(43)-CFA固定收益证券

CFA固定收益证券Chapter5.3ApplicationofDuration,MoneyDurationandKeyRateDuration第五章第三节：债券久期的应用，货币久期与关键利率久期AnExampleExample2:Assumethatthe3.75%USTreasurybondthatmatureson15August

2041ispricedtoyield5.14%forsettlementon15October

2014.Couponsarepaidsemiannuallyon15Februaryand15August.Theyield-to-maturityisstatedonastreet-conventionsemiannualbondbasis.Thissettlementdateis61daysintoa184-daycouponperiod,usingtheactual/actualday-countconvention.ComputetheapproximatemodifieddurationandtheapproximateMacaulaydurationforthisTreasurybondassuminga5bpchangeintheyield-to-maturity.9/13/2023Page1

AnExample9/13/2023Page2

AnExample9/13/2023Page3ModifiedDurationvs.EffectiveDurationModifiedDurationv/sEffectiveDuration:Generally,themodifieddurationandeffectivedurationonatraditionaloption-freebondarenotidentical.Thedifferencebetweenmodifieddurationandeffectivedurationstendstonarrowwhen:Yieldcurveisflatter.Time-to-maturityisshorter.Priceofbondisclosertoitsparvalue,implyingthatthecouponrateisnearlyequaltotheyield-to-maturity.Themodifieddurationandeffectivedurationonanoption-freebondareidenticalonlywhentheyieldcurveiscompletelyflat.9/13/2023Page4Themoneyduration(dollarduration)ofabondmeasuresthechangeinpriceinunitsofthecurrencyinwhichthebondisdenominated.Moneyduration(MoneyDur)=ModDur×PVFullΔPVFull≈-MoneyDur×∆YieldExpectedloss(inmoneyterms)whenyieldincreasesby100bps=MoneyDuration×0.0100Expectedloss(in%)whenyieldincreasesby100bps=(modifiedduration×0.01)×100Pricevalueofabasispoint(PVBP):ThePVBPisanestimateofthechangeinthefullpriceofabondwhentheyield-to-maturitychangesby1bp.ThePVBPisalsocalledthe“PV01”i.e.“pricevalueofan01”or“presentvalueofan01”,where“01”means1bp.PVBP=(PV--PV+)/2Basispointvalue(BPV)=Moneyduration×0.0001(1bp)MoneyDurationofaBondandthePriceValueofaBasis9/13/2023Page5KeyRateDurationAkeyrateduration(orpartialduration)isameasureofabond’ssensitivitytoachangeinthebenchmarkyieldcurveataspecificmaturitysegment.Incontrasttoeffectiveduration,keyratedurationshelpidentify“shapingrisk”forabond—thatis,abond’ssensitivitytochangesintheshapeofthebenchmarkyieldcurve(e.g.,theyieldcurvebecomingsteeperorflatter).Theanalystmaywanttoknowhowthepriceofthecallablebondisexpectedtochangeifbenchmarkratesatshortmaturities(sayupto2years)shiftedupby25bpsbutlongermaturitybenchmarkratesremainedunchanged.Usingkeyratedurations,theexpectedpricechangewouldbeapproximatelyequaltominusthekeyratedurationfortheshortmaturitysegmenttimesthe0.0025interestrateshiftatthatsegment.Ofcourse,fo