国际财务管理课后习题答案chapter-7

word格式-可编辑-感谢下载支持CHAPTER7FUTURES ANDOPTIONS ONFOREIGN EXCHANGESUGGESTEDANSWERS ANDSOLUTIONS TOEND-OF-CHAPTERQUESTIONS ANDPROBLEMSQUESTIONS

1.Explain thebasic differencesbetween theoperation of a currencyforward marketand afutures market.Answer:The forwardmarket is an OTCmarket wherethe forward contract forpurchase orsale offoreign currencyistailor-made betweenthe clientand itsinternational bank.No moneychanges handsuntil thematurity dateof thecontractwhen deliveryand receiptare typicallymade.A futures contract is an exchange-traded instrumentwithstandardized featuresspecifying contractsize and delivery date.Futures contracts are marked-to-market dailytoreflect changes in thesettlement price.Delivery isseldom madein afutures market.Rather a reversing tradeis madetoclose outa long or short position.

2.In orderfor a derivatives marketto functionmost efficiently,two typesof economicagents are needed:hedgersand speculators.Explain.Answer:Two typesof marketparticipants arenecessary for the efficientoperation ofaderivativesmarket:speculators andhedgers.A speculator attempts to profit froma changein the futures price.To dothis,the speculatorwilltake a longorshort position in afutures contractdepending uponhis expectationsof futureprice movement.Ahedger,on-the-other-hand,desires toavoid price variation bylocking in a purchaseprice of the underlyingassetthrough a long position in afutures contractor asales pricethrough a shortposition.In effect,the hedgerpasses offtherisk ofpricevariationto the speculator whois betterable,or at least morewilling,to bearthis risk.

3.Why aremost futures positions closedout througha reversingtrade ratherthan heldto deliveryAnswer:In forwardmarkets,approximately90percent ofall contractsthat areinitially establishedresult in the shortmakingdelivery to the longof theasset underlyingthe contract.This isnatural because the termsof forwardcontractsare tailor-made betweenthe longand short.By contrast,only aboutone percentof currencyfuturescontracts resultin delivery.While futures contractsareuseful forspeculation andhedging,their standardizeddeliverydates makethem unlikely to correspondto theactual futuredates whenforeign exchangetransactions willoccur.Thus,they aregenerally closedout in areversingtrade.In fact,the commissionthat buyersand sellerspay totransactin the futures market is asingle amountthat coversthe round-trip transactionsof initiatingand closingoutthe position.word格式-可编辑-感谢下载支持Solution:PMax[68-70,68-

69.50/

1.0175,0]a Max[-2,-

1.47,0]=0cents

11.Use theEuropean option-pricing modelsdeveloped in the chapterto valuethe callof problem9and theput ofproblem

10.Assume theannualized volatilityof theSwiss francis

14.2percent.This problemcan besolved using theFXOPM.xls spreadsheet.Solution:d[ln

69.50/68+.

5.

142.50]/.142V.50=.26751=2・c2=d

1.142V.50=.2765-.1004=.1671Nd=.60551Nd=.56642M-dJ=.3945N-d=.43362C=[

69.

50.6055-

68.5664]e-.o

35.5o=

3.51centsP=[

68.4336-

69.5O.3945]e,o355o=

2.03centsQ

12.Use thebinomial option-pricing modeldeveloped in the chapterto valuethe callof problem

9.The volatilityof theSwiss francis

14.2percent.Solution:The spotrate atT will be either

77.39C=

70.

0001.1056or

63.32$=

70.00$.9045,where u=e.u2v.5o=

1.1056andd=1/u=.

9045.At the exercise price of E=68,the option will onlybe exercisedat timeT if the Swissfrancappreciates;its exercisevalue would be C=

9.39C=

77.390-

68.If theSwiss francdepreciates itwould notbeuTrational toexercise the option;its valuewouldbeC^=

0.The hedgeratio ish=

9.39-0/

77.39-

63.32=.

6674.Thus,the callpremium is:C=Max{[

69.

