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CHAPTER1Introduction
PracticeQuestions
Problem1.8.
Supposeyouown5,000sharesthatareworth$25each.Howcanputoptionsbeusedtoprovideyouwithinsuranceagainstadeclineinthevalueofyourholdingoverthenextfourmonths?
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Youshouldbuy50putoptioncontracts(eachon100shareswithastrikepriceof$25andan
expirationdateinfourmonths.Ifattheendoffourmonthsthestockpriceprovestobelessthan$25,youcanexercisetheoptionsandsellthesharesfor$25each.
Problem1.9.
Astockwhenitisfirstissuedprovidesfundsforacompany.Isthesametrueofanexchange-tradedstockoption?Discuss.
Anexchange-tradedstockoptionprovidesnofundsforthecompany.Itisasecuritysoldbyoneinvestortoanother.Thecompanyisnotinvolved.Bycontrast,astockwhenitisfirstissuedissoldbythecompanytoinvestorsanddoesprovidefundsforthecompany.Problem1.10.
Explainwhyafuturescontractcanbeusedforeitherspeculationorhedging.
Ifaninvestorhasanexposuretothepriceofanasset,heorshecanhedgewithfutures
contracts.Iftheinvestorwillgainwhenthepricedecreasesandlosewhenthepriceincreases,alongfuturespositionwillhedgetherisk.Iftheinvestorwilllosewhenthepricedecreasesandgainwhenthepriceincreases,ashortfuturespositionwillhedgetherisk.Thuseitheralongorashortfuturespositioncanbeenteredintoforhedgingpurposes.
Iftheinvestorhasnoexposuretothepriceoftheunderlyingasset,enteringintoafuturescontractisspeculation.Iftheinvestortakesalongposition,heorshegainswhentheasset’spriceincreasesandloseswhenitdecreases.Iftheinvestortakesashortposition,heorsheloseswhentheasset’spriceincreasesandgainswhenitdecreases.
Problem1.11.
Acattlefarmerexpectstohave120,000poundsoflivecattletosellinthreemonths.Thelive-cattlefuturescontractontheChicagoMercantileExchangeisforthedeliveryof40,000poundsofcattle.Howcanthefarmerusethecontractforhedging?Fromthefarmer’sviewpoint,whataretheprosandconsofhedging?
Thefarmercanshort3contractsthathave3monthstomaturity.Ifthepriceofcattlefalls,thegainonthefuturescontractwilloffsetthelossonthesaleofthecattle.Ifthepriceofcattlerises,thegainonthesaleofthecattlewillbeoffsetbythelossonthefuturescontract.Usingfuturescontractstohedgehastheadvantagethatitcanatnocostreducerisktoalmostzero.Itsdisadvantageisthatthefarmernolongergainsfromfavorablemovementsincattleprices.



Problem1.12.
ItisJuly2013.Aminingcompanyhasjustdiscoveredasmalldepositofgold.Itwilltakesixmonthstoconstructthemine.Thegoldwillthenbeextractedonamoreorlesscontinuousbasisforoneyear.FuturescontractsongoldareavailableontheNewYorkMercantile
Exchange.TherearedeliverymonthseverytwomonthsfromAugust2013toDecember2014.Eachcontractisforthedeliveryof100ounces.Discusshowtheminingcompanymightusefuturesmarketsforhedging.
Theminingcompanycanestimateitsproductiononamonthbymonthbasis.Itcanthenshortfuturescontractstolockinthepricereceivedforthegold.Forexample,ifatotalof3,000ouncesareexpectedtobeproducedinSeptember2014andOctober2014,thepricereceivedforthisproductioncanbehedgedbyshortingatotalof30October2014contracts.
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Problem1.13.
SupposethataMarchcalloptiononastockwithastrikepriceof$50costs$2.50andishelduntilMarch.Underwhatcircumstanceswilltheholderoftheoptionmakeagain?Underwhatcircumstanceswilltheoptionbeexercised?Drawadiagramshowinghowtheprofitonalongpositionintheoptiondependsonthestockpriceatthematurityoftheoption.Theholderoftheoptionwillgainifthepriceofthestockisabove$52.50inMarch.(Thisignoresthetimevalueofmoney.Theoptionwillbeexercisedifthepriceofthestockisabove$50.00inMarch.TheprofitasafunctionofthestockpriceisshowninFigureS1.1.
20
Profit
15105020-5
30
40
50

