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Contents
PrefaceAboutthisbookAbouttheauthorAcknowledgementsIntroduction
PART1OPTIONSFUNDAMENTALSIntroduction1Thebasicsofcalls2Thebasicsofputs3Pricingandbehaviour4Volatilityandpricingmodels5TheGreeksandriskassessment:delta6Gammaandtheta7Vega
PART2OPTIONSSPREADSIntroduction8Callspreadsandputspreads,oronebyonedirectionalspreads9Onebytwodirectionalspreads10Combosandhybridspreadsformarketdirection11Volatilityspreads12Ironbutterfliesandironcondors:combiningstraddlesandstranglesforreducedrisk13Butterfliesandcondors:combiningcallspreadsandputspreads
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14Thecoveredwrite,thecalendarspreadandthediagonalspread
PART3THINKINGABOUTOPTIONSIntroduction15TheinteractionoftheGreeks16ThecostoftheGreeks17Optionstalk1:technicalanalysisandtheVix18Optionstalk2:tradingoptions19Optionstalk3:troubleshootingandcommonproblems20Volatilityskews
PART4BASICNON-ESSENTIALSIntroduction21Futures,syntheticsandput–callparity22Conversions,reversals,boxesandoptionsarbitrage23Conclusions
QuestionsandanswersGlossaryFurtherreadingIndex
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Thisbookisdedicatedtothememoryofmyparents
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Preface
Whatanoptionis
Thedifferencebetweenacommodity,afuturescontractandanoptionscontractisillustratedinthefollowingthreeparagraphs,whichwilltakeyouaminuteandahalftoread.
Supposeyou’reinthemarketforanorientalrug.Youfindtherugofyourchoiceatalocalshop,youpaytheshopkeeper$500,andhetransferstherugtoyou.Youhavejusttradedacommodity.
Supposeinsteadyouwishtoowntherug,butyouprefertopurchaseitinoneweek’stime.Youmaybeonyourwaytotheairport,ormaybeyouneedtheshort-termuseofyourmoney.Youandtheshopkeeperagree,verballyorinwriting,toexchangethesamerugfor$500oneweekfromnow.Youhavejusttradedafuturescontract.
Alternatively,youmayliketherugonoffer,butyoumaywanttoshoparoundbeforemakingafinaldecision.Youasktheshopkeeperifhewillholdtheruginreserveforyouforoneweek.Herepliesthatyourproposalwilldenyhimtheopportunityofsellingtherug,andascompensation,heasksthatyoupayhim$10.Youandtheshopkeeperagree,verballyorinwriting,thatforafeeof$10hewillholdtherugforyouforoneweek,andthatatanytimeduringtheweekyoumaypurchasethesamerugforacostof$500,excludingthe$10costofyouragreement.You,ontheotherhand,areundernoobligationtobuytherug.Youhavejusttradedanoptionscontract.
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Aboutthisbook
TheFinancialTimesGuidetoOptionsisastraightforwardandpracticalguidetothefundamentalsofoptions.Itincludesonlywhatisessentialtobasicunderstanding.Itpresentsoptionstheoryinconventionalterms,withaminimumofjargon.Itisthorough;notsimplistic.
Thepurposeofthisbookistogiveyouabasisfromwhichtotrademostoftheoptionslistedonmostofthemajorexchanges.Itsprecursor,OptionsPlainandSimple,isusedbytraders,market-makersandbroker-dealers.Itisusedbyinvestmentclubs.Itisusedasatextbookinuniversities.Andithasbeenreadbythosewhoservetheindustry:administrativestaff,accountantsandothers.
Whenyouhavefinishedthisbook,youwillbepreparedforadvancedderivativessubjects,includingquantitativefinance.
Thisbookwillnotmakeyourichin20minutes.Itwill,however,giveyoutoolstomakeprudentinvestmentdecisions.
Likeallinvestmentstrategies,optionsofferpotentialreturnwhileincurringpotentialrisk.Theadvantageofoptionstradingisthatriskcanbemanagedtoagreaterdegreethanwithoutrightbuyingorselling.Thisbookcontinuallydiscussesthelinkbetweenriskandreturn.Itwillhelpyouchoosejustifiableandmanageablestrategies.Readingitwilldevelopanawarenessoftherisksinvolved.
Thisbookistheproductofmytrainingcoursesfornewtraders,brokersandsupportstaff.Mymethodhasbeentestedandrevisedovertheyears.Ithasprovedsuccessfulforthosewhoselivelihoodsdependonthoroughunderstandingandflawlessexecutionundercircumstancesthatallownoerror.BecauseIamanoptionstrader,thestrategiespresentedherearetheverysamethatIhavetradedtimeandagain,daybyday,yearafteryear.
Infact,youandIhavethesamegoals:tomakemoneyandtomanagerisk.
Manytheoreticalconceptsareincluded,butthefocusofthisbookisonpractice,nottheory.Iteachhowtoswingthegolfclub;nothowtodesignit.
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Whileitisimpossibletocoachaninvestoratadistance,itispossibletorecountmanyofthesituationsthatoftenariseinthemarketplace,andtodiscusswaysofapproachingthem.InthisneweditionIhaveaddedmanyexamplesofpracticalapplications,orasitwere,scenariosoranecdotes.
Themathematicsinthisbookinvolveonlyaddition,subtraction,multiplicationanddivision.Thesefourfunctionsplusapricingmodelareallthatweprofessionalsuseinordertotrademostoftheoptionsproductsonthemajorexchanges.
Thefocusofthisbookisoptions:itisnotacomprehensiveguidetotrading.Asprofessionaltradersknow,tradingtechniqueisonlygainedthroughexperience.Forthis,youshouldengageaprofessionaladvisertohelpyoutodecidethebeststrategiestouse.Orbetteryet,[email protected].
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Abouttheauthor
LennyJordanhastrainedcountlesstradersintheoptionsmarketsofChicagoandLondon.Hewasamarket-makerattheChicagoBoardofTrade(CBOT)andattheLondonInternationalFinancialFuturesandOptionsExchange(LIFFE).HenowlecturesforLondon-basedexchangesandinternationalbanks.Hecanbecontactedatlenny@lennyjordan.com.
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Acknowledgements
Theauthorwouldliketothankthefollowingfortheirassistance:
TheChicagoBoardofTradeandtheChicagoMercantileExchange(CBOTandCME)TheChicagoBoardOptionsExchange(CBOE)TheLondonInternationalFinancialFuturesandOptionsExchange(LIFFE)EurexandDeutscheBorsePMPublishingwebsite(pmpublishing.com).MartyO’Connell,oneofthegreattrainers
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Introduction
Whyoptionsareuseful
AwordIoftenhearwhenpeoplearediscussingoptionsis‘risky’.Theothereveningatdinner,aguestmadethesamecomment.Anhourlater,Iwassorrytohearhimsaythathehadrecentlylost84percentofaninvestmentinstocksinemergingmarkets.
Itisanunfortunateandcostlyrealitythatfewinvestorsknowhowtoprotecttheirinvestmentsfromdownsiderisk.Theirsoleinvestmentstrategyistoselectastocktobuy,orafundtobuyinto.Overthelongterm,andifvalueisfoundatthetimeofpurchase,thisstrategymakessense.Unfortunately,ithasn’tmadesensewithmanystocksfrom1999through2009.
Ofcourse,acompetentfinancialadvisercanoutperformtheindexes.Butforthosewhotakeamoreactiveroleintheirinvestments,optionsofferthetwoadvantagesofflexibilityandlimitedrisk.
Callandputpurchasesareexcellentwaysofdevelopingmarketawarenessandbuildingconfidence.Thisisbecausewiththesestrategiestraderscantakeeitherabullishorbearishpositionwhilelimitingtheirmaximumlossattheoutset.Becausethecostofoptionsispaidforupfrontonmostexchanges,theoptionsbuyerisforcedtobemoredisciplinedthanatraderwhomustsimplypostmargin.Andhewon’tbestoppedout.
Becauseoptionshavelivesoftheirown,theyareindicatorsofmarketsentiment.Impliedvolatility,whichwewilldiscuss,oftenanticipateschangesinpriceactivityintheunderlyingcontracts.Simplyknowingaboutoptionscanimprovemarketawareness.
Optionsstrategiesareonly‘risky’when,likeotherinvestments,theirpotentialreturndoesnotjustifytheriskstaken,orwhenthepartiesinvolveddonotknowthefundamentals.Thisbookpresentsasensibleapproachtoprofitopportunitieswithamanageabledegreeofrisk.
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HowtousethisbookThisbookisdesignedforreaderswhosetimeislimited,andforthoseseekingdifferentlevelsofexpertise.Abasicunderstandingofcallsandputs,forthosewhodonotwishtotrade,canbeobtainedbyreadingPart1.Forinvestorswillingtoenterthemarket,Parts1and2provideenoughinformationtotakepositionsundermostmarketconditions.Part3presentsmoresophisticatedwaysofapproachingoptions.Part4coversbasicsthatarenotessentialformostprivateinvestors,butwhichmaybeuseful.Itisrecommendedthatthosewillingtocommitcapitalreadthewholebook.
Eachchapterpresentsexplanatorymaterialfollowedbyasectionwithquestions/examples.Usethelatterasadditionalmaterialfromwhichtolearn;don’texpecttoknowalltheanswersthefirsttimeyougothroughthebook.
Anunderstandingofstocks,bondsorcommoditiesisadvisablebeforeyoustart.Youshouldalsounderstandthesimplemechanicsofbuyingandsellingthroughabrokeroranexchange.Youshouldalsounderstandwhatashortpositionis,andthisisexplainedinPart4.Becausestocks,bondsandcommoditiesareoftentradedasfuturescontracts,abasicexplanationofafuturescontractisgiveninPart4.
Thesubstanceofthisbookisaccessibletoallwhohaveabasicunderstandingofoneoftheprincipalmarketsmentionedabove.Occasionallysubjectsarepresentedthatareataslightlymoreadvancedlevelthantheimmediatecontextinwhichtheyappear.Thesesubjectsarenotdifficult;theymaymerelyrequirerereadingafterlaterportionsofthebookhavebeenassimilated.
Theexamplesinthisbookaredrawnfromexchangelistedproducts.Theseproductsservetheneedsofmostinvestors,andtheirpricesarereportedinmostdailybusinessjournals,ontheinternetandthroughmanydatavendors.Oncetheprinciplesofthisbookareunderstood,youwillbepreparedforforeigncurrencyandOTC(overthecounter)options,aswellasformoreadvancedtopicssuchasexoticoptions.
BecausethisbookisdesignedtohelpUSandEuropeaninvestors,theexampleschosenarefromthesemarkets.IhavetradedmanyproductsintheUSandEurope;alltheoptionsstrategiesdiscussedinthisbookareidentical,andonlythenomenclatureorjargonvaries.
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part1
Optionsfundamentals
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Introduction
Puts
Weencounteroptionsfrequentlyinourdailylives,butweprobablyaren’tawareofthem.Theyoccurinsituationsofuncertainty,andtheyarehelpfulinmanagingrisk.
Forexample,mostofusinsureourhome,ourcarandourhealth.Weprotectthese,ourassets,bytakingoutpoliciesfrominsurancecompanieswhoagreetobearthecostoflossordamagetothem.Weperiodicallypaythesecompaniesafee,orpremium,whichisbasedinpartonthevalueofourassetsandthedurationofcoverage.Inessence,weestablishcontractsthattransferourrisktothecompanies.
Ifbyaccidentourassetssufferdamageandaconsequentlossinvalue,ourcontractgivesustherighttofileaclaimforcompensation.Mostoftenweexercisethisright,butoccasionallywemaynot:forexample,ifthedamagetoourcarissmall,ithasbeenincurredbyourteenageson,andfilingaclaimwouldproduceanundesirableriseinourfuturepremiumlevel.Shouldwefileaclaim,however,ourinsurerhastheobligation,underthetermsofthecontract,topayustheamountofourloss.
Uponreceiptofourpaymentwemightsaythatthecostofouraccidenthasbeen‘putto’theinsurerbyus.Ineffect,ourinsurancecompanyhadsoldusaputoptionwhichweowned,andwhichwehaveexercised.
Inthefinancialmarkets‘puts’,astheyarecalled,operatesimilarly.Pensionfunds,banks,corporationsandprivateinvestorshaveassetsintheformofstocksandbondsthattheyperiodicallyprotectagainstadeclineinvalue.Theydothisbypurchasingputoptionsbasedon,orderivedfrom,theirstocksandbonds.Theseoptionsgivethemtherighttoputtheamountofanasset’sdeclineontotheselleroftheoptions.Theytransferrisk.
Subsequentchaptersexplainhowthisprocessofrisktransferworks,butfornowlet’sturntoanothereverydayuseofoptions.
CallsSupposeweneedtopurchaseawashingmachine.Inourlocalnewspaperwesee
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anadvertisementforthemachinethatwewant.Itis‘onsale’ata20percentdiscountfromalocalretaileruntiltheendoftheweek.Weknowthisretailertobereputableandthatnotricksorgimmicksareinvolved.
Fromourstandpointwehavetherighttobuythismachineatthespecifiedpriceforthespecifiedtimeperiod.Wemaynotexercisethisrightifwefindthemachinecheaperelsewhere.Theretailer,however,hastheobligationtosellthemachineunderthetermsspecifiedintheadvertisement.Ineffect,hehasenteredintoacontractwiththegeneralpublic.
Ifwedecidetoexerciseourright,wesimplyvisittheretailerandpurchaseourwashingmachine.Wemightsaythatwehave‘calledaway’thismachinefromtheretailer.Hehadgivenusacalloptionwhichweacceptedandwhichwehaveexercised.Inthiscaseouroptioniscommonlyknownasa‘call’.Itwasgiventousaspartofthegeneralpublic,freeofcharge.Theretailerborethecostofthecallbecausehehadasupplyofwashingmachinesthathewantedtosell.
Because,underthetermsofthecontract,theretailerisobligatedtosell,hehasalsoincurredarisk.Supposewevisithisshopwithintheweekandfindthatallwashingmachineshavebeensold.Theretailerunderestimatedthedemandthattheadvertisementgenerated,andheisnowshortofsupply.Heandhissalesstaffareanxioustomeetthedemand,andhehashisgoodreputationtouphold.
Ourretailerwillnowtrytorushdeliveryfromadistributor,evenatadditionalcosttohim.Ifnomachinesareavailablethroughthedistributionnetwork,hemaygiveusavoucherforthepurchaseofourmachinewhenmorearrive.
Thisvoucheris,again,acalloption.Itcontainstherighttobuyatthesaleprice,butitsdurationhasbeenextended.Ifinthemeantimethefactoryorwholesalepriceofourmachinerises,theretailerwillstillbeobligatedtosellittousatthesaleprice.Hisprofitmarginwillbecut,andhemayeventakealoss.Thecalloptionthathegaveusmayprovecostlytohim.
Supposethatwebecomeenterprisingwithourvoucher,orcalloption.Earlythenextweekwearetalkingtoourneighbourwhoexpressesdisappointmentathavingmissedthesaleonwashingmachines.Thenewsupplyhasarrived,andthenewpriceisabovetheold,pre-saleprice.Bymissingthesale,hewillneedtopayconsiderablymorethanhewouldhavepaid.We,aftercarefulnegotiationswithourwife,decidethatwecanlivewithouroldmachine.Weoffertosellhimanewmachineforanamountlessthanthenewretailpricebutmorethantheoldsaleprice.Heacceptsouroffer.Wethenreturntotheretailer,exerciseouroption,purchasethemachine,andresellittoourneighbour.Hehasasavingand
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we,includingourwife,haveaprofit.Wearenowoptionstraders.
Callsareasignificantfeatureofcommoditymarkets,wheresupplyshortagesoftenoccur.Adverseweather,strikesordistributionproblemscanresultinunforeseenrisesinthecostsofbasicgoods.Petroleumdistributors,importersandfoodmanufacturersregularlypurchasecallsinordertoensurethattheyhavethecommoditiesnecessarytomeetoutputdeadlines.
OptionsinthemarketsPart1tellsyouwhyoptionsareuseful,andittellsyouhowanoptioncangiveyouanalternativetomakinganoutrightpurchaseorsale.Part1alsolaysdownthefundamentals:whatoptionsdo,howtheyarepriced,theGreeks,volatilityandsubstitutiontrades.Ifyou’regoingtobeinthebusiness,thenyou’dbetterlearnthefundamentals,otherwise,soonerorlater,youoroneofyourclientswilllosealotofmoney.I’veseenithappenmanytimes.
It’spossibletoskipoverthispart,butonlyifyoulimityourtradingtocontractneutralspreadssuchas1×1callandputspreads,andbutterfliesandcondors.ThesearedescribedinPart2.However,it’sbettertoreadPart1–youdon’twanttobecomeoneofthemarketcasualties.
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Thebasicsofcalls
Inthepreviouschapterwesawthatoptionsareusedinassociationwithavarietyofbasic,everydayitems.Theyderivetheirworthfromtheseitems.Forexample,ourhomeinsurancepremiumisderived,naturally,fromthevalueofourhouse.Intheoptionsbusiness,eachofthesebasicitemsisknownasanunderlyingasset,orsimplyan‘underlying’.Itmaybeastockorshare,abondoracommodity.Here,inordertogetstarted,wewilldiscussanunderlyingwithwhichweareallfamiliar,namelystock,bondorcommodityXYZ.
OwningacallXYZiscurrentlytradingatapriceof100.Itmaybe100dollars,euros,orpoundssterling.Supposeyouaregiven,freeofcharge,therighttobuyXYZatthecurrentpriceof100forthenexttwomonths.IfXYZstayswhereitisorifitdeclinesinprice,youhavenouseforyourrighttobuy;youcansimplyignoreit.ButifXYZrisesto105,youcanexerciseyourright:youcanbuyXYZfor100.AsthenewownerofXYZ,youcanthensellitat105orholditasanassetworth105.Ineithercase,youmakeaprofitof5.
Whatyoudobyexercisingyourrightisto‘callXYZaway’fromthepreviousowner.Youroriginalrighttobuyisknownasacalloption,orsimplya‘call’.
Itisimportant,rightfromthestart,tovisualiseprofitandlosspotentialingraphicterms.Figure1.1isaprofit/lossgraphofyourcall,orcallposition,beforeyouexerciseyourright.
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Figure1.1Owningacall
Ifyouchoose,youcanwaitforXYZtorisefurtherbeforeexercisingyourcall.Yourprofitispotentiallyunlimited.IfXYZremainsat100ordeclinesinprice,youhavenolossbecauseyouhavenoobligationtobuy.
OfferingacallNowlet’sconsiderthepositionoftheinvestorwhogaveyouthecall.Bygivingyoutherighttobuy,thispersonhasassumedtheobligationtosell.Consequently,thisinvestor’sprofit/losspositionisexactlytheoppositeofyours.
TheriskforthisinvestoristhatXYZwillriseinpriceandthatitwillbe‘calledaway’fromhim.Hewillrelinquishallprofitabove100.Inthiscase,Figure1.2representstheamountthatisgivenup.
Figure1.2Offeringacall
Ontheotherhand,thisinvestormaynotalreadyownanXYZtobecalledaway.(Rememberourretailerintheintroductiontothispartwhowasshortofwashingmachines.)HemayneedtopurchaseXYZfromathirdpartyinordertomeettheobligationofthecallcontract.Inthiscase,Figure1.2representstheamountthisinvestormayneedtopayforXYZinordertotransferittoyou.Yourpotentialgainishispotentialloss.
BuyingacallObviously,then,theinvestorwhooffersacallalsodemandsafee,orpremium.Thebuyerandthesellermustagreeonapricefortheircallcontract.Supposeinthiscasethepriceagreeduponis4.Acorrectprofit/losspositionforthebuyer,whenthecallcontractexpires,wouldbegraphedasinFigure1.3.
