金融学（中文版）14章金融答案翻译

Instructor’sManual Chapter14 PagePAGE157CHAPTER14FORWARDANDFUTURESPRICESObjectivesToexplaintheeconomicroleoffuturesmarketsToshowwhatinformationcanandcannotbeinferredfromforwardandfuturesprices.OutlineTOC\f14.1 DistinctionsBetweenForwardandFuturesContracts14.2 TheEconomicFunctionofFuturesMarkets14.3 TheRoleofSpeculators14.4 RelationBetweenCommoditySpotandFuturesPrices14.5 ExtractingInformationfromCommodityFuturesPrices14.6 Spot-FuturesPriceParityforGold14.7 FinancialFutures14.8 TheImpliedRisk-FreeRate14.9 TheForwardPriceIsNotaForecastoftheSpotPrice14.10 Forward-SpotParitywithCashPayouts14.11 ImpliedDividends14.12 TheForeign-ExchangeParityRelation14.13 TheRoleofExpectationsinDeterminingExchangeRatesSummaryFuturescontractsmakeitpossibletoseparatethedecisionofwhethertophysicallystoreacommodityfromthedecisiontohavefinancialexposuretoitspricechanges.Speculatorsinfuturesmarketsimprovetheinformationalcontentoffuturespricesandmakefuturesmarketsmoreliquidthantheywouldotherwisebe.Thefuturespriceofwheatcannotexceedthespotpricebymorethanthecostofcarry:Theforward-spotpriceparityrelationforgoldisthattheforwardpriceequalsthespotpricetimesthecostofcarry: Thisrelationismaintainedbytheforceofarbitrage.Onecaninfertheimpliedcostofcarryandtheimpliedstoragecostsfromtheobservedspotandforwardpricesandtherisk-freeinterestrate.Theforward-spotparityrelationforstocksisthattheforwardpriceequalsthespotpricetimes1plustherisk-freeratelesstheexpectedcashdividend.Thisrelationcanthereforebeusedtoinfertheimplieddividendfromtheobservedspotandforwardpricesandtherisk-freeinterestrate.Theforward-spotpriceparityrelationforthedollar/yenexchangerateinvolvestwointerestrates:whereFistheforwardpriceoftheyen,Sisthecurrentspotprice,rYistheyeninterestrate,andr$isthedollarinterestrate.Iftheforwarddollar/yenexchangerateisanunbiasedforecastofthefuturespotexchangerate,thenonecaninferthatforecasteitherfromtheforwardrateorfromthedollar-denominatedandyen-denominatedrisk-freeinterestrates.

SolutionstoProblemsatEndofChapterForwardContractsandForward-SpotParity.SupposethatyouareplanningatriptoEngland.Thetripisayearfromnow,andyouhavereservedahotelroominLondonatapriceof₤50perday.Youdonothavetopayfortheroominadvance.Theexchangerateiscurrently$1.50tothepoundsterling.Explainseveralpossiblewaysthatyoucouldcompletelyhedgetheexchangerateriskinthissituation.Supposethatr₤=.12andr$=.08.BecauseS=$1.50,whatmusttheforwardpriceofthepoundbe?ShowthatifFis$0.10higherthaninyouranswertopartb,therewouldbeanarbitrageopportunity.SOLUTION:Waystohedgetheexchangeraterisk:PayfortheroominadvanceBuythepoundsyouwillneedintheforwardmarket.Investthepresentvalueoftherentalpaymentsinapound-denominatedrisklessasset.对冲外汇风险的几种方法：提前对这个房间付款；在期货市场购买英镑；将与现期价值的租金同等的英镑投资于无风险资产。F=S(1+r$)/(1+r£)=$1.50x1.08/1.12=$1.4464perpound1.4464美元/英镑IfFis$1.55thenarbitrageprofitscanbemadebyborrowingdollars,investinginpoundsandsellingthemforwardattheinflatedforwardprice.Afterpayingoffprincipleandinterestonthedollarsborrowed,youwouldhavepurearbitrageprofitsleftover.如果F是1.55美元，那么套利可以通过买进美元以获取收益，将美元投资于英镑然后在通货膨胀的价格下卖出。在支付完所借到的美元的本金和利息后，你将得到剩下的纯套利收益。Forexample,Borrow$1.50,Convertitinto1pound,Investitinpound-denominatedbondstohave1.12poundsayearfromnow,Sell1.12poundsforwardat$1.55perpoundtohave$1.736ayearfromnow,例如，你可以借进1.50美元，使起转变为1英镑，将起投资于英镑，一年后你会得到1.12英镑的，将这1.12英镑以1.55美元卖出，你将得到1.736美元。After1year,payofftheprincipleandinterestontheloan($1.50x1.08=$1.62).Thisseriesoftransactionsleavesyouwith$.116ayearfromnowwithnoinitialoutlayofyourmoney.