對外經(jīng)濟貿(mào)易大學國際經(jīng)濟貿(mào)易學院固定收益證券部分答案

1、國際經(jīng)濟貿(mào)易學院研究生課程班國際經(jīng)濟貿(mào)易學院研究生課程班《固定收益證券》試題1）Explainwhyyouagreedisagreewiththefollowingstatement:“Thepriceofafloaterwillalwaystradeatitsparvalue.”Answer:Idisagreewiththestatement:“Thepriceofafloaterwillalwaystradeatitsparvalu

2、e.”Firstthecouponrateofafloatingratesecurity(floater)isequaltoareferencerateplussomespreadmargin.FexamplethecouponrateofafloatercanresetattherateonathreemonthTreasurybill(thereferencerate)plus50basispoints(thespread).Nex

3、tthepriceofafloaterdependsontwofacts:(1)thespreadoverthereferencerate(2)anyrestrictionsthatmaybeimposedontheresettingofthecouponrate.Fexampleafloatermayhaveamaximumcouponratecalledacapaminimumcouponratecalledaflo.Thepric

4、eofafloaterwilltradeclosetoitsparvalueaslongas(1)thespreadabovethereferenceratethatthemarketrequiresisunchanged(2)neitherthecapnthefloisreached.Howeverifthemarketrequiresalarger(smaller)spreadthepriceofafloaterwilltradeb

5、elow(above)par.Ifthecouponrateisrestrictedfromchangingtothereferencerateplusthespreadbecauseofthecapthenthepriceofafloaterwilltradebelowpar.2）Aptfoliomanagerisconsideringbuyingtwobonds.BondAmaturesinthreeyearshasacouponr

6、ateof10%payablesemiannually.BondBofthesamecreditqualitymaturesin10yearshasacouponrateof12%payablesemiannually.Bothbondsarepricedatpar.(a)Supposethattheptfoliomanagerplanstoholdthebondthatispurchasedfthreeyears.Whichwould

7、bethebestbondftheptfoliomanagertopurchaseAnswer:Theshtertermbondwillpayalowercouponratebutitwilllikelycostlessfagivenmarketrate.Sincethebondsareofequalriskintermsofcreitquality(Thematuritypremiumfthelongertermbondshouldb

8、egreater)thequestionwhencomparingthetwobondinvestmentsis:WhatinvestmentwillbeexpectetogivethehighestcashflowperdollarinvestedInotherwdswhichinvestmentwillbeexpectedtogivethehighesteffectiveannualrateofreturn.Ingeneralhol

9、dingthelongertermbondshouldcompensatetheinvestinthefmofamaturitypremiumahigherexpectedreturn.Howeverasseeninthediscussionbelowtheactualrealizedreturnfeitherinvestmentisnotknownwithcertainty.Tobeginwithaninvestwhopurchase

10、sabondcanexpecttoreceiveadollarreturnfrom(i)theperiodiccouponinterestpaymentsmadebetheissuer(ii)ancapitalgainwhenthebondmaturesiscalledissold(iii)interestincomegeneratedfromreinvestmentoftheperiodiccashflows.Thelastcompo

11、nentofthepotentialdollarreturnisreferredtoasreinvestmentincome.Fastardbond(oursituation)thatmakesonlycouponpaymentsnoperiodicprincipalpaymentspritothematuritydatetheinterimcashflowsaresimplythecouponpayments.Consequently

12、fsuchbondsthereinvestmentincomeissimplyinterestearnedfromreinvestingthecouponinterestpayments.Fthesebondsthethirdcomponentofthepotentialsourceofdollarreturnisreferredtoastheinterestoninterestcomponents.Ifwearegoingtocoup

13、uteapotentialyieldtomakeadecisionweshouldbeawareofthefactthatBondABondBCoupon8%9%Yieldtomaturity8%8%Maturity(years)25Par$100.00$100.00Price$100.00$104.055(a)Calculatetheactualpriceofthebondsfa100basispointincreaseininter

14、estrates.Answer:FBondAwegetabondquoteof$100fourinitialpriceifwehavean8%couponratean8%yield.Ifwechangetheyield100basispointsotheyieldis9%thenthevalueofthebond(P)isthepresentvalueofthecouponpaymentsplusthepresentvalueofthe

15、parvalue.WehaveC=$40y=4.5%n=4M=$1000.ingthesenumbersintoourpresentvalueofcouponbondfmulaweget:41111(1)(10.045)$40$143.5010.045nrPCr???????????????????????????????Thepresentvalueoftheparmaturityvalueof$1000is:4$1000$838.5

16、61(1)(1.045)nMr???ThusthevalueofbondAwithayieldof9%acouponrateof8%amaturityof2yearsis:P=$143.501$838.561=$982.062.Thuswegetabondquoteof$98.2062.WealreadyknowthatbondBwillgiveabondvalueof$1000abondquoteof$100sinceachangeo

17、f100basispointswillmaketheyieldcouponratethesameFexampleingThusthevalueofbondAwithayieldof9%acouponrateof8%amaturityof2yearsis:P=$143.501$838.561=$982.062.Thuswegetabondquoteof$98.2062.WealreadyknowthatbondBwillgiveabond

18、valueof$1000abondquoteof$100sinceachangeof100basispointswillmaketheyieldcouponratethesameFexampleing(b)Usingdurationestimatethepriceofthebondsfa100basispointincreaseininterestrates.Answer:ToestimatethepriceofbondAwebegin

19、byfirstcomputingthemodifiedduration.WecanuseanalternativefmulathatdoesnotrequiretheextensivecalculationsrequiredbytheMacaulayprocedure.Thefmulais:211(100)1(1)(1)nnCnCyyyyModifiedDurationP?????????????Puttingallapplicable

20、variablesintermsof$100wehaveC=$4n=4y=0.045P=$98.2062.ingthesevaluesinthemodifieddurationfmulagives:212451(100)$414($100$40.045)11(1)(1)0.045(1.045)(1.045)98.2062nnCnCyyyyModifiedDurationP????????????????????????($1975.30