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Figure1.3Buyingacall
Bypaying4forthecalloption,thebuyerdefershisprofituntilXYZreaches104.At104thecallispaidforbytherighttobuypay100forXYZ.Above104theprofitfromthecallequalstheamountgainedbyXYZ.Between100and104apartiallossresults,equaltothedifferencebetween4andanygainsinXYZ.Below100atotallossof4isrealised.Acorrespondingtableofthisprofit/losspositionatexpirationisshowninTable1.1.
Table1.1Buyingacall
Thefirstadvantageofthispositionisthatprofitabove104ispotentiallyunlimited.ThesecondadvantageisthatbybuyingthecallinsteadofXYZ,thecallbuyerisnotexposedtodownsidemovementinXYZ.Hehasapotentialsavings.Thedisadvantageofthispositionisthatthecallbuyermaylosetheamountpaid,4.
Alloptionscontracts,liketheirunderlyingcontracts,havecontractmultipliers.Bothcontractsusuallyhavethesamemultiplier.Ifthemultiplierfortheabovecontractsis$100,thentheactualcostofthecallwouldbe$400.ThevalueofXYZat100wouldactuallybe$1,000.Intheoptionsmarkets,pricesquotedarewithoutcontractmultipliers.
Whentradingoptions,itisimportanttoknowtherisk/returnpotentialatthe
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outset.Inthiscase,thepotentialriskofthecallbuyeristheamountpaidfortheoption,4or$400.Thecallbuyer’spotentialreturnistheunlimitedprofitasXYZrisesabove104.Foradiscussionofanactualrisk/returnscenario,seeQuestion2(concerningUnilever)attheendofthebook.
Callscanbetradedatmanydifferentstrikeprices.Forexample,ifXYZwereat100,callscouldprobablybepurchasedat105,110and115.TheywouldcostprogressivelylessastheirdistancefromthecurrentpriceofXYZincreased.Manyinvestorspurchasethese‘out-of-the-money’calls,astheyareknown,becauseoftheirlowercost,andbecausetheybelievethatthereissignificantupsidepotentialfortheunderlying.
Our100call,withXYZat100,issaidtobe‘atthemoney’.
Inaddition,ifXYZwereat100,callscouldalsobepurchasedat95,90and85.These‘in-the-money’calls,astheyareknown,costprogressivelymoreastheirdistancefromtheunderlyingincreases.Wheretheunderlyingisastock,manyinvestorspurchasethesecallsbecausetheyapproximatepricemovementofthestock,yettheyarelessexpensivethanastockpurchase.Forbothstocksandfutures,thelimitedlossfeatureofthesecallsalsoactsasabuilt-instop-lossorder.
Out-of-the-money,in-the-moneyandat-the-moneycallswillbediscussedinlaterchapters,butfornowlet’sreturntothebasics.
AnexampleofacallpurchaseSupposeGEistradingat18.03,andtheApril18.00callsarepricedat0.58Ifyoupurchasedoneofthesecalls,thebreak-evenlevelwouldbethestrikepriceplusthepriceofthecall,or18.58.IfGEisabovethislevelatexpiration,youwouldprofitone-to-onewiththestock.Below18.00,yourcallexpiresworthless.Between18.00and18.58youtakeapartialloss,equaltothestockpriceminusthestrikepriceminusthecostofthecall.
Table1.2GEApril18.00callprofit/loss
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Ingraphicform,theexpirationprofit/lossissummarisedinFigure1.4.
Figure1.4GE18.00profit/loss
ThecontractmultiplierforGE,andmoststockoptionsattheChicagoBoardOptionsExchange(CBOE),is$100.Therefore,thecostoftheApril18.00call,andyourmaximumrisk,wouldbe0.58×$100=$58.00.Inotherwords,for$58youhavetherighttopurchase100sharesofGEatapriceof$18pershare.Theseshareshaveatotalvalueof$1,800.
SellingacallNowlet’sconsidertheprofit/losspositionoftheinvestorwhosoldyoutheXYZcallfor4.Likethepreviousexample,hisposition,whenthecontractexpires,isexactlytheoppositeofyours(seeFigure1.5).
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Figure1.5Sellingacall
IntabularformthispositionwouldbeasshowninTable1.3.
Table1.3Sellingacall
Consideralsothattherisk/returnpotentialisopposite.Theseller’spotentialreturnisthepremiumcollected,4.Hispotentialriskistheprofitgivenup,ortheunlimitedloss,ifXYZrisesabove104.
TheadvantageforthecallsellerwhoownsXYZisthatbysellingthecallinsteadofXYZ,heretainsownershipwhileearningincomefromthecallsale.ThedisadvantageisthathemaygiveupupsideprofitifhisXYZiscalledaway.ForthecallsellerwhodoesnotownXYZ,i.e.onewhosellsacall‘naked’,thedisadvantageisthathemayneedtopurchaseXYZatincreasinglyhigherlevelsinordertotransferittoyou.Hispotentiallossisunlimited.Forthisreason,itisnotadvisabletosellacallwithoutanadditionalcoveringcontract,eitherapurchasedcallatanotherstrikeoralongunderlying.
Clearly,then,thegreaterrisklieswiththeseller.Throughsellingtherighttobuy,thisinvestorincursthepotentialobligationtosellXYZataloss-takinglevel.Hislossispotentiallyunlimited.Inordertoassumethisrisk,hemust
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receiveajustifiablefee.ThecallsellermustexpectXYZtobestableorslightlylowerwhilethecallpositionisoutstandingor‘open’.
AnexampleofacallsaleAgain,supposethatGEistradingat18.03,andtheApril18.00callsaretradingat0.58.Ifyousoldoneofthesecalls,thenatAprilexpirationthebreak-evenlevelwouldbethestrikepriceplusthepriceofthecall,or18.58.Above18.58youwouldloseone-to-onewiththestock.Below18.00youwouldcollect0.58.Between18.00and18.58youwouldhaveaprofitequaltothestrikepriceminusthestockpriceplusthecallincome.Anexpirationprofit/losstablewouldbeasinTable1.4.
Table1.4SoldGEApril18.00call
Anexpirationgraphofyourprofit/losswouldbeasinFigure1.6.
Figure1.6GE18.00callsite
Again,thecontractmultiplieris$100,andthereforethemaximumprofitonthe
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soldcallwouldbe0.58or×$100=$58.
SummaryofthetermsofthecallcontractAcalloptionistherighttobuytheunderlyingassetataspecifiedpriceforaspecifiedtimeperiod.Thecallbuyerhastheright,butnottheobligation,tobuytheunderlying.Thecallsellerhastheobligationtoselltheunderlyingatthecallbuyer’sdiscretion.Thesearethetermsofthecallcontract.
SummaryoftheintroductiontothecallcontractAcallisusedprimarilyasahedgeforupsidemarketmovement.Itisalsousedtohedgedownsidemovementbecauseit’sanalternativetobuyingtheunderlying.Bybuyingthecallinsteadoftheunderlyingstockorcommodity,etc.youhaveupsidepotentialbuthavelessmoneyatrisk.
Thebuyerandthesellerofacallcontracthaveoppositeviewsaboutthemarket’spotentialtomovehigher.Thecallbuyerhastherighttobuytheunderlyingasset,whilethecallsellerhastheobligationtoselltheunderlyingasset.Becausethecallsellerincursthepotentialforunlimitedloss,hemustdemandafeethatjustifiesthisrisk.Thecallbuyercanprofitsubstantiallyfromasudden,unforeseenriseintheunderlying.Whenexercised,thebuyer’srightbecomestheseller’sobligation.
Bylearningthebasicsofcalloptions,youhavealsolearnedseveralcharacteristicsofoptionsingeneral.Thiswillhelpyoutounderstandthesubjectofthenextchapter,puts.
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Thebasicsofputs
Putoptionsoperateinessentiallythesamemannerascalloptions.Themajordifferenceisthattheyaredesignedtohedgedownsidemarketmovement.Somecommoncharacteristicsofputsandcallsareasfollows:
Thebuyerpurchasesarightfromtheseller,whointurnincursapotentialobligation.Afeeorpremiumisexchanged.Apricefortheunderlyingisestablished.Thecontractisforalimitedtime.Thebuyerandthesellerhaveoppositeprofit/losspositions.Thebuyerandthesellerhaveoppositerisk-returnpotentials.
Aputoptionhedgesadeclineinthevalueofanunderlyingassetbygivingtheputownertherighttoselltheunderlyingataspecifiedpriceforaspecifiedtimeperiod.Theputownerhastherightto‘puttheunderlyingto’theopposingparty.Theotherparty,theputseller,consequentlyincursthepotentialobligationtopurchasetheunderlying.
BuyingputsSupposeyouownXYZ,anditiscurrentlytradingatapriceof100.YouareconcernedthatXYZmaydeclineinvalue,andyouwanttoreceiveasellingpriceof100.Inotherwords,youwanttoinsureyourXYZforavalueof100.YoudothisbypurchasinganXYZ100putforacostof4.IfXYZdeclinesinprice,younowhavetherighttosellitat100.
First,let’sconsidertheprofit/losspositionoftheputitself.Atexpiration,thispositionwouldbegraphedasshowninFigure2.1.
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Figure2.1Buyingaput
Thisgraphshouldappearsimilartothegraphforacallpurchase,Figure1.3.Infact,itistheidenticalprofit/lossbutwithareverseinmarketdirection.Bothgraphsshowthepotentialforalargeprofitattheexpenseofasmallloss.Here,profitismadeasthemarketmovesdownwardratherthanupward.Intabularform,thisprofit/losspositionwouldbeasshowninTable2.1.
Table2.1Buyingaput
Thebreak-evenlevelofthispositionis96.There,thecostoftheputequalstheprofitgainedbytherighttosellXYZat100.Between100and96thecostoftheputispartiallyoffsetbythedeclineinXYZ.Above100,thepremiumpaidistakenasaloss.Below96theprofitontheputequalsthedeclineinXYZ.
AstheownerofXYZ,yourlossisstoppedat96byyourputposition.Thecostoftheputhaseffectivelyloweredyoursellingpriceto96.ButifXYZfallssharply,youhaveasubstantialsavingbecauseyouarefullyprotected.Inotherwords,youareinsured.Inthemeantime,youstillhavetheadvantageofpotentialprofitifXYZgainsinprice.
Thepurchaseofaputoptioncanbeprofitableinitself.Supposethatyoudonot
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actuallyownXYZ,butyoufollowitregularly,andyoubelievethatitisdueforadecline.Justasyoumayhavepurchasedacalltocaptureanupsidemove,younowmaypurchaseaputtocaptureadownsidemove.(Youradvantage,asanalternativetotakingashortpositionintheunderlying,isthatyouarenotexposedtounlimitedlossifXYZmovesupward.)Themostyoucanloseisthepremiumpaid.Figure2.1andtheaccompanyingtable(Table2.1)illustratethepossiblereturnfromyourputpurchase.
Again,notetherisk/returnpotential.Withaputpurchasethepotentialriskisthepremiumpaid,4.ThepotentialreturnisthefullamountthatXYZmaydeclinebelow96.
AnexampleofaputpurchaseSupposeGEistradingat18.03,andtheApril18.00putsaretradingat0.52.Ifyoupurchasedoneoftheseputs,thebreak-evenlevelwouldbethestrikepriceminusthepriceoftheput,or17.48.IfGEisbelowthislevelatexpiration,youwouldprofitonetoonewiththedeclineofthestock.Above18.00,yourputwouldexpireworthless.Between18.00and17.48,youwouldtakeapartialloss,equaltothestrikepriceminusthestockpriceminusthecostoftheput.Atableofyourexpirationprofit/losswouldbeasTable2.2.
Table2.2PurchasedGEApril18.00put
Ingraphicform,yourexpirationprofit/losswouldbeasinFigure2.2.
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Figure2.2Expirationprofit/lossrelatingtoTable2.2
ThemultiplierforstockoptionsattheChicagoBoardOptionsExchange(CBOE)is$100,thereforethecostoftheput,andyourmaximumrisk,wouldbe0.52×$100=$52.
SellingputsNowlet’sconsidertheprofit/losspositionoftheinvestorwhosellstheXYZput.Afterall,youmaydecidethattheputsaleisthebeststrategytopursue.Becausetheputbuyerhastherighttoselltheunderlying,theputseller,asaconsequence,hasthepotentialobligationtobuytheunderlying.
Atexpiration,thesaleoftheXYZ100putfor4wouldbegraphedasinFigure2.3.
Figure2.3Sellingaput
Thispositionshouldappearsimilartothatofthecallsale,Figure1.5.Infact,theprofit/losspotentialisexactlythesame,butthemarketdirectionisopposite,ordownward.
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Intabularform,thisprofit/losspositionwouldbeasshowninTable2.3.
Table2.3Sellingaput
Theputseller’spotentialreturnisamaximumof4ifXYZremainsatorabove100whenthecontractexpires.Between100and96,apartialreturnisgained.Thebreak-evenlevelis96.Below96,theputsellerincursalossequaltotheamountthatXYZmaydecline.
Again,therisk/returnpotentialfortheputsellerisexactlyoppositetotheputbuyer.Thepotentialreturnoftheputsaleisthepremiumcollected,4.ThepotentialriskisthefullamountthatXYZmaydeclinebelow96.
AninvestormaywishtopurchaseXYZatalowerlevelthanthecurrentmarketprice.Asanalternativetoanoutrightpurchase,hemaysellaputandtherebyincurthepotentialobligationtopurchaseXYZatthebreak-evenlevel.Theadvantageisthathereceivesanincomewhileawaitingadecline.ThedisadvantageisthatXYZmayincreaseinprice,andhewillmissabuyingopportunity,althoughheretainstheincomefromtheputsale.Theotherdisadvantageisthesameforallbuyersofanunderlying:XYZmaydeclinesignificantlybelowthepurchaseprice,resultinginaneffectiveloss.
FortheinvestorwhohasashortpositioninXYZ,thesaleofaputgiveshimtheadvantageofanincomewhilehemaintainshisshortposition.ThedisadvantageisthathemaygiveupdownsideprofitifhemustclosehisshortpositionthroughanobligationtobuyXYZ.
Practicallyspeaking,therearefewinvestorswhoadoptthelatterstrategy,althoughmanymarket-makersdo,simplybecausetheysupplythedemandforputs.
Clearlythen,aswithcalls,thegreaterriskoftradingputslieswiththeseller.HemaybeobligatedtobuyXYZinadecliningmarket.Theputsellermust
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thereforeexpectXYZtoremainstableorgoslightlyhigher.Hemustdemandafeethatjustifiesthedownsiderisk.
AnexampleandastrategySupposethatGEis,asbefore,tradingat18.03,andtheApril18.00putsaretradingat0.52.Ifyouaredecidedlybullish,youcouldselloneApril18.00put.Atexpirationyourbreak-evenlevelwouldbethestrikepriceminusthepriceoftheput,or17.48.Above18.00,youwouldcollectthepremium.Below18.00,youwouldbeobligatedtobuythestock,andyourprofit/lossistheclosingpriceofthestockminusthestrikepriceplusthepremiumincome.Atableoftheexpirationprofit/losswouldbeasTable2.4.
Table2.4Expirationprofit/lossforsoldGEApril18.00put
Ingraphicform,theexpirationprofit/losswouldbeasshowninFigure2.4.
Figure2.4GraphofsoldGEApril18.00put
RememberthatifGEdeclinessignificantly,youarestillobligatedtopurchaseitataneffectivepriceof17.48.Bemindfulthatallmarketscandropsuddenly,leavingtheinvestorvirtuallynoopportunitytotakecorrectiveaction.Forthis
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reason,sellingnakedputs,asthisstrategyiscalled,containsahighdegreeofrisk.Apreferredstrategyistheshortputspread,whichisdiscussedinPart2.
Ontheotherhand,supposeyouthinkthatstockinGEwouldbeagoodinvestment.Ifthestockiscurrentlytradingat18.03,youmay,quitereasonably,thinkthataneffectivepurchasepriceof17.48representsgoodvalue.Afterall,thiswouldrepresentadeclineofapproximately3percent,andbearinmindthatyoureceiveanadditional3percentfromthesaleoftheput.YoumaydecidetoselltheApril18.00putasanalternativetobuyingthestock.Ifthestockremainsabove18.00,thenyouarecontenttocollectthe0.52premium.Youmayevendecideonacombinedstrategyofanoutrightstockpurchasewithputsales,i.e.youmightpurchaseanumberofsharesat18.03andsellanumberofApril18.00puts,thereforeaveragingdownthepurchaseprice.
Inordertoapplytheabovestrategyyoumustbeconvincedthatthestockisgoodvalueattheleveloftheeffectivepurchaseprice.Infact,itisnotadvisabletosellnakedputsifyoudonotwishtoownthestockorotherunderlying.Shouldyou,asaresultofemployingthisstrategy,eventuallypurchasethestock,andshouldthestock,asitoftendoes,declinebelowthepurchaseprice,youmustbesecureintheknowledgethatbuyingstockatthelowestpointofamoveisamatteronlyofluck.Fewinvestorsin1932boughtthestocksintheDJIAwhenitwasat41.22.
SummaryofthetermsoftheputcontractAputoptionistherighttoselltheunderlyingassetataspecifiedpriceforaspecifiedtimeperiod.Theputbuyerhastheright,butnottheobligation,toselltheunderlying.Theputsellerhastheobligationtobuytheunderlyingattheputbuyer’sdiscretion.Thesearethetermsoftheputcontract.
AcomparisonofcallsandputsNowthatyou’velearnedhowcallsandputsoperate,itwillbeconstructivetocomparethem.
Thecallbuyerhas the right tobuy theunderlying,consequently thecallsellermayhavetheobligationtoselltheunderlying.Theputbuyer has the right to sell the underlying, consequently theputsellermayhavetheobligationtobuytheunderlying.
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Iftheunderlyingisafuturescontract,theabovetermsaremodified.
The call buyer has the right to take a long position in the underlying,consequently the call seller may have the obligation to take a shortpositionintheunderlying.Theput buyer has the right to take a short position in the underlying,consequentlytheputsellermayhavetheobligationtotakealongpositionintheunderlying.
Ifthesestatementsseemconfusing,bearinmindthattheyarerelatedtoeachotherbysimplelogic:ifoneistrue,thentheothersmustbetrue.Itmaybehelpfultoreviewthegraphsandtablespresented.Asyouworkthroughtheexamplesinthenextfewchapters,familiaritywillhelpcomprehension.
Inconclusion,marketscanbebullish,bearish,orrange-bound,anddifferentoptionsstrategiesaresuitabletoeach.Anyparticularstrategycannotbesaidtobebetterthananyother.Thesestrategies,andthosethatfollow,varyintermsoftheirrisk/returnpotential.Theyaccommodatethedegreeofriskthateachinvestorthinksisappropriate.Itisthisflexibleandlimitingapproachtoriskthatmakesoptionstradingappropriatetomanydifferentkindsofinvestors.
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Pricingandbehaviour
Nowthatyouunderstandthenatureofcallsandputs,youneedtoknowhowtheyarepricedandhowtheybehave.Inthischapteryouwilllearnthatoptionsarebothdependenton,andindependentof,theirunderlyingasset.Theyhavelivesoftheirownbecausetheyaretradedseparatelyashedges.Theyindicatemarketsentiment,ortheoutlookforpricechangesintheunderlying.
PricelevelsWewillbeginwithastraightforwardoptionscontract.Itsunderlyingistheshort-termcostofmoneyintheUS.Table3.1istheEurodollarfuturescontract,tradedattheChicagoMercantileExchange,theCME.1
Table3.1DecemberEurodollaroptions
OnthisdaytheDecemberfuturescontractsettledat94.305,oranequivalentinterestrateof5.695percent.Astheinterestratefalls,thefuturescontractincreases;astheinterestraterises,thepriceofthefuturescontractdecreases.Aninvestorwishingtohedgeariseintheinterestrateto6percentcouldpay0.02forthe94.00put.Aninvestorwishingtohedgeafallintheinterestrateto5.5percentcouldpay0.04forthe94.50call.Thecontractmultiplieris$25,whichmeansthatthe94.50callhasavalueof4×$25,or$100.Thereare132daysuntiltheoptionscontractsexpireon14December.
