14章金融答案翻译Word文件下载.docx
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14.9TheForwardPriceIsNotaForecastoftheSpotPrice
14.10Forward-SpotParitywithCashPayouts
14.11ImpliedDividends
14.12TheForeign-ExchangeParityRelation
14.13TheRoleofExpectationsinDeterminingExchangeRates
Summary
∙Futurescontractsmakeitpossibletoseparatethedecisionofwhethertophysicallystoreacommodityfromthedecisiontohavefinancialexposuretoitspricechanges.
∙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.
SolutionstoProblemsatEndofChapter
ForwardContractsandForward-SpotParity.
1.SupposethatyouareplanningatriptoEngland.Thetripisayearfromnow,andyouhavereservedahotelroominLondonatapriceof₤50perday.Youdonothavetopayfortheroominadvance.Theexchangerateiscurrently$1.50tothepoundsterling.
a.Explainseveralpossiblewaysthatyoucouldcompletelyhedgetheexchangerateriskinthissituation.
b.Supposethatr₤=.12andr$=.08.BecauseS=$1.50,whatmusttheforwardpriceofthepoundbe?
c.ShowthatifFis$0.10higherthaninyouranswertopartb,therewouldbeanarbitrageopportunity.
SOLUTION:
a.Waystohedgetheexchangeraterisk:
Payfortheroominadvance
Buythepoundsyouwillneedintheforwardmarket.
Investthepresentvalueoftherentalpaymentsinapound-denominatedrisklessasset.
对冲外汇风险的几种方法：
提前对这个房间付款；
在期货市场购买英镑；
将与现期价值的租金同等的英镑投资于无风险资产。
b.F=S（1+r$）/（1+r£
）=$1.50x1.08/1.12=$1.4464perpound
1.4464美元/英镑
c.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。
ArbitragePosition
ImmediateCashFlow
CashFlow1YearFromNow
Borrow$1.50
借进1.50美元
$1.50
-$1.62
Buypound-denominatedbond
购买英镑远期合约
-$1.50
S1
Sell1.12poundsforwardat$1.55perpound
以1.55美元/英镑的价格卖出1.12英镑
$1.736-S1
NetCashFlows
净现金流
$1.736-$1.62=$.116
Forward-SpotParityRelationwithKnownCashPayouts
2.SupposethattheTreasuryyieldcurveisflatataninterestrateof7%peryear（compoundedsemiannually）.
a.Whatisthespotpriceofa30-yearTreasurybondwithan8%couponrateassumingcouponsarepaidsemiannually?
b.Whatistheforwardpriceofthebondfordeliverysixmonthsfromnow?
c.Showthatiftheforwardpriceis$1lowerthaninyouranswertopartb,thereshouldbeanarbitrageopportunity.
a.Thespotpriceofthe30-yearTreasuryis$1,124.724:
n
i
PV
FV
PMT
Result
60
3.5
?
1000
40
PV=1124.724
b.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=$1,124.089
d.Iftheforwardpriceisonly$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%for6months
After6months,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。
Sellshorta30-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
$1,163.432
Buyaforwardcontractfora30-yearT-bond
买进30年期的国债远期合同
S1-$1,123.089
$1,163.432-（$1,123.089+$40）=$.343
Forward-SpotParityRelationwithUncertainDividends
3.Astockhasaspotpriceof$100;
therisklessinterestrateis7%peryear（compoundedannually）,andtheexpecteddividendonthestockis$3,tobereceivedayearfromnow.
a.Whatshouldbetheone-yearfuturesprice?
b.Ifthefuturespriceis$1higherthanyouranswertoparta,whatmightthatimplyabouttheexpecteddividend?
a.S=$100,r=.07,D=$3.F=S（1+r）-D=$104
b.IfFis$105,thatmightimplythatDisreallyonly$2.
如果F是105美元，那么说明D真正数值是2美元。
StorageCostsversusDividendYield
4.Comparetheforward-spotprice-parityrelationforgoldtotheoneforstocks.Isitfairtosaythatstockshaveanegativestoragecostequaltothedividendyield?
SOLUTION
Onecoulddefinitelysaythatstockshaveanegativestoragecostequaltothedividend.
确定的说应该是股票的储存成本是股息的负值。
5.Supposeyouareadistributorofcanolaseedandyouobservethespotpriceofcanolatobe$7.45perbushelwhilethefuturespricefordeliveryonemonthfromtodayis$7.60.Assuminga$.10perbushelcarryingcost,whatwouldyoudotohedgeyourpriceuncertainty?
WeseethatF>
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。
6.Inferthespotpriceofanounceofgoldifyouobservethepriceofoneounceofgoldforforwarddeliveryinthreemonthsis$435.00,theinterestrateona91-dayTreasurybillis1%andthequarterlycarryingcostasapercentageofthespotpriceis.2%.（相当于成本是现货价格的2%）
DeducefromthefuturespriceparityconditionforgoldthatF=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.
a.Canyouinfertheannualreturnonarisklesszero-couponsecurityimpliedbytheLawofOnePrice?
b.Canyoudescribeatradingstrategythatwouldgeneratearbitrageprofitsforyouiftheannualreturnontherisklesssecurityisonly5%?
Whatwouldyourarbitrageprofitbe,perounceofkryptonite?
a.Byno-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%
b.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.
First,wesolveitassumingasimplecompoundingmethodfortheriskfreeinterestrate.Over273days,theRiskfreerate
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