CFA一级百题进阶：固收.docx

7.FixedIncomeQ-l.A5-year,5%semiannualcouponpaymentcorporatebondispricedat104.967per100ofparvalue.Thebond'syield-to-maturity,quotedonasemiannualbondbasis,is3.897%.Ananalysthasbeenaskedtoconverttoamonthlyperiodicity.Underthisconversion,theyield-to-maturityisclosestto:A.3.87%.B.4.95%.C.7.67%.Solution:A.门0.03897vHMl2.12212TOf12=O.OO322*12=0.0387Q-2.A10%couponbondwithannualpayments,maturingin3years,ispricedat105.Thebondiscallableinoneyearatacallpriceof104ortwoyearsatacallpriceof102.Thebondsyieldtoworstmostlikelyoccurswhenthebondis:A.Calledinyear1.B.Calledinyear2.C.Helduntilmaturity.Solution:C.Theyieldtoworstforacallablebondisthelowestoftheyieldstocallforeachpossiblecalldateandtheyieldtomaturity.Theyieldtocalloryieldtomaturitysolvesthefollowingequation:P=fcE"l.iy,whereiistheyieldtocall,oryieldtomaturityCFisthecashflowatdatet,andTisthematurityorcalldate.Theyieldtocallifthebondiscalledinoneyearis8.57%zbecause105=°*"1.0857lTheyieldtocallifthebondiscalledintwoyearsis8.15%,because105=")一.")'"心.l.O815,l.08152Theyieldtomaturityofthebondis8,06%,because105，"°°.The1.080611.080621.08063yieldtoworstisthelowestoftheseandoccurswhenthebondishelduntilmaturity(i.e.,itistheyieldtomaturity).Q-3.AssumetheUSTreasuryforwardratesasfollows,thevalueofa2year$1000parvaluesemi-annuallyTreasurybondwitha6%couponrateisclosestto:PeriodForwardRate11.40%22.00%32.50%42.90%A.$1076.82B.$107433C.$1072.46Solution:B.Thevalueofthebondis303030(U0.014/2)U0.014/2)(1+0.02/2)1.0.014/2)(U0.02/2)(U0.025/2)1030*(U0.014/2Xk0.02/2)(U0.025/2)(k0.029/2)$1074.33Q-4.Whichofthefollowing90-daymoneymarketinstrumentsmostlikelyofferstheinvestorthehighestrateofreturn?MoneyMarketInstrumentQuotedRateQuotationBasisDayConventionInstrumentA5.80%360DiscountrateInstrumentB5,65%365DiscountrateInstrumentC5.88%365Add-onrateA,InstrumentCB.InstrumentAC.InstrumentBSolution:B.InstrumentCprovidesabondequivalentyieldof5.88%,comparedwith5.97%forInstrumentAand5.73%forInstrumentB.ForInstrumentA:assumeFV=100,守需W55.IOo-9&55365AOR=×=0.059798.5590ForInstrumentB:assumeFV=100,舒9°MPVW100-98.6068365AOR=X三0.057398.606890ForInstrumentC=5.88%Q-5.Anoption-adjusted-spread(OAS)onacallablebondistheZ-spread:A.Overthebenchmarkspotcurve.B.Minusthestandardswaprateinthatcurrencyofthesametenor.C.Minusthevalueoftheembeddedcalloptionexpressedinbasispointsperyear.Solution:C.TheoptionvalueinbasispointsperyearissubtractedfromtheZ-spreadtocalculatetheoption-adjustedspread(OAS).TheZ-spreadistheconstantyieldspreadoverthebenchmarkspotcurve.Thel-spreadistheyieldspreadofaspecificbondoverthestandardswaprateinthatcurrencyofthesametenor.Q-6.Whichofthefollowingsourcesofreturnismostlikelyexposedtointerestrateriskforaninvestorofafixed-ratebondwhoholdsthebonduntilmaturity?A.CapitalgainorlossB.RedemptionofprincipalC.ReinvestmentofcouponpaymentsSolution:C.Becausethefixed-ratebondisheldtomaturity(a"buy-and-hold"investor),interestrateriskarisesentirelyfromchangesincouponreinvestmentrates.Higherinterestratesincreaseincomefromreinvestmentofcouponpayments,andlowerratesdecreaseincomefromcouponreinvestment.Therewillnotbeacapitalgainorlossbecausethebondisheldtomaturity.Thecarryingvalueatthematuritydateisparvalue,thesameastheredemptionamount.Theredemptionofprincipaldoesnotexposetheinvestortointerestraterisk.Therisktoabond'sprincipaliscreditrisk.Q-7.Aninvestorbuysathree-yearbondwitha5%couponratepaidannually.Thebond,withayield-to-maturityof3%zispurchasedatapriceof105.657223per100ofparvalue.Assuminga5-basispointchangeinyield-to-maturity,thebond'sapproximatemodifieddurationisclosestto:A.2.78.B.2.86.C.5.56Solution:A.105.804232105.510494loweryield-to-maturityby5bpsto2.95%(1.0.0295)(I0.0295)2(1*0.0295)ahigheryield-Fo-nuturityby5bpsto3.05%_55105(1.00305)*(1÷0,0305)2(1*O.O3O5)3approximate modified duration -105.804232-1055 0494 ? g2*0.0(X)5*105.657223"Q-8.Inarecentpresentation,TerrymadetwostatementsaboutMacaulayduration:Statement1:"Macaulaydurationwilldecreaseastimepassesandimmediatelyincreaseaftercouponpayment."Statement2:"Macaulaydurationwillincreaseastimepassesandimmediatelydecreaseaftercouponpayment."AreTerry'stwostatementscorrect?A.YesforStatement1andnoforStatement2B.NoforStatement1andyesforStatement2C.NoforbothstatementsSolution:A.Astimepassesduringthecouponperiod,theMacaulaydurationdeclinessmoothlyandthenjumpsupwardafterthecouponispaid.MacauIayDurationQ-9.Abondwithexactlynineyearsremaininguntilmaturityoffersa3%couponratewithannualcoupons.Thebond,withayield-to-maturityof5%,ispricedat85.784357per100ofparvalue.Theestimatedpricevalueofabasispointforthebondisclosestto:A.0.0086.B.0.0648.C.0.1295.Solution:B.1.oweringtheyield-to-maturitybyonebasispointto4.99%resultsinabondpriceof85.849134:3103PV：85.849134(L0.0499j(10.0499)sIncreasingtheyield-to-m