20196二級(jí)jc網(wǎng)課719cfa2更至第9講題目固定收益

PAGE1專業(yè)·創(chuàng)新·FixedWinterasksMadisonaboutherpreferencesconcerningtermstructuremodels.Madison“Ipreferarbitrage-models.Eventhoughequilibriummodelsrequirefewerparameterstobeestimatedrelativetoarbitrage-models,arbitrage-modelsallowfortime-varyingparameters.Ingeneral,thisallowanceleadstoarbitrage-modelsbeingabletomodelthemarketyieldcurvemorepreciselythanequilibriummodels.”IsMadisoncorrectindescribingkeydifferencesinequilibriumandarbitrage-modelsastheyrelatetothenumberofparametersandmodelaccuracy?No,sheisincorrectaboutwhichtypeofmodelrequiresfewerparameterNo,sheisincorrectaboutwhichtypeofmodelismorepreciseatmodelingmarketyieldSolution:ConsistentwithMadison’sstatement,equilibriumtermstructuremodelsrequirefewerparameterstobeestimatedrelativetoarbitrage-models,andarbitrage-modelsallowfortime-varyingparameters.Consequently,arbitrage-modelscanmodelthemarketyieldcurvemorepreciselythanequilibriummodels.Exhibit1.SelectedExhibit1.SelectedBondCouponBondAyrault,lnc.CaIlableatparinoneyearandtwoyearsBlum,lnc.EnterprisesPutableatparinoneyearfromNote:Eachbondhasaremainingmaturityofthreeyears,annualcouponpayments,andaratingofToassesstheinterestrateriskofthethreebonds,Bianchiconstructstwobinomialinterestratetreesbasedona10%interestratevolatilityassumptionandacurrentone-yearrateof1%.PanelAofExhibit2providesaninterestratetreeassumingthebenarkyieldcurveshiftsdownby30bps,andPanelBprovidesaninterestratetreeassumingthebenarkyieldcurveshiftsupby30bps.BianchideterminesthattheAIbondiscurrentlytradingatanPAGE2option-adjustedspread(OAS)of13.95bpsrelativetothebenarkyieldExhibit2.BinomialInterestRateTreesPanelAInterestRatesShiftDownby30YearYearYearYearYearPanelBInterestRatesShiftUpby30YearYearYearYearYearBasedonExhibits1and2,theeffectivedurationfortheAIbondisclosestSolution:TheAIbond'svalueifinterestratesshiftdownby30bps(PV-)isYear YearYearYearYearYearCalledatCalledatCalledatCalledatYearYearYearYearYear Effectiveduration=(100.870?99.487)/(2?0.003?100.200)Tyothensuggeststhatthefirmwasabletoaddreturnbyridingtheyieldcurve.Thefundnstocontinuetousethisstrategybutonlyinmarketswithanattractiveyieldcurveforthisstrategy.Shemovesontopresenthermarketviewsontherespectiveyieldcurvesforfive-yearinvestmentPAGE4專業(yè)·創(chuàng)新·"Toimproveliquidity,CountryC'scentralbankisexpectedtointervene,leadingtoareversalintheslopeoftheexistingyieldcurve.Weassumethatfuturespotrateswillbelowerthantoday'sforwardratesforallmaturities.”Tyo'sassistantasks,“Assuminginvestorsrequireliquiditypremiums,howcanayieldcurveslopedownward?Whatdoesthisimplyaboutforwardrates?"Tyoanswers,“Evenifinvestorsrequirecompensationforholdinglonger-termbonds,yieldcurvecanslopedownwardforexample,ifthereisanexpectationofseveredeflation.Regardingforwardrates,itcanbehelpfultounderstandyieldcurvedynamicsbycalculatingimpliedforwardrates.ToseewhatImean,wecanuseExhibit1tocalculatetheforwardrateforatwo-yearCountryCloanbeginninginthreeyears.”Exhibit1ernmentSpotCOI.mtll'yCountll'yCountryOneTwoThreeFourFiveTyo'sassistantshouldcalculateaforwardrateclosestSolution:Fromtheforwardratemodel,f(3,2),isfoundasUsingthethree-yearandfive-yearspotrates,we(10.107)5(10.118)3[1f(3,2)]2, WilliamRogers,afixed-incomeportfoliomanager,needstoeliminatealargecashpositioninhisportfolio.Hewouldliketopurchasesomecorporatebonds.TwobondsthatheisevaluatingareshowninExhibit1.Thesetwobondsarefromthesameissuer,andthecurrentcallpriceforthecallablebondis100.AssumethattheissuerwillcallifthebondPAGE5priceexceedsthecallDuringthediscussions,RogersmakesthefollowingStatement1:Ifthevolatilityofinterestratesdecreases,thevalueofthecallablebondwillStatement2:Thenoncallablebondwillnotbeaffectedbyachangeinthevolatilityorlevelofinterestrates.Statement3:Wheninterestratesdecrease,thevalueofthenoncallablebondincreasesbymorethanthecallablebond.EvaluateRogers’sstatements1andOnlyStatement1isOnlyStatement3isBothstatementsareSolution:Statement1iscorrect.Ifthevolatilityofinterestratesdecreases,thecalloptionislessvaluable,whichincreasesthevalueofthecallablebond.RecallthatVcalllable=Vnoncallable—Vcall.Statement3isalsocorrect.Thevalueofthenoncallablebondincreasesbymorethanthecallablebondbecauseasyieldfalls,thevalueofthecallgoesup.Asthecallvalueincreases,thecallablevalue(noncallvalue-calloptionvalue)goesupbylessthanthenoncallvalue.DanielaIbarraisaseniorystinthe