Thenumberofdifferentoptionscontractslistedisdesignedtoaccommodateinvestorswithdifferentlevelsofinterestrateexposure.Eachlistedpricelevelisknownasastrikeprice,e.g.94.00,94.25,94.50,etc.
Whenanoptionisclosesttotheunderlying,itistermedat-the-money(ATM).Here,boththe94.25callandthe94.25putareat-the-money.Whenacallisabovetheunderlying,itistermedout-of-the-money(OTM),e.g.allthecallsat
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94.50,94.75and95.00.Whenaputisbelowtheunderlying,itisalsoout-of-the-money,e.g.theputsat93.75and94.00.
Whenacallisbelowtheunderlying,itistermedin-the-money(ITM),e.g.thecallsat93.75and94.00.Whenaputisabovetheunderlying,itisalsoin-the-money,e.g.alltheputsat94.50,94.75and95.00.
Generallyspeaking,theoptionsmosttradedarethoseat-the-moneyorout-of-the-money.Ifanupsidehedgeisneeded,thenat-the-moneyorout-of-themoneycallswillwork,andtheyarelesscostlythanin-the-moneycalls.Foradownsidehedge,thesamereasoningappliestoputs.
AspectsofpremiumThepremiumofanoptioncorrespondstoitsprobabilityofexpiringinthemoney.The94.75callandthe94.00putareeachworthonly0.02becausemostlikelytheunderlyingwillnotreachtheselevelsbeforeexpiration.Morespecifically,the0.02valueofeachoftheseistermedthetimepremium.
Thepremiumofanin-the-moneyoptionconsistsoftwocomponents.Thefirstoftheseistheamountequaltothedifferencebetweenthestrikepriceandthepriceoftheunderlying,anditistermedtheintrinsicvalue.Thesecondcomponentisthetimepremium.The94.00call,withtheunderlyingat94.305,isworth0.32;ithasanintrinsicvalueof0.305andcontainsatimepremiumof0.015.
Whenanoptionisdeeplyinthemoney,itwilltradeasaproxyfortheunderlying,anditspremiumwillconsistofintrinsicvalueonly.Thiskindofoptionissaidtobeatparitywiththeunderlying.The93.50call,withavalueof0.805,isatparitywiththeunderlyingat94.305.
Anat-the-moneyoptionwillcontainthemosttimepremiumbecausetherethetwoadvantagestoowninganoptionareequalandgreatest.Acallthatisexactlyat-the-money,whosestrikepriceequalsthepriceoftheunderlying,canprofitfullyfromupsidemarketmovement,lessthecostofthecall.Asanalternativetopurchasingtheunderlying,itcanalsosavethecallbuyerthefullamountthattheunderlyingmaydecline,lessthecostofthecall.Withanat-the-moneycall,thepotentialprofittheoreticallyequalsthepotentialsavings.Anat-the-moneyputhasthesameprofit/savingspotential.
DurationandtimedecayAnotheraspectthatdeterminestheamountofanoption’spremiumis,quite
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reasonably,thetimeuntilexpiration.Along-termhedgewillcostmorethanashort-termhedge.Timedecay,however,isnotlinear.Figure3.1illustratesthatanoptionlosesitsvalueatanacceleratingrateasitapproachesexpiration.
Figure3.1Valueofoptionwithrespecttotime
Anotherwayofstatingthisisthattheproportionofanoption’sdailytimedecaytoitsvalueincreasestowardexpiration.UsingtwooptionsbasedonCornfutures,Table3.2illustratesthisinpercentageterms.
Table3.2DecemberCorncalls2
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DatacourtesyofFutureSource–Bridge;thepercentagecalculationsaretheauthor’s.
Notethattheout-ofthe-moneyoptionentersitsacceleratedtimedecayperiodmuchearlierthantheat-the-moneyoption.Thisistrueforin-the-moneyoptionsaswell.
Tothetraderthismeansthattherisk/returnpotentialalsoaccelerateswithtime.Becausenear-termoptionscostless,theyhavethepotentialtoprofitmorefromanunexpected,largemoveintheunderlying.However,theirtimedecaycanbesevere.Theriskoftimedecayisgreat,butthereturnofsubstantialsavingsorlargeprofitisalsogreat.
Optionswithacceleratedtimedecayarebestutilisedbyprofessionalswhoarecertainoftheiroutlookfortheunderlyingatexpiration.Theriskscanbereducedbyspreading,butformostinvestorsastraightlongcallorputpositionwith2percenttimedecayshouldeitherbeclosedorbe‘rolled’toalatercontractmonth.TradingtimedecayisdiscussedfurtherinPart3.
Interestrates,dividendsandmarginversuscashpaymentItisbesttocheckwiththeexchangewhereyouwishtotradeastowhether
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marginorcashpaymentapplies.Thefollowingaregeneralguidelinesforinterestrateanddividendpricingcharacteristics.Exceptunderspecialcircumstances,interestrateanddividendpricingcomponentsareoutweighedbythevolatilitycomponentofoptions.
FuturesoptionsOnmostexchangesapurchasedoptiononafuturescontractmustbepaidforinfullattheoutset.Accordingly,itspricewillbediscountedbythecostofcarryontheoptionuntilexpiration.Giventhecurrentlowratesofinterest,thisdiscountisminorwhencomparedtootherpricingcomponents.Thisdiscountbecomesgreater,however,withdeepin-the-moneyoptions.
TheLIFFE,however,chargesmarginforpurchasedoptionsonfuturescontracts,andthereforetheinterestonthecashorbondsheldbytheclearingfirmisretainedbytheoptionsbuyer.
Allsoldorshortoptionsonmostexchangeshavemarginrequirementsbecausetheirpotentialrisksaregreaterthanboughtorlongoptions.
StockoptionsThesituationisdifferentforoptionsonstocks.Becauseacallisanalternativetobuyingstock,thecallholderhastheuseofthecashthathewouldotherwiseusetopurchasethestock.Thecostofacallisthereforeincreasedbythecostofcarryonthestockviathestrikepriceoftheoption,untiltheoption’sexpiration.
Becausetheholderofacallonstocksdoesnotreceivedividends,thecostofthecallisdiscountedbytheamountofdividendsforthedurationofthecallcontract.
Forexample,supposeDuPontpaysadividendof$0.35on14December.Thecurrentshort-terminterestrateis5percentasdeterminedbytheDecemberEurodollarfuturescontractat95.00.Thereare60daysuntiltheDuPontoptionsexpireonthethirdFridayofJanuary.TheinterestrateanddividendcomponentsoftheDuPontJanuary55callcanbeestimatedasfollows.Amoreaccuratecalculationisobtainedwithanoptionsmodel.
1. $55×60/360×0.05=$0.46interestaddedtocallprice2. $0.35dividendsubtractedfromcallprice3. $0.46–0.35=$0.11,totaladdedtocallprice
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Notethatthepriceofthestockisnotafactorinthiscalculation.Infact,DuPontwastradingat57atthetimeofthisexample.Thereisadifferenceofopinion,however.Sometradersthinkthatthecurrentpriceofthestockisamoreaccuratebasisfromwhichtocalculatetheinterestratecomponentoftheoption.Practicallyspeaking,thedifferencebetweenthesetwomethodsisnotsignificantunlesstheoptionsarefarout-of-the-moneywithmanydaysuntilexpiration.Again,anoptionsmodelaccountsforthis.Moreimportantwouldbeachangeinthedividendortheinterestrateuntilexpiration.Alsonotethatunlessspecialcircumstancesoccurwithrespecttodividendsandinterestrates,thesepricingcomponentsarefarlesssignificantthanthevolatilitycomponent.
Putsonstockshavetheoppositepricingcharacteristicstocallswithrespecttocostofcarryanddividends.Purchasedcallsandputsonstocksarepaidforincashup-frontonmostexchanges.Soldorshortoptions,however,aremarginedbecauseshortcallsincurpotentiallyunlimitedrisk,andshortputsincurextremerisk.
OptionsonstockindexesAstockindexisaproxyforallthestocksthatcompriseit.Callsandputsonastockindexarepricedaccordingtothecostofcarryoftheindex,andtheamountofdividendscontainedintheindex.Thecostsofcarryanddividendsareaddedanddiscountedinthesamemannerasoptionsonindividualstocks.Theseoptionsarealsopaidforincash.
LongandshortoptionspositionsInpractice,onceacallorputisbought,itisconsideredtobealongoptionsposition.‘I’mlong10,June550puts,’youmightsay.Conversely,acallorputsoldisconsideredtobeashortoptionsposition.‘I’mtooshortformyowngood,’meansthatyouhavesoldtoomanycallsorputs,orboth,foryourpeaceofmind.
Itmaybehelpfultothinkthatwhentheterms‘long’and‘short’areappliedtooptions,theydesignateownership.Thesametermsappliedtoapositionintheunderlyingdesignateexposuretomarketdirection.Tobeshortputsistobelongthemarket,i.e.youwantthemarkettomoveupward.Thefollowingchapterondeltasclarifiesthis.
Exerciseandassignment
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Inpractice,mostoptionsarenotheldthroughexpiration.Theyareclosedbeforehandbecausetheholdersofoptionsdonotwanttotakedeliveryoftheunderlyings.Theexceptionsareoptionsonstockindexesandoptionsonshort-terminterestratecontractssuchasEurodollars.Inthesecontracts,nodeliveryofanunderlyingisinvolved.
Longandshortoptionspositionsthatareinthemoneyatexpirationwillbeconvertedintounderlyingpositionsthroughexerciseandassignment,respectively.Theclearingfirmsmanagethisprocedure.TheresultingpositionsaresimilartothosestatedattheendofChapter2underacomparisonofcallsandputs(page24).Thereareslightdifferencesforeachtypeofcontract.
StocksThroughexercise,theholderofalongcallwillbuy,atthestrikeprice,thenumberofsharesintheunderlyingcontract.Throughassignment,theholderofashortcallwillselltheshares.Iftheshortcallholderdoesnotownstocktosell,hewillbeassignedashortstockposition.
Throughexercise,theholderofalongputwillsell,atthestrikeprice,thenumberofsharesintheunderlyingcontract.Ifthelongputholderdoesnotownsharestosell,hewillbeassignedashortstockposition.Throughassignment,theholderofashortputwillbuytheshares.
FuturesThroughexercise,theholderofalongcallwillacquire,atthestrikeprice,alongfuturespositionintheunderlying.Throughassignment,theholderofashortcallwillacquireashortfuturespositionatthestrikeprice.Onmanyfuturesexchanges,anoptionscontractexpiresonemonthbeforeitsunderlyingfuturescontract.
Forexample,expirationforoptionsonNovembersoybeansattheChicagoBoardofTrade(CBOT)normallyoccursonthethirdFridayinOctober.IfonthedayofexpirationtheNovemberfuturescontractsettlesat552,thentheholderofalongNovember550callwillexercisetoalongNovemberfuturespositionatthepriceof550.TheholderofashortNovember550callwillbeassignedashortNovemberfuturespositionatapriceof550.Inthiscasetheformerlongcallholderobviouslyhasacreditof2,buthemayhaveoriginallypaidmoreorlessthanthatforhisNovember550call.
Throughexercise,theholderofalongputwillacquire,atthestrikeprice,ashortfuturespositionintheunderlying.Throughassignment,theholderofashortput
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willacquirealongfuturespositionatthestrikeprice.
Forexample,ifonthedayofexpirationtheNovembersoybeansfuturescontractsettlesat552,thentheholderofalongNovember575putexercisestoashortNovemberfuturespositionatapriceof575.TheholderofashortNovember575putisassignedalongNovemberfuturespositionat575.The23creditfortheformerlongputholderisnoindicationofthepriceatwhichheoriginallytradedtheoption.
Cashsettledcontracts:stockindexesandshort-terminterestratecontractsThroughexercise,theholderofalongcallwillreceivethecashdifferentialbetweenthepriceoftheindexorunderlyingandthestrikepriceofthecall.Throughassignment,theholderofashortcallwillpaythecashdifferential.
Forexample,ifatexpirationtheOEXsettlesat527.00,theholderofanexpiringlong525callpositionreceives2.00,whiletheholderofanexpiringshort525callpositionpays2.00.ThecontractmultiplierfortheOEXis$100,sointhiscase$200changeshands.
Throughexercise,theholderofalongputwillreceivethecashdifferentialbetweenthestrikepriceoftheputandthepriceoftheindexorunderlying.Throughassignment,theholderofashortputwillpaythecashdifferential.
Forexample,ifatexpirationtheOEXsettlesat527.00,theholderofanexpiringlong530putpositionreceives3.00,whiletheholderofanexpiringshort530putpositionpays3.00.
Thesameproceduresapplytoshort-terminterestratecontractssuchasEurodollarsandShortSterling.Forexample,ineitherofthesecontractsifanoptionsettlesonetickinthemoney,thenthelongiscreditedwithoneticktimesthecontractmultiplier,andtheshortisdebitedoneticktimesthecontractmultiplier.ThemultiplierforEurodollarsis$25,andthemultiplierforShortSterlingis£12.50.
PinriskPinriskisrare,butitisimportanttoknowaboutit.Occasionally,optionsexpireexactlyat-the-money,i.e.theunderlyingequalsthestrikepriceatthetimeofexpiration.Wesaythattheseoptions,boththecallandtheput,arepinned.Thiscausesaproblemforoptionsonstocksandoptionsonfuturescontracts,butnot
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foroptionsonstockindexesandshort-terminterestratefuturescontracts.
Whilethereisnoimmediateprofittobemadefromexercisingtheseoptions,thosewhoholdthemmayhaveashort-termdirectionaloutlookfortheunderlyingthatwarrantsexercisingthem.
Forexample,iftheexpirationpriceofXYZis100,theownerofa100callmayexercisebecausehethinksthatXYZwillincreaseinpriceduringthenexttradingsession,orhemaysimplywanttoownitwhileriskingashort-termdecline.Theownerofa100putmayexercisefortheoppositereasons.
Theproblemlieswiththeholderofashortpositionineitheroftheseoptions.HemayormaynotbeassignedapositioninXYZ.Theassignmentprocessiscarriedoutonarandombasisbytheclearingfirms.Iftheshortoptionholderisassigned,hewillbenotifiedbytheopeningofthenexttradingsession.IfasusualhedoesnotwanttokeepapositioninXYZ,hewillneedtomakeanoffsettingbuy/selltransactionattheopening.Ifthemarketopensagainsthim,hewillcoverhispositionataloss.
ThereisnopinriskwithcashsettledindexoptionssuchastheOEXandtheFTSE-100becausewiththesecontractsthereisnounderlyingfuturescontractorquantityofsharestobeassigned,ortoexerciseto.Thesameistrueofmostshort-terminterestratecontractssuchasEurodollarsandShortSterling.
HowtomanagepinriskIfyouareshortanoptionthatisclosetotheunderlyingwithaweekuntilexpiration,itisadvisabletobuyitbackratherthanringthelastamountoftimedecayfromitandriskanunwantedpositionintheunderlying.Ifyouwaituntilthemorningofexpiration,youmayfindthatyouarejoinedbyotherswiththesameposition,andyoumaybeforcedtopayuptogetout.
EuropeanversusAmericanstyleAnoptionisEuropeanstyleifitcannotbeexercisedbeforeexpiration.Theonlywaytoclosethisstyleofoptionbeforeexpirationistomaketheopposingbuy/selltransaction.OneexampleistheSPXoptionsontheStandardandPoor’s500Index(S&P500)tradedattheCBOE.AnotherexampleistheESXoptions(atthe25and75strikes)ontheFinancialTimes100Index(FTSE-100)tradedattheLondonInternationalFinancialFuturesandOptionsExchange(LIFFE).
AlsoavailableistheAmerican-styleoption,whichcanbeexercisedatanytime
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beforeexpiration.Ifsuchanoptionbecomessodeeplyin-the-moneythatittradesatparitywiththeunderlying,thenithasserveditspurposeandrepresentscashtiedup.Asaresult,itcanbesold,oritcanbeexercisedtoapositionintheunderlyingstockorfuturescontract.Inthecaseofastockindex,suchastheOEX,itcanbeexercisedforthecashdifferential.MoststockoptionsandfuturesoptionsareAmericanstyle.
Black–ScholesandothermodelsTheBlack–Scholesoptionspricingmodelwasthefirsttosucceed.Byitselfitpracticallycreatedanindustry.Itassumesthattheoptionishelduntilexpiration.ThismodelisthereforeappropriateforEuropean-styleoptions,butitislessappropriateforAmerican-styleoptions.Forindexoptionssubjecttoearlyexercise,itmustbe,andhasbeen,modifiedsignificantly.
Mostoptionsmodelsassumethatvolatilityisconstantthroughexpiration,whichitseldomis.Thisbringschallengestobothoptionsbuyersandoptionssellers.Thesechallengesarediscussedlaterinthischapter.
Formoreonmodelsandtheirassumptionspleaserefertothereadinglistgivenattheendofthebook.
EarlyexercisepremiumBecauseAmerican-styleoptionscanbeexercisedbeforeexpiration,thosein-the-moneywilloftencontainanadditionalearlyexercisepremium.Thisisnotasignificantamountformostoptionsonfuturescontracts.Itismoresignificantforputsonindividualstocksbecausetheycanbeexercisedtosellstockandasaresult,interestisearnedonthecash.
Earlyexercisepremiumisahighlysignificantamountforin-the-moneyindexoptionssuchastheOEXoptionsontheS&P100tradedattheCBOE.Thereasonisthatattheendofeachtradingsession,thiscontractclosesatadifferenttimefromitsindex.Theirin-the-moneyoptions,especiallytheirputs,canbedriventoparitywiththecashindex,andcanthenbecomeanexercise.Tobeassignedinthismanneroftenresultsinaloss.Itisadvisablenottosell,orhaveashortpositionin,thein-the-moneyoptionsofthisandsimilarcontracts.
Conversely,becauseofthepotentialforearlyexercise,longout-of-the-moneyorat-the-moneypositionsintheabovetwocontractscanprofitsignificantly.Astheseoptionsbecomein-the-money,theirearlyexercisepremiumincreases
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drastically.Holdersoftheseoptionsthenprofittwofold.
Atrader’sstoryThisbringstomindastoryconcerningriskandearlyexercisepremium.
IhaveapersonalrulewithAmericanstyledindexoptions,andthatisalwaystocoverashortpositionwhenitbecomes0.50delta.ImadethisruleafteroneortwoincidentswhenIwasshorttheformerFTSE-100Americanstyledoptions3andtheywentdeepin-the-moneyonme.Theirearlyexercisepremiummounted,andIbecamereluctanttopayupinordertobuythemback.Ilostmoresleepthanusual,andtheneventually,afewdaysorweekslater,theybecameanexerciseattheclose.Asaresult,Ilostmyhedge,i.e.Iwasnolongerdeltaneutral,whichiswhatallmarket-makersstrivetobe.Thenextmorningattheopening,themarketmovedagainstmeandItookaloss.
Oneortwoincidentssuchasthisarenotserious,butIcouldseethepotentialforseriousdamageinahighlyvolatilemarket.ItwasthenthatIdecidedonmyrule.Subsequently,IpaidupwheneverIhadashortpositionthatwentto0.50deltas.Thiswasn’toften,butitseemedasifitwasbecauseitalwayscostme.Anyway,thatwasthepriceofagoodnight’ssleep,orjustabetternight’ssleep.
