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.docx
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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.docx
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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
国际经济贸易学院研究生课程班
《固定收益证券》试题
1)Explainwhyyouagreeordisagreewiththefollowingstatement:
“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
Answer:
Theshortertermbondwillpayalowercouponratebutitwilllikelycostlessforagivenmarketthebondsareofequalriskintermsofcreitquality(Thematuritypremiumforthelongertermbondshouldbegreater),thequestionwhencomparingthetwobondinvestmentsis:
WhatinvestmentwillbeexpectetogivethehighestcashflowperdollarinvestedInotherwords,whichinvestmentwillbeexpectedtogivethehighesteffectiveannualrateofgeneral,holdingthelongertermbondshouldcompensatetheinvestorintheformofamaturitypremiumandahigherexpected,asseeninthediscussionbelow,theactualrealizedreturnforeitherinvestmentisnotknownwithcertainty.
Tobeginwith,aninvestorwhopurchasesabondcanexpecttoreceiveadollarreturnfrom(i)theperiodiccouponinterestpaymentsmadebetheissuer,(ii)ancapitalgainwhenthebondmatures,iscalled,orissold;and(iii)interestincomegeneratedfromreinvestmentoftheperiodiccashlastcomponentofthepotentialdollarreturnisreferredtoasreinvestmentastandardbond(oursituation)thatmakesonlycouponpaymentsandnoperiodicprincipalpaymentspriortothematuritydate,theinterimcashflowsaresimplythecoupon,forsuchbondsthereinvestmentincomeissimplyinterestearnedfromreinvestingthecouponinterestthesebonds,thethirdcomponentofthepotentialsourceofdollarreturnisreferredtoastheinterest-on-interestcomponents.
Ifwearegoingtocouputeapotentialyieldtomakeadecision,weshouldbeawareofthefactthatanymeasureofabond’spotentialyieldshouldtakeintoconsiderationeachofthethreecomponentsdescribedcurrentyieldconsidersonlythecouponinterestconsiderationisgiventoanycapitalgainorinterestonyieldtomaturitytakesintoaccountcouponinterestandanycapitalalsoconsiderstheinterest-on-interest,implicitintheyield-to-maturitycomputationistheassumptionthatthecouponpaymentscanbereinvestedatthecomputedyieldtoyieldtomaturityisapromisedyieldandwillberealizedonlyifthebondisheldtomaturityandthecouponinterestpaymentsarereinvestedattheyieldtothebondisnotheldtomaturityandthecouponpaymentsarereinvestedattheyieldtomaturity,thentheactualyieldrealizedbyaninvestorcanbegreaterthanorlessthantheyieldtomaturity.
Giventhefactsthat(i)onebond,ifbought,willnotbeheldtomaturity,and(ii)thecouponinterestpaymentswillbereinvestedatanunknownrate,wecannotdeterminewhichbondmightgivethehighestactualrealized,wecannotcomparethembaseduponthis,iftheportfoliomanagerisriskinverseinthesensethatsheorhedoesn’twanttobuyalongertermbond,whichwilllikelhavemorevariabilityinitsreturn,thenthemanagermightprefertheshortertermbond(bondA)ofthresbondalsomatureswhenthemanagerwantstocashinthe,themanagerwouldnothavetoworryaboutanypotentialcapitallossinsellingthelongertermbond(bondB).Themanagerwouldknowwithcertaintywhatthecashflows
Thesecashflowsarespentwhenreceived,themanagerwouldknowexactlyhowmuchmoneycouldbespentatcertainpointsintime.
Finally,amanagercantrytoprojectthetotalreturnperformanceofabondonthebasisofthepannedinvestmenthorizonandexpectationsconcerningreinvestmentratesandfuturemarketermitstheportfoliomanagertoevaluatethichofseveralpotentialbondsconsideredforacquisitionwillperformbestovertheplannedinvestmentwejustrgued,thiscannotbedoneusingtheyieldtomaturityasameasureofrelativetotalreturntoassessperformanceoversomeinvestmenthorizoniscalledhorizonatotalreturniscalculatedovenaninvestmenthorizon,itisreferredtoasahorizonhorizonanalysisframworenabledtheportfoliomanagertoanalyzetheperformanceofabondunderdifferentinterest-ratescenariosforreinvestmentratesandfuturemarketbyinvestigatingmultiplescenarioscantheportfoliomanagerseehowsensitivethebond’sperformancewillbetoeachcanhelpthemanagerchoosebetweenthetwobondchoices.
