(42)-CFA固定收益證券

CFA固定收益證券Chapter5.2MacaulayDuration,ModifiedDurationandEffectiveDuration第五章第二節(jié)：麥考利久期，修正久期和有效久期DurationofABondTheduration(久期)ofabondmeasuresthesensitivityofthebond’sfullprice(includingaccruedinterest)tochangesinthebond’syield-to-maturity(changesinbenchmarkinterestrates),allelsebeing(particularlythetime-to-maturity)constant.Thedurationmeasurestheinstantaneous(or,atleast,same-day)changeinthebondprice.Ifthebondisheldforthedurationperiod,anincreasefromreinvestingcouponsisoffsetbyadecreaseinpriceifinterestratesincreaseandadecreasefromreinvestingcouponsisoffsetbyanincreaseinpriceifinterestratesdecrease.9/13/2023Page1MacaulayDurationAbond’sMacaulaydurationiscalculatedastheweightedaverageofthenumberofyearsuntileachofthebond’spromisedcashflowistobepaid,wheretheweightsarethepresentvaluesofeachcashflowasapercentageofabond’sfullprice.Supposea4%3-yrsannualbondwithaYTMof5%,foreachyearCF1=40,PV1=40/1.05=38.10,Weight1=38.1/972.77=3.92%CF2=40,PV2=40/1.052=36.28,Weight2=36.28/972.77=3.73%CF3=1040,PV3=1040/1.053=898.39,Weight3=898.39/972.77=92.35%PV0=38.1+36.28+898.39=972.77Macaulaydurationofthisbond=3.92%(1)+3.73%(2)+92.35%(3)=2.883yearsTheMacaulaydurationofasemiannualbondcanbecalculatedinthesameway;asaweightedaverageofthenumberofsemiannualperiodsuntilcashflowaretobereceived.9/13/2023Page2

ModifiedDuration9/13/2023Page3ModifiedDuration9/13/2023Page4

EffectiveDuration9/13/2023Page5EffectiveDurationModifiedDurationdoesmakesnodistinctionbetweenchangesinthebenchmarkandchangeinthespreads.Effectivedurationreflectsonlythesensitivityofthebond’svaluetochangesinthebenchmarkyieldcurve.Changes