50.6674-6870/

68.6674-1+1]/

1.0175,70-68}o=Max[

1.64,2]=2cents perSF.word格式-可编辑-感谢下载支持MINI CASE:THE OPTIONSSPECULATORA speculatoris considering the purchaseof fivethree-month Japaneseyen call options with a striking price of96cents per100yen.The premiumis

1.35cents per100yen.The spot price is

95.28cents per100yen and the90-day forwardrate is

95.71cents.The speculatorbelieves theyen willappreciate to$

1.00per100yen over the nextthree months.As thespeculators assistant,you havebeen askedto preparethe following:

1.Graph the call optioncash flowschedule.

2.Determine thespeculators profitif theyen appreciates to$

1.00/100yen.

3.Determine thespeculators profitif theyen onlyappreciatesto the forwardrate.

4.Determine the future spot price atwhich thespeculator willonly breakeven.Suggested Solutionto theOptions Speculator:

2.5x¥6,250,000x[100-96-

1.35]/10000=$8,

281.

25.

3.Since the option expiresout-of-the-money,thespeculatorwill lettheoptionexpire worthless.He willonly losetheoption premium.

4.S=E+C=96+

1.35=

97.35cents per100yen.T

5.How canthe FXfutures marketbe usedfor price discoveryAnswer:To theextent thatFX forward prices arean unbiased predictor offuture spot exchange rates,the marketanticipateswhether onecurrency willappreciate ordepreciate versusanother.Because FXfutures contractstradein anexpiration cycle,different contractsexpire atdifferent periodicdates into the future.The patternof the pricesof thesecontracts providesinformation asto themarket9s currentbelief aboutthe relativefuture value of onecurrencyversus anotherat thescheduled expirationdates of the contracts.One willgenerally seea steadilyappreciating ordepreciatingpattern;however,it maybe mixedat times.Thus,the futuresmarketisuseful forpricediscovery,i.e.,obtaining themarkets forecastof the spotexchangerate atdifferent futuredates.

6.What is the majordifference in the obligationof onewith along position inafutures or forward contractincomparison toan optionscontractAnswer:A futures orforwardcontract is a vehiclefor buyingor sellinga statedamount offoreign exchangeat astatedprice perunit ata specifiedtime in thefuture.If the long holdsthe contract to the delivery date,he paystheeffective contractualfuturesorforwardprice,regardless ofwhether itis anadvantageous price in comparisontothe spot price at thedeliverydate.By contrast,an option is acontract givingthelongthe rightto buyor sella givenquantityof anasset ata specifiedprice atsome timein thefuture,but notenforcing anyobligation onhim if the spotprice is morefavorable thantheexerciseprice.Because theoption ownerdoes not have toexercise theoption ifitis tohis disadvantage,theoptionhas a price,or premium,whereas nopriceispaid atinception toenter intoafutures orforwardcontract.

7.What ismeant by the terminologythat anoption isin-,at-,or out-of-the-moneyAnswe匚A call put optionwith SE ES isreferred toas tradingin-the-money.If S^E theoption istradingt tat-the-money.If SE ES thecall put optionistrading out-of-the-money.tword格式-可编辑-感谢下载支持

8.List thearguments variablesof whichan FX call orput optionmodel priceisafunction.How doesthecallandput premiumchange withrespect toa changein theargumentsAnswer:Both calland putoptions arefunctions ofonly sixvariables:S,E,r,T ando.When all elset IIipremains thesame,theprice ofa European FX callputoption will increase:

1.the largersmaller isS,

2.the smallerlarger isE,

3.the smallerlarger isr,

4.the largersmaller is

5.the largersmaller rjsrelative tor,and

6.the greaterisa.When randrare nottoo muchdifferent insize,a EuropeanFXcalland putwillincrease in pricewhen theoptionterm-to-maturity increases.However,when Qis verymuch largerthan r.,aEuropeanFXcallw川3Iincrease inprice,but theput premiumwill decrease,when theoption term-to-maturity increases.The oppositeistrue whenris verymuch greaterthan r$.For AmericanFX optionsthe analysisis lesscomplicated.Since alongerterm Americanoption can be exercisedon anydate thata shorterterm optioncan beexercised,or asome laterdate,it followsthat theallelseremaining thesame,the longerterm Americanoptionwillsell atapriceatleastaslarge asthe shorterterm option.PROBLEMS

1.Assume todayssettlement priceon aCME EURfutures contractis$

1.3140/EUR.You havea shortposition in onecontract.Your performance bond accountcurrently has a balance of$1,

700.The nextthree days9settlement pricesare$

1.3126,$

1.3133,and$

1.

