对外经济贸易大学国际经济贸易学院固定收益证券部分答案Word格式文档下载.docx
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“Thepriceofafloaterwillalwaystradeatitsparvalue.”
Answer:
Idisagreewiththestatement:
“Thepriceofafloaterwillalwaystradeatitsparvalue.”First,thecouponrateofafloating-ratesecurity(orfloater)isequaltoareferencerateplussomespreadormargin.Forexample,thecouponrateofafloatercanresetattherateonathree-monthTreasurybill(thereferencerate)plus50basispoints(thespread).Next,thepriceofafloaterdependsontwofactors:
(1)thespreadoverthereferencerateand
(2)anyrestrictionsthatmaybeimposedontheresettingofthecouponrate.Forexample,afloatermayhaveamaximumcouponratecalledacaporaminimumcouponratecalledafloor.Thepriceofafloaterwilltradeclosetoitsparvalueaslongas
(1)thespreadabovethereferenceratethatthemarketrequiresisunchangedand
(2)neitherthecapnorthefloorisreached.However,ifthemarketrequiresalarger(smaller)spread,thepriceofafloaterwilltradebelow(above)par.Ifthecouponrateisrestrictedfromchangingtothereferencerateplusthespreadbecauseofthecap,thenthepriceofafloaterwilltradebelowpar.
2)Aportfoliomanagerisconsideringbuyingtwobonds.BondAmaturesinthreeyearsandhasacouponrateof10%payablesemiannually.BondB,ofthesamecreditquality,maturesin10yearsandhasacouponrateof12%payablesemiannually.Bothbondsarepricedatpar.
(a)Supposethattheportfoliomanagerplanstoholdthebondthatispurchasedforthreeyears.Whichwouldbethebestbondfortheportfoliomanagertopurchase?
Theshortertermbondwillpayalowercouponratebutitwilllikelycostlessforagivenmarketrate.Sincethebondsareofequalriskintermsofcreitquality(Thematuritypremiumforthelongertermbondshouldbegreater),thequestionwhencomparingthetwobondinvestmentsis:
Whatinvestmentwillbeexpectetogivethehighestcashflowperdollarinvested?
Inotherwords,whichinvestmentwillbeexpectedtogivethehighesteffectiveannualrateofreturn.Ingeneral,holdingthelongertermbondshouldcompensatetheinvestorintheformofamaturitypremiumandahigherexpectedreturn.However,asseeninthediscussionbelow,theactualrealizedreturnforeitherinvestmentisnotknownwithcertainty.
Tobeginwith,aninvestorwhopurchasesabondcanexpecttoreceiveadollarreturnfrom(i)theperiodiccouponinterestpaymentsmadebetheissuer,(ii)ancapitalgainwhenthebondmatures,iscalled,orissold;
and(iii)interestincomegeneratedfromreinvestmentoftheperiodiccashflows.Thelastcomponentofthepotentialdollarreturnisreferredtoasreinvestmentincome.Forastandardbond(oursituation)thatmakesonlycouponpaymentsandnoperiodicprincipalpaymentspriortothematuritydate,theinterimcashflowsaresimplythecouponpayments.Consequently,forsuchbondsthereinvestmentincomeissimplyinterestearnedfromreinvestingthecouponinterestpayments.Forthesebonds,thethirdcomponentofthepotentialsourceofdollarreturnisreferredtoastheinterest-on-interestcomponents.
Ifwearegoingtocouputeapotentialyieldtomakeadecision,weshouldbeawareofthefactthatanymeasureofabond’spotentialyieldshouldtakeintoconsiderationeachofthethreecomponentsdescribedabove.Thecurrentyieldconsidersonlythecouponinterestpayments.Noconsiderationisgiventoanycapitalgainorinterestoninterest.Theyieldtomaturitytakesintoaccountcouponinterestandanycapitalgain.Italsoconsiderstheinterest-on-interestcomponent.Additionally,implicitintheyield-to-maturitycomputationistheassumptionthatthecouponpaymentscanbereinvestedatthecomputedyieldtomaturity.Theyieldtomaturityisapromisedyieldandwillberealizedonlyifthebondisheldtomaturityandthecouponinterestpaymentsarereinvestedattheyieldtomaturity.Ifthebondisnotheldtomaturityandthecouponpaymentsarereinvestedattheyieldtomaturity,thentheactualyieldrealizedbyaninvestorcanbegreaterthanorlessthantheyieldtomaturity.
Giventhefactsthat(i)onebond,ifbought,willnotbeheldtomaturity,and(ii)thecouponinterestpaymentswillbereinvestedatanunknownrate,wecannotdeterminewhichbondmightgivethehighestactualrealizedrate.Thus,wecannotcomparethembaseduponthiscriterion.However,iftheportfoliomanagerisriskinverseinthesensethatsheorhedoesn’twanttobuyalongertermbond,whichwilllikelhavemorevariabilityinitsreturn,thenthemanagermightprefertheshortertermbond(bondA)ofthresyears.Thisbondalsomatureswhenthemanagerwantstocashinthebond.Thus,themanagerwouldnothavetoworryaboutanypotentialcapitallossinsellingthelongertermbond(bondB).Themanagerwouldknowwithcertaintywhatthecashflowsare.If
Thesecashflowsarespentwhenreceived,themanagerwouldknowexactlyhowmuchmoneycouldbespentatcertainpointsintime.