edepartmentofalargewealthmanagementfirm.MartenKoningisajuniorystinthesamedepartment,andDavidLokisamemberofthecreditresearchteam.Thefirminvestsinavarietyofbonds.Ibarraispresentlyyzingasetofbondswithsomesimilarcharacteristics,suchasfouryearsuntilmaturityandaparvalueof€1,000.Exhibit1includesdetailsofthesebonds. Azero-coupon,four-yearcorporatebondwithaparvalueof€1,000.Thewealthmanagementfirm’sresearchteamhasestimatedthattherisk-neutralprobabilityofdefault(thehazardrate)foreachdateforthebondis1.50%,andtherecoveryrateisIbarraasksKoningtoassistherwithyzingthebonds.Shewantshimtoperformtheysiswiththeassumptionsthatthereisnointerestratevolatilityandthattheernmentbondyieldcurveisflatat3%.ThemarketpriceofbondB1is€875.ThebondfairlySolution:Thefollowingtableshowsthatthecreditvaluationadjustment(CVA)forthebondis€36.49,thesumofthepresentvaluesofexpectedloss.Thestepstakentocompletethetableareasfollows.Step1:ExposureatDateTis€1,000/(1+r)4?T,whereris3%.Thatis,exposureiscomputedbydiscountingthefacevalueofthebondusingtherisk-rateandthenumberofyearsuntilStep2:Recovery=Exposure×RecoveryStep3:Lossgivendefault(LGD)=Exposure–Step4:Probabilityofdefault(POD)onDate1is1.50%,theassumedhazardrate.Theprobabilityofsurvival(POS)onDate1is98.50%.Forsubsequentdates,PODiscalculatedasthehazardratemultipliedbythepreviousdate’sPOS.Forexample,todeterminetheDate2POD(1.4775%),thehazardrateof(1.50%)ismultipliedbytheDate1POS(98.50%).Step5:POSinDates2–4=POSinthepreviousyear–POD(Thatis,POSinYearT=POSinyear[T–1]–PODinYearT.)POScanalsobedeterminedbysubtractingthehazardratefrom100%andraisingittothepowerofthenumberofyears:(100%–1.5000%)1=(100%–1.5000%)2=(100%–1.5000%)3=(100%–1.5000%)4=Step6:Expectedloss=LGD×Step7:Discountfactor(DF)forDateTis1/(1+r)T,wherer 0e12金程教金程教專業(yè)·創(chuàng)新·增PAGE734CVAValueofthebondifthebondweredefaultwouldbe1,000×DFforDate4=€888.49.FairvalueofthebondconsideringCVA=€888.49–CVA=€888.49–€36.49=€852.00.Becausethemarketpriceofthebond(€875)isgreaterthanthefairvalueof€852,BisAisincorrectbecausethemarketpriceofthebonddiffersfromitsfairvalue.Cisincorrectbecausealthoughthebond’svalueifthebondweredefaultisgreaterthanthemarketprice,thebondhasariskofdefault,andCVAlowersitsfairvaluetobelowthemarketprice.On1January20X2,DeemAdvisorspurchaseda$10millionsix-yearseniorunsecuredbondissuedbyUNABCorporation.Sixmonthslater(1July20X2),concernedabouttheportfolio’screditexposuretoUNAB,DorisMorrison,thechiefinvestmentofficeratDeemAdvisors,purchasesa$10millionCDSwithastandardizedcouponrateof5%.ThereferenceobligationoftheCDSistheUNABbondownedbyDeemAdvisors.On1January20X3,MorrisonasksBillWatt,aderivativesyst,toassessthecurrentcreditqualityofUNABbondsandthevalueofDeemAdvisor’sCDSonUNABdebt.WattgathersthefollowinginformationontheUNAB’sdebtissuescurrentlytradinginthemarket:Bond1:Atwo-yearseniorunsecuredbondtradingat40%ofparBond2:Asix-yearseniorunsecuredbondtradingat50%ofparBond3:Asix-yearsubordinatedunsecuredbondtradingat20%ofWithrespecttothecreditqualityofUNAB,Wattmakesthefollowing‘’Thereisseverenear-termstressinthefinancialmarketsandUNAB’screditcurveclearlyreflectsthedifficultenvironment.”O(jiān)n1July20X3,UNABfailstomakeascheduledinterestpaymentontheoutstandingsubordinatedunsecuredobligationafteragraceperiod;however,thedoesnotfileforbankruptcy.MorrisonasksWatttodetermineifUNABexperiencedacrediteventand,ifso,torecommendasettlementpreference.IfUNABexperiencedacrediteventon1July,Wa