Hull OF OD8e Solutions Ch05英.docx

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1、CHAPTER5DeterminationofForwardandFuturesPricesPracticeQuestionsProb1em5.1.Exp1ainwhathappenswhenaninvestorshortsacertainshare.Theinvestorsbrokerborrowsthesharesfromanotherc1ienfsaccountandse11sthemintheusua1way.Toc1oseouttheposition,theinvestormustpurchasetheshares.Thebrokerthenrep1acesthemintheacco

2、untofthec1ientfromwhomtheywereborrowed.Thepartywiththeshortpositionmustremittothebrokerdividendsandotherincomepaidontheshares.Thebrokertransfersthesefundstotheaccountofthec1ientfromwhomtheshareswereborrowed.Occasiona11ythebrokerrunsoutofp1acesfromwhichtoborrowtheshares.Theinvestoristhenshortsqueezed

3、andhastoc1oseoutthepositionimmediate1y.Prob1em5.2.Whatisthedifferencebetweentheforwardpriceandtheva1ueofaforwardcontract?Theforwardpriceofanassettodayisthepriceatwhichyouwou1dagreetobuyorse11theassetatafuturetime.Theva1ueofaforwardcontractiszerowhenyoufirstenterintoit.Astimepassestheunder1yingassetp

4、ricechangesandtheva1ueofthecontractmaybecomepositiveornegative.Prob1em5.3.Supposethatyouenterintoasix-monthforwardcontractonanon-dividend-payingstockwhenthestockpriceis$30andtherisk-freeinterestrate(withcontinuouscompounding)is12%perannum.Whatistheforwardprice?Theforwardpriceis30*23=$3186Prob1em5.4.

5、Astockindexcurrent1ystandsat350.Therisk-freeinterestrateis8%perannum(withcontinuouscompounding)andthedividendyie1dontheindexis4%perannum.Whatshou1dthefuturespriceforafour-monthcontractbe?Thefuturespriceis350do.O8-OO4)xO3333=$3547Prob1em5.5.Exp1aincarefu11ywhythefuturespriceofgo1dcanheca1cu1atedfromi

6、tsspotpriceandotherobservab1evariab1eswhereasthefuturespriceofcoppercannot.Go1disaninvestmentasset.Ifthefuturespriceistoohigh,investorswi11finditprofitab1etoincreasetheirho1dingsofgo1dandshortfuturescontracts.Ifthefuturespriceistoo1ow,theywi11finditprofitab1etodecreasetheirho1dingsofgo1dandgo1ongint

7、hefuturesmarket.Copperisaconsumptionasset.Ifthefuturespriceistoohigh,astrategyofbuycopperandshortfuturesworks.However,becauseinvestorsdonotingenera1ho1dtheasset,thestrategyofse11copperandbuyfuturesisnotavai1ab1etothem.Thereisthereforeanupperbound,butno1owerbound,tothefuturesprice.Prob1em5.6.Exp1ainc

8、arefu11ythemeaningofthetermsconvenienceyie1dandcostofcarry.Whatisthere1ationshipbetweenfuturesprice,spotprice,convenienceyie1d,andcostofcarry?Convenienceyie1dmeasurestheextenttowhichtherearebenefitsobtainedfromownershipofthephysica1assetthatarenotobtainedbyownersof1ongfuturescontracts.Thecostofcanyi

9、stheinterestcostp1usstoragecost1esstheincomeearned.Thefuturesprice,Fq,andspotprice,SO,arere1atedbywherecisthecostofcarry,yistheconvenienceyie1d,andTisthetimetomaturityofthefuturescontract.Prob1em5.7.Exp1ainwhyaforeigncurrencycanbetreatedasanassetprovidingaknownyie1d.Aforeigncurrencyprovidesaknownint

10、erestrate,buttheinterestisreceivedintheforeigncurrency.Theva1ueinthedomesticcurrencyoftheincomeprovidedbytheforeigncurrencyisthereforeknownasapercentageoftheva1ueoftheforeigncurrency.Thismeansthattheincomehasthepropertiesofaknownyie1d.Prob1em5.8.Isthefuturespriceofastockindexgreaterthanor1essthanthe

11、expectedfutureva1ueoftheindex?Exp1ainyouranswer.Thefuturespriceofastockindexisa1ways1essthantheexpectedfutureva1ueoftheindex.Thisfo11owsfromSection5.14andthefactthattheindexhaspositivesystematicrisk.Forana1ternativeargument,1etbetheexpectedreturnrequiredbyinvestorsontheindexsothatE(S)=SOeS-g.Because

12、randFq=S0eirqy,itfo11owsthatE(Sr)Fq.Prob1em5.9.Aone-year1ongforwardcontractonanon-dividend-payingstockisenteredintowhenthestockpriceis$40andtherisk-freerateofinterestis10%perannumwithcontinuouscompounding.a) Whataretheforwardpriceandtheinitia1va1ueoftheforwardcontract?b) SiXmonths1ater,thepriceofthe

13、stockis$45andtherisk-freeinterestrateissti1110%.Whataretheforwardpriceandtheva1ueoftheforwardcontract?a) Theforwardprice,Fq,isgivenbyequation(5.1)as:/r=40eoj,=44.21or$44.21.Theinitia1va1ueoftheforwardcontractiszero.b) Thede1iverypriceKinthecontractis$44.21.Theva1ueofthecontract,f,aftersixmonthsisgiv

14、enbyequation(5.5)as:/=45-44.21权5=2.951 .e.,itis$2.95.Theforwardpriceis:45ex5=47.31or$47.31.Prob1em5.10.Therisk-freerateOfinterestis7%perannumwithcontinuouscompounding,andthedividendyie1donastockindexis3.2%perannum.Thecurrentva1ueoftheindexis150.Whatisthesix-monthfuturesprice?Usingequation(5.3)thesix

15、monthfuturespriceis150*07FQ32)x05=52.88or$152.88.Prob1em5.11.Assumethattherisk-freeinterestrateis9%perannumwithcontinuouscompoundingandthatthedividendyie1donastockindexvariesthroughouttheyear.InFebruary,May,August,andNovember,dividendsarepaidatarateof5%perannum.Inothermonths,dividendsarepaidatarateo

16、f2%perannum.Supposethattheva1ueoftheindexonJu1y31is1,300.Whatisthefuturespriceforacontractde1iverab1eonDecember31ofthesameyear?Thefuturescontract1astsforfivemonths.Thedividendyie1dis2%forthreeofthemonthsand5%fortwoofthemonths.Theaveragedividendyie1distherefore(3225)=3.2%Thefuturespriceistherefore1300d09-0032)Mi67=,33i80or$1331.80.Prob1em5.12.Supposethattherisk-freein