(b)Supposethattheportfoliomanagerplanstoholdthebondthatispurchasedforsixyearsinsteadofthreeyears.Inthiscase,whichwouldbethebestbondfortheportfoliomanagertopurchase
Answer:
Simileartoourdiscussioninpart(a),wedonotknowwhichinvestmentwouldgivethehighestactualrelizedreturninsixyearswhenweconsiderreinvestingallcashthemanagerbuysathree-yearbond,thentherewouldbetheadditionaluncertaintyofnowknowingwhatthree-yearbondrateswouldbeinthreepurchaseoftheten-yearbondwouldbeheldlongerthanpreviously(sixyearscomparedtothreeyears)andrendercouponpaymentsforasix-yearperiodthatarethesecashflowsarespentwhenreceived,themanagerwillknowexactlyhowmuchmoneycouldbespentatcertainpointsintimeNotknowingwhichbondinvestmentwouldgivethehighestrealizedreturn,theportfoliomanagerwouldchoosethebondthatfitsthefirm’sgoalsintermsofmaturity.
3)AnswerthebelowquestionsforbondsAandB.
BondA
BondB
Coupon
8%
9%
Yieldtomaturity
8%
8%
Maturity(years)
2
5
Par
$
$
Price
$
$
(a)Calculatetheactualpriceofthebondsfora100-basis-pointincreaseininterestrates.
Answer:
ForBondA,wegetabondquoteof$100forourinitialpriceifwehavean8%couponrateandan8%yield.Ifwechangetheyield100basispointsotheyieldis9%,thenthevalueofthebond(P)isthepresentvalueofthecouponpaymentsplusthepresentvalueoftheparvalue.WehaveC=$40,y=%,n=4,andM=$1,000.Insertingthesenumbersintoourpresentvalueofcouponbondformula,weget:
Thepresentvalueoftheparormaturityvalueof$1,000is:
Thus,thevalueofbondAwithayieldof9%,acouponrateof8%,andamaturityof2yearsis:
P=$+$=$.Thus,wegetabondquoteof$.WealreadyknowthatbondBwillgiveabondvalueof$1,000andabondquoteof$100sinceachangeof100basispointswillmaketheyieldandcouponratethesame,Forexample,insertingThus,thevalueofbondAwithayieldof9%,acouponrateof8%,andamaturityof2yearsis:
P=$+$=$.Thus,wegetabondquoteof$.WealreadyknowthatbondBwillgiveabondvalueof$1,000andabondquoteof$100sinceachangeof100basispointswillmaketheyieldandcouponratethesame,Forexample,inserting
(b)Usingduration,estimatethepriceofthebondsfora100-basis-pointincreaseininterestrates.
Answer:
ToestimatethepriceofbondA,webeginbyfirstcomputingthemodifiedduration.WecanuseanalternativeformulathatdoesnotrequiretheextensivecalculationsrequiredbytheMacaulayprocedure.Theformulais:
Puttingallapplicablevariablesintermsof$100,wehaveC=$4,n=4,y=,andP=$.Insertingthesevalues,inthemodifieddurationformulagives:
($1,[]+$/$=($+$/$=$/$=orabout.Convertingtoannualnumberbydividingbytwogivesamodifieddurationof(beforetheincreasein100basispointsitwas.Wenextsolveforthechangeinpriceusingthemodifieddurationofanddy=100basispoints=.Wehave:
WecannowsolveforthenewpriceofbondAasshownbelow:
Thisisslightlylessthantheactualpriceof$.Thedifferenceis$–$=$.ToestimatethepriceofbondB,wefollowthesameprocedurejustshownforbondA.UsingthealternativeformulaformodifieddurationthatdoesnotrequiretheextensivecalculationsrequiredbytheMacaulayprocedureandnotingthatC=$45,n=10,y=,andP=$100,weget:
($+$0)/$100=orabout(beforetheincreasein100basispointsitwasorabout.Convertingtoanannualnumberbydividingbytwogivesamodifieddurationof(beforetheincreasein100basispointsitwas.WewillnowestimatethepriceofbondBusingthemodifieddurationmeasure.With100basispointsgivingdy=andanapproximatedurationof,wehave:
Thus,thenewpriceis(1–$1,=$1,=$.
Thisisslightlylessthantheactualpriceof$1,000.Thedifferenceis$1,000–$=$.
(c)Usingbothduration
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