Ayearorsolater,duringmid-1997,theemergingmarketcrisisstartedtodevelop.Atfirst,theUSseemedtoignoreit,andthatheldLondonup.Still,IthoughtitwastimetobuyalittleextrapremiumincasetheUSchangeditsmind.Theextrapremiumcostmeintimedecay,especiallybecausetheFTSEimpliedwasaround20percent.Inthebackofmymindwas,andalwaysis,19October1987.
InOctober1997theUKmarketstartedtoweakenbecauseofitsexposuretoHongKong,andonedaytowardstheclose,Ifoundmyselfshortanumberof4800putswhichwereat-the-money,or0.50deltas.Aruleisarule,Isaid,whichwassomeconsolationfortheamountIpaiduptobuythemback.IwasnowlongerpremiumthanIgenerallyliketobe,andbecausewewereattheclose,IknewIwasgoingtobearthecostofthetimedecay.
ThatnighttheUScracked.Thenextmorning,theBBCnewswascallingforseriouslossesinLondon,andIknewthereweregoingtobecasualtiesattheopening.Iarrivedearlyattheoffice,andIhadmyclerksdoanextensiveriskanalysis,thoughIknew,asallmarket-makersdo,thatatatimelikethis,optionstheorytakesabackseat.Iwenttothefloorandwedgedmywayintothecrowd,andIwaited,knowingthatIwascovered.
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Thebellsoundedandtheshoutingbegan,andafterafewbriefstopstheFTSElandedat4400.Thetraderswhowereshortoptionswerescreamingtobuythemback,payinganypricefromthosewillingtosell.Theimpliedvolatilityleapedto70percentbeforesettlingdowntoacool50percentaftertheopening.Imadefewtradesthatday,buttheyweretheonesIwantedtomake.Ihadmybestdayever.
Onelessonfromthisisobvious.Makeaplantocoveryourriskandsticktoit.Yourgoalhereisnottomakemoneybuttoavoidtakingaseriousloss.HadInotcoveredmyshortoptionsoverthecourseofayearormore,Iwouldhavebeenoneofthecasualties.Myprofitonthatdaymorethanoffsetallmydaysofpayingup.
Anotherlessonisthatbycoveringrisk,youleaveyourmindcleartodealwiththecircumstanceathand.Youcanmakerationaltradingdecisions.Thisisequallytrueforanextraordinaryeventorforamoreroutinetradingday.
____________1Becausecurrentshort-terminterestratesareatunsustainablylowlevels,thisexampleisleftatamorehistoricallevel.Itstillservestheneedofthisdiscussion.
2Corniscurrentlytradingmuchhigher,butthisexamplecanstillbeappliedtoitandotheroptionsproducts.
3Theseoptionsarenolongerlisted.
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Volatilityandpricingmodels
Themostsophisticatedandthemostsignificantaspectofoptionspricingisthatofvolatility.Afterall,theprimarypurposeofoptionsistohedgeexposuretomarketvolatility.Increasedmarketvolatilityleadstoincreasedoptionspremiums,whiledecreasedmarketvolatilityhastheoppositeeffect.Althoughathoroughreviewofvolatilityinvolvesastudyofstatistics,alayman’sexplanationispracticalandsufficientforthepurposeoftradingoptions.
Volatilityisgenerallydescribedintermsofnormalpricedistribution.Onmostdays,anunderlyingsettlesatapricethatisnotverydifferentfromthepreviousday’ssettlement.Occasionally,thereoccursalargepricechangefromonedaytothenext.Onecansafelysaythatthegreaterthepricechange,thelessfrequentitsoccurrencewillbe.
Atypicalsetofpricechangesforanunderlyingcanbegraphedwithabellcurve(seeFigure4.1).
Figure4.1Lowvolatility
Thebellcurveplaceseachday’sclosingpriceatthecentre,andplotsthenextclosingday’spricetotherightorleft,dependingonwhetherthenextday’spriceisupwardordownward,respectively.Thex-axisdenotesthemagnitudeofthepricechanges,andthey-axisdenotestheirfrequency.
Someunderlyingcontractsroutinelyhavegreaterdailypricechangesthan
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others.Theyaresaidtobemorevolatile.Inthesecasestheirbellcurvesindicategreaterpricedistributionbyexibitingalower,flattercurve.Aparticularcontractmayalsoundergoperiodsofhighervolatility.InbothcasesthebellcurvebecomesmoreliketheexampleshowninFigure4.2.
Figure4.2Highvolatility
Thebellcurveisahelpfulwayofvisualisingtheconceptofvolatility.Itillustratestheneedforhigheroptionspricesduetohighervolatility.
Normalpricedistributionissimilartowaitingforpublictransport.Innormalcircumstances,thebusappearsshortlybeforeorafteryouarriveatthebusstop.Occasionally,thepreviousbushasalreadydepartedsometimeago,andthenextbusarrivesatthestopjustasyoudo.Atothertimes,youjustmissthebus,andyouneedtowaitlongerthanusual.
Unfortunately,normalcircumstances,likenormalmarkets,arethemselvesunusual.Arrivalsanddeparturesaresubjecttoavarietyoftraffic,weatherandprofessionalcomplications,makingitdifficulttoanticipatebusmovements.Sometimes,thestreetisbumpertobumperwithbuses.Atothertimes,youmaywaitfor20ormoreminutesintherain,andthenfindyourselfpassedbyabuswithasignthatsays‘OutofService’.Atthesetimesyouareattheendsofthebellcurve.
Therearetwotypesofvolatilityusedintheoptionsmarkets:thehistoricalvolatilityoftheunderlying,andtheimpliedvolatilityoftheoptionsontheunderlying.
Historicalvolatility
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Thehistoricalvolatilitydescribestherangeofpricemovementoftheunderlyingoveragiventimeperiod.If,foracertaintimeperiod,anunderlying’sdailysettlementpricesarethreetofivepointsaboveorbelowitspreviousdailysettlementprices,thenitwillhaveagreaterhistoricalvolatilitythanifitssettlementpricesareonetotwopointsaboveorbelow.Historicalvolatilityisconcernedwithpricemovement,notwithpricedirection.
Properlyspeaking,volatilityitselfiscalculatedasaone-day,onestandarddeviationmove,annualised.Theannualisedfigureisusedincomputinghistoricalvolatility.Forexample,astock,bondorcommoditywithavolatilityof20percenthasa68percentprobabilityofbeingwithina20percentrangeofitspresentpriceoneyearfromnow;andithasa95percentprobabilityofbeingwithina40percentrangeofitspresentpriceoneyearfromnow.IfXYZiscurrentlyat100andthecurrenthistoricalvolatilityis20percent,thenwecanbe68percentcertainthatitwillbebetween80and120oneyearfromnow.Wecanbe95percentcertainthatXYZwillbebetween60and140oneyearfromnow.
Mosttradingfirmshavemathematicalmodelstocalculatevolatility,butformostunderlyingsthereisasimplifiedwaytocalculateanannualisedvolatilitybasedonaday’spricemovement.
Anannualisedvolatilityforanunderlyingcanbecomputedbymultiplyingtheday’spercentagepricechangeby16.1Forexample,ifXYZsettlesat100,andthenextdayitsettlesat102:2/100=2%.2%×16=32%annualisedvolatility.NotethatifonthefollowingdayXYZretracesto100:2/102=1.96%.1.96%×16=31.36%annualisedvolatility.
Thiswayofcalculatingvolatilityis,asmentionedbefore,simplified,butitwillprovideinsightintohowpricechangesandthevalueoftheunderlyingaffectthevolatilitycalculation.Theaboveformulaisinsufficientforshort-terminterestratecontractssuchasEurodollars,wherethevolatilitycalculationshouldbebasedonthechangeintheyieldorinterestrate,andnotonthechangeintheunderlyingfuturescontract.
Volatilityfluctuatesfromdaytoday,butoveratimeperioditoftentrendsupordown,orremainsinarange.Inordertoputdailyvolatilityfluctuationsinperspective,theyareaveragedintotimeintervalsof10,20,30daysormore.Thisprocessofaveragingcreatesausefulhistoricalvolatility.Itissimilartothemorefamiliarmovingaverageofdailysettlementprices.
Becausemarketsfrequentlychangetheirvolatilitylevels,andbecauseoptions
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areshort-terminvestments,manytradersusea20-dayaverageinordertocomputetheirhistoricalvolatility.Forlonger-termoptionsitisbeneficialtoexaminethe20-dayhistoricalvolatilityoverlongertimeperiods,perhapsayearormore.Inmarketsthatareundergoingasuddenchangeofvolatility,afive-dayaverageorlessmaybeusedfornear-termcontracts.Itisparticularlyusefultoknowwhatacontract’shistoricalvolatilitycanbeunderextraordinarycircumstances,bothactiveandquiet.SeeFigure4.3foranexample.
Figure4.3ChartofhistoricalvolatilityofFTSE-100indexcomparedtodailypricechanges,January–November1998Source:FutureSource–Bridge.
PricingmodelsOncethehistoricalvolatilityisknown,itbecomesaninputforanoptionspricingmodel.TheprimarymodelusedintheoptionsindustryistheBlack–Scholesmodel;almostallothermodelsusedarevariationsofit.Thismodelhasbeenrevisedoverthepast35yearsorsoinordertopriceoptionsondifferentunderlyings,butitremainsthefoundationofthebusiness.2
Theotherpricinginputsarethosealreadydiscussed:
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strikepriceoftheoptionpriceoftheunderlyingtimeuntilexpirationshort-terminterestratedividendsvolatility,historicalorimplied.
Withtheseinputsthemodelyieldsanoptionpricewhichcanbecomeabasisfromwhichtotrade.Ifwecomparethisoptionpricetoitscurrentmarketprice,however,wewillprobablyfindadiscrepancy.Thereasonforthisissimplyadifferencebetweentheoryandpractice.
ImpliedvolatilityAlthoughatheoreticalvalueforanoptioncanbedeterminedbythehistoricalvolatility,anoption’smarketpriceisdeterminedbysupplyanddemand.Anoptionsmarketaccountsforpastpricemovement,butitalsotriestoanticipatefuturepricemovement.Themarketpriceofanoption,then,impliesarangeofexpectedpricemovementsfortheunderlyingthroughexpiration.
Ifweinsertthemarketpriceoftheoptionintothepricingmodel,andifwedeletetheformerhistoricalvolatility,themodelsubstitutesanothervolatilitynumber,theimpliedvolatilityoftheoption.
Thisimpliedvolatilitycanthenbeusedastheimpliedvolatilitytocalculatemarketpricesofoptionsatotherstrikepriceswithinthesamecontractmonth.Asaresult,marketpricesofoptionsspreadscanalsobecalculated.
Forexample,iftheDecemberCornfuturescontractisat220,3andtheDecember220calls,with60daysuntilexpiration,arepricedat7($350),anoptionsmodelcancalculatethatthesecallshaveanimpliedvolatilityof20percent.Ifthedemandfortheseoptionsbidsuptheirpriceto10.5($525),whileatthesametimethepriceoftheunderlyingandthedaysuntilexpirationremainconstant,themodelwillcalculatethattheyhaveanimpliedvolatilityof30percent.
Ifdemandhasbidupthe220calls,thenthe240callsarealsoworthmorebecausetheyareahedgeforunderlyingpricemovementaswell.Thelasttradedpriceofthe240callsmayhavebeen1.375butthatwasbeforethe220callsbecamebidup.Supposewewanttoestimatethenewtheoreticalvalueforthe240calls.
Ifweknowthatthe220callshaveincreasedtheirimpliedto30percent,wecan
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assumethattheimpliedforalltheoptions,includingthe240calls,hasincreasedto30percent.4Wecanassumethisbecausethemarketisimplyinganewvolatilityfortheunderlyingthroughexpiration,andalltheoptionswillbepricedtoaccountforit.
Wetheninsertthe30percentimpliedintotheoptionsmodel,andityieldsapriceof3.375($193.75)fortheDecember240calls.
Youcanexperimentwiththeeffectofimpliedvolatilitychangesonoptionspricesbyusinganoptionscalculator.Severaloptions’websites,includingcboe.com,offeroneofthese.Infact,anyonewhoseriouslywantstolearnabouttheeffectsofalltheoptionsvariablesonoptionspricesshouldspendaminimumofseveralhourswiththisdevice.
ComparinghistoricalandimpliedvolatilityHistoricalandimpliedvolatilitymoveintandem;theyseldomcoincide.Figure4.4comparesthehistoricalandimpliedvolatilitiesforJanuaryCrudeOil,tradedattheNewYorkMercantileExchange(NYMEX).5Here,thedottedlineisthehistoricalvolatilityandthesolidlineistheimpliedvolatility.
Figure4.4Historicalandimpliedvolatilities,JanuaryCrudeOil1998Source:pmpublishing.com.
Thischartcanbeinterpretedinatleasttwoways.Becauseitisanindicatorofexpectedpricemovementfortheunderlying,theimpliedvolatilitycanbeseenastheleaderofhistoricalvolatility.Conversely,thehistoricalvolatilitycanbeseenasthetrendvolatilityoftheunderlying,towhichmovementsintheimpliedvolatilityeventuallyreturn.Again,thiskindofanalysisissimilartothatassociatedwithmovingaveragesandtrendlines.Thestudyofvolatilityisaform
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oftechnicalanalysis.
ConventionalusageAlthoughitisconfusing,intheoptionsmarketstheterm‘volatility’canrefertothedaily,historical,orimpliedvolatility.Butwhenanoptionstradersays‘Exxon’sat20percent,’heisreferringtotheimpliedvolatilityofthefront-month,at-the-moneycallandput.ThisisthebasisoftheVixcontractattheCBOE.
Risk/returnBynow,itshouldbeapparentthatvolatilitycanbetradedinitsownright,independentlyofmarketdirection.Therearemanyapproachestothis,andseveralarediscussedinlaterchapters.Fornow,bearinmindthatifthevolatilityofanunderlyingcontractincreasesordecreases,thevolatilitycomponentofanoptionwilllikelyincreaseordecreaserespectively.
Becausevolatilitycantrend,thereisarisk/returnpotentialassociatedwithvolatilitydirection.Likemoreconventionalkindsofdirectionaltrading,anoptionstradercantakeapositionthatfollowsthevolatilitytrend,ornot.Theoptionsbuyerisactuallyavolatilitybuyer,whiletheoptionsselleristheopposite.
Forthevolatilitybuyer,thepotentialreturnistheincreasedvolatilitycomponent,ortimepremium,oftheoptionastheunderlyingbecomesmoreactive.Hecanprofitsignificantlyiftheunderlyingmakesanunexpected,largemove.Thevolatilitybuyer’smajorriskisthattheunderlyingmaysuddenlycometoahalt,andthatoptionspremiumscollapse.
Forthevolatilityseller,thepotentialreturnisthedecreasedvolatilitycomponentoftheoptionastheunderlyingbecomeslessactive.Hecanprofitsignificantlyiftheunderlyingquicklysettlesintoarange.Thevolatilityseller’smajorrisk(andnightmare)isthatanunexpectedeventwillcausetheunderlyingtomovesharplywhileoptionspremiumsexplode.
Themainproblemforoptionstradersistoanticipatechangesinvolatility.Itiscomparabletotheproblemofpricedirectionforstockorcommoditytraders.
TradersandthebellcurveThebellcurvecanbeausefulreferencewhenevaluatingyourperformance.
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PleaserefertoFigures4.1and4.2earlier.Imaginethatprofitabledaysfalltotherightoftheverticaldottedline(themean)whilelossdaysfalltotheleft.
Nowlet’sassumethatyou’vesurvivedyourfirstyearorso,andthatyou’veestablishedatradingstyle.SometradershaveP/LswingslikethecurveinFigure4.1:theyarenipandtucktraders.Theytrytomakesmallprofitsandtakesmalllosseswhileearningagoodliving.Theirresultsarenotspectacular,buttheydon’ttakealotofriskeither.
OthertradershaveP/LswingslikethecurveinFigure4.2.Theytakemorerisk.Ontheprofitdaystheyarehandsomelyrewarded.Onlossdays,theyhavetheirriskmanagersemailingtheirrésumés.
AlltradershaveoccasionallargeP/Lswings,i.e.furtherfromthemean.Justbecauseatradermakesalargeprofitdoesn’tnecessarilymeanthathe’sahero,andconversely,ifhetakesabigloss,itdoesn’tmeanthathe’sabum.Tradersarelikeunderlyingcontracts:theyhaveprofitswingsthatresemblestandarddeviationmoves.
Manypeopleintheindustry,including,itseems,seniormanagementofsomeverylargebanks,insurancefirmsandhedgefunds,don’thaveapracticalunderstandingofthebellcurve.Keepthebellcurveinmind.
AfinalnoteThevolatilitycalculationisbasedonstatisticalanalysisofassetpricemovement.Ithasthebenefitofagreatdealofdata,butlikeanyotherformofanalysis,itcannotpredictthefuture.Ultimately,itisthemostcomprehensivemeansofdeterminingthevalueofanoption.
Athoroughunderstandingofvolatilityrequiresresearchandexperience,butevenabasicunderstandingcanbeprofitablefortheoptionstrader.Youmaywishtorereadthischapterasyouworkthroughthisbook.
____________116istheapproximatesquarerootof250,theapproximatenumberoftradingdaysinayear.2Therearemanybooksthatdiscussthedifferencesbetweenoptionsmodels.Needlesstosaythistopicrequiresanextensivemathsbackground.Seethebibliographyforrecommendedreadings.
3Cornisnowpricedmuchhigher,butthisexamplestillholdstrue.4Thisassumptionbecomesmodifiedwithrespecttovolatilityskews,whicharediscussedinPart3.5Agreatchartfromthestartofthebullmarketincommodities.Itshowsperfectlyhowtheimplied
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volatilitycananticipateanincreaseinthehistoricalvolatility.
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TheGreeksandriskassessment:delta
Becausethereareseveralcomponentsthatcontributetothepriceofanoption,itisessentialtounderstandhoweachofthesecomponentscanbeaffectedbychangesinthemarket.Short-terminterestratesanddividends,especiallywithrespecttoastockindex,arefairlypredictable.Thethreemajorvariablesthataffectanoption’spriceare:
achangeintheunderlyingthepassageoftimeachangeintheimpliedvolatility.
Optionstheoryisabletoquantifyexposuretothesevariables.Thetermsthatareappliedtothecalculationsareborrowedfromothermathematicalfields,andtheyareGreek:
deltaandgammaexpressexposuretoachangeintheunderlyingthetaexpressesexposuretothepassageoftimevegaexpressesexposuretoachangeintheimpliedvolatility.
‘TheGreeks’,astheyarecalled,areinvaluableaidesindeterminingtherisk/returnpotentialofanoptionsposition.Theyarethefundamentalparametersofriskassessment.
DeltaDeltaistheamountthatanoptionchangeswithrespecttoasmallchangeintheunderlying.
Ifanoptionissodeeplyin-the-moneythatitisatparitywiththeunderlying,itspricewillchangeoneforonewiththeunderlying.Itsdeltaistherefore1.00.Tradersoftensaythatthisoptionhasa‘one-hundreddelta’becauseithasa100percentcorrelationwiththeunderlying.
Anoptionthatisat-the-moneychangespriceathalftherateoftheunderlying,
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andthereforehasadeltaof0.50.Tradersoftensaythatthisoptionhasa‘fiftydelta’.
Inanextremecase,anoptionmaybesofarout-of-the-moneythatitisvirtuallyworthless.Practicallyanychangeintheunderlyingcannotaffectitsprice.Itsdeltaistherefore0.00.
Table5.1givesatypicalexampleofasetofoptionswiththeirdeltasforonecontractmonth:
DecemberCornat$3.8090daysuntilexpirationImpliedvolatilityat30percentInterestrateat3percentOptionsmultiplierat$50,somultiplycallandputvaluestimes$50.
