国际财务管理课后习题答案chapter-7

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CHAPTER7FUTURESANDOPTIONSONFOREIGNEXCHANGE

SUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTER

QUESTIONSANDPROBLEMS

QUESTIONS

1.Explainthebasicdifferencesbetweentheoperationofacurrencyforwardmarketandafuturesmarket.

Answer:TheforwardmarketisanOTCmarketwheretheforwardcontractforpurchaseorsaleofforeigncurrencyistailor-madebetweentheclientanditsinternationalbank.Nomoneychangeshandsuntilthematuritydateofthecontractwhendeliveryandreceiptaretypicallymade.Afuturescontractisanexchange-tradedinstrumentwithstandardizedfeaturesspecifyingcontractsizeanddeliverydate.Futurescontractsaremarked-to-marketdailytoreflectchangesinthesettlementprice.Deliveryisseldommadeinafuturesmarket.Ratherareversingtradeismadetocloseoutalongorshortposition.

2.Inorderforaderivativesmarkettofunctionmostefficiently,twotypesofeconomicagentsareneeded:hedgersandspeculators.Explain.

Answer:Twotypesofmarketparticipantsarenecessaryfortheefficientoperationofaderivativesmarket:speculatorsandhedgers.Aspeculatorattemptstoprofitfromachangeinthefuturesprice.Todothis,thespeculatorwilltakealongorshortpositioninafuturescontractdependinguponhisexpectationsoffuturepricemovement.Ahedger,on-the-other-hand,desirestoavoidpricevariationbylockinginapurchasepriceoftheunderlyingassetthroughalongpositioninafuturescontractorasalespricethroughashortposition.Ineffect,thehedgerpassesofftheriskofpricevariationtothespeculatorwhoisbetterable,oratleastmorewilling,tobearthisrisk.

3.Whyaremostfuturespositionsclosedoutthroughareversingtraderatherthanheldtodelivery?

Answer:Inforwardmarkets,approximately90percentofallcontractsthatareinitiallyestablishedresultintheshortmakingdeliverytothelongoftheassetunderlyingthecontract.Thisisnaturalbecausethetermsofforwardcontractsaretailor-madebetweenthelongandshort.Bycontrast,onlyaboutonepercentofcurrencyfuturescontractsresultindelivery.Whilefuturescontractsareusefulforspeculationandhedging,theirstandardizeddeliverydatesmakethemunlikelytocorrespondtotheactualfuturedateswhenforeignexchangetransactionswilloccur.Thus,theyaregenerallyclosedoutinareversingtrade.Infact,thecommissionthatbuyersandsellerspaytotransactinthefuturesmarketisasingleamountthatcoverstheround-triptransactionsofinitiatingandclosingouttheposition.

4.HowcantheFXfuturesmarketbeusedforpricediscovery?

Answer:TotheextentthatFXforwardpricesareanunbiasedpredictoroffuturespotexchangerates,themarketanticipateswhetheronecurrencywillappreciateordepreciateversusanother.BecauseFXfuturescontractstradeinanexpirationcycle,differentcontractsexpireatdifferentperiodicdatesintothefuture.Thepatternofthepricesofthesecontractsprovidesinformationastothemarket’scurrentbeliefabouttherelativefuturevalueofonecurrencyversusanotheratthescheduledexpirationdatesofthecontracts.Onewillgenerallyseeasteadilyappreciatingordepreciatingpattern;however,itmaybemixedattimes.Thus,thefuturesmarketisusefulforpricediscovery,i.e.,obtainingthemarket’sforecastofthespotexchangerateatdifferentfuturedates.

5.Whatisthemajordifferenceintheobligationofonewithalongpositioninafutures(orforward)contractincomparisontoanoptionscontract?

Answer:Afutures(orforward)contractisavehicleforbuyingorsellingastatedamountofforeignexchangeatastatedpriceperunitataspecifiedtimeinthefuture.Ifthelongholdsthecontracttothedeliverydate,hepaystheeffectivecontractualfutures(orforward)price,regardlessofwhetheritisanadvantageouspriceincomparisontothespotpriceatthedeliverydate.Bycontrast,anoptionisacontractgivingthelongtherighttobuyorsellagivenquantityofanassetataspecifiedpriceatsometimeinthefuture,butnotenforcinganyobligationonhimifthespotpriceismorefavorablethantheexerciseprice.Becausetheoptionownerdoesnothavetoexercisetheoptionifitistohisdisadvantage,theoptionhasaprice,orpremium,whereasnopriceispaidatinceptiontoenterintoafutures(orforward)contract.

6.Whatismeantbytheterminologythatanoptionisin-,at-,orout-of-the-money?

Answer:Acall(put)optionwithSt>E(E>St)isreferredtoastradingin-the-money.IfStEtheoptionistradingat-the-money.IfSt<E(E<St)thecall(put)optionistradingout-of-the-money.

