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-maturitybyonebasispointto5.01%resultsinabondpriceof85.719638:3(E 0.0501)'+ (U 0.0501)903：3=85.719638W*85.84913485.719638=03752Q>10.Abondiscurrentlytradingfor98.722per100ofparvalue.Ifthebond*syield-to-maturity(YTM)risesby10basispoints,thebond'sfullpriceisexpectedtofallto98.669.ifthebond'sYTMdecreasesby10basispoints,thebond,sfullpriceisexpectedtoincreaseto98.782.Thebond,sapproximateconvexityisclosestto:A.0.0071.B.70.906.C.1144.628.Solution:B.(YTM)2Vcapproximateconvexityapproximateconvexity98.78298.669(2*98.722)/(0.001%98722)70.906Q-ll.Thedurationofanoption-freebondpricedat$900is8.5.Ifyieldsdecreaseby150basispoints,themostaccuratestatementabouttheactualpriceofthebondafterthedecreaseinyieldsisthattheactualpricewillbe:A.Equalto$1,014.75.B.Greaterthanlz014.75.C.Lessthan1,014.75becausethelowerlevelofyieldsincreasesthebond'sinterestraterisk.Solution:B.Thepriceadjustmentfordurationcanbecalculatedasfollows:8.5×(0.015)X100=12.75%.$900(1.1275)=$1,014.75Thisadjuststhepricefordurationonly.Becausethebondisoption-freeandthechangeinyieldislarge,usingdurationaloneunderestimatestheactualpriceofthebondbecauseoftheeffectofconvexity.Onceanadjustmentismadeforconvexity,thepricewouldbegreaterthan$1,014.75.Q>12.Aninvestorpurchasesanannualcouponbondwitha8%couponrateandexactly20yearsremaininguntilmaturityatapriceequaltoparvalue.Theinvestor'sinvestmenthorizoniseightyears.Themodifieddurationofthebondis12.480years.Thedurationgapatthetimeofpurchaseisclosestto:A.-6.842.B.4480.C.5.478.Solution:C.Thedurationgapisclosestto4.158.Thedurationgapisabond'sMacaulaydurationminustheinvestmenthorizon.TheapproximateMacaulaydurationistheapproximatemodifieddurationtimesoneplustheyield-to-maturity.Itis13.478(=12.480×1.08).Givenaninvestmenthorizonofeightyears,thedurationgapforthisbondatpurchaseispositive:13.478-8=5.478.WhentheinvestmenthorizonislessthantheMacaulaydurationofthebond,thedurationgapispositive,andpriceriskdominatescouponreinvestmentrisk.Q-13.AcreditanalystobservesthefollowinginformationforAlphaCo.atfiscalyearsending20X7and20X8.ExcerptfromtheConsolidatedIncomeStatementofAlphaCo.forthefiscalyearsending31December20X7and20X8(inmillions)20X720X8Grossprofit$549.0$506.0Operatingexpenses451.0372.0Operatingprofit98.0134.0Interestexpense29.035,0Incomebeforetaxes69.099,0Incometaxes(at30%)22.031.0Netincome47.068.0AdditionalinformationDepreciationandamortization26.034.0Basedonthisinformation,overthisperiodAlpha,sinterestcoverageratiohas:A.Remainedunchanged.B.Improved.C.Deteriorated.Solution:B.Thecompany'sinterestcoverageratiocanbecomputedas:EBITDA/lnterestexpense.Thatis:20X720X8EBITDA124.0168.0Interestexpense29.03S.0EBITDA/lnterestexpense4.284.8EBITDA=Operatingprofit+DepreciationandamortizationThecompany'sEBITDAinterestcoverageratiohasimprovedoverthisperiod.IfEBITisusedtocalculatethecoverageratiosyoureachthesameconclusion,for20X7theratiois338andfor20X8itis3.83.Q>14.Thefundmanagerisconcernaboutthefactthatmarketinterestrateswillgoupunexpectedlyandleadtoprepaymentratesthataremuchlowerthanpreviousexpectation.Healsoexpresseshisexpectationforarelativelylong-terminvestment(averagelifeofgreaterthanfiveyears)anddoesnotwanttoreceiveanycashflowfromcomingyears.Theendowmentfundmanager'sconcernabouttheimpactofmovementsinmarketinterestratesisbestdescribedasaconcernabout:A.Extensionrisk.B.Prepaymentrisk.C.Contractionrisk.Solution:A.Iftheprepaymentratefalls,itusuallyresultinalengtheningofthesecurity'slifewhichiscalledextensionriskandisalsofundmanager'sconcern.Q-15.Twodifferentstructuresofcollateralizedmortgageobligations(CMO)arebeingconsideredforissuance:Structure1:$400millionofpass-throughwillbeusedascollateralfortwosequentialpaytranches:$325millionworthofbondsOfTrancheXand$75millionofbondsofTrancheY.TheprincipalforTrancheXmustbecompletelypaidoffbeforeanypaymentsaremadetoTrancheY.Structure2:$400millionofpass-throughwillbeusedascollateralfor$325millionofEbondsinaplannedamortizationclass(PAC)trancheand$75millionofFbondsinasupporttranche.Whichofthefollowingstatementsisleastaccurate?The:A.XbondshavelesscontractionriskthantheYbonds.B.XbondshavelessextensionriskthantheYbonds.C.EbondshavelesscontractionriskthantheFbonds.Solution:A.Instructurelzwehavetwosequentialpaytranches.Ifprepaymentsslow,itwilltakelongerforcashflowstogettheYbonds,sotheXbondshavelessextensionrisk.TheXbondshavemorecontractionriskthantheYbondsbecausetheywillgetcashflowsmorequicklyifprepaymentsaccelerate.TheXbondsprotecttheYbondsagainstcontractionrisk.InthecaseofStructure2wheretherearetwoPACtranches,theFsupporttranchewillabsorbtheimpactofbothacceleratedandslowerthanexpectedprepayments,resultingintheEbondshavingbothlesscontractionriskandlessextensionriskthantheFbonds.