Table5.1DecemberCornat380
Strike
Callvalue×$50
Calldelta
Putvalue×$50
Putdelta
320
63.00
0.90
3¼
0.10
340
47.00
0.80
7.00
0.20
360
33⅞
0.67
14.00
0.33
380
22.00
0.53
22.00
0.47
400
15.00
0.40
35.00
0.60
420
8⅝
0.27
48½
0.73
440
8½
0.19
65¼
0.81
IftheDecemberfuturescontractmovesupbyonepoint,thenthe380callmoves
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upby½point,to22½;the380putthenmovesdownby½point,to21½.IftheDecemberfuturescontractmovesdownby1point,thenthe380callmovesto21½andthe380putmovesto22½.
Notethatthe440callispricedhigherthanthe320puteventhoughtheyareequallyoutofthemoney.ThisisbecausethemodelassumesthatCorncanrallyfurtherthanitcanbreak.1Thisisareasonableassumption,butisitatradableassumption?Inotherwords,isittrueforallpricelevels?Isittrueunderanykindofweather?Noteaswellthata380callcosts22×$50=$1,100.
Asanunderlyingchanges,thedeltaitselfchanges.Alargemoveintheunderlyingcanchangeanoption’sstatusfromin-the-moneytoat-the-moneyorout-of-the-money,orviceversa.Theoption’sdeltawillchangetooradicallyforthepurposeofpriceassessment.Thedeltacalculationthereforeonlyappliestoasmallchangeintheunderlying.
DeltaandtimedecayThedeltaofanout-of-the-moneyoptiondecreaseswithtime.Thisisbecausetheprobabilityoftheunderlyingreachingitsstrikepricealsodecreaseswithtime.Thedeltaofanin-the-moneyoptionincreaseswithtime.Thisisbecausetheprobabilityofitsstrikepriceremaininginthemoneyalsoincreaseswithtime.Thedeltaofanat-the-moneyoptionremainsat0.50.Table5.2isanothersetofoptionscontractsontheaboveunderlying;itisthesamecontractmonthwithfewerdaysuntilexpiration:
Table5.2DecemberCornat$3.80×5,000bushels
Strike
Callvalue×$50
Calldelta
Putvalue×$50
Putdelta
320
60⅛
0.99
⅛
0.01
340
41⅛
0.92
1¼
0.08
360
24⅝
0.76
4¾
0.24
380
12½
0.51
12½
0.48
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400 5⅜ 0.28 25¼ 0.72
420
1⅞
0.12
41⅞
0.83
440
⅝
0.04
60½
0.96
30daysuntilexpiration; impliedvolatilityat30percent; interest rateat3percent;optionsmultiplierat$50.
AcomparisonofeachstrikepricefromTable5.1toTable5.2demonstratestheeffectoftimedecayondeltas.
Deltaposition:equivalencetounderlyingAdeltapositioncorrespondstoalongorshortpositionintheunderlying.Forexample,alongcallhasalongdeltapositionwhichcorrespondstoalongunderlyingposition.Allthedeltacorrespondencesaresummarisedbelow:
longcall=longdelta=longunderlyingshortcall=shortdelta=shortunderlyinglongput=shortdelta=shortunderlyingshortput=longdelta=longunderlying.
Aconsequenceofthesecorrespondencesisthatadeltabecomesequivalenttoapercentageoftheunderlyingcontract.Oneshort,at-the-moneycallwitha0.50deltaequalshalfofashortunderlyingcontract.Foursuchcallsequaltwoshortunderlyings,andsoon.
Allthedeltasinanoptionspositioncanthenbesummarisedintoanetdeltaposition.Table5.3isanexampleofasmallposition.
Table5.3Sampleoptionsposition,DecemberCorn,90DTE,impliedat30%
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Here,anequivalentlongunderlyingpositionisgivenaplussign(+),andanequivalentshortunderlyingpositionisgivenaminussign(–).Thenetdeltapositionof–3.00isequivalenttoanunderlyingpositionthatisshortthreecontracts.Rememberthatthisequivalencyonlyappliestoasmallmoveintheunderlying.2
HedgeratioBecauseanetdeltapositionisanequivalentfuturesposition,itcanindicateexposuretoanunwantedmovebytheunderlying.Thisexposurewouldbehedgedsimplybybuyingorsellingthenumberofunderlyingcontractsneededtocreateadeltaneutralposition.Asahedgeratio,thedeltaindicatesthenumberofcontractstobuyorsell.
Forexample,anoptionwitha0.50deltaishedgedbyhalftheamountofunderlyingcontracts.Apositionof10long,0.50deltacallsisequivalenttoapositionoflongfiveunderlyingcontracts.Thispositionisexposedtodownwardmovebytheunderlying,andsomaybehedgedbyselling,orgoingshort,fiveunderlyingcontracts.Thetotaldeltapositionisthenzero,or,aswesay,thepositionisdeltaneutral.Forasmallmovebytheunderlyingineitherdirection,theprofit/lossofthetotalpositionchangeslittle,ifatall.
Thehedgeratioisespeciallyusefultoriskmanagerswithlargeoptionsportfolios.Theyregularlyadjusttheirexposuretomarketdirectionwithoffsettingtransactionsintheunderlyingcontracts.SupposeyouareariskmanagerwiththepositiongiveninTable5.3.Howdoyouhedgethisposition?3
Deltaandprobability
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Ausefulwaytothinkofdeltaisthatitindicatestheprobabilityofanoptionexpiringin-the-money.Anoptionthatisat-the-money,witha0.50delta,hasanevenchanceofexpiringin-the-money.Byassociatingdeltawithprobability,wecandeterminethemarket’sassessmentoftherangeoftheunderlyinguntilexpiration.Thiscanhelpusdecidehowmuchriskliesinanoptionsposition.
Forexample,theaboveDecember440call,withan0.19delta,hasa19percentprobabilityofexpiringin-the-money,andmightbeconsideredalow-risksale.Thereturnonthesaleofthiscallwouldalsobelow,butthisisajustifiablerisk/returnscenarioforsomeinvestors.
Ontheotherhand,a19percentprobabilityofDecemberCornmovingto440byexpirationmaybethepointatwhichanotherinvestorwishestocoverashortpositionintheunderlying.Althoughthemarketcurrentlyindicatesthatsuchamoveisunlikely,thisinvestoriswillingtopaythesmallpremiumthatwouldenablehimtoretainhisshortposition.
Asanindicatorofprobability,adeltaisonlyasgoodasthecurrentmarketassessmentofpricemovementuntilexpiration.Thisassessmentiscontinuallysubjecttonewinformation,andasaresultitiscontinuallyrevised.Profitableoptionstradingisoftenamatterofanticipating,orbeingoneofthefirsttodiscern,changesinprobability.
SummaryofdeltaTherearefourwaystothinkofdelta;thefirstisthedefinition,andthefollowingthreearetheuses:
the rate of change of the option with respect to a small change in theunderlyingapercentageofanunderlyingcontractahedgeratiotheprobabilityofanoptionexpiringin-the-money.
DeltaisdiscussedfurtherinPart3.
____________1ThecallsherecanactuallybepricedhigherthanI’vegiven.ThisisbecauseIhaveeliminatedthevolatilityskewforthepurposeofdemonstration.Tolearnaboutvolatilityskews,turntoChapter20.
2Occasionallyintheoptionsbusiness,theplussign(+)isusedtorefertoacalldeltaandtheminussign(–)
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isusedtorefertoaputdelta.Thispracticeconfusestheprocessofcalculatinganetdeltaposition;itisnotusedinthisbook.
3Buy,orgolong,threeunderlyingcontracts.
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Gammaandtheta
Itshouldbeapparentafterreadingthepreviouschapterthatdeltaisanindispensabletoolforunderstandinganoption’sbehaviour.Butbecauseanoption’sdeltachangescontinuallywiththeunderlying,weneedtobeabletoassessitsownrateofchange.Gammaquantifiestherateofchangeofthedeltawithrespecttoachangeintheunderlying.
Tounderstandgammaistounderstandhowquicklyorslowlyadeltacanchange.SupposeXYZistradingatapriceof100,andtherearejusttwohoursuntilthefront-monthoptionscontractexpires.ThetypicaldailyrangeofXYZistwopoints,soweexpectittobebetween99and101atthetimeofexpiration.
NowsupposethatXYZstartstomoveerratically,andforthenexttwohoursittradesbetween99and101.Duringthistime,whatisthedeltaoftheexpiring100call?IfXYZsettlesbelow100,the100callwillexpireworthless,withadeltaofzero.IfXYZsettlesabove100,thecallwillcloseatparity,withadeltaof1.00.
Duringtheselasttwohoursitwouldhavebeenpointlesstocalculatethedeltabecauseitischangingsorapidly.Thisrapidandmostextremechangeofdelta,however,isanexampleofthehighestpossiblegammathatanoptioncanhave.
Ifweconsidertheout-of-the-moneyoptionsinthesamecontractmonth,suchasthe105callsandthe95puts,wecanbealmostcertainthattheywillexpireworthless.Theirdeltasarezeroandwillnotchange.Theyhavenogamma.Likewisein-the-money,parityoptionssuchasthe90callsandthe110putshavenogammabecausetheirdeltaswillremainat1.00throughexpiration.
Thefirstsituationaboveoccasionallyoccurs,butmostoptionscontractsexpirewellout-oforin-the-money.Nevertheless,severalpointsaboutgammaareillustrated.Inanycontractmonth,gammaisthehighestwiththeat-the-moneyoptions,anditdecreasesasthestrikepricesbecomemoredistantfromthemoney,whethertheyarein-the-moneyorout-of-the-money.
Asacontractmonthapproachesexpiration,thegammasofboththeat-the-moneyoptions,andtheoptionsnear-the-money,increase.Theeffectoftimedecay,however,causesthegammasofthefarout-of-the-moneyandfarin-the-
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moneyoptionstoapproachzero.Generallyspeaking,however,timedecayleastaffectsthegammasofoptionsinthe0.10and0.90deltaranges.Thisallbecomescomplicated,ofcourse,bythefactthatdeltaschangewithtime.Youshouldsimplyrememberthatastimepasses,theneareranoptionistotheunderlying,themoreitsgammaincreases.
Table6.1isatypicalexampleofasetofoptionswithdeltasandgammasinonecontractmonth:
Table6.1DecemberCornat$3.80
90daysuntilexpiration;impliedvolatilityat30percent;interestrateat3percent;optionsmultiplierat$50,somultiplycallandputvaluestimes$50.
Thegamma-deltacalculationisamatterofsimpleadditionorsubtraction.Here,theDecember400callwitha0.40deltahasagammaof0.007.ThismeansthatiftheDecemberfuturescontractmovesuponepoint,from380to381,thedeltaofthecallwillincreaseto0.407,roundedto0.41.Ifthefuturescontractmovesdownonepoint,thedeltaofthesamecallwilldecreaseto0.393,roundedto0.39.Accordingly,ifthefuturescontractmovesup20points,thenthedeltaofthe400callwillincreaseby0.14,to0.54,theequivalentdeltaofthe380callatpresent.
IftheDecemberfuturescontractmovesdownbyonepoint,thenthedeltaoftheDecember340putwillincreasebyitsgammaof0.005,from0.20to0.205(or0.21rounded);ifthefuturescontractmovesupbyonepoint,thedeltawilldecreaseby0.005.
Notethatgammadescribestheabsolutechangeindelta,whetherincreasedor
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decreased.
Anoption’sgamma,likeitsdelta,changesastheunderlyingchanges.IfyoucalculatethenewtheoreticaldeltafortheDecember420calloveranincreaseof40pointsinthefuturescontract(corn,likeallcommodities,canbeextremelyvolatile),theresultwillbe(0.006×40)+0.27=0.51.YoushouldinsteadexpectthenewdeltatobeequivalenttothatofthepresentDecember380callat0.53Thisdiscrepancyisduetothefactthatthegammaisincreasingfrom0.006to0.008asthefuturescontractmovesup.Thegamma-deltacalculationisthereforebestappliedtoasmallchangeinthedelta.
Table6.2liststhesamesetofoptionsbutwithlesstimeuntilexpiration.IfwecompareitwithTable6.1,thepointspreviouslymadeaboutgammabecomeevident.Withthepassageoftime,thedeepin-the-moneyandfarout-of-the-moneyoptionshavegammasthatareunchangedtodecreased,whileat-the-moneyandnear-the-moneyoptionshaveincreasedgammas:
Table6.2DecemberCornat$3.80×5,000bushels
Gammacanbethoughtofastheheatofanoption.Ittellsushowfastouroption’sdelta,orourequivalentunderlyingposition,ischanging.
30daysuntilexpiration; impliedvolatilityat30percent; interest rateat3percent;optionsmultiplierat$50.
PositiveandnegativegammaBecausegammadeterminestheabsolute(increasedordecreased)changeindelta,anddeltadeterminestheabsolutechangeinanoption’sprice,gamma
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helpsusdetermineourexposuretoabsoluteunderlyingmovement.
Rememberthatalongcallisanalternativetoapurchaseoftheunderlying.Itisahedgeforunderlyingmovementineitherdirection:itgainspriceappreciationontheupside,anditofferspriceprotectiononthedownside.Alongcallyieldsabenefitwhenthemarketmoves;itsvaluehasapositivecorrelationwithmarketmovement.
Thesameistrueforalongputasanalternativetoasaleorshortpositionintheunderlying.Ifyoubuyaputinsteadofsellingyourstock,you’llbeverycontentifthestockmakesalargemoveineitherdirection.
Positivecorrelationwithmarketmovementiscommonlyknownaspositivegamma.Justasalongat-the-moneyoptionhasthemostprofit/savingspotential,alongat-the-moneyoptionhasthemostpositivegamma.
Conversely,negativecorrelationwithmarketmovementisknownasnegativegamma.Ifyousellanat-the-moneycallinsteadofsellingyourstock,you’llbedisappointedifthestockmovesaboveorbelowtheamountofthecallsale.Ifyousellanat-the-moneyputinsteadofbuyingstock,youmaycurseyourluckifthestockmovesoutsidetherangeofthesaleprice.Shouldthisbeunclear,imagineyourselfwithapotentialXYZpositionat100andwithapotential100callorputpricedat4.
Thefollowingdiscussionbecomessomewhatmoreadvanced.Youmayreturntoitlater,orhaveaglancenow.
GammaandvolatilitytradingThegammacalculationisparticularlyusefultothosewhotradevolatility,i.e.absolutepricemovementorpricemovementineitherdirection.
Longoptionscanbecombinedinordertoprofitfromabsolutemarketmovement,andshortoptionscanbecombinedtoprofitfromastaticmarket.
IfweusethesetofoptionsinTable6.2,apositionoflong1December380callpluslong1December380putwillhaveatotalpositivegammaof+0.013×2,or+0.026.Thispositionisknownasalongstraddle,anditwillprofitfromanunderlyingmoveineitherdirectiongreaterthatthepurchasepriceof12.5+12.5=25.Ithastwobreak-evenlevels,at405and355.
Becausethispositionislongbothacallandaput,thegammafiguretellsusthatitscombineddeltaincreasesby0.026foreach1pointincreaseintheunderlying:
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thecallincreasesitsdeltaby0.013,andtheputdecreasesitsdeltaby0.013.Thegammafigurealsotellsusthatforeach1pointdecreaseintheunderlying,thecombineddeltadecreasesby0.026:theputincreasesitsdeltaby0.013,andthecalldecreasesitsdeltaby0.013.
Inotherwords,astheunderlyingrallies,thispositionbecomeslonger,andastheunderlyingbreaks,thispositionbecomesshorter.Asconfirmedbythebreak-evenlevels,thelongstraddleprofitsfromincreasedvolatility,orabsolutepricemovement.
Conversely,theoppositeposition,ashortstraddle,willhaveanegativegammapositionof–0.026,andwillprofitifDecemberCornremainsbetween355and405.Thesetwopositionsarediscussedfurtherinthechapteronstraddles(Chapter11).
Thegammacalculationisusefultomarket-makerswhocarrylargepositionsontheirbooks.Theabovegammareadingof+/–0.026indicatesmoreexposuretomarketmovementthan,forexample,+/–0.0.11,whichwouldbeobtainedbybuyingorsellingboththeDecember420callandtheDecember340put.Here,thebreak-evenlevelsare423.13and336.88.Thispositionisknownasthestrangle,anditisalsodiscussedinChapter11.
Positiveandnegativegammahelptoquantifytherisk/returnpotentialofapositionwithrespecttoabsolutemarketmovement.
ThetaComparedtogammaanddelta,thetaisastraightforwardconcept.Thethetaofanoptionistheamountthattheoptiondecaysinoneday.Ashortoptionspositionreceivesincomefromtimedecayandthereforehaspositivetheta.Alongoptionspositionincursanexpensefromtimedecayandthereforehasnegativetheta.
Tables6.3and6.4aresimilartothepreviousTables6.1and6.2,buttheyincludethedailythetanumbersforallthecontractslisted.Here,thethetafiguresareexpressedinactualdollarsandcents(theycanalsobeexpressedinoptionsticks):
90daysuntilexpiration; impliedvolatilityat30percent; interest rateat3percent;optionsmultiplierat$50,somultiplycallandputvaluestimes$50.
Table6.3DecemberCornat$3.80
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30daysuntilexpiration; impliedvolatilityat30percent; interest rateat3percent;optionsmultiplierat$50.
Table6.4DecemberCornat$3.80×5,000bushels
AswesaidinChapter3,alloptionslosetheirvalueatanacceleratedrateastheyapproachexpiration.Theat-the-moneyoptions,the380s,havethemostincreaseinthetabecausetheycontainthemosttimepremium.Thosenearestthemoney,the360sandthe400s,alsohaveincreasedtheta.Thefarout-of-the-moneyanddeepin-the-moneyoptionscanhavedecreasedtheta,butthisisbecausethey
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containonlyasmallamountoftimepremiumwith30DTE.
UseandabuseofthetaThetaquantifiestheexpenseofowning,ortheincomefromselling,anoptionforadayoftheoption’slife.Youmayhaveanoutlookformovementinaparticularunderlying.Whatisthecostofalongoptionspositionforthedurationofyouroutlook?Ifyouroutlookisforastablemarket,whatisyourexpectedreturnfromashortoptionspositionduringthistimeperiod?
Thesubjectofthetagivesrisetoafewwordsofcaution.Itistemptingtoselloptionssimplytocollectmoneyfromtimedecay.Thisstrategycontainsahiddenrisk.Itcanbecomehabitualbecauseitoftenworksonashort-andmedium-termbasis.Inthelongterm,however,itusuallyfails.Thereasonisthatitignoresthebasisofoptionstheory:thattimepremiumisafairexchangeforvolatilitycoverage.Manytradershavegonebustbyignoringthisbasicprinciple.Toselloptionsinsuchamanneristoignoreprobability,andtohopethatyouareoutofthemarketwheniteventuallymoves.
AstoryaboutthetaThefollowingstorytellswhatcangowrongwithashortoptionsposition,butalsohowtroublecanbeavoided.
AfewyearsagoIworkedforoneofthemoreprominenttradersinindexoptionsinChicago.HisstrategywastosellindexcallsandhedgethemwithlongS&P500futurescontracts.Wewereinabearmarket.Stocksandtheindeximpliedvolatilitywerebothinadowntrend.ThetraderIworkedfor,Bobby,routinelyleanedshort,i.e.hisoveralldeltapositionwasnegativefromdaytoday.Hehadmadesubstantialprofitsinthisway.
IdidthenasIdonow,followanumberoftechnicalindicators.Oneofthemwasthe200-daymovingaverage.TheS&P500washoldingatthislevelafteranextensivedecline,andIbecameworriedthatBobby’sstrategy,whichhadworkedsowellformanymonths,mighthaverunitscourse,atleastforthetimebeing.BecauseIwasnewtothebusiness,Bobbywouldhavenoneofmybeginner’sadvice.Afterall,hewasmyboss,andhehadrecentlymadeasubstantialamountofmoney.Hehadalsosubstantiallyincreasedthesizeofhispositions.