在一年之后，将本金和利息支付，也就是1.50*1.08=1.62美元，这一系列的交易在没有创始费用的状况下将给你留下1.16美元。ArbitragePositionImmediateCashFlowCashFlow1YearFromNowBorrow$1.50借进1.50美元$1.50-$1.62Buypound-denominatedbond购买英镑远期合约-$1.50S1Sell1.12poundsforwardat$1.55perpound以1.55美元/英镑的价格卖出1.12英镑0$1.736-S1NetCashFlows净现金流0$1.736-$1.62=$.116Forward-SpotParityRelationwithKnownCashPayoutsSupposethattheTreasuryyieldcurveisflatataninterestrateof7%peryear(compoundedsemiannually).Whatisthespotpriceofa30-yearTreasurybondwithan8%couponrateassumingcouponsarepaidsemiannually?Whatistheforwardpriceofthebondfordeliverysixmonthsfromnow?Showthatiftheforwardpriceis$1lowerthaninyouranswertopartb,thereshouldbeanarbitrageopportunity.SOLUTION:a. Thespotpriceofthe30-yearTreasuryis$1,124.724:niPVFVPMTResult603.5?100040PV=1124.724b. Theforwardpricefordeliverysixmonthsfromnowis$1,124.089:6个月后交割的债券远期价格是1,124.089美元F=S(1+r)-C=$1,124.724x1.035-40=$1,124.089Iftheforwardpriceisonly$1,123.089,thenarbitrageprofitscanbemadebysellingthebondshortandbuyingitforwardatthelowforwardprice.Itcanbedescribedasfollows:如果远期价格仅仅是1,123.089美元，那么套利获得收益可以这样进行：将近期的美元卖出，并在将来以较低的价格买进。可以通过如下来描述：Sellshortabondat$1,124.724;buyitforwardat$1,123.089;investtheproceedsoftheshortsaletoearn3.5%for6monthsAfter6months,takedeliveryofthebondandcoveryourshortsale将$1,124.724卖出，并在将来买进$1,123.089；6个月后将从购买中获得3.5%的收益。ArbitragePositionImmediateCashFlowCashFlow1YearFromNowSellshorta30-yearT-bond卖出30年期国债$1,124.089-(S1+$40)Buy6-monthT-billspaying3.5%买进6个月国债制服3.5%-$1,124.089$1,163.432Buyaforwardcontractfora30-yearT-bond买进30年期的国债远期合同0S1-$1,123.089NetCashFlows净现金流0$1,163.432-($1,123.089+$40)=$.343Forward-SpotParityRelationwithUncertainDividendsAstockhasaspotpriceof$100;therisklessinterestrateis7%peryear(compoundedannually),andtheexpecteddividendonthestockis$3,tobereceivedayearfromnow.Whatshouldbetheone-yearfuturesprice?Ifthefuturespriceis$1higherthanyouranswertoparta,whatmightthatimplyabouttheexpecteddividend?SOLUTION:S=$100,r=.07,D=$3.F=S(1+r)-D=$104IfFis$105,thatmightimplythatDisreallyonly$2.如果F是105美元，那么说明D真正数值是2美元。StorageCostsversusDividendYieldComparetheforward-spotprice-parityrelationforgoldtotheoneforstocks.Isitfairtosaythatstockshaveanegativestoragecostequaltothedividendyield?SOLUTIONOnecoulddefinitelysaythatstockshaveanegativestoragecostequaltothedividend.确定的说应该是股票的储存成本是股息的负值。Supposeyouareadistributorofcanolaseedandyouobservethespotpriceofcanolatobe$7.45perbushelwhilethefuturespricefordeliveryonemonthfromtodayis$7.60.Assuminga$.10perbushelcarryingcost,whatwouldyoudotohedgeyourpriceuncertainty?SOLUTIONWeseethatF>S+C.Ifyoushortthefuturescontract,youcansellyourseedat$7.60perbushel.我们发现F>S+C.如果你缩短期货交易合同的时限，你将可以把你的种子以7.6美元/蒲式耳。Inferthespotpriceofanounceofgoldifyouobservethepriceofoneounceofgoldforforwarddeliveryinthreemonthsis$435.00,theinterestrateona91-dayTreasurybillis1%andthequarterlycarryingcostasapercentageofthespotpriceis.2%.（相当于成本是现货价格的2%）SOLUTIONDeducefromthefuturespriceparityconditionforgoldthatF=S0(1+r+s)sothatS0=$429.84.