HullOFOD9eSolutionsCh02第九版期權(quán)期貨及其他衍生品課后答案4269

CHAPTER2

MechanicsofFuturesMarkets

PracticeQuestions

Problem2.1.

Distinguishbetweenthetermsopeninterestandtradingvolume.

Theopeninterestofafuturescontractataparticulartimeisthetotalnumberoflongpositions

outstanding.(Equivalently,itisthetotalnumberofshortpositionsoutstanding.)Thetrading

volumeduringacertainperiodoftimeisthenumberofcontractstradedduringthisperiod.

Problem2.2.

Whatisthedifferencebetweenalocalandafuturescommissionmerchant?

Afuturescommissionmerchanttradesonbehalfofaclientandchargesacommission.Alocal

tradesonhisorherownbehalf.

Problem2.3.

SupposethatyouenterintoashortfuturescontracttosellJulysilverfor$17.20perounce.The

sizeofthecontractis5,000ounces.Theinitialmarginis$4,000,andthemaintenancemarginis

$3,000.Whatchangeinthefuturespricewillleadtoamargincall?Whathappensifyoudonot

meetthemargincall?

Therewillbeamargincallwhen$1,000hasbeenlostfromthemarginaccount.Thiswilloccur

whenthepriceofsilverincreasesby1,000/5,000$0.20.Thepriceofsilvermustthereforerise

to$17.40perouncefortheretobeamargincall.Ifthemargincallisnotmet,yourbrokercloses

outyourposition.

Problem2.4.

SupposethatinSeptember2015acompanytakesalongpositioninacontractonMay2016

crudeoilfutures.ItclosesoutitspositioninMarch2016.Thefuturesprice(perbarrel)is

$88.30whenitentersintothecontract,$90.50whenitclosesoutitsposition,and$89.10atthe

endofDecember2015.Onecontractisforthedeliveryof1,000barrels.Whatisthecompany’s

totalprofit?Whenisitrealized?Howisittaxedifitis(a)ahedgerand(b)aspeculator?

AssumethatthecompanyhasaDecember31year-end.

Thetotalprofitis($90.50$88.30)1,000$2,200.Ofthis($89.10$88.30)1,000or

$800isrealizedonaday-by-daybasisbetweenSeptember2015andDecember31,2015.A

further($90.50$89.10)1,000or$1,400isrealizedonaday-by-daybasisbetweenJanuary

1,2016,andMarch2016.Ahedgerwouldbetaxedonthewholeprofitof$2,200in2016.A

speculatorwouldbetaxedon$800in2015and$1,400in2016.

Problem2.5.

Whatdoesastopordertosellat$2mean?Whenmightitbeused?Whatdoesalimitorderto

sellat$2mean?Whenmightitbeused?

Astopordertosellat$2isanordertosellatthebestavailablepriceonceapriceof$2orlessis

reached.Itcouldbeusedtolimitthelossesfromanexistinglongposition.Alimitordertosellat

$2isanordertosellatapriceof$2ormore.Itcouldbeusedtoinstructabrokerthatashort

positionshouldbetaken,providingitcanbedoneatapricemorefavorablethan$2.

Problem2.6.

Whatisthedifferencebetweentheoperationofthemarginaccountsadministeredbyaclearing

houseandthoseadministeredbyabroker?

Themarginaccountadministeredbytheclearinghouseismarkedtomarketdaily,andthe

clearinghousememberisrequiredtobringtheaccountbackuptotheprescribedleveldaily.The

marginaccountadministeredbythebrokerisalsomarkedtomarketdaily.However,theaccount

doesnothavetobebroughtuptotheinitialmarginlevelonadailybasis.Ithastobebroughtup

totheinitialmarginlevelwhenthebalanceintheaccountfallsbelowthemaintenancemargin

level.Themaintenancemarginisusuallyabout75%oftheinitialmargin.

Problem2.7.