Aweekortwolater,Iwasonthefloorearlyforagovernmenteconomicindicator.Thereportwasbullish,bondswereup,andsowasthecallforstocks.I
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phonedinmyreport,andBobbygreetedthenewswithdeadsilence.Afewminuteslater,hejoinedmeinthepit,andthestockmarketgappedopenhigherwithnochancetocoverhisposition.Westoodthereforabouthalfanhourjustwatchingtheorderflowandtheindexesamidfrenetictrading.Thenthingsstartedtoquietdown.Theindexesdowntickedalittle,buttheyweren’tpickingupmomentum.
Bobbymadehisfirsttrades,bigones–hesoldcalls.Itappedhimontheshoulderandtriedtosay,‘Bobby,they’renotgoingdown,’buthecutmeoffbysaying,‘Shutupandgimmethecount,’meaningcalculatehisposition.Severalminuteslater,themarketmadeitssecondmove,fastandhigher.Again,therewasnochancetocover.Itlevelledoffatabouthalfagainthedistanceofthefirstmove.Bobbythencoveredasbestashecouldbybuyingincalls,whichwerewellbid,andbybuyingfutures.Heleftthepitwithoutsayingaword,andIstayedontotallyhisposition.
Ahalfhourlater,Ijoinedhimupstairsinhisofficetogivehimmyreport.Hewassittinginhischair,staringthroughhistradingscreen.Hedidn’thearawordIwassaying;hewasspeechlessandcatatonic.Hehadlostagreatdealofmoney.Iknewhispositionwassafeforthemoment,soIlefttheoffice.
Thereareafewlessonstobelearnedfromthisstory.Oneistoknowwhyyourstrategyisworking.Ofcourseyou’retalented,astuteandyouworkhard,butisyourstyleoftradingoryourstrategyparticularlysuitedtoacertainkindofmarket?Whathappensifthemarketchangesitscharacter?
Anotherlessonistheconverse.Perhapsthestrategiesthatyou’remostcomfortablewitharen’ttheonesthatprofitinthecurrentmarket.Canyouadapt?Ifyoudon’tfeelcomfortablewithadifferentstyleorstrategy,thenbyallmeanstakeabreakfromthemarket.
Finally,rememberthatoptionsarederivatives.Onceyou’reinthebusinessawhile,itbecomeseasytolosetouchwiththefundamentalandtechnicalanalysesofunderlyingcontracts.Lackofawarenesssoonerorlaterprovescostly.
ThetraderIworkedforeventuallyworkedhiswaybackintothemarket,andhasdoneverywellinrecentyears.We’vestillneverdiscussedthe200-daymovingaverage.
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Vega
Ofteninanoptionsmarketcircumstancesarisethatcausethevolatilityoftheunderlyingtoincreaseordecreasesuddenly.Thismaybetheresultoftheinceptionorconclusionofanunforseenmarketevent.Duringsuchcircumstancestheimpliedvolatilityofeachoptionscontractmonthreactstoadifferentdegree,andthisinturnaffectsthepriceofeachoptionofeachcontractmonthtoadifferentdegree.Undertheseaswellasmoreusualcircumstancesthereisaneedtoquantifytheeffectofachangeinimpliedvolatilityonthepriceofaparticularoption.Vegaistheamountthatanoptionchangesiftheimpliedvolatilitychangesbyonepercentagepoint.
Vegaitselfcanbeexpressedineitheroptionsticksorinanactualcurrencyamount.Table7.1showsasetofoptionswiththeirvegasforonecontractmonth.Thevegasareexpressedindollarsthenroundedintoticks.
30daysuntilexpirationImpliedvolatilityat30percentInterestrateat3percent.
Anincreaseinimpliedvolatilityleadstoanincreaseinoptionspremiums,whileadecreaseinimpliedvolatilityhastheoppositeeffect.Ifthecurrentimpliedvolatilityincreasesfrom30percentto31percent,thevalueoftheDecember380callincreasesfrom12½to13.Iftheimpliedvolatilitydecreasesfrom30percentto29percent,thevalueoftheDecember380calldecreasesfrom12½to12.
Table7.1DecemberCornat$3.80×5,000bushels
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Notethatthevega,orthenumberofoptionsticks,ismultipliedbythenumberofpercentagepointsthattheimpliedvolatilitychanges.Theaboveimpliedmayincrease3percent(commonlymeaning3percentagepoints),from30percentto33percent.ThenewvalueoftheDecember380callwillthenbe14.
Forout-of-andin-the-moneyoptions,thevegaitselfincreasesastheimpliedincreases,anditdecreasesastheimplieddecreases.Thereforewiththeseoptionsthevegacalculationismostaccurateforasmallchangeintheimplied.Forat-the-moneyoptions,thevegaremainsconstantthroughchangesintheimplied.
At-the-moneyoptionshavelargervegasthanout-of-andin-the-moneyoptions.Thisisbecauseachangeinvolatilityincreasesordecreasestheirrangeofcoveragemorethanout-of-andin-the-moneyoptions.Theirvaluebecomesincreasedordecreasedaccordingly.
Table7.2showsasetoflonger-termoptions,withtheirvegas,onthesameunderlying:
90daysuntilexpiration; impliedvolatilityat30percent; interest rateat3percent;optionsmultiplierat$50,somultiplycallandputvaluestimes$50.
Table7.2DecemberCornat$3.80
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Thevegaofanoptionincreaseswiththetimeuntilexpiration.Thisisbecauseanincreaseinimpliedvolatilityoveralongertermnecessitatesagreaterincreaseintheoptionspremiums.Consequently,iftheimpliedvolatilityincreasesequallyforbothanear-andalong-termcontract,theoptionsinthelatterwillincreasemore.
Alongoptionspositionprofitsfromanincreaseinimpliedvolatility,andthereforeithasapositivevega.Ashortoptionspositionprofitsfromadecreaseinimpliedvolatility,andthereforeithasanegativevega.
VegaandimpliedvolatilitytrendsPracticallyspeaking,theimpliedvolatilityoflong-termcontractsismorestablethanthoseofnear-termcontracts.Front-monthimpliedvolatilityisthemostreactivetocurrentevents,orcurrentnon-events.
Inquietmarkets,thefront-monthimpliedcantrendlowerandlowerformonthsinanticipationofcontinuedconditions.Eachpointthattheimplieddecreasesinturnmultiplies,bythevega,thenumberofoptionsticksthattheoptions’valuesdecrease.Thefrustrationof,andtheriskto,thepremiumholdersbecomesalmostunbearableastheiraccountsdiminish,whilethepremiumsellersnonchalantlycollecttheirtimedecay.
Ifanunexpectedeventshocksthemarket,thefront-monthimpliedcanleap5,10,30ormorepercentagepointswithinminutes.Asthevegasbecome
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multipliedbytheincreaseintheimpliedvolatility,evensmallpositionstakeonalmostunmanageableproportions.Thepremiumholdersbecomevindicated,whilethepremiumsellersseemonthsofprofitseliminated.
Risk/returnofvegaBecauseat-the-moneyoptionshavethelargestvegas,theyarethemostexposedtoachangeinimpliedvolatility.Alloptions,ofcourse,facethisexposure.Inquietmarkets,ashortoptionspositioncanprofitnotonlyfromtimedecay,butalsofromadeclineintheimplied.Inactivemarkets,alongoptionspositioncanprofitfromanincreaseintheimpliedthatmorethanoffsetsthecostoftimedecay.
Itisimportanttoknowhowmuchthevegasofoptionsonaparticularcontractcanbeaffectedbychangesinvolatility,andforthatyouneedtoresearchthepasthistoricalandimpliedvolatilityranges.Mostdatavendors,theexchangesandmanywebsiteshavethisinformation.Forexample,ifyouwanttoknowhowthecrashof1987andthegrindingretracementof1988affectedOEXimplieds,howinturntheimpliedsmultipliedthevegas,andhowinturnthevegasaffectedtheoptionsprices,consulttheCBOE.
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part2
Optionsspreads
Introduction
Spreadingrisk‘I’mbullish,whatdoIdo?’OccasionallyIamaskedthisquestion,andIusuallybeginmyresponsewithanotherquestion:‘Howmuchriskdoyouwanttotake?’Intheoptionsbusinesstherearemanywaysoftakingaposition,andtheyallhavevaryingdegreesofrisk.Aswithallkindsofinvestments,thereisarisk/returntrade-off.Highriskcorrespondstohighreturn,whilelowriskcorrespondstolowreturn.Theadvantageofoptionsspreadsisthateachinvestorcantaketheamountofriskthatheisabletojustifyandmanage.Thispartoutlinesthemajorstrategiesthatspreadrisk.Thesestrategiescanbetradedonalltheexchanges,and,withfewexceptions,theycanbetradedinonetransaction.
Attheoutset,itisimportanttoknowwhatrisksyouwanttospread.Premiumsmaybetoohightojustifyanoutrightoptionspurchase.Thepotentialforunlimitedriskfromashortcallorputpositionmaybeunjustified,eventhoughpremiumsareatahighanddeclininglevel.Youroutlookmaybeforadirectionalmove,butitmaybeuncertainoftheextent.Themarketmaybedueforalargemovebutthedirectionmaybedifficulttoassess.Impliedvolatilitiesmaybedecreasingbuttheymaybesubjecttofrequent,upwardspikes.Youmaywanttobuyashort-termoption,butitscostintermsoftimedecaymaybetoogreat.Thesearejustafewofthereasonsforspreadingrisk.
Mostoptionsspreadscanbeclassifiedaseitherdirectionalorvolatilityspreads.Directionalspreadsarethosethatprofitfromeitherbullishorbearishmarketmovement.Volatilityspreadsprofitfromeitherincreasedordecreasedabsolutemarketmovement,regardlessofdirection.
Anyspreadhastheoppositeriskandreturnpotentialdependingonwhetheritisboughtorsold.
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Belowisanindexofthemajorspreads.Itwillserveasaquickreferenceinselectingstrategies.Inafewcasesthetermsthatareappliedtothesespreadsvary,butthesewillbenoted.Ifyouarefirststartingtotrade,orifthisisyourfirstreading,focusonthespreadsmarkedwithanasterisk(*),becausetheyhavetheleast,andmostmanageable,risk.
Indexofspreads
ATM=at-the-money;OTM=out-of-the-money.
Termstousewhenplacingspreadorders
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Wheneveryouplaceanorderforoneofthesespreads,omitthejargon.Itismostimportanttoknowthepriceatwhichyouwanttotradethespread.Then,youmustknowthepricesoftheindividualoptions,orthepieces,thatyouwanttotrade.
Whenyouringyourbroker,statethatyouareplacinganorderforanoptionsspread,andstatethestockorotherunderlying.Next,specifythefollowing:buyorsell,quantity,month,strikeprice,andcall(s)orput(s).Dothisforeachoptionsstrike.Next,specifythenetdebitorcreditforonespread.Then,specifythetotaldebitorcreditforthetrade.Makesureyourbrokerrepeatsallthespecificationstoyou.Lastofall,usethejargon,butonlyifyouandyourbrokerhavepreviouslyagreedontheterms.Yourconversationwithyourbrokershouldsoundlikethefollowing:
You:
Hi,IwanttoplaceanoptionsspreadorderinIBM.
Broker:
Goahead.
You:
Onaspreadbuy5July130calls,andsell5July135callsforanetdebitof1.27times5.Totaldebitis6.35.[Youshouldknowthat6.35equals$635.00.]
Broker:
Checking,inIBMoptionsyouarebuying5July130calls,andselling5July135callsasaspread,foradebitof1.27times5.Yourtotaldebitis6.35.
You:
Yes,that’scorrect.
Broker:
Working,I’llcallyouback.
Whenyourbrokercallsyoubacktoconfirm,heorsheshouldspecifyalloftheaboveplusthepricesofeachoption.
Broker:
Hi,you’refilledonyourspread.
You:
Good,readitoff.
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Broker:
OnaspreadinIBMyoubought5July130calls,andsold5July135callsforadebitof1.27times5.Yourtotaldebitis6.35.Youpaid2.87for5oftheJuly130calls,andyousold5oftheJuly135callsat1.60.
You:
Yes,that’scorrect.
Broker:
Checking,youpaid1.27for5July130–135callspreads.
You:
Yes,Ipaid1.27togolong(tobuy)5July130–135callspreads.
Broker:
Canyouconfirmthatagain?
You:
Haveaniceday,wiseguy.
Notethatwhenreportingthepricesoftheoptions,yourbrokershouldusethefollowingterms:
whenbuying:priceforquantitywhenselling:quantityatprice.
Thesetermsavoidconfusion,andtheyhavebeenusedformanyyearsonmostofthemajorexchanges,includingtheCBOTandtheLIFFE.Learntousethem.
AdviceforbeginnersBeforewebeginourdiscussionofspreading,herearetwopiecesofadvice:
The first is not to change your risk/return profile in order to reduce yourpremium outlay or to pay less commissions. Trade an options positionbecause your outlook tells you it is the best position to take under thecurrentmarketconditions.Specifically,sellingextraoptionsmayreducethecost of your spread, or failing to buy protective options may reduce theamount of your brokerage bill, but in both cases, you incur added andunjustifiablerisk.
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Second,ifyouarenewtotradingoptions,donottakeapositionthatisnetshortanoptionoroptions.Therearemanywaystotradefromtheshortsidewithouttakingunlimited,orpracticallyunlimited,risk.Theyallinvolvethepurchaseofoneormorerisklimitingoptions.Eachshortoptionshouldbecoveredbyalongoption.
Itishelpfultodiscusstheprofit/losspotentialofspreadsintermsoftheirvalueatexpiration.Practicallyspeaking,however,youwillmostoftencloseaspreadbeforeexpirationbecauseyouwillnotwanttoexerciseorbeassignedtoanunderlyingcontract.Youalsodonotwantpinrisk.
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Callspreadsandputspreads,oronebyonedirectionalspreads
Investorswithadirectionaloutlookoftenfindtherisksofastraightlongorshortoptionspositiontobeundesirable.Astockindexmaybeatahistoricallyhighlevel,andthereforeaninvestormaywanttosellcallsorbuyputsinordertoprofitfromadecline.Butperhapsthemarketisstilltoostrongtosell‘naked’calls,i.e.shortcallswithoutahedge.Ifpremiumlevelsarehigh,thentheinvestormaynotwanttoriskinvestinginastraightputpurchase.Asensiblealternativeistospreadtheriskofastraightoptionspositionbytakingtheoppositelongorshortpositionatastrikepricethatismoredistantfromtheunderlying.
Forexample,ifXYZistradingat100,wemaybuythe95putandsimultaneouslysellthe90put,therebycreatingalongputspread,abearishstrategy.Ifinsteadwearebullish,wemaysellthe95putandbuythe90put,creatingashortputspread.
Anotherbullishstrategyistobuythe105callwhilesellingthe110call,creatingalongcallspread.Ifinsteadwesellthe105callwhilebuyingthe110call,wecreateashortcallspread,analternativebearishstrategy.Thesefourspreadsarealsoknownasverticalspreads.
Inpractice,bothstrikesofthecallorputspreadareusuallyplacedout-of-the-money.Thekeytoallthesespreadsistheoptionthatisat,ornearestto,theunderlying.Wewilldiscusseachofthem.
Inaddition,byspreadingoneoptionagainsttheother,youarealsospreadingcostagainstcost,soifoneoptionisdear,thenitisfinancedbyanotherthatisdear.YoualsominimiseyourexposuretotheGreeks.Irepeat:youminimiseyourexposuretotheGreeks.
Theprofit/losscalculationsthatformthebasisofthesespreadscanbeappliedtoanyunderlyinginstocks,bonds,commoditiesorFX.Forthepurposeofillustration,asetofoptionsonastockindexisgiveninTable8.1:
SPDRat115.22
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45daysuntilJuneexpirationContractmultiplierof$100
Table8.1SPYoptions
*LongcallspreadBullishstrategyTheSPDR1(‘Spider’)iscurrentlytradingat115.22.Youmaywishtopurchasethe117calltoprofitfromanupsidemove.It’sclosetoexpiration,timedecayiscostly,andtheimpliedvolatilityishigherthanithasbeenrecently,soanexpenditureof2.60×$100,or$260mayseemtoogreat.Youcouldsellthe119callfor1.70atthesametimeasyoubuythe117call,foratotaldebitof0.90or$90.Yourshortcalltheneffectivelyfinancesthepurchaseofyourlongcall,andminimisesyourexposuretotheGreeks.
Withthisspread,youhaveapotentialbuyat117andapotentialsellat119,forwhichyoupayapremium.Youranalysismayindicatethatthenear-termpricegainfortheSPDRisexpectedtobe119.Youarewillingtotradeunlimitedupsidepotentialforareducedriskinyourpremiumexposure.
Thispositionisknownasthelongcallspreadbecauseitissimilartoalongcall.2Inordertoassesstheprofit/losspotentialofthespreadatexpiration,firstthepriceofthespreadisconsideredasaunit,0.90.
Themaximumprofitisgainedifthestockisatorabovethehigherstrike,or119,atexpiration.Thisiscalculatedasthedifferencebetweenthestrikepricesminusthecostofthespread,or(119–117)–0.90=1.10.
Themaximumlossofthespreadisequaltoitscost,or0.90.Thislossisincurredifthestockisatorbelowthelowerstrike,or117,atexpiration.
Thebreak-evenlevelisthelevelatwhichanincreaseinthestockpaysforthespread.Thisiscalculatedasthelowerstrikepriceplusthecostofthespread,or117+0.90=117.90.Hereisasummaryofthisspread’sprofit/lossatexpiration:
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DebitfromlongJune117call:
–2.60
CreditfromshortJune119call:
1.70
Totaldebit:
–0.90
Maximumprofit:differencebetweenstrikes–costofspread:(119–117)–0.90=1.10
Maximumloss:costofspread:0.90
Break-evenlevel:lowerstrike+costofspread:117+0.90=117.90
Therisk/returnpotentialofthisspreadismaximumlossdividedbymaximumprofit,or0.90/1.10=0.82.Inotherwords,ariskof0.82hasapotentialgainof1.00,or1.6to2.3
Table8.2showstheexpirationprofit/lossforthisspread.
Table8.2LongSPYJune117–119callspread
Ingraphicterms,theexpirationprofit/losscanbeillustratedasshowninFigure8.1.
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Figure8.1Expirationprofit/lossrelatingtoTable8.2
*ShortcallspreadNeutraltobearishstrategySupposeyouareneutraltobearishontheS&P500.With45daystillexpiration,Junetimedecayisbeginningtoaccelerate.Youwouldliketocollectpremiumiftheindexstaysinitscurrentrangeorifitdeclines,butyoudon’twanttorisktheunlimitedlossfromashortcall.YoumaythenselltheJune117callat2.60,andinthesametransactionpay1.70fortheJune119call,foranetcreditof0.90Yourpositionisknownastheshortcallspreadbecauseitissimilartoashortcall.4
Theadvantageofyourspreadisthatithasabuilt-instop-losscoveratthehigherstrike,or119.Youmaythinkofthisspreadasapotentialsaleofthestockat117,andapotentialbuyofthestockat119.Forthisrisk,youcollectapremium.
Theexpirationprofit/lossofthisspreadisoppositetotheabovelongcallspread,butthebreak-evenlevelisthesame.Here,themaximumprofitisthecreditreceivedfromthespread,or0.90.Thisprofitisearnedifthestockisatorbelowthelowerstrike,or117.
Themaximumlossoccursifthestockisatorabovethehigherstrike.Thisiscalculatedasthedifferencebetweenstrikepricesminustheincomefromthespread,or(119–117)–0.90=1.10.