StockPrice
70
60
FigureS1.1ProfitfromlongpositioninProblem1.13
Problem1.14.
SupposethataJuneputoptiononastockwithastrikepriceof$60costs$4andishelduntilJune.Underwhatcircumstanceswilltheholderoftheoptionmakeagain?Underwhatcircumstanceswilltheoptionbeexercised?Drawadiagramshowinghowtheprofitonashortpositionintheoptiondependsonthestockpriceatthematurityoftheoption.Theselleroftheoptionwillloseifthepriceofthestockisbelow$56.00inJune.(Thisignoresthetimevalueofmoney.Theoptionwillbeexercisedifthepriceofthestockisbelow$60.00inJune.TheprofitasafunctionofthestockpriceisshowninFigureS1.2.


60504030201000-10
20
40
60

Profit
StockPrice
80
100
120
FigureS1.2ProfitfromshortpositioninProblem1.14
Problem1.15.
ItisMayandatraderwritesaSeptembercalloptionwithastrikepriceof$20.Thestockpriceis$18,andtheoptionpriceis$2.Describetheinvestor’scashflowsiftheoptionishelduntilSeptemberandthestockpriceis$25atthistime.
Thetraderhasaninflowof$2inMayandanoutflowof$5inSeptember.The$2isthecashreceivedfromthesaleoftheoption.The$5istheresultoftheoptionbeingexercised.Theinvestorhastobuythestockfor$25inSeptemberandsellittothepurchaseroftheoptionfor$20.
Problem1.16.
AninvestorwritesaDecemberputoptionwithastrikepriceof$30.Thepriceoftheoptionis$4.Underwhatcircumstancesdoestheinvestormakeagain?
Theinvestormakesagainifthepriceofthestockisabove$26atthetimeofexercise.(Thisignoresthetimevalueofmoney.
Problem1.17.
TheCMEGroupoffersafuturescontractonlong-termTreasurybonds.Characterizetheinvestorslikelytousethiscontract.
Mostinvestorswillusethecontractbecausetheywanttodooneofthefollowing:aHedgeanexposuretolong-terminterestrates.
bSpeculateonthefuturedirectionoflong-terminterestrates.
cArbitragebetweenthespotandfuturesmarketsforTreasurybonds.Problem1.18.
Anairlineexecutivehasargued:“Thereisnopointinourusingoilfutures.Thereisjustasmuchchancethatthepriceofoilinthefuturewillbelessthanthefuturespriceasthereisthatitwillbegreaterthanthisprice.”Discusstheexecutive’sviewpoint.

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Itmaywellbetruethatthereisjustasmuchchancethatthepriceofoilinthefuturewillbeabovethefuturespriceasthatitwillbebelowthefuturesprice.Thismeansthattheuseofafuturescontractforspeculationwouldbelikebettingonwhetheracoincomesupheadsortails.Butitmightmakesensefortheairlinetousefuturesforhedgingratherthan
speculation.Thefuturescontractthenhastheeffectofreducingrisks.Itcanbearguedthatanairlineshouldnotexposeitsshareholderstorisksassociatedwiththefuturepriceofoilwhentherearecontractsavailabletohedgetherisks.
Problem1.19.
“Optionsandfuturesarezero-sumgames.”Whatdoyouthinkismeantbythisstatement?Thestatementmeansthatthegain(losstothepartywiththeshortpositionisequaltotheloss(gaintothepartywiththelongposition.Intotal,thegaintoallpartiesiszero.Problem1.20.
Atraderentersintoashortforwardcontracton100millionyen.Theforwardexchangerateis$0.0080peryen.Howmuchdoesthetradergainorloseiftheexchangerateattheendofthecontractis(a$0.0074peryen;(b$0.0091peryen?
aThetradersells100millionyenfor$0.0080peryenwhentheexchangerateis$0.0074
peryen.Thegainis10000006millionsofdollarsor$60,000.
bThetradersells100millionyenfor$0.0080peryenwhentheexchangerateis$0.0091
peryen.Thelossis10000011millionsofdollarsor$110,000.Problem1.21.
Atraderentersintoashortcottonfuturescontractwhenthefuturespriceis50centsperpound.Thecontractisforthedeliveryof50,000pounds.Howmuchdoesthetradergainorloseifthecottonpriceattheendofthecontractis(a48.20centsperpound;(b51.30centsperpound?
aThetradersellsfor50centsperpoundsomethingthatisworth48.20centsperpound.
Gain=($0.5000$0.4820×50,000=$900.
bThetradersellsfor50centsperpoundsomethingthatisworth51.30centsperpound.
Loss=($0.5130$0.5000×50,000=$650.Problem1.22.
Acompanyknowsthatitisduetoreceiveacertainamountofaforeigncurrencyinfourmonths.Whattypeofoptioncontractisappropriateforhedging?
Alongpositioninafour-monthputoptioncanprovideinsuranceagainsttheexchangeratefallingbelowthestrikeprice.Itensuresthattheforeigncurrencycanbesoldforatleastthestrikeprice.
Problem1.23.
AUnitedStatescompanyexpectstohavetopay1millionCanadiandollarsinsixmonths.Explainhowtheexchangerateriskcanbehedgedusing(aaforwardcontract;(banoption.
Thecompanycouldenterintoalongforwardcontracttobuy1millionCanadiandollarsin

