HullOFOD9eSolutionsCh07

CHAPTER7SwapsPracticeQuestionsProblem7.1.CompaniesAandBhavebeenofferedthefollowingratesperannumona$20millionfive-yearloan:FixedRateFloatingRateCompanyA5.0%LIBOR+0.1%CompanyB6.4%LIBOR+0.6%CompanyArequiresafloating-rateloan;companyBrequiresafixed-rateloan.Designaswapthatwillnetabank,actingasintermediary,0.1%perannumandthatwillappearequallyattractivetobothcompanies.Ahasanapparentcomparativeadvantageinfixed-ratemarketsbutwantstoborrowfloating.Bhasanapparentcomparativeadvantageinfloating-ratemarketsbutwantstoborrowfixed.Thisprovidesthebasisfortheswap.Thereisa1.4%perannumdifferentialbetweenthefixedratesofferedtothetwocompaniesanda0.5%perannumdifferentialbetweenthefloatingratesofferedtothetwocompanies.Thetotalgaintoallpartiesfromtheswapistherefore140509%perannum.Becausethebankgets0.1%perannumofthisgain,theswapshouldmakeeachofAandB0.4%perannumbetteroff.ThismeansthatitshouldleadtoAborrowingatLIBOR03%andtoBborrowingat6.0%.TheappropriatearrangementisthereforeasshowninFigureS7.1.FigureS7.1:SwapforProblem7.1Problem7.2.CompanyXwishestoborrowU.S.dollarsatafixedrateofinterest.CompanyYwishestoborrowJapaneseyenatafixedrateofinterest.Theamountsrequiredbythetwocompaniesareroughlythesameatthecurrentexchangerate.Thecompanieshavebeenquotedthefollowinginterestrates,whichhavebeenadjustedfortheimpactoftaxes:YenDollarsCompanyX5.0%9.6%CompanyY6.5%10.0%Designaswapthatwillnetabank,actingasintermediary,50basispointsperannum.Maketheswapequallyattractivetothetwocompaniesandensurethatallforeignexchangeriskisassumedbythebank.Xhasacomparativeadvantageinyenmarketsbutwantstoborrowdollars.Yhasacomparativeadvantageindollarmarketsbutwantstoborrowyen.Thisprovidesthebasisfortheswap.Thereisa1.5%perannumdifferentialbetweentheyenratesanda0.4%perannumdifferentialbetweenthedollarrates.Thetotalgaintoallpartiesfromtheswapistherefore150411%perannum.Thebankrequires0.5%perannum,leaving0.3%perannumforeachofXandY.TheswapshouldleadtoXborrowingdollarsat960393%perannumandtoYborrowingyenat650362%perannum.TheappropriatearrangementisthereforeasshowninFigureS7.2.Allforeignexchangeriskisbornebythebank.FigureS7.2:SwapforProblem7.2Problem7.3.A$100millioninterestrateswaphasaremaininglifeof10months.Underthetermsoftheswap,six-monthLIBORisexchangedfor7%perannum(compoundedsemiannually).Theaverageofthebid–offerratebeingexchangedforsix-monthLIBORinswapsofallmaturitiesiscurrently5%perannumwithcontinuouscompounding.Thesix-monthLIBORratewas4.6%perannumtwomonthsago.Whatisthecurrentvalueoftheswaptothepartypayingfloating?Whatisitsvaluetothepartypayingfixed?Infourmonths$3.5million(05007$100million)willbereceivedand$2.3million(050046$100million)willbepaid.(Weignoredaycountissues.)In10months$3.5millionwillbereceived,andtheLIBORrateprevailinginfourmonths’timewillbepaid.Thevalueofthefixed-ratebondunderlyingtheswapis0054120051012351035$102718millioneeThevalueofthefloating-ratebondunderlyingtheswapis005412(10023)$100609millioneThevalueoftheswaptothepartypayingfloatingis$102718$100609$2109million.Thevalueoftheswaptothepartypayingfixedis$2109million.Theseresultscanalsobederivedbydecomposingtheswapintoforwardcontracts.Considerthepartypayingfloating.Thefirstforwardcontractinvolvespaying$2.3millionandreceiving$3.5millioninfourmonths.Ithasavalueof00541212$1180emillion.Tovaluethesecondforwardcontract,wenotethattheforwardinterestrateis5%perannumwithcontinuouscompounding,or5.063%perannumwithsemiannualcompounding.Thevalueoftheforwardcontractis0051012100(0070500506305)$0929millioneThetotalvalueoftheforwardcontractsistherefore$1180$0929$2109million.Problem7.4.Explainwhataswaprateis.Whatistherelationshipbetweenswapratesandparyields?AswaprateforaparticularmaturityistheaverageofthebidandofferfixedratesthatamarketmakerispreparedtoexchangeforLIBORinastandardplainvanillaswapwiththatmaturity.TheswaprateforaparticularmaturityistheLIBOR/swapparyieldforthatmaturity.Problem7.5.Acurrencyswaphasaremaininglifeof15months.Itinvolvesexchanginginterestat10%on£20millionforinterestat6%on$30milliononceayear.ThetermstructureofinterestratesinboththeUnitedKingdomandtheUnitedStatesiscurrentlyflat,andiftheswapwerenegotiatedtodaytheinterestratesexchangedwouldbe4%indollarsand7%insterling.Allinterestratesarequotedwithannualcompounding.Thecurrentexchangerate(dollarsperpoundsterling)is1.5500.Whatisthevalueoftheswaptothepartypayingsterling?Whatisthevalueoftheswaptothepartypayingdollars?Theswapinvolvesexchangingthesterlinginterestof20010or£2millionforthedollarinterestof3000618$million.Theprincipalamountsarealsoexchangedattheendofthelifeoftheswap.Thevalueofthesterlingbondunderlyingtheswapis145422222182millionpounds(107)(107)Thevalueofthedollarbondunderlyingtheswapis145418318$32061million(104)(104)Thevalueoftheswaptothepartypayingsterlingistherefore32.061−(22.182×1.55)=−$2.321millionThevalueoftheswaptothepartypayingdollarsis$2.321million.Theresultscanalsobeobtainedbyviewingtheswapasaportfolioofforwardcontracts.Thecontinuouslycompo