Whatdifferencesexistinthewaypricesarequotedintheforeignexchangefuturesmarket,the

foreignexchangespotmarket,andtheforeignexchangeforwardmarket?

Infuturesmarkets,pricesarequotedasthenumberofUSdollarsperunitofforeigncurrency.

SpotandforwardratesarequotedinthiswayfortheBritishpound,euro,Australiandollar,and

NewZealanddollar.Forothermajorcurrencies,spotandforwardratesarequotedasthenumber

ofunitsofforeigncurrencyperUSdollar.

Problem2.8.

Thepartywithashortpositioninafuturescontractsometimeshasoptionsastotheprecise

assetthatwillbedelivered,wheredeliverywilltakeplace,whendeliverywilltakeplace,andso

on.Dotheseoptionsincreaseordecreasethefuturesprice?Explainyourreasoning.

Theseoptionsmakethecontractlessattractivetothepartywiththelongpositionandmore

attractivetothepartywiththeshortposition.Theythereforetendtoreducethefuturesprice.

Problem2.9.

Whatarethemostimportantaspectsofthedesignofanewfuturescontract?

Themostimportantaspectsofthedesignofanewfuturescontractarethespecificationofthe

underlyingasset,thesizeofthecontract,thedeliveryarrangements,andthedeliverymonths.

Problem2.10.

Explainhowmarginaccountsprotectinvestorsagainstthepossibilityofdefault.

Amarginisasumofmoneydepositedbyaninvestorwithhisorherbroker.Itactsasa

guaranteethattheinvestorcancoveranylossesonthefuturescontract.Thebalanceinthe

marginaccountisadjusteddailytoreflectgainsandlossesonthefuturescontract.Iflossesare

aboveacertainlevel,theinvestorisrequiredtodepositafurthermargin.Thissystemmakesit

unlikelythattheinvestorwilldefault.Asimilarsystemofmarginaccountsmakesitunlikelythat

theinvestor’sbrokerwilldefaultonthecontractithaswiththeclearinghousememberand

unlikelythattheclearinghousememberwilldefaultwiththeclearinghouse.

Problem2.11.

AtraderbuystwoJulyfuturescontractsonfrozenorangejuice.Eachcontractisforthedelivery

of15,000pounds.Thecurrentfuturespriceis160centsperpound,theinitialmarginis$6,000

percontract,andthemaintenancemarginis$4,500percontract.Whatpricechangewouldlead

toamargincall?Underwhatcircumstancescould$2,000bewithdrawnfromthemargin

account?

Thereisamargincallifmorethan$1,500islostononecontract.Thishappensifthefutures

priceoffrozenorangejuicefallsbymorethan10centstobelow150centsperpound.$2,000

canbewithdrawnfromthemarginaccountifthereisagainononecontractof$1,000.Thiswill

happenifthefuturespricerisesby6.67centsto166.67centsperpound.

Problem2.12.

Showthat,ifthefuturespriceofacommodityisgreaterthanthespotpriceduringthedelivery

period,thenthereisanarbitrageopportunity.Doesanarbitrageopportunityexistifthefutures

priceislessthanthespotprice?Explainyouranswer.

Ifthefuturespriceisgreaterthanthespotpriceduringthedeliveryperiod,anarbitrageurbuys

theasset,shortsafuturescontract,andmakesdeliveryforanimmediateprofit.Ifthefutures

priceislessthanthespotpriceduringthedeliveryperiod,thereisnosimilarperfectarbitrage

strategy.Anarbitrageurcantakealongfuturespositionbutcannotforceimmediatedeliveryof

theasset.Thedecisiononwhendeliverywillbemadeismadebythepartywiththeshort

position.Neverthelesscompaniesinterestedinacquiringtheassetmayfinditattractivetoenter

intoalongfuturescontractandwaitfordeliverytobemade.

Problem2.13.

Explainthedifferencebetweenamarket-if-touchedorderandastoporder.