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sixmonths.Thiswouldhavetheeffectoflockinginanexchangerateequaltothecurrentforwardexchangerate.Alternativelythecompanycouldbuyacalloptiongivingittheright(butnottheobligationtopurchase1millionCanadiandollarsatacertainexchangerateinsixmonths.ThiswouldprovideinsuranceagainstastrongCanadiandollarinsixmonthswhilestillallowingthecompanytobenefitfromaweakCanadiandollaratthattime.Problem1.24
Atraderbuysacalloptionwithastrikepriceof$30for$3.Doesthetradereverexercisetheoptionandlosemoneyonthetrade.Explain.
Yes,thetraderwillexerciseiftheassetpriceisgreaterthan$30,butwillcoverthecostofthecalloptiononlyifthepriceisgreaterthan$33.Thetraderexercisesandlosesmoneyifthepriceisbetween$30and$33.
Problem1.25
Atradersellsaputoptionwithastrikepriceof$40for$5.Whatisthetrader’smaximumgainandmaximumloss?Howdoesyouranswerchangeifitisacalloption?
Thetrader’smaximumgainfromtheputoptionis$5.Themaximumlossis$35,
correspondingtothesituationwheretheoptionisexercisedandtheassetpriceiszero.Iftheoptionwereacall,thetrader’smaximumgainwouldstillbe$5,buttherewouldbenoboundtothelossasthereisintheorynolimittohowhightheassetpricecouldrise.Problem1.26
‘‘Buyingastockandaputoptiononthestockisaformofinsurance.’’Explainthisstatement.
Ifthestockpricedeclinesbelowthestrikepriceoftheputoption,thestockcanbesoldforthestrikeprice.
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FurtherQuestions
TraderAmakesaprofitofST1000andTraderBmakesaprofitofmax(ST1000,0–100
whereSTisthepriceoftheassetinoneyear.TraderAdoesbetterifSTisabove$900asindicatedinthediagrambelow

Problem1.27(Excelfile
TraderAentersintoaforwardcontracttobuyanassetfor$1000anounceinoneyear.TraderBbuysacalloptiontobuytheassetfor$1000inoneyear.Thecostoftheoptionis$100.Whatisthedifferencebetweenthepositionsofthetraders?Showtheprofitasafunctionofthepriceoftheassetinoneyearforthetwotraders.