推断黄金的期货价格应该是F=S（1+r+s）因而S=429.84美元7.Youareadealerinkryptoniteandarecontemplatingatradeinaforwardcontract.Youobservethatthecurrentspotpriceperounceofkryptoniteis$180.00,theforwardpricefordeliveryofoneounceofkryptoniteinoneyearis$205.20,andannualcarryingcostsofthemetalare4%ofthecurrentspotprice.Canyouinfertheannualreturnonarisklesszero-couponsecurityimpliedbytheLawofOnePrice?Canyoudescribeatradingstrategythatwouldgeneratearbitrageprofitsforyouiftheannualreturnontherisklesssecurityisonly5%?Whatwouldyourarbitrageprofitbe,perounceofkryptonite?SOLUTIONByno-arbitrage,werequirethattherisklessratersatisfy:在没有套利的情况下，无风险零息债券的年利率是： F=S0(1+r+s) 205.2=180(1+r+.04)=187.2+180r r=18/180=.10or10%Theimplicitrisk-freeratethatyoucanearnbybuyingkryptonite,storingit,andsellingitforwardat$205.2perounceis10%.Iftherisklessborrowingrateisfivepercent,youshouldborrowatthatrateandinvestinhedgedkryptonite.Ifyoubuyanounceofkryptonitefor$180,youwillget$205.2foritforsureayearfromnow.Ifyouborrowthe$180,youwillhavetopayprincipalandinterestof$180x1.05plusanother.04x$180instoragecosts.Thistotals$196.2,thusleavingyouwith$9inarbitrageprofits.你可以通过买kryptonite并储存后在将来以205.2美元/盅司的价格卖出赚取10%隐含的无风险利率。如果无风险借贷利率是5%，你可以以那样的比例借进并投资于kryptonite。如果你以$180/盅司买进，你将会在一年后得到$205.2。如果你借进的是180美元，你将归坏本金和利息$180x1.05以及.04x$180的储藏成本。这总共是$196.2，因而你可以从套利中获得$9。8.Calculatetheimplicitcostofcarryinganounceofgoldandtheimpliedstoragecostperounceofgoldifthecurrentspotpriceofgoldperounceis$425.00,theforwardpriceofanounceofgoldfordeliveryin273daysis$460.00,theyieldover91daysonazero-couponTreasurybillis2%andthetermstructureofinterestratesisflat.SOLUTIONFirst,wesolveitassumingasimplecompoundingmethodfortheriskfreeinterestrate.Over273days,theRiskfreerateis2%*3=6%.Thereforewehave,首先，我们通过假设一个零风险利率的简单组合方法来解决这个问题。273天，零息国债收益率是2%*3=6%。因而我们有， F=S(1+r+s) 460=425(1.06+s) s=(460-450.5)/425=9.5/425=.02235for273daysThusthecarryingcostsareroughly8.24%for273daysor10.98%peryear.所以持有成本粗率的计算为8.24%以237天计算或者是10.98%/年。Second,wesolveitassumingweneedtocompoundtheinterestrates.Theriskfreerateover273dayswill be(1+2%)3-1=6.12%. plugintheaboveformulaewegets=.021145for273days. Thusthecarryingcostsareroughly8.23%for273daysor11.13%peryear.其次，我们需要连续复利。零息无风险利率在273天应该是(1+2%)3-1=6.12%。再上式中我们得出s=021145/273天。所以持有成本应该是8.23%/273天or11.13%/年。9Theforwardpriceforashareofstocktobedeliveredin182daysis$410.00,whereasthecurrentyieldona91-dayT-billis2%.Ifthetermstructureofinterestratesisfiat,whatspotpriceforthestockisimpliedbytheLawofOnePrice?SOLUTION F=$410;r=.02perquarter.（每季度） S=F/(1+r)2=$394.0810Youobservethattheone-yearforwardpriceofashareofstockinKramer,Inc.,aNewYorktour-buscompanyandpurveyoroffineclothing,is$45.00whilethespotpriceofashareis$41.00.Iftherisklessyieldonaone-yearzero-coupongovernmentbondis5%:WhatistheforwardpriceimpliedbytheLawofOnePrice?Canyoudeviseatradingstrategytogeneratearbitrageprofits?Howmuchwouldyouearnpershare?SOLUTIONTheno-arbitragevalueoftheforwardpriceisF=$43.05.股票的远期价格是F=$43.05Theobservedforwardpriceisexcessive.Considershort-sellingaforwardcontractandtakingalongpositioninaportfolioconsistingofonestockandthesaleofabondwithfacevalueofF.Futureliabilitiesforthispositionarezero,whilethecurrentcashinflowis$1.86.观察到的远期价格是更高的。考虑短期卖出期货合同并采取面值为F的股票和债券的组合。这样的决定将来的债务是0，并且现金流是$1.86。11Infertheyieldona273-day,zero-couponJapanesegovernmentsecurityifthespotpriceofashareofstockinMifuneandAssociatesis4,750yenwhereastheforwardpricefordeliveryofasharein273daysis5,000yen.SOLUTIONTheimpliedyieldoverthe273daytermisr=5.26%.273天的收益率是5.26%。12OnyourfirstdayoftradinginVietnameseforwardcontracts,youobservethatthesharepriceofGiapIndustriesiscurrently54,000dongwhiletheone-yearforwardpriceis60,000dong.Iftheyieldonaone-yearrisklesssecurityisfifteenpercent,arearbitrageprofitspossibleinthismarket?Ifnot,explainwhynot.Ifso,deviseanappropriatetradingstrategy.SOLUTIONArbitrageprofitswouldseemtobepossible,sincetheno-arbitrageforwardpri