Finally,amanagercantrytoprojectthetotalreturnperformanceofabondonthebasisofthepannedinvestmenthorizonandexpectationsconcerningreinvestmentratesandfuturemarketyields.Thisermitstheportfoliomanagertoevaluatethichofseveralpotentialbondsconsideredforacquisitionwillperformbestovertheplannedinvestmenthorizon.Aswejustrgued,thiscannotbedoneusingtheyieldtomaturityasameasureofrelativevalue.Usingtotalreturntoassessperformanceoversomeinvestmenthorizoniscalledhorizonanalysis.Whenatotalreturniscalculatedovenaninvestmenthorizon,itisreferredtoasahorizonreturn.Thehorizonanalysisframworenabledtheportfoliomanagertoanalyzetheperformanceofabondunderdifferentinterest-ratescenariosforreinvestmentratesandfuturemarketyields.Onlybyinvestigatingmultiplescenarioscantheportfoliomanagerseehowsensitivethebond’sperformancewillbetoeachscenario.Thiscanhelpthemanagerchoosebetweenthetwobondchoices.
(b)Supposethattheportfoliomanagerplanstoholdthebondthatispurchasedforsixyearsinsteadofthreeyears.Inthiscase,whichwouldbethebestbondfortheportfoliomanagertopurchase?
Simileartoourdiscussioninpart(a),wedonotknowwhichinvestmentwouldgivethehighestactualrelizedreturninsixyearswhenweconsiderreinvestingallcashflows.Ifthemanagerbuysathree-yearbond,thentherewouldbetheadditionaluncertaintyofnowknowingwhatthree-yearbondrateswouldbeinthreeyears.Thepurchaseoftheten-yearbondwouldbeheldlongerthanpreviously(sixyearscomparedtothreeyears)andrendercouponpaymentsforasix-yearperiodthatareknown.Ifthesecashflowsarespentwhenreceived,themanagerwillknowexactlyhowmuchmoneycouldbespentatcertainpointsintimeNotknowingwhichbondinvestmentwouldgivethehighestrealizedreturn,theportfoliomanagerwouldchoosethebondthatfitsthefirm’sgoalsintermsofmaturity.
3)AnswerthebelowquestionsforbondsAandB.
BondA
BondB
Coupon
8%
9%
Yieldtomaturity
Maturity(years)
2
5
Par
$100.00
Price
$104.055
(a)Calculatetheactualpriceofthebondsfora100-basis-pointincreaseininterestrates.
ForBondA,wegetabondquoteof$100forourinitialpriceifwehavean8%couponrateandan8%yield.Ifwechangetheyield100basispointsotheyieldis9%,thenthevalueofthebond(P)isthepresentvalueofthecouponpaymentsplusthepresentvalueoftheparvalue.WehaveC=$40,y=4.5%,n=4,andM=$1,000.Insertingthesenumbersintoourpresentvalueofcouponbondformula,weget:
Thepresentvalueoftheparormaturityvalueof$1,000is:
Thus,thevalueofbondAwithayieldof9%,acouponrateof8%,andamaturityof2yearsis:
P=$143.501+$838.561=$982.062.Thus,wegetabondquoteof$98.2062.WealreadyknowthatbondBwillgiveabondvalueof$1,000andabondquoteof$100sinceachangeof100basispointswillmaketheyieldandcouponratethesame,Forexample,insertingThus,thevalueofbondAwithayieldof9%,acouponrateof8%,andamaturityof2yearsis:
P=$143.501+$838.561=$982.062.Thus,wegetabondquoteof$98.2062.WealreadyknowthatbondBwillgiveabondvalueof$1,000andabondquoteof$100sinceachangeof100basispointswillmaketheyieldandcouponratethesame,Forexample,inserting
(b)Usingduration,estimatethepriceofthebondsfora100-basis-pointincreaseininterestrates.
ToestimatethepriceofbondA,webeginbyfirstcomputingthemodifiedduration.WecanuseanalternativeformulathatdoesnotrequiretheextensivecalculationsrequiredbytheMacaulayprocedure.Theformulais:
Puttingallapplicablevariablesintermsof$100,wehaveC=$4,n=4,y=0.045,andP=$98.2062.Insertingthesevalues,inthemodifieddurationformulagives:
($1,975.308642[0.161439]+$35.664491)/$98.2062=($318.89117+$35.664491)/$98.2062=$354.555664/$98.2062=3.6103185orabout3.61.Convertingtoannualnumberbydividingbytwogivesamodifieddurationof1.805159(beforetheincreasein100basispointsitwas1.814948).Wenextsolveforthechangeinpriceusingthemodifieddurationof1.805159anddy=100basispoints=0.01.Wehave:
WecannowsolveforthenewpriceofbondAasshownbelow:
Thisisslightlylessthantheactualpriceof$982.062.Thedifferenceis$982.062–$981.948=$0.114.ToestimatethepriceofbondB,wefollowthesameprocedurejustshownforbondA.UsingthealternativeformulaformodifieddurationthatdoesnotrequiretheextensivecalculationsrequiredbytheMacaulayprocedur