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

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:

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?

Answer:

Simileartoourdiscussioninpart（a）,wedonotknowwhichinvestmentwouldgivethehighestactualrelizedreturninsixyearswhenweconsiderreinvestingallcashflows.Ifthemanagerbuysathree-yearbond,thentherewouldbetheadditionaluncertaintyofnowknowingwhatthree-yearbondrateswouldbeinthreeyears.Thepurchaseoftheten-yearbondwouldbeheldlongerthanpreviously（sixyearscomparedtothreeyears）andrendercouponpaymentsforasix-yearperiodthatareknown.Ifthesecashflowsarespentwhenreceived,themanagerwillknowexactlyhowmuchmoneycouldbespentatcertainpointsintimeNotknowingwhichbondinvestmentwouldgivethehighestrealizedreturn,theportfoliomanagerwouldchoosethebondthatfitsthefirm’sgoalsintermsofmaturity.

3）AnswerthebelowquestionsforbondsAandB.

BondA

BondB

Coupon

8%

9%

Yieldtomaturity

8%

8%

Maturity（years）

2

5

Par

$100.00

$100.00

Price

$100.00

$104.055

（a）Calculatetheactualpriceofthebondsfora100-basis-pointincreaseininterestrates.

Answer:

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.

Answer:

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.Usingthealternativeformulaformodifieddurationthatdoesnotrequiretheextensivecalculationsrequiredbyt