HullOFOD9eSolutionsCh06

CHAPTER6InterestRateFuturesPracticeQuestionsProblem6.1.AU.S.Treasurybondpaysa7%coupononJanuary7andJuly7.Howmuchinterestaccruesper$100ofprincipaltothebondholderbetweenJuly7,2014andAugust8,2014?Howwouldyouranswerbedifferentifitwereacorporatebond?Thereare32calendardaysbetweenJuly7,2014andAugust8,2014.Thereare184calendardaysbetweenJuly7,2014andJanuary7,2015.Theinterestearnedper$100ofprincipalistherefore3.5×32/184=$0.6087.Foracorporatebondweassume31daysbetweenJuly7andAugust8,2014and180daysbetweenJuly7,2014andJanuary7,2015.Theinterestearnedis3.5×31/180=$0.6028.Problem6.2.ItisJanuary9,2015.ThepriceofaTreasurybondwitha12%couponthatmaturesonOctober12,2030,isquotedas102-07.Whatisthecashprice?Thereare89daysbetweenOctober12,2014,andJanuary9,2015.Thereare182daysbetweenOctober12,2014,andApril12,2014.Thecashpriceofthebondisobtainedbyaddingtheaccruedinteresttothequotedprice.Thequotedpriceis732102or102.21875.Thecashpriceistherefore89102218756$10515182Problem6.3.HowistheconversionfactorofabondcalculatedbytheCMEGroup?Howisitused?Theconversionfactorforabondisequaltothequotedpricethebondwouldhaveperdollarofprincipalonthefirstdayofthedeliverymonthontheassumptionthattheinterestrateforallmaturitiesequals6%perannum(withsemiannualcompounding).Thebondmaturityandthetimestothecouponpaymentdatesareroundeddowntothenearestthreemonthsforthepurposesofthecalculation.Theconversionfactordefineshowmuchaninvestorwithashortbondfuturescontractreceiveswhenbondsaredelivered.Iftheconversionfactoris1.2345theamountinvestorreceivesiscalculatedbymultiplying1.2345bythemostrecentfuturespriceandaddingaccruedinterest.Problem6.4.AEurodollarfuturespricechangesfrom96.76to96.82.Whatisthegainorlosstoaninvestorwhoislongtwocontracts?TheEurodollarfuturespricehasincreasedby6basispoints.Theinvestormakesagainpercontractof256$150or$300intotal.Problem6.5.WhatisthepurposeoftheconvexityadjustmentmadetoEurodollarfuturesrates?Whyistheconvexityadjustmentnecessary?SupposethataEurodollarfuturesquoteis95.00.Thisgivesafuturesrateof5%forthethree-monthperiodcoveredbythecontract.Theconvexityadjustmentistheamountbywhichfuturesratehastobereducedtogiveanestimateoftheforwardratefortheperiod.Theconvexityadjustmentisnecessarybecausea)thefuturescontractissettleddailyandb)thefuturescontractexpiresatthebeginningofthethreemonths.Bothoftheseleadtothefuturesratebeinggreaterthantheforwardrate.Problem6.6.The350-dayLIBORrateis3%withcontinuouscompoundingandtheforwardratecalculatedfromaEurodollarfuturescontractthatmaturesin350daysis3.2%withcontinuouscompounding.Estimatethe440-dayzerorate.Fromequation(6.4)therateis3290335030409440or3.0409%.Problem6.7.ItisJanuary30.Youaremanagingabondportfolioworth$6million.Thedurationoftheportfolioinsixmonthswillbe8.2years.TheSeptemberTreasurybondfuturespriceiscurrently108-15,andthecheapest-to-deliverbondwillhaveadurationof7.6yearsinSeptember.Howshouldyouhedgeagainstchangesininterestratesoverthenextsixmonths?Thevalueofacontractis1532108100010846875$.Thenumberofcontractsthatshouldbeshortedis6000000825971084687576Roundingtothenearestwholenumber,60contractsshouldbeshorted.ThepositionshouldbeclosedoutattheendofJuly.Problem6.8.Thepriceofa90-dayTreasurybillisquotedas10.00.Whatcontinuouslycompoundedreturn(onanactual/365basis)doesaninvestorearnontheTreasurybillforthe90-dayperiod?ThecashpriceoftheTreasurybillis90100109750360$Theannualizedcontinuouslycompoundedreturnis36525ln1102790975%Problem6.9.ItisMay5,2014.Thequotedpriceofagovernmentbondwitha12%couponthatmaturesonJuly27,2024,is110-17.Whatisthecashprice?ThenumberofdaysbetweenJanuary27,2014andMay5,2014is98.ThenumberofdaysbetweenJanuary27,2014andJuly27,2014is181.Theaccruedinterestistherefore98632486181Thequotedpriceis110.5312.Thecashpriceistherefore1105312324861137798or$113.78.Problem6.10.SupposethattheTreasurybondfuturespriceis101-12.Whichofthefollowingfourbondsischeapesttodeliver?BondPriceConversionFactor1125-051.21312142-151.37923115-311.11494144-021.4026Thecheapest-to-deliverbondistheoneforwhichQuotedPriceFuturesPriceConversionFactorisleast.Calculatingthisfactorforeachofthe4bondswegetBond112515625101375121312178Bond214246875101375137922652Bond311596875101375111492946Bond414406250101375140261874Bond4isthereforethecheapesttodeliver.Problem6.11.ItisJuly30,2015.Thecheapest-to-deliverbondinaSeptember2015Treasurybondfuturescontractisa13%couponbond,anddeliveryisexpectedtobemadeonSeptember30,2015.CouponpaymentsonthebondaremadeonFebruary4andAugust4eachyear.Thetermstructureisflat,andtherateofinterestwithsemiannualcompoundingis12%perannum.Theconversionfactorforthebondis1.5.Thecurrentquotedbondpriceis$110.Calculatethequotedfuturespriceforthecontract.Thereare176daysbetweenFebruary4andJuly30and181daysbetweenFebruary4andAugust4.Thecashpriceofthebondis,therefore:1761106511632181Therateofinterestwithcontinuouscompoundingis2ln10601165or11.65%perannum.Acouponof6.5willbereceivedin5daysor0.1370years)time.Thepresentvalueofthecouponis490.651165.01370.0