300
Profit
2001000700-100
AssetPrice

TraderA
900
1100
1300
TraderB
-200-300
Problem1.28
OnJune25,2012,asindicatedinTable1.2,thespotofferpriceofGooglestockis$561.51andtheofferpriceofacalloptionwithastrikepriceof$560andamaturitydateof
Septemberis$30.70.Atraderisconsideringtwoalternatives:buy100sharesofthestockandbuy100Septembercalloptions.Foreachalternative,whatis(atheupfrontcost,(bthetotalgainifthestockpriceinSeptemberis$620,and(cthetotallossifthestockpriceinSeptemberis$500.AssumethattheoptionisnotexercisedbeforeSeptemberandifstockispurchaseditissoldinSeptember.
aTheupfrontcostforthesharealternativeis$56,151.Theupfrontcostfortheoptionalternativeis$3,070.
bThegainfromthestockalternativeis$62,000−$56,151=$5,849.Thetotalgainfromtheoptionalternativeis($620-$560×100−$3,070=$2,930.
cThelossfromthestockalternativeis$56,151−$50,000=$6,151.Thelossfromthe
optionalternativeis$3,070.Problem1.29
Whatisarbitrage?Explainthearbitrageopportunitywhenthepriceofaduallylisted
miningcompanystockis$50ontheNewYorkStockExchangeand$52CADontheTorontoStockExchange.Assumethattheexchangerateissuchthat1USDequals1.01CAD.Explainwhatislikelytohappentopricesastraderstakeadvantageofthisopportunity.Arbitrageinvolvescarryingouttwoormoredifferenttradestolockinaprofit.Inthiscase,traderscanbuysharesontheNYSEandsellthemontheTSXtolockinaUSDprofitof52/1.01−50=1.485pershare.AstheydothistheNYSEpricewillriseandtheTSXpricewillfallsothatthearbitrageopportunitydisappears
Problem1.30
InMarch,aUSinvestorinstructsabrokertoselloneJulyputoptioncontractonastock.Thestockpriceis$42andthestrikepriceis$40.Theoptionpriceis$3.Explainwhatthe
investorhasagreedto.Underwhatcircumstanceswillthetradeprovetobeprofitable?Whataretherisks?

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Theinvestorhasagreedtobuy100sharesofthestockfor$40inJuly(orearlierifthepartyontheothersideofthetransactionchoosestosell.Thetradewillproveprofitableiftheoptionisnotexercisedorifthestockpriceisabove$37atthetimeofexercise.Therisktotheinvestoristhatthestockpriceplungestoalowlevel.Forexample,ifthestockpricedropsto$1byJuly(unlikelybutpossible,theinvestorloses$3,600.Thisisbecausetheputoptionsareexercisedand$40ispaidfor100shareswhenthevaluepershareis$1.Thisleadstoalossof$3,900whichisoffsetbythepremiumof$300receivedfortheoptions.Problem1.31
AUScompanyknowsitwillhavetopay3millioneurosinthreemonths.Thecurrent
exchangerateis1.4500dollarspereuro.Discusshowforwardandoptionscontractscanbeusedbythecompanytohedgeitsexposure.
Thecompanycouldenterintoaforwardcontractobligatingittobuy3millioneurosinthreemonthsforafixedprice(theforwardprice.Theforwardpricewillbeclosetobutnotexactlythesameasthecurrentspotpriceof1.4500.Analternativewouldbetobuyacalloptiongivingthecompanytherightbutnottheobligationtobuy3millioneurosforaa
particularexchangerate(thestrikepriceinthreemonths.Theuseofaforwardcontractlocksin,atnocost,theexchangeratethatwillapplyinthreemonths.Theuseofacalloptionprovides,atacost,insuranceagainsttheexchangeratebeinghigherthanthestrikeprice.Problem1.32(Excelfile
Astockpriceis$29.Aninvestorbuysonecalloptioncontractonthestockwithastrikepriceof$30andsellsacalloptioncontractonthestockwithastrikepriceof$32.50.Themarketpricesoftheoptionsare$2.75and$1.50,respectively.Theoptionshavethesamematuritydate.Describetheinvestor'sposition.
ThisisknownasabullspreadandwillbediscussedinChapter11.Theprofitisshowninthediagrambelow
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Problem1.33
Thepriceofgoldiscurrently$1,800perounce.Forwardcontractsareavailabletobuyorsellgoldat$2,000perouncefordeliveryinoneyear.Anarbitrageurcanborrowmoneyat5%perannum.Whatshouldthearbitrageurdo?Assumethatthecostofstoringgoldiszeroandthatgoldprovidesnoincome.
Thearbitrageurshouldborrowmoneytobuyacertainnumberofouncesofgoldtodayandshortforwardcontractsonthesamenumberofouncesofgoldfordeliveryinoneyear.Thismeansthatgoldispurchasedfor$1800perounceandsoldfor$2000perounce.Thecostoftheborrowingis$90perounce.Arisklessprofitof$110perounceisgenerated.
Problem1.34.
DiscusshowforeigncurrencyoptionscanbeusedforhedginginthesituationdescribedinExample1.1sothat(aImportCoisguaranteedthatitsexchangeratewillbelessthan1.5800,and(bExportCoisguaranteedthatitsexchangeratewillbeatleast1.5400.ImportCocanbuycalloptionson$10,000,000withastrikepriceof1.5800.Thiswillensurethatitneverpaysmorethan$15,800,000forthesterlingitrequires.ExportCocanbuyputoptionson$30,000,000withastrikepriceof1.5400.Thiswillensurethatthepricereceivedforthesterlingwillbeabove1.5430,000,000$46,200,00.
Problem1.35.
Thecurrentpriceofastockis$94,andthree-monthcalloptionswithastrikepriceof$95currentlysellfor$4.70.Aninvestorwhofeelsthatthepriceofthestockwillincreaseistryingtodecidebetweenbuying100sharesandbuying2,000calloptions(20contracts.Bothstrategiesinvolveaninvestmentof$9,400.Whatadvicewouldyougive?Howhighdoesthestockpricehavetorisefortheoptionstrategytobemoreprofitable?
Theinvestmentincalloptionsentailshigherrisksbutcanleadtohigherreturns.Ifthestockpricestaysat$94,aninvestorwhobuyscalloptionsloses$9,400whereasaninvestorwhobuyssharesneithergainsnorlosesanything.Ifthestockpricerisesto$120,theinvestorwhobuyscalloptionsgains
2000(120959400$40600
Aninvestorwhobuyssharesgains
100(12094$2600
Thestrategiesareequallyprofitableifthestockpricerisestoalevel,S,where
100(S942000(S959400
or
S100
Theoptionstrategyisthereforemoreprofitableifthestockpricerisesabove$100.Problem1.36.
OnJune25,2012,aninvestorowns100Googleshares.AsindicatedinTable1.3,thebidsharepriceis$561.32andaDecemberputoptionwithastrikeprice$520costs$26.10.The