Amarket-if-touchedorderisexecutedatthebestavailablepriceafteratradeoccursata

specifiedpriceoratapricemorefavorablethanthespecifiedprice.Astoporderisexecutedat

thebestavailablepriceafterthereisabidorofferatthespecifiedpriceoratapriceless

favorablethanthespecifiedprice.

Problem2.14.

Explainwhatastop-limitordertosellat20.30withalimitof20.10means.

Astop-limitordertosellat20.30withalimitof20.10meansthatassoonasthereisabidat

20.30thecontractshouldbesoldprovidingthiscanbedoneat20.10orahigherprice.

Problem2.15.

Attheendofonedayaclearinghousememberislong100contracts,andthesettlementpriceis

$50,000percontract.Theoriginalmarginis$2,000percontract.Onthefollowingdaythe

memberbecomesresponsibleforclearinganadditional20longcontracts,enteredintoata

priceof$51,000percontract.Thesettlementpriceattheendofthisdayis$50,200.Howmuch

doesthememberhavetoaddtoitsmarginaccountwiththeexchangeclearinghouse?

Theclearinghousememberisrequiredtoprovide20$2000$40000asinitialmarginfor

thenewcontracts.Thereisagainof(50,200

50,000)100$20,000ontheexisting

contracts.Thereisalsoalossof(5100050200)20$16000onthenewcontracts.The

membermustthereforeadd

400002000016000$36000

tothemarginaccount.

Problem2.16.

ExplainwhycollateralrequirementswillincreaseintheOTCmarketasaresultofnew

regulationsintroducedsincethe2008creditcrisis.

RegulationsrequiremoststandardOTCtransactionsenteredintobetweenderivativesdealersto

beclearedbyCCPs.Thesehaveinitialandvariationmarginrequirementssimilartoexchanges.

Thereisalsoarequirementthatinitialandvariationmarginbeprovidedformostbilaterally

clearedOTCtransactions.

Problem2.17.

TheforwardpriceontheSwissfrancfordeliveryin45daysisquotedas1.1000.Thefutures

priceforacontractthatwillbedeliveredin45daysis0.9000.Explainthesetwoquotes.Which

ismorefavorableforaninvestorwantingtosellSwissfrancs?

The1.1000forwardquoteisthenumberofSwissfrancsperdollar.The0.9000futuresquoteis

thenumberofdollarsperSwissfranc.Whenquotedinthesamewayasthefuturespricethe

forwardpriceis11100009091.TheSwissfrancisthereforemorevaluableintheforward

marketthaninthefuturesmarket.Theforwardmarketisthereforemoreattractiveforaninvestor

wantingtosellSwissfrancs.

Problem2.18.

SupposeyoucallyourbrokerandissueinstructionstoselloneJulyhogscontract.Describe

whathappens.

LivehogfuturesaretradedbytheCMEGroup.Thebrokerwillrequestsomeinitialmargin.The

orderwillberelayedbytelephonetoyourbroker’stradingdeskonthefloor

oftheexchange(or

tothetradingdeskofanotherbroker).Itwillthenbesentbymessengertoacommissionbroker

whowillexecutethetradeaccordingtoyourinstructions.Confirmationofthetradeeventually

reachesyou.Ifthereareadversemovementsinthefuturespriceyourbrokermaycontactyouto

requestadditionalmargin.

Problem2.19.

“Speculationinfuturesmarketsispuregambling.Itisnotinthepublicinteresttoallow

speculatorstotradeonafuturesexchange.”Discussthisviewpoint

.

Speculatorsareimportantmarketparticipantsbecausetheyaddliquiditytothemarket.However,

contractsmustbeusefulforhedgingaswellasspeculation.Thisisbecauseregulatorsgenerally

onlyapprovecontractswhentheyarelikelytobeofinteresttohedgersaswellasspeculators.

Problem2.20.

ExplainthedifferencebetweenbilateralandcentralclearingforOTCderivatives.

