Fixed-Income-securities教材练习题及答案

ProblemsandSolutions1CHAPTER1—Problems1.1ProblemsonBondsExercise1.1On12/04/01,considerafixed-couponbondwhosefeaturesarethefollowing:•facevalue:$1,000•couponrate:8%•couponfrequency:semiannual•maturity:05/06/04Whatarethefuturecashflowsdeliveredbythisbond?Solution1.11.Thecouponcashflowisequalto$40Coupon=8%×$1,0002=$40Itisdeliveredonthefollowingfuturedates:05/06/02,11/06/02,05/06/03,11/06/03and05/06/04.Theredemptionvalueisequaltothefacevalue$1,000andisdeliveredonmaturitydate05/06/04.Exercise1.3Aninvestorhasacashof$10,000,000atdisposal.Hewantstoinvestinabondwith$1,000nominalvalueandwhosedirtypriceisequalto107.457%.1.Whatisthenumberofbondshewillbuy?2.Samequestionifthenominalvalueandthedirtypriceofthebondarerespec-tively$100and98.453%.Solution1.31.ThenumberofbondshewillbuyisgivenbythefollowingformulaNumberofbondsbought=CashNominalValueofthebond×dirtypriceHere,thenumberofbondsisequalto9,306n=10,000,0001,000×107.457%=9,306.0482.nisequalto101,562n=10,000,000100×98.453%=101,571.31Exercise1.4On10/25/99,considerafixed-couponbondwhosefeaturesarethefollowing:•facevalue:Eur1002ProblemsandSolutions•couponrate:10%•couponfrequency:annual•maturity:04/15/08Computetheaccruedinteresttakingintoaccountthefourdifferentday-countbases:Actual/Actual,Actual/365,Actual/360and30/360.Solution1.4Thelastcouponhasbeendeliveredon04/15/99.Thereare193daysbetween04/15/99and10/25/99,and366daysbetweenthelastcoupondate(04/15/99)andthenextcoupondate(04/15/00).•TheaccruedinterestwiththeActual/Actualday-countbasisisequaltoEur5.273193366×10%×Eur100=Eur5.273•TheaccruedinterestwiththeActual/365day-countbasisisequaltoEur5.288193365×10%×Eur100=Eur5.288•TheaccruedinterestwiththeActual/360day-countbasisisequaltoEur5.361193360×10%×Eur100=Eur5.361Thereare15daysbetween04/15/99and04/30/99,5monthsbetweenMayandSeptember,and25daysbetween09/30/99and10/25/99,sothatthereare190daysbetween04/15/99and10/25/99onthe30/360day-countbasis15+(5×30)+25=190•Finally,theaccruedinterestwiththe30/360day-countbasisisequaltoEur5.278190360×10%×Eur100=Eur5.278Exercise1.8Aninvestorwantstobuyabulletbondoftheautomotivesector.Hehastwochoices:eitherinvestinaUScorporatebonddenominatedineurosorinaFrenchcorporatebondwithsamematurityandcoupon.Arethetwobondscomparable?Solution1.8Theanswerisno.First,thecouponandyieldfrequencyoftheUScorporatebondissemiannual,whileitisannualfortheFrenchcorporatebond.Tocomparetheyieldsonthetwoinstruments,youhavetoconverteitherthesemiannualyieldoftheUSbondintoanequivalentlyannualyieldortheannualyieldoftheFrenchbondintoanequivalentlysemiannualyield.Second,thetwobondsdonotnecessarilyhavethesamerating,thatis,thesamecreditrisk.Third,theydonotnecessarilyhavethesameliquidity.3ProblemsandSolutionsExercise1.15WhatisthepricePofthecertificateofdepositissuedbybankXon06/06/00,withmaturity08/25/00,facevalue$10,000,000,aninterestrateatissuanceof5%fallingatmaturityandayieldof4.5%asof07/31/00?Solution1.15RecallthatthepricePofsuchaproductisgivenbyP=F×
1+c×ncB
1+ym×nmBwhereFisthefacevalue,ctheinterestrateatissuance,ncisthenumberofdaysbetweenissueandmaturity,Bistheyear-basis(360or365),ymistheyieldonamoney-marketbasisandnmisthenumberofdaysbetweensettlementandmaturity.Then,thepricePofthecertificateofdepositissuedbybankXisequaltoP=$10,000,000×1+5%×803601+4.5%×25360=$10,079,612.3Indeed,thereare80calendardaysbetween06/06/00and08/25/00,and25calendardaysbetween07/31/00and08/25/00.2CHAPTER2—ProblemsExercise2.1Supposethe1-yearcontinuouslycompoundedinterestrateis12%.Whatistheeffectiveannualinterestrate?Solution2.1TheeffectiveannualinterestrateisR=e0.12−1=0.1275=12.75%.Exercise2.2Ifyoudeposit$2,500inabankaccountthatearns8%annuallyonacontinuouslycompoundedbasis,whatwillbetheaccountbalancein7.14years?Solution2.2Theaccountbalancein7.14yearswillbe$2,500.e8%×7.14=$4,425.98Exercise2.3Ifaninvestmenthasacumulative63.45%rateofreturnover3.78years,whatistheannualcontinuouslycompoundedrateofreturn?Solution2.3TheannualcontinuouslycompoundedrateofreturnRissuchthat1.6345=e3.78RcWefindRc=ln(1.6345)/3.78=13%.4ProblemsandSolutionsExercise2.71.Whatisthepriceofa5-yearbondwithanominalvalueof$100,ayieldtomaturityof7%(withannualcompoundingfrequency),a10%couponrateandanannualcouponfrequency?2.Samequestionforayieldtomaturityof8%,9%and10%.Conclude.Solution2.71.ThepricePofabondisgivenbytheformulaP=ni=1N×c(1+y)i+N(1+y)nwhichsimplifiesintoP=N×cy1−1(1+y)n+N(1+y)nwhereN,c,yandnarerespectivelythenominalvalue,thecouponrate,theyieldtomaturityandthenumberofyearstomaturityofthebond.Here,weobtainforPP=107%1−1(1+7%)5+100(1+7%)5Pisthenequalto112.301%ofthenominalvalueor$112.301.NotethatwecanalsousetheExcelfunction“Price”toobtainP.2.Pricesofthebondfordifferentyieldstomaturity(YTM)aregiveninthefol-lowingtableYTM(%)Price($)8107.9859103.89010100Bondpricesdecreaseasratesincrease.Exercise2.14Weconsiderthefollowingzero-couponcurve:Maturity(years)Zero-CouponRate(%)14.0024.5034.7544.9055.001.Whatisthepriceofa5-yearbondwitha$100facevalue,whichdeliversa5%annualcouponrate?2.Whatistheyieldtomaturityofthisbond?3.Wesupposethatthezero-couponcurveincr