Thebreak-evenlevelisthesameasthelongcallspread.Thisisthelevelatwhichalossduetoanincreaseinthestockpricematchestheincomefromthespread.Thecalculationisthelowerstrikepriceplusthepriceofthespread,or117+0.90=117.90.Belowisasummaryofthisspread’sexpirationprofit/loss:
CreditfromshortJune117call:
2.60
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DebitfromlongJune119call:
–1.70
Totalcredit:
0.90
Maximumprofit:creditfromspread:0.90
Maximumloss:(differencebetweenstrikes)–creditfromspread:(119–117)–0.90=1.10
Break-evenlevel:lowerstrike+creditfromspread:117+0.90=117.90
Therisk/returnpotentialfromthisspreadisalsooppositetothelongcallspread,ormaximumlossdividedbymaximumreturnat1.10/0.90.Here,ariskofeach$110offersapotentialreturnof$90.
Table8.3showstheexpirationprofit/lossforthisshortcallspread.
Table8.3ShortSPYJune117–119callspread
Theexpirationprofit/lossforthisspreadisgraphedinFigure8.2.
Figure8.2Expirationprofit/lossrelatingtoTable8.3
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*LongputspreadBearishstrategyTheSPDRiscurrentlytradingat115.22,andyouarebearish,shortterm,ontheS&P500index.YoumaywishtopurchasetheJune113puttoprofitfromadownsidemove.With45daystillexpiration,timedecayisacceleratingandtheimpliedvolatilityishigherthanithasbeenrecently,soanexpenditureof3.10or$310,mayseemtoogreat.
Instead,youcouldselltheJune111putat2.60,andinthesametransactionpay3.10fortheJune113put,foratotaldebitof0.50.Yourshortputtheneffectivelyfinancesthepurchaseofyourlongput,andminimisesyourexposuretotheGreeks.
Thetrade-offisthatyourdownsideprofitislimitedbythe111put,butatthatpointyouhaveprobablycapturedthebestpartofthemove.YouranalysismaytellyouthattheSPXissupportedbelow111,inwhichcaseyour111putwouldeffectivelybethelevelatwhichyoutaketheprofitfromyour113put.
Inthiscase,youarebuyingtheJune113–111putspread.Thispositionisknownasthelongputspreadbecauseitissimilartoalongput.5Youmaysimplythinkofthisspreadasapotentialsaleoftheindex(theETF)at113,andapotentialbuyoftheindexat111.Forthisprofitpotentialyoupayapremium.
Inordertoassesstheprofit/losspotentialofthespreadatexpiration,firstthepriceofthespreadisconsideredasaunit:0.50.
Atexpiration,themaximumprofitisgainedifthestockisatorbelowthelowerstrike,or111.Thisiscalculatedasthedifferencebetweenstrikepricesminusthecostofthespread,or(113–111)–0.50=1.50.
Themaximumlossistakenifthestockisatorabovethehigherstrike,or113,atexpiration.Thisiscalculatedsimplyasthecostofthespread,or0.50.
Thebreak-evenlevelisthelevelatwhichadeclineinthestockpaysforthecostofthespread.Thisiscalculatedasthehigherstrikeminusthecostofthespread,or113–0.50=112.50.Theexpirationprofit/lossissummarisedasfollows:
DebitfromlongJune113put:
–3.10
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CreditfromshortJune111put: 2.60
Totaldebit:
–0.50
Maximumprofit:differencebetweenstrikes–costofspread:(113–111)–0.50=1.50
Maximumloss:costofspread:0.50
Break-evenlevel:higherstrike–costofspread:113–0.50=112.50
Therisk/returnpotentialofthisspreadismaximumlossdividedbymaximumprofit,or0.50/1.50.Inotherwordsyouarerisking$0.33foreachpotentialprofitof$1.00,orarisk/returnratioof1/3.6
Intabularformtheexpirationprofit/lossisasinTable8.4.
Table8.4LongSPYJune113–111putspread
Ingraphicterms,theprofit/lossofthisspreadisillustratedinFigure8.3.
Figure8.3Expirationprofit/lossrelatingtoTable8.4
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*ShortputspreadNeutraltobullishstrategyOntheotherhand,supposethatyouareneutraltobullishontheSPXortheSPDR.Youranalysistellsyouthatitisoversold,orthatearningsprospectsarebetterthanexpected.Youwouldliketosellaputinordertoprofiteitherfromtimedecayiftheindexstabilisesorfromadeclineintheput’svalueiftheindexrallies.Atthesametime,youdonotwanttheexposureofanakedshortput.
YoumaythenselltheJune113putat3.10,andinthesametransactionpay2.60fortheJune111put,foranetcreditof0.50.Thispositionisknownastheshortputspreadbecauseitissimilartoashortput.7Theadvantageofthisspreadisthatifthestockdeclines,apossiblelossiscutatthelowerstrike,or111.Youmaythinkofthisspreadasapotentialbuyofthestockatthehigherstrike,or113,andapotentialsaleofthestockatthelowerstrike,or111.Forthispotentialriskyoucollectapremium.
Theexpirationprofit/lossofthisshortputspreadisexactlyoppositetotheformerlongputspread.Themaximumprofitisearnedifthestockisatorabovethehigherstrike,or113.Thisamountissimplythepremiumcollectedforthespread,or0.50.
Themaximumlossoccursifthestockisatorbelowthelowerstrike,or111.Thisiscalculatedasthedifferencebetweenthestrikepricesminustheincomefromthespread:(113–111)–0.50=1.50.
Thebreak-evenlevelisthelevelatwhichadeclineinthestockmatchesthespreadincome.Thisiscalculatedasthehigherstrikeminusthepriceofthespread,or113–0.50=112.50.
Theprofit/lossatexpirationissummarisedasfollows:
CreditfromshortJune113put:
3.10
DebitfromlongJune111put:
–2.60
Totalcreditfromspread:
0.50
Maximumprofit:creditfromspread:
0.50
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Maximumloss:differencebetweenstrikes–creditfromspread:(113–111)–0.50=1.50
Break-evenlevel:higherstrike–creditfromspread:113–0.50=112.50
Therisk/returnpotentialforthisspreadisalsooppositetothelongputspread,atmaximumlossdividedbymaximumprofit,or1.50/0.50.Here,yourisk3.0tomake1.00.8
Intabularformtheexpirationprofit/lossisshowninTable8.5.
Table8.5ShortSPYJune113–111putspread
Thegraphoftheprofit/losspositionatexpirationisshowninFigure8.4.
Figure8.4Expirationprofit/lossrelatingtoTable8.5
LongversusshortcallandputspreadsSofarwehaveseenthatbothalongcallspreadandashortputspreadprofitfromanupsidemove.Likewisebothalongputspreadandashortcallspreadprofitfromadownsidemove.Thequestionmayariseastowhichoneis
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preferable.Thebasicdifferenceisthatofbuyingorsellingpremium,andthetrade-offsaresimilartostraightlongorshortpositionsincallsorputs.
Ifalongandashortspreadarebothout-of-the-moneyandequidistantfromtheunderlying,themaximumprofitofthelongspreadisgreaterthanthemaximumprofitoftheshortspread,buttheshortspreadhasthegreaterprobabilitytoprofit.
Theprobabilityofeitherspreadexpiringinthemoneycanbeapproximatedbythedeltaofthestrikethatisnearesttheunderlying.Intheaboveexamples,boththe117callandthe113puthaveadeltathatisapproximately0.40.Iftheindexhasa40percentprobabilityofmovingtoastrikeineitherdirection,thenthedirectionwhichisshorthasa60percentprobabilityofcollectingitspremium.Themaximumloss,however,isgreaterwiththeshortspread.Themaximumprofit,ofcourse,favoursthelongspread,andthisisafairreturnforanoutcomethatislessprobable.
Premiumsellersoftenshortout-of-the-moneyspreadsthatareatasafedistancefromtheunderlyingbecausethesespreadshavelimitedrisk.Premiumbuyers,however,canaffordtoplacetheirpositionclosertotheunderlyingbecausethecostofthespreadislessthanthecostofastraightcallorput.
Whichstrikes?Callspreadsandputspreadscanbecreatedwithanytwostrikes.Ofcourse,therearetrade-offs.(Theydon’tcallthem‘options’fornothing.)Ifyouspreadthestrikes,thenyougetagreaterprofitrangebutyoupaymore.Youneedtodotechnicalanalysistodeterminewhichstrikestospread.Also,callspreadsandputspreadscanbeanydistancefromtheunderlying.Thetrade-offsaresimilartothosebetweenstraightout-of-the-moneyandat-the-moneycallsorputs.Thefurtheraspreadisfromtheunderlying,thelesscostorincomeithas,andthelessprobabilityithasofbecomingin-the-money.
1×1sandvolatilityskewsInthestockorbondmarkets,theout-of-the-moneyputspreadoftencostslessthantheequidistantout-of-the-moneycallspread.Thisisbecausethelowerstrikeputispricedhigherthanthehigherstrikecall,althoughtheyarethesamedistancefromtheunderlying.Intheaboveexample,the111putis2.60whilethe119callis1.70.Thisisafunctionofwhatareknownasvolatilityskews,whicharediscussedinPart3.
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Incommodities,however,thecallspreadsareoftencheaperthantheequidistantputspreadsbecausethereisapositivecallskew.
Butdon’tbebewilderedatthispoint.Ifyouspread1×1sthenyouminimiseyourexposuretotheskews.Longcallspreadsandlongputspreadsarethesafestwaytotradeoptions.
AfinalnoteThedifferencebetweenaspreadandastraightcallorputisthatthespread’smaximumprofit/losscanbequantifiedattheoutset.Forthelongs,thecostofthespreadisthemaximumloss,andifthetraderisgoodwithtechnicals,hecanpickhislevels.Fortheshorts,thesespreadsallowforpremiumsellingwithabuilt-instop-lossorder.Onarisk/returnbasistheycanberecommendedtoeveryone,especiallybeginners.
____________1S&P500ETFTrust.TheoptionstradeatChicago’sCBOE.TheSPDRisamutualfundbasedontheS&P500.JustthinkofitastheS&P500.Thecurrentopeninterestonthisoptionscontractisamassive13million.Inotherwords,everybodyandhisuncletradeit.Becauseit’s1/10ththesizeoftheSpu’s,it’saffordable.
2Thisspreadisalsoknownasthebullcallspreadandthelongverticalcallspread.3Inpractice,Iprefertohavearisk/returnratioof0.5orbetterunlessI’mverybullish,whichIwaswhenIlookedatthisspread.We’lltalkaboutR/Raswemoveon.
4Thisspreadisalsoknownasthebearcallspreadandtheshortverticalcallspread.5Thisspreadisalsoknownasthebearputspreadandthelongverticalputspread.6ThisisamorejustifiableR/Rthanwehadwiththe117–119callspread.Thereasonwhythisputspreadischeaperthanthecallspreadisbecauseofthesteepputskew.We’lldiscussthislater.
7Thisspreadisalsoknownasthebullputspreadandtheshortverticalputspread.8Iwouldn’t,butmanydobecausesupposedly‘It’llneverhappen’.
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Onebytwodirectionalspreads
Thereareotherwaysoffinancingthepurchaseofadirectionalposition.Thosethatwewilldiscussinthischapterarevariationsofthelongcallandputspreads.Again,theyinvolvebuyinganoptiontotakeadvantageofachosenmarketdirection.Butinsteadofsellingone,theyselltwooptionsatthestrikepricethatismoredistantfromtheunderlying.
Thespreadsinthischapteraresuitableforslowlytrendingmarkets,andtheyareunsuitableformarketsthataretrendingrapidlyhigherorlower,orvolatilemarketsthataresubjecttosuddenshiftsindirection.
LongonebytwocallspreadBullishstrategyThelongonebytwocallspreadisalongcallspreadwithanadditionalshortcallatthehigherstrike.IfXYZisat100,youcouldbuyone105callandselltwo115callsinthesametransaction.Thisspreadisalsoknownastheonebytworatiocallspreadortheonebytwoverticalcallspread.
Inordertotradethisspread,youroutlookshouldcallfortheunderlyingtoincreasetoalevelthatisnear,butnotsubstantiallyabove,thehigherstrike.Thisspread,likethelongcallspread,hasitsmaximumprofitiftheunderlyingisatthehigherstrikeatexpiration.Itislesscostlythanthelongcallspreadbecauseitisfinancedbyanextrashortcall.Butbecauseoftheextrashortcall,thisspreadhasthepotentialforunlimitedlossiftheunderlyingralliessubstantially.TheextrashortcallincludesaddedexposuretotheGreeks.
WithCoca-Colaat52.67,examinetheAugustoptionsonoffer1(60daysuntilexpiration):
Here,youcouldpay1.45foroneAugust55callandselltwoAugust60callsat
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0.34foranetdebitof0.77.Atexpiration,themaximumprofitoccursifthestockclosesatthehigherstrike;thisisthesamelevelaswithalongcallspreadatthesamestrike.Thisprofitiscalculatedasthedifferencebetweenthestrikepriceslessthecostofthespread,or60–55–0.77=4.23.
Becauseoftheextrashortcalltherearetwobreak-evenlevels.Thelowerbreak-evenlevelis,likethelongcallspread,thelowerstrikepriceplusthecostofthespread,or55+0.77=55.77.
Theupperbreak-evenlevelisthemaximumprofitplusthehigherstrikeprice,or60+4.23=64.23.
Abovetheupperbreak-evenlevelthisspreadtakesalossequivalenttotheamountthatthestockincreases.Asummaryoftheprofit/lossatexpirationisasfollows.
DebitfromAugust55call:
1.45
CreditfromtwoAugust60calls:2×0.34=
–0.68
Totaldebit:
–0.77
Maximumprofit:(differencebetweenstrikes)minuscostofspread:(60–55)–0.77=4.23
Lowerbreak-evenlevel:lowerstrikepluscostofspread:55+0.77=55.77
Upperbreak-evenlevel:maximumprofitplushigherstrike:60+4.23=64.23
Maximumloss:unlimitedupside
Inordertoevaluatetherisk/returnpotentialofthisspread,youmustconsidertheupsidepotentialofthestockorunderlying.Rememberthatthemaximumlossispotentiallyunlimited.
Intabularform,theexpirationprofit/lossisasshowninTable9.1.
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Table9.1Coca-ColalongAugust55-60onebytwocallspread
Ingraphicform,theexpirationprofit/lossofthisspreadisasshowninFigure9.1.
Figure9.1Expirationprofit/lossrelatingtoTable9.1
LongonebytwocallspreadforacreditBearishtoslightlybullishstrategyWithadjacentstrikes,orstrikesthatareclosetoeachother,thelongonebytwocallspreadcanoftenbedoneforacredit.Effectively,then,thereisnolowerbreak-evenlevel,andthespreadwillprofitfromadownsidemarketmove.The
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upperbreak-evenlevel,however,becomesmuchclosertotheunderlying.Butthereisahiddendangerinthisspread.
Forexample,usingtheabovestrikes,youcouldpay1.45foroneAuggie55callandselltwoAuggie57.50callsat0.79foranetcreditof0.13onthespread.
Theupperbreak-evenleveliscalculatedasthehigherstrikeplusthemaximumprofit,or57.50+0.13=57.63.
Rememberthatabovetheupperbreak-evenlevelthisspreadhasthepotentialforunlimitedloss.
Thisspreadmaylooklikeeasymoney,butdon’tbemisled.Iftheonebytwocall(orput)spreadcanbedoneforacredit,themarketisprobablytellingyouthattheunderlyingissufficientlyvolatiletobeabovetheupperbreak-evenlevelatexpiration.Perhapsforthisreasontheonebytwospreadforacreditisnotoftentraded.If,afterconsideringthesefactors,youroutlookstillcallsforthestocktoremainbelowtheupperbreak-evenlevelthroughexpiration,thenthelongonebytwocallspreadforacreditisajustifiablestrategy.Thisisnotrecomendedforbeginners.
LongonebytwoputspreadBearishstrategyThelongonebytwoputspreadisalongputspreadwithanextrashortputatthelowerstrike.Itisalsoknownastheonebytworatioputspreadortheonebytwoverticalputspread.IfXYZisat100,youcouldbyone95putandselltwo85putsinthesametransaction.
Inordertotradethisspread,youroutlookshouldcallfortheunderlyingtodeclinetoalevelthatisnear,butnotsubstantiallybelow,thelowerstrike.Atexpirationthemaximumprofitisearnedifthestockclosesatthelowerstrike,butbecauseoftheextrashortput,themaximumdownsidelossispotentiallygreat.TheextrashortputincludesaddedexposuretotheGreeks.Thisspreadislesscostlythanthelongputspreadbecauseitisfinancedbytheextrashortput.
WithCoca-Colaat52.67,examinetheAugustoptionsonoffer2(60daysuntilexpiration):
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WithCoca-Colaat52.67,intheAugustoptions,youcouldpay2.05forthe50.00putandselltwo45.00putsat0.82foranetdebitof0.41($41).Atexpiration,themaximumprofitoccursifthestockclosesat45.00.Thisprofitiscalculatedasthedifferencebetweenstrikesminusthecostofthespread,or(50.00–45.0)–0.41=4.59.
Likethelongonebytwocallspread,therearetwobreak-evenlevels.Theupperbreak-evenleveliscalculatedasthehigherstrikeminusthecostofthespread,or50.00–0.41=49.59Thelowerbreak-evenleveliscalculatedasthelowerstrikeminusthemaximumprofit,or45.00–4.59=40.41.
Belowthelowerbreak-evenlevelthespreadlosespointforpointwiththedeclineofthestock.
Asummaryoftheexpirationprofit/lossisasfollows:
DebitfromlongAugust50.00put:
–2.05
CreditfromtwoshortAugust45.00puts:2×0.82=
1.64
Totaldebit:
–0.41
Maximumprofit:(differencebetweenstrikes)minuscostofspread:50.00–45.00–0.41=4.59
Upperbreak-evenlevel:higherstrikeminuscostofspread:50.00–0.41=49.59
Lowerbreak-evenlevel:lowerstrikeminusmaximumprofit:45.00–4.59=40.41
Maximumloss:amountofstockdeclinebelowlowerbreak-evenlevel
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Therisk/returnpotentialofthisspreadmustconsiderthatthepotentiallossisthefullamountthatthestockmaydeclinebelowthelowerbreak-evenlevel.
Intabularform,theexpirationprofit/lossisasshowninTable9.2.
Table9.2Coca-ColalongAugust50–45onebytwoputspread:Coca-Colaat52.67,100daysuntilexpiration
Ingraphicform,theexpirationprofit/lossofthisspreadisshowninFigure9.2.
Figure9.2Expirationprofit/lossrelatingtoTable9.2
Howtomanagetheriskofthelongonebytwospreads
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Thereturnscenarioforthesespreadsisagradualunderlyingmovefromthelongtowardstheshortstrike.If,however,theunderlyingmakesasuddenmovetotheshortstrike,withnosignofaretracement,thespreadbecomessubjecttothedeltaandvegariskoftheextrashortoption.Itisthenadvisabletocovertheriskofthisoption.Therearetwopracticalsolutions:
The first is simply to buy back the extra short. This cuts the loss on thepositionandleavesanetlongcallorputspreadwithlimitedrisk.The second solution is less costly, and it is to buy an out-of-the-moneyoptionthatisthesamedistancefromthetwoshortoptionsastheyarefromthe longoption.Forexample, if thespread is longone105callandshorttwo115calls,andifXYZralliesto115,thenthesolutionistobuyone125call.Likewise,ifthespreadislongone95putandshorttwo85puts,andifXYZbreaksto85,thenthesolutionistobuyone75put.
Inthefirstcase,theresultingpositionisalongcallbutterfly,andinthesecondcase,theresultingpositionisalongputbutterfly.Bothpositionshavelimitedriskbecausetheyhavecoveredthenakedshortoption.Theyalsohavethepotentialtorecoupsomeofthelossthroughtimedecay.Thebutterflyspreadisdiscussedinaseparatechapter.