Inbilateralclearingthetwosidesenterintoanagreementgoverningthecircumstancesunder

whichtransactionscanbeclosedoutbyoneside,howtransactionswillbevaluedifthereisa

closeout,howthecollateralpostedbyeachsideiscalculated,andsoon.Incentralclearinga

CCPstandsbetweenthetwosidesinthesamewaythatanexchangeclearinghousestands

betweentwosidesfortransactionsenteredintoonanexchange

Problem2.21.

Whatdoyouthinkwouldhappenifanexchangestartedtradingacontractinwhichthequality

oftheunderlyingassetwasincompletelyspecified?

Thecontractwouldnotbeasuccess.Partieswithshortpositionswouldholdtheircontractsuntil

deliveryandthendeliverthecheapestformoftheasset.Thismightwellbeviewedbytheparty

withthelongpositionasgarbage!Oncenewsofthequalityproblembecamewidelyknownno

onewouldbepreparedtobuythecontract.Thisshowsthatfuturescontractsarefeasibleonly

whentherearerigorousstandardswithinanindustryfordefiningthequalityoftheasset.Many

futurescontractshaveinpracticefailedbecauseoftheproblemofdefiningquality.

Problem2.22.

“Whenafuturescontractistradedontheflooroftheexchange,itmaybethecasethattheopen

interestincreasesbyone,staysthesame,ordecreasesbyone.”Explainthisstatement.

Ifbothsidesofthetransactionareenteringintoanewcontract,theopeninterestincreasesbyone.

Ifbothsidesofthetransactionareclosingoutexistingpositions,theopeninterestdecreasesby

one.Ifonepartyisenteringintoanewcontractwhiletheotherpartyisclosingoutanexisting

position,theopenintereststaysthesame.

Problem2.23.

SupposethatonOctober24,2015,acompanysellsoneApril2016live-cattlefuturescontracts.

ItclosesoutitspositiononJanuary21,2016.Thefuturesprice(perpound)is121.20centswhen

itentersintothecontract,118.30centswhenitclosesoutitsposition,and118.80centsatthe

endofDecember2015.Onecontractisforthedeliveryof40,000poundsofcattle.Whatisthe

totalprofit?Howisittaxedifthecompanyis(a)ahedgerand(b)aspeculator?Assumethatthe

companyhasaDecember31yearend.

Thetotalprofitis

40,000×(1.2120?1.1830)=$1,160

Ifthecompanyisahedgerthisisalltaxedin2016.Ifitisaspeculator

40,000×(1.2120?1.1880)=$960

istaxedin2015and

40,000×(1.1880?1.1830)=$200

istaxedin2016.

Problem2.24.

Acattlefarmerexpectstohave120,000poundsoflivecattletosellinthreemonths.Thelive-

cattlefuturescontracttradedbytheCMEGroupisforthedeliveryof40,000poundsofcattle.

Howcanthefarmerusethecontractforhedging?Fromthefarmer’sviewpoint,whatarethe

prosandconsofhedging?

Thefarmercanshort3contractsthathave3monthstomaturity.Ifthepriceofcattlefalls,the

gainonthefuturescontractwilloffsetthelossonthesaleofthecattle.Ifthepriceofcattlerises,

thegainonthesaleofthecattlewillbeoffsetbythelossonthefuturescontract.Usingfutures

contractstohedgehastheadvantagethatthefarmercangreatlyreducetheuncertaintyaboutthe

pricethatwillbereceived.Itsdisadvantageisthatthefarmernolongergainsfromfavorable

movementsincattleprices.

Problem2.25.

ItisJuly2014.Aminingcompanyhasjustdiscoveredasmalldepositofgold.Itwilltakesix

monthstoconstructthemine.Thegoldwillthenbeextractedonamoreorlesscontinuousbasis

foroneyear.Futurescontractsongoldareavailablewithdeliverymonthseverytwomonths

fromAugust2014toDecember2015.Eachcontractisforthedeliveryof100ounces.Discuss

howtheminingcompanymightusefuturesmarketsforhedging.