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investoriscomparingtwoalternativestolimitdownsiderisk.ThefirstinvolvesbuyingoneDecmberputoptioncontractwithastrikepriceof$520.Thesecondinvolvesinstructingabrokertosellthe100sharesassoonasGoogle’spricereaches$520.Discusstheadvantagesanddisadvantagesofthetwostrategies.
Thesecondalternativeinvolveswhatisknownasastoporstop-lossorder.Itcostsnothingandensuresthat$52,000,orcloseto$52,000,isrealizedfortheholdingintheeventthe
stockpriceeverfallsto$520.Theputoptioncosts$2,610andguaranteesthattheholdingcanbesoldfor$52,000anytimeuptoDecember.Ifthestockpricefallsmarginallybelow$520andthenrisestheoptionwillnotbeexercised,butthestop-lossorderwillleadtotheholdingbeingliquidated.Therearesomecircumstanceswheretheputoptionalternativeleadstoabetteroutcomeandsomecircumstanceswherethestop-lossorderleadstoabetteroutcome.Ifthestockpriceendsupbelow$520,thestop-lossorderalternativeleadstoabetteroutcomebecausethecostoftheoptionisavoided.Ifthestockpricefallsto$480in
Novemberandthenrisesto$580byDecember,theputoptionalternativeleadstoabetteroutcome.Theinvestorispaying$2,610forthechancetobenefitfromthissecondtypeofoutcome.
Problem1.37.
AtraderbuysaEuropeancalloptionandsellsaEuropeanputoption.Theoptionshavethesameunderlyingasset,strikepriceandmaturity.Describethetrader’sposition.Underwhatcircumstancesdoesthepriceofthecallequalthepriceoftheput?
ThetraderhasalongEuropeancalloptionwithstrikepriceKandashortEuropeanputoptionwithstrikepriceK.SupposethepriceoftheunderlyingassetatthematurityoftheoptionisST.IfSTK,thecalloptionisexercisedbytheinvestorandtheputoptionexpiresworthless.ThepayofffromtheportfolioisSTK.IfSTK,thecalloptionexpiresworthlessandtheputoptionisexercisedagainsttheinvestor.ThecosttotheinvestorisKST.AlternativelywecansaythatthepayofftotheinvestorisSTK(anegative
amount.Inallcases,thepayoffisSTK,thesameasthepayofffromtheforwardcontract.Thetrader’spositionisequivalenttoaforwardcontractwithdeliverypriceK.
SupposethatFistheforwardprice.IfKF,theforwardcontractthatiscreatedhaszerovalue.Becausetheforwardcontractisequivalenttoalongcallandashortput,thisshowsthatthepriceofacallequalsthepriceofaputwhenthestrikepriceisF.

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