3049.Calculate thechangesin the performancebond accountfrom dailymarking-to-marketand the balanceof the performancebond accountafter thethird day.Solution:$1,700+[$

1.3140-$

1.3126+$

1.3126-$

1.3133+$

1.3133-$

1.3049]x EUR125,000=$2,

837.50,where EUR125,000is thecontractual sizeof oneEUR contract.

2.Do problem1again assuming you havealong position in the futures contract.Solution:$1,700+[$

1.3126-$

1.3140+$

1.3133-$

1.3126+$

1.3049-$

1.3133]x EUR125,000=$

562.50,where EUR125,000is thecontractual sizeof oneEUR contract.With only$

562.50in your performancebond account,you wouldexperience amargin callrequesting thatadditionalfunds beadded toyourperformancebondaccountto bringthebalanceback uptotheinitialperformance bondlevel.

3.Using thequotations inExhibit

7.3,calculate theface value of theopen interestinthe June2005Swiss francfuturescontract.Solution:2,101contracts xSF125,000=SF262,625,

000.where SF125,000is thecontractual sizeof oneSF contract.

4.Using thequotations inExhibit

7.3,note that the June2005Mexican pesofuturescontract has aprice of$

0.

08845.You believethespotpriceinJune will be$

0.

09500.What speculativeposition wouldyou enterinto toattempttoprofit from yourbeliefs Calculateyour anticipatedprofits,assumingyoutake apositioninthreecontracts.What is the sizeof yourprofit lossifthe futures priceis indeedan unbiased predictor of thefuture spotprice andthis pricematerializesSolution:If youexpect theMexican pesoto risefrom$

0.08845to$

0.09500,you wouldtake alongpositioninfutures sincethe futures priceof$

0.08845is lessthan yourexpected spotprice.Your anticipatedprofit fromalongpositioninthree contractsis:3x$

0.09500-$

0.08845xword格式-可编辑-感谢下载支持MP500Q00=$9,

825.00,where MP500,000is thecontractual sizeof oneMP contract.If thefutures priceis anunbiasedpredictorofthe expected spotprice,theexpected spotpriceisthefuturesprice of$

0.08845/MP.If thisspotpricematerializes,you willnothaveany profitsor lossesfrom yourshort positioninthree futures contracts:3x$

0.08845-$

0.08845x MP500,000=

0.

5.Do problem4again assumingyou believetheJune2005spotpricewill be$

0.

08500.Solution:If youexpect theMexican pesoto depreciatefrom$

0.08845to$

0.07500,you wouldtake ashort positioninfutures sincethefuturespriceof$

0.08845is greaterthan yourexpectedspotprice.Your anticipatedprofitfromashortpositioninthree contractsis:3x$

0.08845-$

0.07500x MP500,000=$20,

175.

00.If thefuturespriceis anunbiasedpredictorofthefuturespotprice andthis pricematerializes,you willnotprofit orlose fromyour longfutures position.

6.George Johnson is considering a possiblesix-month$100million LIBOR-based,floating-rate bankloan tofunda projectat termsshown inthe tablebelow.Johnson fearsa possiblerise inthe LIBOR rate byDecember andwantsto usethe December Eurodollar futurescontractto hedge thisrisk.The contract expires December20,1999,has aUS$1million contractsize,and adiscount yield of

7.3percent.Johnson willignore the cash flowimplications ofmarking tomarket,initial marginrequirements,and anytimingLoan Firstloan payment9%Second paymentinitiatedand futurescontract expiresand principal9/20/9912/20/993/20/00mismatch betweenexchange-traded futurescontract cash flows and the interest payments duein March.Loan TermsSeptember20,1999December20,1999March20,2000•Pay backprincipal plus•Borrow$100million atSeptemberinterest20LIBOR+200basis pointsbps•Pay interestfor firstthreemonths•September20LIBOR=7%•Roll loanover atDecember20LIBOR+200bpsword格式-可编辑-感谢下载支持a.Formulate JohnsonsSeptember20floating-to-fixed-rate strategyusingtheEurodollar futurecontractsdiscussed inthe textabove.Show thatthis strategywould resultina fixed-rate loan,assuming anincrease intheLIBOR rate to

