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1、WhatPractitionersNeedToKnow...AboutDurationandConvexityMarkKHtzman,Windhamcouponpaymentsandprepay-receiptof7.75years.ButthisCapitalManagementmentofprincipal.measuretooisdeficientbecauseitignoresthetimevalueofConsidertwobonds,bothofmoney.A$100couponpaymentIn1938,FrederickMacaulaypub-whichma
2、turein10years.Sup-tobereceivedtwoyearsfromlishedhisclassicbook.SomeThe-posethefirstbondisazero-todayislessvaluablethana$100oreticalProblemsSuggestedbycouponbondthatpays$2000atcouponpaymenttobereceivedtheMovementsofInterestRates,maturity,whilethesecondbondoneyearhence.BondYieldsandStockPric
3、esinpaysacouponof$100annuallytheUnitedStatesSince1865^Al-and$1000atmaturity.AlthoughthoughMacaulayfocusedprima-bothbondsyieldthesametotalMacaulayrecognizedthisdistinc-rilyonthetheoryofinterestrates,cashflow,thebondholdermusttionanddeterminedthatthetimeasanasideheintroducedthewait10yearstor
4、eceivethecashtoreceiptofeachcashflowconceptofdurationasamoreflowfromthezero-couponbond,shouldbeweighted,notbytheprecisealternativetomaturityforwhilehereceivesalmosthalftherelativemagnitudeofthecashmeasuringthelifeofabond.Ascashflowfromthecoupon-flow,butbythepresentvalueofwithmanyoftheimpor
5、tantinno-bearingbondpriortoitsmatu-itsrelativemagnitude.Macaulay'svationsinfinance,theinvestmentrity.Therefore,theaveragetimeduration,therefore,equalstheav-communitywasslowtoappreci-toreceiptofthecashflowoftheeragetimetoreceiptofabond'scoupon-bearingbondissignifi-ateMacaulay'sdiscoveryofdu
6、ra-cashflows,inw^hicheachcashcantlyshorterthanitisforthetion.Itwasnotuntilthe1970szero-couponbond.flow'stimetoreceiptisweightedthatprofessionaiinvestorsbeganbyitspresentvaiueasapercent-tosubstitutedurationformaturityThefirstcashflowfromthecou-ageofthetotaipresentvalueofinordertomeasureafix
7、edin-pon-bearingbondcomesafterallthecashflows.Thesumofthecomeportfolio'sexposuretoin-oneyear,thesecondaftertwopresentvaluesofallthecashterestraterisk.^Today,durationyears,andsoon.Onaverage,theflows,ofcourse,equalsthepriceandconvexity—theextenttobondholderrecei
