投资学题库Chap011

Chapter11-ManagingBondPortfolios11-1CHAPTER11MANAGINGBONDPORTFOLIOS1.Durationcanbethoughtofasaweightedaverageofthe‘maturities’ofthecashflowspaidtoholdersoftheperpetuity,wheretheweightforeachcashflowisequaltothepresentvalueofthatcashflowdividedbythetotalpresentvalueofallcashflows.Forcashflowsinthedistantfuture,presentvalueapproacheszero(i.e.,theweightbecomesverysmall)sothatthesedistantcashflowshavelittleimpact,andeventually,virtuallynoimpactontheweightedaverage.2.Alowcoupon,longmaturitybondwillhavethehighestdurationandwill,therefore,producethelargestpricechangewheninterestrateschange.3.Arateanticipationswapshouldwork.Thetradewouldbetolongthecorporatebondsandshortthetreasuries.Arelativegainwillberealizedwhenratespreadsreturntonormal.4.-25=-(D/1.06)x.0025x1050…solvingforD=10.095.d.6.Theincreasewillbelargerthanthedecreaseinprice.7.Whileitistruethatshort-termratesaremorevolatilethanlong-termrates,thelongerdurationofthelonger-termbondsmakestheirratesofreturnmorevolatile.Thehigherdurationmagnifiesthesensitivitytointerest-ratesavings.Thus,itcanbetruethatratesofshort-termbondsaremorevolatile,butthepricesoflong-termbondsaremorevolatile.8.Computationofduration:a.YTM=6%(1)(2)(3)(4)(5)TimeuntilPayment(Years)PaymentPaymentDiscountedat6%WeightColumn(1)×Column(4)16056.600.05660.056626053.400.05340.106831060890.000.89002.6700ColumnSum:1000.001.00002.8334Duration=2.833yearsChapter11-ManagingBondPortfolios11-2b.YTM=10%(1)(2)(3)(4)(5)TimeuntilPayment(Years)PaymentPaymentDiscountedat10%WeightColumn(1)×Column(4)16054.550.06060.060626049.590.05510.110131060796.390.88442.6531ColumnSum:900.531.00002.8238Duration=2.824years,whichislessthanthedurationattheYTMof6%9.Thepercentagebondpricechangeis:–Duration0327.010.10050.0194.7y1yora3.27%decline10.Computationofduration,interestrate=10%:(1)(2)(3)(4)(5)TimeuntilPayment(Years)Payment(inmillionsofdollars)PaymentDiscountedAt10%WeightColumn(1)×Column(4)110.90910.27440.2744221.65290.49890.9977310.75130.22670.6803ColumnSum:3.31331.00001.9524Duration=1.9524years11.Thedurationoftheperpetuityis:(1+y)/y=1.10/0.10=11yearsLetwbetheweightofthezero-couponbond.Thenwefindwbysolving:(w1)+[(1–w)11]=1.9523w=9.048/10=0.9048Therefore,yourportfolioshouldbe90.48%investedinthezeroand9.52%intheperpetuity.12.Thepercentagebondpricechangewillbe:–Duration00463.008.10010.00.5y1yora0.463%increaseChapter11-ManagingBondPortfolios11-313.a.BondBhasahigheryieldtomaturitythanbondAsinceitscouponpaymentsandmaturityareequaltothoseofA,whileitspriceislower.(Perhapstheyieldishigherbecauseofdifferencesincreditrisk.)Therefore,thedurationofBondBmustbeshorter.b.BondAhasaloweryieldandalowercoupon,bothofwhichcauseittohavealongerdurationthanthatofBondB.Moreover,BondAcannotbecalled.Therefore,thematurityofBondAisatleastaslongasthatofBondB,whichimpliesthatthedurationofBondAisatleastaslongasthatofBondB.14.Choosethelonger-durationbondtobenefitfromaratedecrease.a.TheAaa-ratedbondhastheloweryieldtomaturityandthereforethelongerduration.b.Thelower-couponbondhasthelongerdurationandmoredefactocallprotection.c.Thelowercouponbondhasthelongerduration.15.a.Thepresentvalueoftheobligationis$17,832.65andthedurationis1.4808years,asshowninthefollowingtable:Computationofduration,interestrate=8%(1)(2)(3)(4)(5)TimeuntilPayment(Years)PaymentPaymentDiscountedat8%WeightColumn(1)×Column(4)110,0009,259.260.51920.51923210,0008,573.390.48080.96154ColumnSum:17,832.651.00001.48077b.Toimmunizetheobligation,investinazero-couponbondmaturingin1.4808years.Sincethepresentvalueofthezero-couponbondmustbe$17,832.65,thefacevalue(i.e.,thefutureredemptionvalue)mustbe:$17,832.65(1.08)1.4808=$19,985.26c.Iftheinterestrateincreasesto9%,thezero-couponbondwouldfallinvalueto:92.590,17$)09.1(26.985,19$4808.1Thepresentvalueofthetuitionobligationwouldfallto$17,591.11,sothatthenetpositionchangesby$0.19.Iftheinterestratefallsto7%,thezero-couponbondwouldriseinvalueto:Chapter11-ManagingBondPortfolios11-499.079,18$)07.1(26.985,19$4808.1Thepresentvalueofthetuitionobligationwouldincreaseto$18,080.18,sothatthenetpositionchangesby$0.19.Thereasonthenetpositionchangesatallisthat,astheinterestratechanges,sodoesthedurationofthestreamoftuitionpayments.16.a.PVofobligation=$2million/0.16=$12.5millionDurationofobligation=1.16/0.16=7.25yearsCallwtheweightonthefive-yearmaturitybond(withdurationof4years).Then:(w4)+[(1–w)11]=7.25w=0.5357Therefore:0.5357$12.5=$6.7millioninthe5-yearbond,and0.4643$12.5=$5.8millioninthe20-yearbond.b.Thepriceofthe20-yearbondis:[60Annuityfactor(16%,20)]+[1000PVfactor(16%,20)]=$407.12Therefore,thebondsellsfor0.4071timesitsparvalue,sothat:Marketvalue=Parvalue0.4071$5.8million=Parvalue0.4071Parvalue=$14.25millionAnotherwaytoseethisistonotethateachbondwithparvalue$1000sellsfor$407.11.Iftotalmarketvalueis$5.8million,thenyouneedtobuy:$5,800,000/407.11=14,250bondsTherefore,totalparvalueis$14,250,000.17.a.Thedurationoftheperpetuityis:1.05/0.05=21yearsLetwbetheweightofthezero-couponbond,sothatwefindwbysolving:(w5)+[(1–w)21]=10w=11/16=0.6875Therefore,thepo