7.8percent byDecember20,which remainsat

7.8percent throughMarch

20.Show allcalculations.Johnsonisconsideringa12-month loanas analternative.This approachwill resultin twoadditional uncertaincashLoan FirstSecond ThirdFourth paymentinitiatedpayme paymentpayment andprincipalnt9%9/20/9912/20/993/20/006/20/009/20/00flows,as follows:b.Describe thestrip hedge that Johnsoncould useand explainhow ithedges the12-month loanspecify numberof contracts.No calculationsareneeded.CFA GuidelineAnswera.The basis point valueBPV ofa Eurodollar futurescontractcan befound bysubstituting thecontractspecifications intothe followingmoney marketrelationship:BPV=Change inValue=face valuex daysto maturity/360x changein yield=$1million x90/FUT360x.0001=$25The number ofcontract,N,can befound by:N=BPV spot/BPV futures=$2,500/$25=100ORN=value ofspot position/face value of eachfuturescontract=$100million/$1million=100ORN=valueofspot position/valueof futures position=$100,000,000/$981,750where valueoffuturesposition=$1,000,000x[1-

0.073/4]必102contractsTherefore onSeptember20,Johnson wouldsell100or102DecemberEurodollar futures contractsatthe

7.3percent yield.The implied LIBOR ratein Decemberis

7.3percent asindicated bythe DecemberEurofuturesdiscount yieldof

7.3percent.Thus aborrowing rateof

9.3percent

7.3percent+200basis pointscanbelocked inifthe hedgeis correctlyimplemented.A riseintherateto

7.8percent representsa50basis pointbp increaseovertheimpliedLIBORrate.For a50basispointincreaseinLIBOR,the cash flow onthe shortfuturespositionis:=$25per basispoint percontract x50bp x100contracts=$125,

000.However,the cash flow onthe floating rate liabilityis:=-

0.098x$100,000,000/4=-$2,450,

000.Combining the cash flow from thehedge with thecashflow fromthe loanresults ina netoutflow of$2,325,000,which translatesinto anannual rateof

9.3percent:=$2,325,000x4/$100,000,000=

0.093This isprecisely theimplied borrowingrate thatJohnson lockedinonSeptember

20.Regardless ofthe LIBORrateon December20,the netcash outflowwill be$2,325,000,which translatesinto anannualized rateof

9.3percent.Consequently,the floatingrate liabilityhas beenconverted toafixedrate liabilityinthesense thatthe interest rateuncertainty associatedwiththeMarch20payment usingthe December20contracthasbeen removedas ofSeptember

20.b.In a strip hedge,Johnson wouldsell100December futuresfor theMarch payment,100March futuresfor theJunepayment,and100June futuresfor theSeptember payment.The objectiveis to hedge eachinterest ratepaymentseparately usingthe appropriatenumberofcontracts.The problemisthesame asin Part A exceptherethree cashflows aresubject torising ratesand a strip offutures isused to hedge thisinterest raterisk.Thisproblem issimplified somewhatbecause thecashflowmismatch betweenthefuturesandtheloan paymentisignored.Therefore,in ordertohedgeeach cashflow,Johnson simplysells100contracts foreach payment.Thestrip hedgetransforms thefloatingrateloan intoastripof fixedrate payments.As wasdone inPartA,the fixedratesare foundby adding200basis pointstotheimplied forwardLIBORrateindicated bythe discountyieldofthethree differentEurodollar futures contracts.The fixedpayments willbe equalwhen theLIBOR term structure isflatfor thefirst year.

