HullOFOD8eSolutionsCh05Word格式.doc
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HullOFOD8eSolutionsCh05Word格式.doc
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Explainwhathappenswhenaninvestorshortsacertainshare.
Theinvestor’sbrokerborrowsthesharesfromanotherclient’saccountandsellsthemintheusualway.Tocloseouttheposition,theinvestormustpurchasetheshares.Thebrokerthenreplacesthemintheaccountoftheclientfromwhomtheywereborrowed.Thepartywiththeshortpositionmustremittothebrokerdividendsandotherincomepaidontheshares.Thebrokertransfersthesefundstotheaccountoftheclientfromwhomtheshareswereborrowed.Occasionallythebrokerrunsoutofplacesfromwhichtoborrowtheshares.Theinvestoristhenshortsqueezedandhastocloseoutthepositionimmediately.
Problem5.2.
Whatisthedifferencebetweentheforwardpriceandthevalueofaforwardcontract?
Theforwardpriceofanassettodayisthepriceatwhichyouwouldagreetobuyorselltheassetatafuturetime.Thevalueofaforwardcontractiszerowhenyoufirstenterintoit.Astimepassestheunderlyingassetpricechangesandthevalueofthecontractmaybecomepositiveornegative.
Problem5.3.
Supposethatyouenterintoasix-monthforwardcontractonanon-dividend-payingstockwhenthestockpriceis$30andtherisk-freeinterestrate(withcontinuouscompounding)is12%perannum.Whatistheforwardprice?
Theforwardpriceis
Problem5.4.
Astockindexcurrentlystandsat350.Therisk-freeinterestrateis8%perannum(withcontinuouscompounding)andthedividendyieldontheindexis4%perannum.Whatshouldthefuturespriceforafour-monthcontractbe?
Thefuturespriceis
Problem5.5.
Explaincarefullywhythefuturespriceofgoldcanbecalculatedfromitsspotpriceandotherobservablevariableswhereasthefuturespriceofcoppercannot.
Goldisaninvestmentasset.Ifthefuturespriceistoohigh,investorswillfinditprofitabletoincreasetheirholdingsofgoldandshortfuturescontracts.Ifthefuturespriceistoolow,theywillfinditprofitabletodecreasetheirholdingsofgoldandgolonginthefuturesmarket.Copperisaconsumptionasset.Ifthefuturespriceistoohigh,astrategyofbuycopperandshortfuturesworks.However,becauseinvestorsdonotingeneralholdtheasset,thestrategyofsellcopperandbuyfuturesisnotavailabletothem.Thereisthereforeanupperbound,butnolowerbound,tothefuturesprice.
Problem5.6.
Explaincarefullythemeaningofthetermsconvenienceyieldandcostofcarry.Whatistherelationshipbetweenfuturesprice,spotprice,convenienceyield,andcostofcarry?
Convenienceyieldmeasurestheextenttowhichtherearebenefitsobtainedfromownershipofthephysicalassetthatarenotobtainedbyownersoflongfuturescontracts.Thecostofcarryistheinterestcostplusstoragecostlesstheincomeearned.Thefuturesprice,,andspotprice,,arerelatedby
whereisthecostofcarry,istheconvenienceyield,andisthetimetomaturityofthefuturescontract.
Problem5.7.
Explainwhyaforeigncurrencycanbetreatedasanassetprovidingaknownyield.
Aforeigncurrencyprovidesaknowninterestrate,buttheinterestisreceivedintheforeigncurrency.Thevalueinthedomesticcurrencyoftheincomeprovidedbytheforeigncurrencyisthereforeknownasapercentageofthevalueoftheforeigncurrency.Thismeansthattheincomehasthepropertiesofaknownyield.
Problem5.8.
Isthefuturespriceofastockindexgreaterthanorlessthantheexpectedfuturevalueoftheindex?
Explainyouranswer.
Thefuturespriceofastockindexisalwayslessthantheexpectedfuturevalueoftheindex.ThisfollowsfromSection5.14andthefactthattheindexhaspositivesystematicrisk.Foranalternativeargument,letbetheexpectedreturnrequiredbyinvestorsontheindexsothat.Becauseand,itfollowsthat.
Problem5.9.
Aone-yearlongforwardcontractonanon-dividend-payingstockisenteredintowhenthestockpriceis$40andtherisk-freerateofinterestis10%perannumwithcontinuouscompounding.
a)Whataretheforwardpriceandtheinitialvalueoftheforwardcontract?
b)Sixmonthslater,thepriceofthestockis$45andtherisk-freeinterestrateisstill10%.Whataretheforwardpriceandthevalueoftheforwardcontract?
a)Theforwardprice,,isgivenbyequation(5.1)as:
or$44.21.Theinitialvalueoftheforwardcontractiszero.
b)Thedeliverypriceinthecontractis$44.21.Thevalueofthecontract,,aftersixmonthsisgivenbyequation(5.5)as:
i.e.,itis$2.95.Theforwardpriceis:
or$47.31.
Problem5.10.
Therisk-freerateofinterestis7%perannumwithcontinuouscompounding,andthedividendyieldonastockindexis3.2%perannum.Thecurrentvalueofth
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