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Chapter11-ManagingBondPortfolios
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Chapter11
ManagingBondPortfolios
Durationcanbethoughtofasaweightedaverageofthe‘maturities’ofthecashflowspaidtoholdersoftheperpetuity,wheretheweightforeachcashflowisequaltothepresentvalueofthatcashflowdividedbythetotalpresentvalueofallcashflows.Forcashflowsinthedistantfuture,presentvalueapproacheszero(i.e.,theweightbecomesverysmall)sothatthesedistantcashflowshavelittleimpact,andeventually,virtuallynoimpactontheweightedaverage.
Alowcoupon,longmaturitybondwillhavethehighestdurationandwill,therefore,producethelargestpricechangewheninterestrateschange.
Anintermarketspreadswapshouldwork.Thetradewouldbetolongthecorporatebondsandshortthetreasuries.Arelativegainwillberealizedwhentheratespreadsreturntonormal.
ChangeinPrice=–(ModifiedDuration?ChangeinYTM)?Price
=-MacaulaysDuration1+YTM?ChangeinYTM
Giventhecurrentbondpriceis$1,050,yieldtomaturityis6%,andtheincreaseinYTMandnewprice,wecancalculateD:
$1,025–$1,050=–MacaulaysDuration1+0.06?0.0025?$1,050?
d.Noneoftheabove.
Theincreasewillbelargerthanthedecreaseinprice.
Whileitistruethatshort-termratesaremorevolatilethanlong-termrates,thelongerdurationofthelonger-termbondsmakestheirratesofreturnmorevolatile.Thehigherdurationmagnifiesthesensitivitytointerest-ratesavings.Thus,itcanbetruethatratesofshort-termbondsaremorevolatile,butthepricesoflong-termbondsaremorevolatile.
WhenYTM=6%,thedurationis2.8334.
(1)
(2)
(3)
(4)
(5)
TimeuntilP
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