Loan Firstloanpayment(9%) Secondpayment

initiated andfuturescontractexpires andprincipal

9/20/99 12/20/99 3/20/00

a.FormulateJohnson’sSeptember20floating-to-fixed-ratestrategyusingtheEurodollarfuturecontractsdiscussedinthetextabove.Showthatthisstrategywouldresultinafixed-rateloan,assuminganincreaseintheLIBORrateto7.8percentbyDecember20,whichremainsat7.8percentthroughMarch20.Showallcalculations.

Johnsonisconsideringa12-monthloanasanalternative.Thisapproachwillresultintwoadditionaluncertaincashflows,asfollows:

Loan First Second Third Fourthpayment

initiated payment(9%) payment payment andprincipal

9/20/99 12/20/99 3/20/00 6/20/00 9/20/00

b.DescribethestriphedgethatJohnsoncoulduseandexplainhowithedgesthe12-monthloan(specifynumberofcontracts).Nocalculationsareneeded.

CFAGuidelineAnswer

a.Thebasispointvalue(BPV)ofaEurodollarfuturescontractcanbefoundbysubstitutingthecontractspecificationsintothefollowingmoneymarketrelationship:

BPVFUT=ChangeinValue=(facevalue)x(daystomaturity/360)x(changeinyield)

=($1million)x(90/360)x(.0001)

=$25

Thenumberofcontract,N,canbefoundby:

N=(BPVspot)/(BPVfutures)

=($2,500)/($25)

=100

OR

N =(valueofspotposition)/(facevalueofeachfuturescontract)

=($100million)/($1million)

=100

OR

N =(valueofspotposition)/(valueoffuturesposition)

=($100,000,000)/($981,750)

wherevalueoffuturesposition=$1,000,000x[1–(0.073/4)]

102contracts

ThereforeonSeptember20,Johnsonwouldsell100(or102)DecemberEurodollarfuturescontractsatthe7.3percentyield.TheimpliedLIBORrateinDecemberis7.3percentasindicatedbytheDecemberEurofuturesdiscountyieldof7.3percent.Thusaborrowingrateof9.3percent(7.3percent+200basispoints)canbelockedinifthehedgeiscorrectlyimplemented.

Ariseintherateto7.8percentrepresentsa50basispoint(bp)increaseovertheimpliedLIBORrate.Fora50basispointincreaseinLIBOR,thecashflowontheshortfuturespositionis:

=($25perbasispointpercontract)x50bpx100contracts

=$125,000.

However,thecashflowonthefloatingrateliabilityis:

=-0.098x($100,000,000/4)

=-$2,450,000.

Combiningthecashflowfromthehedgewiththecashflowfromtheloanresultsinanetoutflowof$2,325,000,whichtranslatesintoanannualrateof9.3percent:

=($2,325,000x4)/$100,000,000=0.093

ThisispreciselytheimpliedborrowingratethatJohnsonlockedinonSeptember20.RegardlessoftheLIBORrateonDecember20,thenetcashoutflowwillbe$2,325,000,whichtranslatesintoanannualizedrateof9.3percent.Consequently,thefloatingrateliabilityhasbeenconvertedtoafixedrateliabilityinthesensethattheinterestrateuncertaintyassociatedwiththeMarch20payment(usingtheDecember20contract)hasbeenremovedasofSeptember20.

b.Inastriphedge,Johnsonwouldsell100Decemberfutures(fortheMarchpayment),100Marchfutures(fortheJunepayment),and100Junefutures(fortheSeptemberpayment).Theobjectiveistohedgeeachinterestratepaymentseparatelyusingtheappropriatenumberofcontracts.TheproblemisthesameasinPartAexceptherethreecashflowsaresubjecttorisingratesandastripoffuturesisusedtohedgethisinterestraterisk.Thisproblemissimplifiedsomewhatbecausethecashflowmismatchbetweenthefuturesandtheloanpaymentisignored.Therefore,inordertohedgeeachcashflow,Johnsonsimplysells100contractsforeachpayment.Thestriphedgetransformsthefloatingrateloanintoastripoffixedratepayments.AswasdoneinPartA,thefixedratesarefoundbyadding200basispointstotheimpliedforwardLIBORrateindicatedbythediscountyieldofthethreedifferentEurodollarfuturescontracts.ThefixedpaymentswillbeequalwhentheLIBORtermstructureisflatforthefirstyear.

7.JacobBowerhasaliabilitythat:

hasaprincipalbalanceof$100milliononJune30,1998,

accruesinterestquarterlystartingonJune30,1998,

paysinterestquarterly,

hasaone-yeartermtomaturity,and

calculatesinterestduebasedon90-dayLIBOR(theLondonInterbankOffered

Rate).

Bowerwishestohedgehisremaininginterestpaymentsagainstchangesininterestrates.

Bowerhascorrectlycalculatedthatheneedstosell(short)300Eurodollarfuturescontractstoaccomplishthehedge.Heisconsideringthealternativehedgingstrategiesoutlinedinthefollowingtable.

InitialPosition(6/30/98)in

90-DayLIBOREurodollarContracts

StrategyA StrategyB

ContractMonth (contracts) (contracts)

September1998 300 100

December1998 0 100

March1999 0 100

a.ExplainwhystrategyBisamoreeffectivehedgethanstrategyAwhentheyieldcurve

undergoesaninstantaneousnonparallelshift.

b.DiscussaninterestratescenarioinwhichstrategyAwouldbesuperiortostrategyB.