Theminingcompanycanestimateitsproductiononamonthbymonthbasis.Itcanthenshort

futurescontractstolockinthepricereceivedforthegold.Forexample,ifatotalof3,000ounces

areexpectedtobeproducedinSeptember2015andOctober2015,thepricereceivedforthis

productioncanbehedgedbyshorting30October2015contracts.

Problem2.26.

ExplainhowCCPswork.Whataretheadvantagestothefinancialsystemofrequiringall

standardizedderivativestransactionstobeclearedthroughCCPs?

ACCPstandsbetweenthetwopartiesinanOTCderivativetransactioninmuchthesameway

thataclearinghousedoesforexchange-tradedcontracts.Itabsorbsthecreditriskbutrequires

initialandvariationmarginfromeachside.Inaddition,CCPmembersarerequiredtocontribute

toadefaultfund.Theadvantagetothefinancialsystemisthatthereisalotmorecollateral(i.e.,

margin)availableanditisthereforemuchlesslikelythatadefaultbyonemajorparticipantin

thederivativesmarketwillleadtolossesbyothermarketparticipants.Thereisalsomore

transparencyinthatthetradesofdifferentfinancialinstitutionsaremorereadilyknown.The

disadvantageisthatCCPsarereplacingbanksasthetoo-big-to-failentitiesinthefinancial

system.ThereclearlyneedstobecarefuloversightofthemanagementofCCPs.

FurtherQuestions

Problem2.27.

TraderAentersintofuturescontractstobuy1millioneurosfor1.3milliondollarsinthree

months.TraderBentersinaforwardcontracttodothesamething.Theexchangerate(dollars

pereuro)declinessharplyduringthefirsttwomonthsandthenincreasesforthethirdmonthto

closeat1.3300.Ignoringdailysettlement,whatisthetotalprofitofeachtrader?Whenthe

impactofdailysettlementistakenintoaccount,whichtraderdoesbetter?

Thetotalprofitofeachtraderindollarsis0.03×1,000,000=30,000.TraderB’sprofitisrealized

attheendofthethreemonths.TraderA’sprofitisrealizedday-by-dayduringthethreemonths.

Substantiallossesaremadeduringthefirsttwomonthsandprofitsaremadeduringthefinal

month.ItislikelythatTraderBhasdonebetterbecauseTraderAhadtofinanceitslossesduring

thefirsttwomonths.

Problem2.28.

Explainwhatismeantbyopeninterest.Whydoestheopeninterestusuallydeclineduringthe

monthprecedingthedeliverymonth?Onaparticularday,therewere2,000tradesina

particularfuturescontract.Thismeansthattherewere2000buyers(goinglong)and2000

sellers(goingshort).Ofthe2,000buyers,1,400wereclosingoutpositionsand600were

enteringintonewpositions.Ofthe2,000sellers,1,200wereclosingoutpositionsand800were

enteringintonewpositions.Whatistheimpactoftheday'stradingonopeninterest?

Openinterestisthenumberofcontractoutstanding.Manytraderscloseouttheirpositionsjust

beforethedeliverymonthisreached.Thisiswhytheopeninterestdeclinesduringthemonth

precedingthedeliverymonth.Theopeninterestwentdownby600.Wecanseethisintwoways.

First,1,400shortsclosedoutandtherewere800newshorts.Second,1,200longsclosedoutand

therewere600newlongs.

Problem2.29.

Oneorangejuicefuturecontractison15,000poundsoffrozenconcentrate.Supposethatin

September2014acompanysellsaMarch2016orangejuicefuturescontractfor120centsper

pound.InDecember2014thefuturespriceis140cents;inDecember2015thefuturespriceis

110cents;andinFebruary2016itisclosedoutat125cents.ThecompanyhasaDecemberyear

end.Whatisthecompany'sprofitorlossonthecontract?Howisitrealized?Whatisthe

accountingandtaxtreatmentofthetransactionifthecompanyisclassifiedasa)ahedgerandb)

aspeculator?

