriceasaFunctionofChangeinYieldtoMaturityFigure16.1ChangeinBondPriAsmaturityincreases,pricesensitivityincreasesatadecreasingratePricesensitivityisinverselyrelatedtoabond’scouponratePricesensitivityisinverselyrelatedtotheyieldtomaturityatwhichthebondissellingBondPricingRelationshipsContinuedAsmaturityincreases,pricesTable16.1Pricesof8%CouponBond(CouponsPaidSemiannually)Table16.1Pricesof8%CouponTable16.2PricesofZero-CouponBond(SemiannuallyCompounding)Table16.2PricesofZero-CoupAmeasureoftheeffectivematurityofabondTheweightedaverageofthetimesuntileachpaymentisreceived,withtheweightsproportionaltothepresentvalueofthepaymentDurationisshorterthanmaturityforallbondsexceptzerocouponbondsDurationisequaltomaturityforzerocouponbondsDurationAmeasureoftheeffectivematDuration:CalculationDuration:CalculationSpreadsheet16.1CalculatingtheDurationofTwoBondsSpreadsheet16.1CalculatingtPricechangeisproportionaltodurationandnottomaturityD*

=modifieddurationDuration/PriceRelationshipPricechangeisproportionaltRulesforDurationRule1Thedurationofazero-couponbondequalsitstimetomaturityRule2Holdingmaturityconstant,abond’sdurationishigherwhenthecouponrateislowerRule3Holdingthecouponrateconstant,abond’sdurationgenerallyincreaseswithitstimetomaturityRule4Holdingotherfactorsconstant,thedurationofacouponbondishigherwhenthebond’syieldtomaturityislowerRules5Thedurationofalevelperpetuityisequalto:(1+y)/yRulesforDurationRule1ThedFigure16.2BondDurationversus

BondMaturityFigure16.2BondDurationversTable16.3BondDurations(YieldtoMaturity=8%APR;SemiannualCoupons)Table16.3BondDurations(YieConvexityTherelationshipbetweenbondpricesandyieldsisnotlinearDurationruleisagoodapproximationforonlysmallchangesinbondyieldsConvexityTherelationshipbetwFigure16.3BondPriceConvexity:30-YearMaturity,8%Coupon;InitialYieldtoMaturity=8%Figure16.3BondPriceConvexiCorrectionforConvexityCorrectionforConvexity:CorrectionforConvexityCorrecFigure16.4ConvexityofTwoBondsFigure16.4ConvexityofTwoBCallableBondsAsratesfall,thereisaceilingonpossiblepricesThebondcannotbeworthmorethanitscallpriceNegativeconvexityUseeffectiveduration:CallableBondsAsratesfall,tFigure16.5Price–YieldCurveforaCallableBondFigure16.5Price–YieldCurveMortgage-BackedSecuritiesAmongthemostsuccessfulexamplesoffinancialengineeringSubjecttonegativeconvexityOftensellformorethantheirprincipalbalanceHomeownersdonotrefinancetheirloansassoonasinterestratesdropMortgage-BackedSecuritiesAmonFigure16.6Price-YieldCurveforaMortgage-BackedSecurityFigure16.6Price-YieldCurveMortgage-BackedSecuritiesContinuedTheyhavegivenrisetomanyderivativesincludingtheCMO(collateralizedmortgageobligation)UseoftranchesMortgage-BackedSecuritiesConFigure16.7PanelA:CashFlowstoWholeMortgagePool;PanelsB–DCashFlowstoThreeTranchesFigure16.7PanelA:CashFlowBond-IndexFundsImmunizationofinterestraterisk:NetworthimmunizationDurationofassets=DurationofliabilitiesTargetdateimmunizationHoldingPeriodmatchesDurationPassiveManagementBond-IndexFundsPassiveManageFigure16.8StratificationofBondsintoCellsFigure16.8StratificationofTable16.4TerminalvalueofaBondPortfolioAfter5Years(AllProceedsReinvested)Table16.4TerminalvalueofaFigure16.9GrowthofInvestedFundsFigure16.9GrowthofInvestedFigure16.10ImmunizationFigure16.10ImmunizationTable16.5MarketValueBalanceSheetTable16.5MarketValueBalancCashFlowMatchingandDedicationAutomaticallyimmunizetheport

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