7.Jacob Bower has aliability that:•has aprincipal balanceof$100million on June30,1998,•accrues interestquarterly startingonJune30,1998,•pays interestquarterly,•hasaone-year termto maturity,and•calculates interestdue basedon90-day LIBORthe LondonInterbank OfferedRate.Bower wishestohedgehis remaininginterestpaymentsagainst changesin interest rates.Bowerhascorrectly calculatedthat he needs tosell short300Eurodollarfuturescontracts toaccomplish thehedge.He isconsideringthealternative hedgingstrategies outlinedinthefollowing table.Initial Position6/30/98in90-Day LIBOREurodollar ContractsContractMonth Strategy A contractsStrategy BcontractsSeptember1998300100December19980100March19990100a.Explain whystrategy Bisa moreeffective hedgethan strategyA when the yield curve undergoesaninstantaneous nonparallel shift.b.Discuss aninterestrate scenario in which strategyA wouldbe superiorto strategyB.CFA GuidelineAnswera.Strategy BsSuperiorityStrategy Bisastrip hedgethatis constructedby selling shorting100futurescontractsmaturing ineach ofthe nextthreequarters.With thestriphedgein place,each quarterofthecoming yearis hedgedagainst shiftsin interestratesfor thatquarter.The reasonStrategy B willbea moreeffective hedgethan Strategy A forJacob Boweris thatStrategy B islikelytowork wellwhether aparallelshiftoranonparallel shiftoccurs overthe one-year termof Bowersliability.That is,regardless ofwhat happenstothetermstructure,Strategy Bstructures thefutures hedgeso thatthe ratesreflectedbytheEurodollarfuturescash pricematch theapplicable ratesfortheunderlying liability-the90dayLIBOR-based rateon Bowers liability.The sameis nottrue forStrategy A.Because JacobBowersliabilitycarries afloating interestratethat resetsquarterly,heneedsa strategy that providesa seriesof three-month hedges.Strategy A will needto berestructuredwhenthethreemonth Septembercontractexpires.In particular,ifthe yieldcurvetwists upwardfuturesyields risemore fordistant expirationsthan fornear expirations,Strategy A will produceinferior hedgeresults.b.Scenario inWhich Strategy A isSuperiorStrategy Aisastack hedgestrategythatinitially involvessellingshorting300September contracts.StrategyAisrarely better than Strategy B asa hedgingor risk-reduction strategy.Only fromthe perspectiveof favorablecashflows isStrategyAbetterthanStrategy B.Such cashflows occuronly incertain interestrate scenarios.For exampleStrategyAwillwork aswell asStrategy Bfor Bowersliability ifinterestratesinstantaneously changein parallelfashion.Another interestratescenariowhere StrategyA outperformsStrategyB is oneinwhichtheyieldcurve risesbutwith atwist sothat futuresyields risemore fornear expirationsthan fordistant expirations.Upon expirationof theSeptembercontract,Bower will have toroll outhis hedgeby selling200December contractstohedgetheremaining interestpayments.This actionwillhavethe effectthatthecashflow from StrategyAwillbe largerthanthe cashflowfrom StrategyBbecausetheappreciation onthe300short Septemberfuturescontractswillbelargerthan thecumulative appreciationinthe300contracts shortedin StrategyBi.e.,100September,100December,and100March.Consequently,thecashflowfromStrategyAwill morethan offsetthe increaseintheinterestpayment onthe liability,whereas thecashflowfromStrategyBwillexactly offsetthe increaseintheinterestpayment onthe liability.

8.Use thequotations inExhibit

7.7to calculatethe intrinsicvalue andthe timevalueofthe97SeptemberJapanese yenAmerican calland putoptions.Solution:Premium-Intrinsic Value=Time Value97Sep Call

2.08-Max[

95.80-

97.00=-

1.20,0]=

2.08cents per100yen97Sep Put

2.47-Max[

97.00-

95.80=

1.20,0]=

1.27cents per100yen

9.Assume spotSwiss francis$

0.7000andthesix-month forwardrate is$

0.

6950.What isthe minimumprice thatasix-month Americancalloptionwithastrikingpriceof$

0.6800should sellfor ina rationalmarket Assumetheannualized six-month Eurodollarrate is31/2percent.Solution:Note toInstructor:A completesolution tothis problemrelies onthe boundaryexpressions presentedin footnote3ofthetext ofChapter

7.C Max[70-68,

69.50-68/

1.0175,0]a Max[2,

1.47,0]=2cents

10.Do problem9again assumingan Americanputoptioninstead ofa calloption.。