CFAGuidelineAnswer

a. StrategyB’sSuperiority

StrategyBisastriphedgethatisconstructedbyselling(shorting)100futurescontractsmaturingineachofthenextthreequarters.Withthestriphedgeinplace,eachquarterofthecomingyearishedgedagainstshiftsininterestratesforthatquarter.ThereasonStrategyBwillbeamoreeffectivehedgethanStrategyAforJacobBoweristhatStrategyBislikelytoworkwellwhetheraparallelshiftoranonparallelshiftoccursovertheone-yeartermofBower’sliability.Thatis,regardlessofwhathappenstothetermstructure,StrategyBstructuresthefutureshedgesothattheratesreflectedbytheEurodollarfuturescashpricematchtheapplicableratesfortheunderlyingliability-the90dayLIBOR-basedrateonBower’sliability.ThesameisnottrueforStrategyA.BecauseJacobBower’sliabilitycarriesafloatinginterestratethatresetsquarterly,heneedsastrategythatprovidesaseriesofthree-monthhedges.StrategyAwillneedtoberestructuredwhenthethree-monthSeptembercontractexpires.Inparticular,iftheyieldcurvetwistsupward(futuresyieldsrisemorefordistantexpirationsthanfornearexpirations),StrategyAwillproduceinferiorhedgeresults.

b.ScenarioinWhichStrategyAisSuperior

StrategyAisastackhedgestrategythatinitiallyinvolvesselling(shorting)300Septembercontracts.StrategyAisrarelybetterthanStrategyBasahedgingorrisk-reductionstrategy.OnlyfromtheperspectiveoffavorablecashflowsisStrategyAbetterthanStrategyB.Suchcashflowsoccuronlyincertaininterestratescenarios.ForexampleStrategyAwillworkaswellasStrategyBforBower’sliabilityifinterestrates(instantaneously)changeinparallelfashion.AnotherinterestratescenariowhereStrategyAoutperformsStrategyBisoneinwhichtheyieldcurverisesbutwithatwistsothatfuturesyieldsrisemorefornearexpirationsthanfordistantexpirations.UponexpirationoftheSeptembercontract,Bowerwillhavetorollouthishedgebyselling200Decembercontractstohedgetheremaininginterestpayments.ThisactionwillhavetheeffectthatthecashflowfromStrategyAwillbelargerthanthecashflowfromStrategyBbecausetheappreciationonthe300shortSeptemberfuturescontractswillbelargerthanthecumulativeappreciationinthe300contractsshortedinStrategyB(i.e.,100September,100December,and100March).Consequently,thecashflowfromStrategyAwillmorethanoffsettheincreaseintheinterestpaymentontheliability,whereasthecashflowfromStrategyBwillexactlyoffsettheincreaseintheinterestpaymentontheliability.

8.UsethequotationsinExhibit7.7tocalculatetheintrinsicvalueandthetimevalueofthe97SeptemberJapaneseyenAmericancallandputoptions.

Solution:Premium-IntrinsicValue=TimeValue

97SepCall2.08-Max[95.80–97.00=-1.20,0]=2.08centsper100yen

97SepPut2.47-Max[97.00–95.80=1.20,0]=1.27centsper100yen

9.AssumespotSwissfrancis$0.7000andthesix-monthforwardrateis$0.6950.Whatistheminimumpricethatasix-monthAmericancalloptionwithastrikingpriceof$0.6800shouldsellforinarationalmarket?Assumetheannualizedsix-monthEurodollarrateis3½percent.

Solution:

NotetoInstructor:Acompletesolutiontothisproblemreliesontheboundaryexpressionspresentedinfootnote3ofthetextofChapter7.

CaMax[(70-68),(69.50-68)/(1.0175),0]

Max[2,1.47,0]=2cents

10.Doproblem9againassuminganAmericanputoptioninsteadofacalloption.

Solution:PaMax[(68-70),(68-69.50)/(1.0175),0]

Max[-2,-1.47,0]=0cents

11.UsetheEuropeanoption-pricingmodelsdevelopedinthechaptertovaluethecallofproblem9andtheputofproblem10.AssumetheannualizedvolatilityoftheSwissfrancis14.2percent.ThisproblemcanbesolvedusingtheFXOPM.xlsspreadsheet.

Solution:

d1=[ln(69.50/68)+.5(.142)2(.50)]/(.142).50=.2675

d2=d1-.142.50=.2765-.1004=.1671

N(d1)=.6055

N(d2)=.5664

N(-d1)=.3945

N(-d2)=.4336

Ce=[69.50(.6055)-68(.5664)]e-(.035)(.50)=3.51cents

Pe=[68(.4336)-69.50(.3945)]e-(.035)(.50)=2.03cents

12.Usethebinomialoption-pricingmodeldevelopedinthechaptertovaluethecallofproblem9.

ThevolatilityoftheSwissfrancis14.2percent.

Solution:ThespotrateatTwillbeeither77.39¢=70.00¢(1.1056)o