Thepricegoesupduringthetimethecompanyholdsthecontractfrom120to125centsper

pound.Overallthecompanythereforetakesalossof15,000×0.05=$750.Ifthecompanyis

classifiedasahedgerthislossisrealizedin2016,Ifitisclassifiedasaspeculatoritrealizesa

lossof15,000×0.20=$3000in2014,againof15,000×0.30=$4,500in2015,andalossof

15,000×0.15=$2,250in2016.

Problem2.30.

Acompanyentersintoashortfuturescontracttosell5,000bushelsofwheatfor750centsper

bushel.Theinitialmarginis$3,000andthemaintenancemarginis$2,000.Whatpricechange

wouldleadtoamargincall?Underwhatcircumstancescould$1,500bewithdrawnfromthe

marginaccount?

Thereisamargincallif$1000islostonthecontract.Thiswillhappenifthepriceofwheat

futuresrisesby20centsfrom750centsto770centsperbushel.$1500canbewithdrawnifthe

futurespricefallsby30centsto720centsperbushel.

Problem2.31.

Supposethattherearenostoragecostsforcrudeoilandtheinterestrateforborrowingor

lendingis5%perannum.HowcouldyoumakemoneyiftheJuneandDecemberfutures

contractsforaparticularyeartradeat$80and$86?

YoucouldgolongoneJuneoilcontractandshortoneDecembercontract.InJuneyoutake

deliveryoftheoilborrowing$80perbarrelat5%tomeetcashoutflows.Theinterest

accumulatedinsixmonthsisabout80×0.05×1/2or$2.InDecembertheoilissoldfor$86per

barrelwhichismorethanthe$82thathastoberepaidontheloan.Thestrategythereforeleads

toaprofit.NotethatthisprofitisindependentoftheactualpriceofoilinJuneandDecember.It

willbeslightlyaffectedbythedailysettlementprocedures.

Problem2.32.

WhatpositionisequivalenttoalongforwardcontracttobuyanassetatKonacertaindate

andaputoptiontosellitforKonthatdate?

ThelongforwardcontractprovidesapayoffofST?KwhereSTistheassetpriceonthedateand

Kisthedeliveryprice.Theputoptionprovidesapayoffofmax(K?ST,0).IfST>Kthesumof

thetwopayoffsisST–K.IfST<Kthesumofthetwopayoffsis0.Thecombinedpayoffis

thereforemax(ST–K,0).Thisisthepayofffromacalloption.Theequivalentpositionis

thereforeacalloption.

Problem2.33.

AcompanyhasderivativestransactionswithBanksA,B,andCwhichareworth+$20million,

?$15million,and?$25million,respectivelytothecompany.Howmuchmarginorcollateral

doesthecompanyhavetoprovideineachofthefollowingtwosituations?

a)Thetransactionsareclearedbilaterallyandaresubjecttoone-waycollateralagreements

wherethecompanypostsvariationmargin,butnoinitialmargin.Thebanksdonothavetopost

collateral.

b)ThetransactionsareclearedcentrallythroughthesameCCPandtheCCPrequiresatotal

initialmarginof$10million.

Ifthetransactionsareclearedbilaterally,thecompanyhastoprovidecollateraltoBanksA,B,

andCof(inmillionsofdollars)0,15,and25,respectively.Thetotalcollateralrequiredis$40

million.Ifthetransactionsareclearedcentrallytheyarenettedagainsteachotherandthe

company’stotalvariationmargin(inmillionsofdollars)is–20+15+25or$20millionintotal.

Thetotalmarginrequired(includingtheinitialmargin)istherefore$30million.

Problem2.34.

Abank’sderivativestransactionswithacounterpartyareworth+$10milliontothebank

andareclearedbilaterally.Thecounterpartyhasposted$10millionofcashcollateral.

Whatcreditexposuredoesthebankhave?

Thecou