HullOFOD9eSolutionsCh03第九版期权期货及其他衍生品课后答案

CHAPTER3HedgingStrategiesUsingFuturesPracticeQuestionsProblem3.1.Underwhatcircumstancesare(a)ashorthedgeand(b)alonghedgeappropriate?Ashorthedgeisappropriatewhenacompanyownsanassetandexpectstosellthatassetinthefuture.Itcanalsobeusedwhenthecompanydoesnotcurrentlyowntheassetbutexpectstodosoatsometimeinthefuture.Alonghedgeisappropriatewhenacompanyknowsitwillhavetopurchaseanassetinthefuture.Itcanalsobeusedtooffsettheriskfromanexistingshortposition.Problem3.2.Explainwhatismeantbybasisriskwhenfuturescontractsareusedforhedging.Basisriskarisesfromthehedger’suncertaintyastothedifferencebetweenthespotpriceandfuturespriceattheexpirationofthehedge.Problem3.3.Explainwhatismeantbyaperfecthedge.Doesaperfecthedgealwaysleadtoabetteroutcomethananimperfecthedge?Explainyouranswer.Aperfecthedgeisonethatcompletelyeliminatesthehedger’srisk.Aperfecthedgedoesnotalwaysleadtoabetteroutcomethananimperfecthedge.Itjustleadstoamorecertainoutcome.Consideracompanythathedgesitsexposuretothepriceofanasset.Supposetheasset’spricemovementsprovetobefavorabletothecompany.Aperfecthedgetotallyneutralizesthecompany’sgainfromthesefavorablepricemovements.Animperfecthedge,whichonlypartiallyneutralizesthegains,mightwellgiveabetteroutcome.Problem3.4.Underwhatcircumstancesdoesaminimum-variancehedgeportfolioleadtonohedgingatall?Aminimumvariancehedgeleadstonohedgingwhenthecoefficientofcorrelationbetweenthefuturespricechangesandchangesinthepriceoftheassetbeinghedgediszero.Problem3.5.Givethreereasonswhythetreasurerofacompanymightnothedgethecompany’sexposuretoaparticularrisk.(a)Ifthecompany’scompetitorsarenothedging,thetreasurermightfeelthatthecompanywillexperiencelessriskifitdoesnothedge.(SeeTable3.1.)(b)Theshareholdersmightnotwantthecompanytohedgebecausetherisksarehedgedwithintheirportfolios.(c)Ifthereisalossonthehedgeandagainfromthecompany’sexposuretotheunderlyingasset,thetreasurermightfeelthatheorshewillhavedifficultyjustifyingthehedgingtootherexecutiveswithintheorganization.Problem3.6.Supposethatthestandarddeviationofquarterlychangesinthepricesofacommodityis$0.65,thestandarddeviationofquarterlychangesinafuturespriceonthecommodityis$0.81,andthecoefficientofcorrelationbetweenthetwochangesis0.8.Whatistheoptimalhedgeratioforathree-monthcontract?Whatdoesitmean?Theoptimalhedgeratiois065080642081Thismeansthatthesizeofthefuturespositionshouldbe64.2%ofthesizeofthecompany’sexposureinathree-monthhedge.Problem3.7.Acompanyhasa$20millionportfoliowithabetaof1.2.Itwouldliketousefuturescontractsonastockindextohedgeitsrisk.Theindexfuturesiscurrentlystandingat1080,andeachcontractisfordeliveryof$250timestheindex.Whatisthehedgethatminimizesrisk?Whatshouldthecompanydoifitwantstoreducethebetaoftheportfolioto0.6?Theformulaforthenumberofcontractsthatshouldbeshortedgives20000000128891080250Roundingtothenearestwholenumber,89contractsshouldbeshorted.Toreducethebetato0.6,halfofthisposition,orashortpositionin44contracts,isrequired.Problem3.8.Inthecornfuturescontract,thefollowingdeliverymonthsareavailable:March,May,July,September,andDecember.Statethecontractthatshouldbeusedforhedgingwhentheexpirationofthehedgeisina)June,b)July,andc)JanuaryAgoodruleofthumbistochooseafuturescontractthathasadeliverymonthascloseaspossibleto,butlaterthan,themonthcontainingtheexpirationofthehedge.Thecontractsthatshouldbeusedaretherefore(a)July(b)September(c)MarchProblem3.9.Doesaperfecthedgealwayssucceedinlockinginthecurrentspotpriceofanassetforafuturetransaction?Explainyouranswer.No.Consider,forexample,theuseofaforwardcontracttohedgeaknowncashinflowinaforeigncurrency.Theforwardcontractlocksintheforwardexchangerate—whichisingeneraldifferentfromthespotexchangerate.Problem3.10.Explainwhyashorthedger’spositionimproveswhenthebasisstrengthensunexpectedlyandworsenswhenthebasisweakensunexpectedly.Thebasisistheamountbywhichthespotpriceexceedsthefuturesprice.Ashorthedgerislongtheassetandshortfuturescontracts.Thevalueofhisorherpositionthereforeimprovesasthebasisincreases.Similarly,itworsensasthebasisdecreases.Problem3.11.ImagineyouarethetreasurerofaJapanesecompanyexportingelectronicequipmenttotheUnitedStates.Discusshowyouwoulddesignaforeignexchangehedgingstrategyandtheargumentsyouwouldusetosellthestrategytoyourfellowexecutives.Thesimpleanswertothisquestionisthatthetreasurershould1.Estimatethecompany’sfuturecashflowsinJapaneseyenandU.S.dollars2.EnterintoforwardandfuturescontractstolockintheexchangeratefortheU.S.dollarcashflows.However,thisisnotthewholestory.AsthegoldjewelryexampleinTable3.1shows,thecompanyshouldexaminewhetherthemagnitudesoftheforeigncashflowsdependontheexchangerate.Forexample,willthecompanybeabletoraisethepriceofitsproductinU.S.dollarsiftheyenappreciates?Ifthecompanycandoso,itsforeignexchangeexposuremaybequitelow.Thekeyestimatesrequiredarethoseshowingtheoveralleffectonthecompany’sprofitabilityofchangesintheexchangerateatvarioustimesinthefuture.Oncetheseestimateshavebeenproducedthecompanycanchoosebetweenusingfuturesandoptionstohedgeitsrisk.Theresultsoftheanalysisshouldbepresentedcarefullytoot