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1、BoridPortfolioAnalysisGroup•DurationandMaturityforNonzero-CouponBonds3•TheEffectoftheYieldLevel6•TheEffectoftheCouponFrequency7•DurationasTimeElapses(andMaturityApproaches)7•DurationBetweenCouponDates8•DurationofaPortfolio10III.ModifiedDuration11IV.Volati

2、lityWeightingforHedging,BondSwapsandArbitrage11•TheHedgeRatio12•PriceValueofaBasisPoint13•YieldValueof1/3214•UsingDurationinVolatilityWeighting16•DurationCanMislead—ATreasuryBondExample17•MoreonthePriceValueofaBasisPoint18V.Convexity20•AMorePronouncedExam

3、ple23•Convexity,RealSecuritiesandtheMarket25VI.DurationforOtherSecurities25Summary27Appendix29Figure1.CashFlowsandPresentValuesofaSeven-Year12%Bond2Figure2.CashFlowsandtheDurationFulcrum3Figure3.DurationofParandPremiumBonds4Figure4.DurationofDiscountBonds

4、5Figure5.DurationversusMaturity—Premium,ParandDiscountBonds5Figure6.EffectofYieldLevel6Figure7.Durationvs.PassageofTime—100-Year12%Bond(Annual-Pay)BondatPar7Figure8.CashFlowsandPresentValuesImmediatelyBeforeCouponPayment8Figure9.TheEffectoftheCouponPaymen

5、t9Figure10.CouponPaymentIncreasesDuration9Figure11.DurationThroughTime—LastEightCouponPeriodsofaBond10Figure12.Price-YieldCurveandPriceValueofBasisPoint(PVBP)13Figure13.YieldValueof1/3215Figure14.TreasuryHedgeExample17Figure15.TreasuryHedgeExample17Figure

6、16.HedgeRatios18Figure17.PVBPversusDurationasTimeElapses19Figure18.PVBP:EffectofYieldandCoupon19Figure19.NominalFlowandPresentValue20Figure20.PricesatDifferentYields21Figure21.PricesatDifferentYields21Figure22.DurationasRatesChange22Figure23.Durationversu

7、sYieldLevel23Figure24.Security4—CashFlowandDuration23Figure25.PricesatDifferentYields—EffectofConvexity24Figure26.DurationatDifferentYields24Figure27.DurationatDifferentYields25UnderstandingDurationandVolatilityI.IntroductionDurationisnotanewconcept:Itwas

8、firstdescribedbyFrederickMacaulayin1938.1Afterbeing"rediscovered"inthe1970s,durationhasbecomeoneofthemostcommonlyusedtoolsoffixed-incomemanagers.Oneuseisimmunization,whenaportfolioofassetsisselectedsuchthatitsdurati