Beforeyoutradeanyspreadthatisnetshortanoption,youshouldhaveacontingencyplanaspartofyourriskscenario.Atthesametimeasyouplaceyourspreadorder,youshouldalsoplaceabuy-stop,marketorderforacoveringoptionthatisactivatedatapredeterminedleveloftheunderlying.
Longcallladder(UK),orlongcallChristmastree(US)BullishstrategyAvariationofthelongonebytwoisaspreadthatplacesthetwoshortoptionsatdifferentstrikes.Thelongcallladderisalongcallspreadwithanextrashortcallatathirdstrikethatisabovethelowertwostrikes.IfXYZisat100,thenyoucanbuyone105call,sellone110call,andsellone115callinthesametransaction.ThisspreadisalsoknownasthelongChristmastree,orsimply,the‘tree’.3Inpractice,itisplacedout-of-the-money.
InAugust,withtheCoca-Colastockat52.67,youcouldpay1.45forone55.00
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call,sellone57.50callat0.79,andsellone60.00callat0.34foranetdebitof0.32.
Atexpiration,themaximumprofitfortheladderisearnedwhenthestockclosesatthetwoupperstrikes,57.50and60.Thisprofitiscalculatedasthedifferencebetweenthetwolowerstrikesminusthedebit,or57.50–55.00–0.32=2.18.Thelowerbreak-evenleveliscalculatedastheloweststrikeplusthespreaddebit,or55.00+0.32=55.32.
Theupperbreak-evenlevelisthehigheststrikeplusthemaximumprofit.Inthiscase,thecalculationis60.00+2.18=62.18.Abovetheupperbreak-evenlevelthespreadlosespointforpointwiththestock,andfacesthepossibilityofunlimitedloss.Theexpirationprofit/lossisasfollows:
DebitfromlongAugust55.00call:
–1.45
CreditfromshortAugust57.50call:
0.79
CreditfromshortAugust60.00call:
0.34
Totaldebit:
–0.32
Maximumprofit:(middlestrikeminuslowerstrike)minusdebitfromspread:here,(57.50–55.00)–0.32=2.18
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:55.00+0.32=55.32
Upperbreak-evenlevel:higheststrikeplusmaximumprofit:60.00+2.18=62.18
Maximumloss:potentiallyunlimited
Noteagainthepotentialforunlimitedlosscomparedtoamaximumprofitof2.18.Theexpirationprofit/lossofthisspreadisshowninTable9.3.
Table9.3Coca-ColalongAugust55.00–57.50–60.00callladder
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Figure9.3isagraphofthisspreadatexpiration.
Figure9.3Expirationprofit/lossrelatingtoTable9.3
Youcancomparethisladdertothe55–60onebytwo.Itwouldcost0.75,andthebreak-evenlevelsare55.75and64.25.Themaximumprofitofthe1×2is4.25,butthisprofitlevelis60.00.Thisladderisafairalternativeintermsofrisk/return.
Longputladder(UK),orlongputChristmastree
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(US)BearishstrategyThelongputladderisalongputspreadwithanextrashortputatathirdstrikebelowtheputspread.IfXYZisat100,thenyoucouldbuyone95put,sellone90putandsellone85putinthesametransaction.ThisspreadisalsoknownasthelongputChristmastree.
WithCoca-Colaat52.67youcouldpay2.05foroneAugust50put,selloneAugust45putat0.82andselloneAugust40putat0.34.Here,thespreadtradesforanetdebitof–0.89.
Atexpiration,themaximumprofitisearnedwhenthestockclosesbetweenthelowertwostrikes,45–40.Inthiscase,becauseofthesmallspreaddebit,thisprofitiscalculatedasthedifferencebetweenthehighertwostrikesminusthecostofthespread,or(50–45)–0.89=4.11.
Theupperbreak-evenlevelisthehigheststrikeminusthecostofthespread,or50–0.89=49.11.Thelowerbreak-evenlevelistheloweststrikeminusthemaximumprofit,or40–4.11=35.89.
Themaximumlosscanbesignificant;itisthefullamountthatthestockdeclinesbelowthelowerbreak-evenlevel.Theexpirationprofit/lossforthisspreadisasfollows:
DebitfromlongAugust50put:
–2.05
CreditfromshortAugust45put:
0.82
CreditfromshortAugust40put:
0.34
Totaldebit:
–0.89
Maximumprofit/loss:(higheststrikeminusmiddlestrike)minuscostofspread:(50–45)–0.89=4.11
Upperbreak-evenlevel:higheststrike–costofspread:50–0.89=49.11
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Lowerbreak-evenlevel:loweststrikeminusmaximumprofit:40–4.11=35.89
Maximumloss:amountofstockdeclinebelowlowerbreak-evenlevel
Therisk/returnpotentialofthisspreadshouldaccountforadeclineinthestockbelowthelowerbreak-evenlevel.Theexpirationprofit/lossintabularformisshowninTable9.4.
Table9.4Coca-ColalongAugust50–45–40putladder
Figure9.4isagraphoftheexpirationprofit/loss.
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Figure9.4Expirationprofit/lossrelatingtoTable9.4
YoumightcomparethisputladdertotheCoca-Colacallladder.Here,wehavesplitstrikes,whilethecallladderhasadjacentstrikes.Fortheputladderwepaid0.82,whileforthecallladderwepaid0.30.Withtheputladder,however,wehavedoubledourprofitrangefrom2.50pointsto5.00points.Wehavealsoplacedourbreak-evenpointfurtherfromtheunderlying.
HowtomanagetheriskofthelongladderTheriskofthelongladderismanagedsimilarlytothatofthelongonebytwo.Iftheunderlyingsuddenlymovestotheshortstrikethatwasformerlyfurthestout-of-the-money,thefirstsolutionistobuybackthatstrike.
Thesecondsolutionistobuytheout-of-the-moneyoptionthatisasfarfromtheladderasthethreeoptionsintheladderarefromeachother.Forexample,iftheladderislongone105call,shortone110callandshortone115call,andifXYZquicklyralliesto115,thenthesolutionistobuyone120call.Likewise,iftheladderislongone95put,shortone90putandshortone85put,andifXYZsuddenlybreaksto85,thenthesolutionistobuyone80put.Inthefirstcase,theresultingpositionisalongcallcondor,andinthesecondcase,theresultingpositionisalongputcondor.Bothofthesespreadshavelimitedrisk;theyarediscussedinChapter13.
LaddersatdifferentstrikepricesWiththeladdertheconsecutivestrikepricesareusuallyequidistantfromeachother.Theequidistance4mayvary,however,fromadjacenttoanynumberofnon-adjacentstrikes.Forexample,ifXYZisat100,acallladdermayhavestrikepricesat105,110and115,oritmayhavestrikepricesat105,115and125.Thesecondladdercostsmorebecausethesumoftheoptionssoldisless.Itsprofitpotential,however,is10pointsinsteadof5,lesscost.Itsupperbreak-evenlevel,orpointofpotentialunlimitedrisk,isfurtherfromtheunderlying.Withladders,themajorriskconsiderationisthatthestrikefurthestout-of-the-moneyshouldbeatasafedistancefromtheunderlying.
AsymmetricorbrokenladderFinally,thereisnoreasonwhythestrikesofaladderneedtobeequidistantfromeachother.Asymmetricladdersareoccasionallytraded,andtheyhavedifferent
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risk/returnprofiles.Forexample,youmaywishtoplacethesecondshortstrikefurtherfromtheunderlying.IfXYZisat100,insteadofplacingyourcallladderat105,110and115,youmayplaceitat105,110and120.Thesecondspreadcostsmoreandthereforehaslessprofitpotential,butithaslessriskbecauseitsupperbreak-evenlevelisfurtherfromtheunderlying.
Alternatively,youmayplaceyourladderat105,115and120.Thisspreadcostsmorethanthetwoabovebecausethetwooptionssoldaretheleastexpensive,butithasthegreatestprofitpotential.Italsohastheleastpotentialriskbecauseitsupperbreak-evenlevelisthefurthestfromtheunderlying.Justrememberthatthemajorriskoftheladderlieswiththeextrashortoption.
Comparingcallspreads,1×2sandladdersAtthispoint,itwillbeconstructivetocomparethedatafromthespreadsalreadydiscussed.Wewanttoexaminecosts,profitpotentials,risksandbreak-evenlevels.Ifweexaminethecallspreads,thenwecanapplytheconclusionstotheputspreads.RefertothetableofCoca-Colaoptionsabove.
Coca-Colaat52.67Augustoptions,100daysuntilexpiration
TrytodevelopyouroptionsawarenessbytakingafewminutestoanalysethedatainTable9.5.Comparethecostsorincomestothepotentialprofits,andcomparethepotentialprofitstotheupperbreak-evenlevels,etc.
Themostriskaversespreadsareobviouslythetwoonebyonecallspreads.Concerningtheothers,ifthemarketmovesinthedirectionofyourshortstrikeyoumayhavetocoversimplyoutofworry.Itismucheasiertomaketradingdecisionswhenyourjudgementisnotimpairedbyproximaterisk.
Ananalysisproceduresuchastheaboveshouldalwaysbeusedwhendecidingwhichspreadtotrade.
Table9.5Comparingcallspreads,1×2sandladders
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Astoryabout1×2sandladdersSeveralyearsagoIwasaclientstrategistforaboutiqueLondonbrokeragefirm.Iwouldgivelecturestoclientsaboutthesamestrategiesthatyouarelearning.Myjobwastogettheclientsuptospeedwithoptionssothatwhenourbrokersphonedthemtheywouldknowwhatourbrokersweretalkingabout.
Wecoveredthefundamentalspreads,therisk/returntrade-offs,theuseoftechnicalanalysis,etc:inotherwords,thebasicsofoptions.
Ialsoincreasedourbrokers’knowledge,butmostlyintermsofapplications.(Brokersseldomwanttoknowabouttheory.)Thentogetherwedevisedtraderecommendationswhichthebrokerspassedontotheirclients.
Theclientsdidwell.OneofthemtookoneofourrecommendationsandboughtaBundputladderatjusttherighttime.TheGreeksandthelevelsworkedinherfavour.AnotherdidwellintheEuriborforthesamereasons.
Butlater,oneofthebrokersfalselyassumedthathehadmasteredwhatIhadtaughthim,andhebegantorecommend1×2sandladderswithoutconsultingme.Itledtodisaster.
Oneofourclientswasaatraderforamajorhedgefundwhogotcaughtoutonaput1×2.Hebegantocovertheirriskbysellingfutures.Thentheotherplayersinthemarketneededtosellfuturesinordertocovertheirrisk.Themarketwentdownanddown.Traderswereringingusup,asking‘What’sgoingon?This
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don’tmakesense.’Finallythespread-arbsstabilisedthemarket,butourclienthadlostbig,andhewasfurious.
Therewerephonecallsandmeetings,butfortunatelyitdidn’tgetugly.Intheendheforgaveusoursinsbecauseheacceptedthatthebrokermadeanhonestmistake.(Likenotknowingwhathewasdoing.)Thelessonis:eitheryouworkwithanoptionsstrategistoryoustickto1×1s,longvanillas,andbutterfliesorcondors.
____________1DatacourtesyoftheChicagoBoardOptionsExchange,CBOE.2DatacourtesyoftheChicagoBoardOptionsExchange,CBOE.3Thistermprobablysignifiesthattheoptionsareplacedathigherandhigherlevels,likeornamentsonaChristmastree.Rememberthatthisspreadisnetshortanoption,soyouwillwanttoputoutthefirebeforeitreachesthetop.
4i.e.,thedistancethatisequal.Thisword,foundintheLennyJordanDictionary,willcomeinhandywhenwediscussspreadswithfourcomponents.
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10
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Combosandhybridspreadsformarketdirection
Longcall,shortputcomboorcylinderBullishstrategyStillanotherwayoffinancingalongcallpositionistosellaput.Usuallybothstrikesareout-of-the-money,andthisspreadiscalledthelongcall,shortputcombo.Itisalsocalledthecylinder.IfXYZisat100,youmaybuythe110callandsellthe85putinthesametransaction.Inordertotradethisspread,youmustbereasonablycertainthattheunderlyingisduetoincreaseinvalue,becausetheshortputincursthepotentialobligationtobuytheunderlying.Thedownsideriskisgreat,butsoistheupsidepotential.
Thisspreadisoftentradedbyprofessionalswhowanttobuytheunderlying.Thelongcallservesasabuy-stoporder,whiletheshortputservesasarestingbuyorderwherevalueisestimatedtobe.
Considerthefollowing:Coca-Colaat52.6760daysuntilAugustexpirationContractmultiplierof$100TheAugustoptionsareshowninTable10.1.
Table10.1Coca-ColaAugustoptions
DatacourtesyoftheChicagoBoardOptionsExchange,CBOE.
Here,youcouldpay0.79foroneAugust57.50call,andselloneAugust45.00
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putat0.82foranetcreditof0.03.1Ontheupside,thespreadbehaveslikealong57.50callsoldfor0.03.Thebreak-evenlevelisthecallstrikepriceminusthecostofthespread,or57.50–0.03=57.47.Youarelongacall,soyouhaveunlimitedupsidepotential.
Onthedownside,thespreadbehaveslikeashort45putforwhichyoureceiveacreditof0.03.Ifatexpiration,thestockclosesbelowtheputstrike,or45,youwillbeassignedontheshortput,andyouwillbeobligatedtobuythestockatthestrikeprice,or45.Thecostofyourstockpurchasewillbeeffectivelyreducedbythecreditofthespread.Forexample,ifthestockclosesat45andyouareassignedontheput,thepurchasepriceofCoca-Colawouldbe45–0.03=44.97.Ifthestockcontinuestodecline,youarestillobligatedtomakepurchaseforaneffectivepriceof44.97.Becauseofthenaked,shortput,thepotentiallossislarge.
Itisadvisabletoplacetheputatagreaterdistancefromtheunderlyingthanthecall,unlessyouareconvincedthatthestockhasbottomedout.Usethetechnicalstofindasupportarea.
Ifatexpirationthestockclosesbetween45and57.50,thecreditfromthespread,or0.03inthiscase,isearned.Theexpirationprofit/lossissummarisedasfollows:
DebitfromAugust57.50call:
–0.79
CreditfromAugust45put:
0.82
Totalcredit:
0.03
Becauseyouhavetradedthisspreadforacredit,thereisnoupsidebreak-evenlevel.
Maximumupsideprofit:potentiallyunlimitedDownsidepotentialpurchaseprice:lowerstrikepriceminuscreditfromspread:45.00–0.03=44.97Maximumdownsideloss:declineofstockbelowdownsidepotentialpurchaseprice:44.97Profit/lossbetweenstrikes:creditfromspread:0.03profitbetween45and57.50
Therisk/returnpotentialis,practicallyspeaking,equalandgreat.Intabular
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form,theexpirationprofit/lossisshowninTable10.2.
Table10.2Coca-ColalongAugust57.50call,short45putcombo
Ingraphicterms,theexpirationprofit/lossisshowninFigure10.1.
Figure10.1Expirationprofit/lossrelatingtoTable10.2
Thelongcall,shortputcomboisoftentradedinbullmarkets,andespeciallybullmarketsincommoditiesthatarestartingfromlong-termsupportlevels.
Longput,shortcallcombo,orfenceBearishstrategyAmorecommonuseofthisspreadiswithalongout-of-the-moneyputcoupledwithashortout-of-the-moneycall,knownasthelongput,shortcallcombo.Itisalsocalledthecylinderorthecollar.IfXYZisat100,youcouldbuyone95putandsellone110callinthesametransaction.Bothoptionspositionsareapotentialsaleoftheunderlying.
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Thisspreadisoftenusedasahedgebyinvestorswhoownorarelonganunderlyingcontract.Theywanttheircashbackifthemarketdeclines,buttheywanttotaketheirprofitifthemarketrallies.Thelongputactsasastop-lossorderontheirunderlyingpositionwhiletheshortcallactsasarestingsellorderatafavourableprice.Whenusedinthismannerthisspreadiscalledthefence.2
Thecallandtheputcanbeplacedatwhateverlevelsaredesirable,butoften10percentout-of-the-moneylevelsareusedasareference.
InCoca-Colayoucouldpay1.30foroneAuggie47.50putandselloneAuggie60callat0.34foranetdebitof0.96.Onthedownside,yourspreadbehaveslikealong47.50putpurchasedfor0.96.Yourbreak-evenlevelistheputstrikeminusthecostofthespread,or47.50–0.96=46.54.Belowthislevelyouprofitonetoonewiththedeclineofthestock,oryouhedgeyourinvestmentonetoone.
Ontheupside,yourspreadbehaveslikeashort60callforwhichyouhavepaid0.96.Ifthestockclosesabove60atexpiration,youwillbeassignedonyourshortcall,andyouwillbeobligatedtosellthestockat60.Thespreadwastradedforadebitof0.96,soyoureffectivesalepricewouldbethecallstrikeminusthespreaddebit,or60–0.96=59.04.Nomatterhowfarthestockrisesabove60,youwillstillbeobligatedtosellitforaneffectivepurchasepriceof59.04.Theloss,aswithanyshortcallposition,ispotentiallyunlimited.Youhadbetterownthestock.
Atexpiration,ifthestockclosesbetweenthestrikeprices,thespreaddebitistakenasaloss.Here,ifthestockclosesbetween47.50and60,thelossonthepositionis0.96.
Asummaryoftheexpirationprofit/lossisasfollows:
DebitfromlongAugust47.50put:
–1.30
CreditfromshortAugust60call:
0.34
Totaldebit:
–0.96
Downsidebreak-evenlevel:putstrikeminuscostofspread:47.50–0.96=46.54Maximumdownsideprofit:declineofstockbelowlowerbreak-evenlevel:46.54
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Upsidepotentialsaleprice:higherstrikeminusdebitfromspread:60–0.96=59.04Maximumupsideloss:potentiallyunlimitedProfit/lossifstockclosesbetweenstrikes:lossofspreaddebit:0.96
Again,therisk/returnpotential,practicallyspeaking,isequalandgreat.Theexpirationprofit/lossisshowninTable10.3.
Table10.3Coca-ColaAugustlong47.50put,short60callcombo
Figure10.2showsagraphofthiscombo.
Figure10.2Expirationprofit/lossrelatingtoTable10.3
IfyouweretheownerofCoca-Colastock,andifyouappliedthisspreadasafence,thenyoureffectivesellinglevelsatexpirationwouldbeeither46.54or59.04.
Directionalhybridspreads
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Thedirectionalspreadsthatwehavediscussedarethemostcommon,buttheyarenottheonlychoicesavailable.Manyinvestorscreatespreadsthatcombinecomponentsofthestandardspreadstosuitaparticularoutlookandstrategy.Therearenospecialtermsforthesehybridspreads,buttheycanbetradedinonetransactiononmost,ifnotall,open-outcryexchanges.Youmaynottradethesespreads,butyoumightreviewtheminordertoimproveyouroptionsawareness.
Aswithallspreads,ahybridcanbecreatedprovidedyouroutlookaccountsfor:
directionlevelofsupportlevelofresistance.
Therisk/returnpotentialshouldalsobeassessed,andanycontingencyplansprepared.Thefollowingisjustoneexampleofahybridspread.
BullishstrategyIfacallpurchasecanbefinancedbythesaleofaput,thenacallspreadpurchasecanbefinancedbythesaleofaput.IfXYZisat100,youcouldbuythe105–115callspreadandsellthe85put.Onmostopen-outcryexchanges,thisthree-waycanbetradedinonetransaction,andthebid–askspreadforitwillbemarginallygreaterthanwithasingleoption.
Theadvantageofthisspreadisthatthelongcallisfinancedwithtwooptions,butthedisadvantageisthattheshortputcontainsthepotentialobligationtopurchasetheunderlyingifthemarketdeclines.Also,theupsideislimited.
WithCoca-Colaat52.67,youcouldpay1.45foroneAugust55call,selloneAugust60callat0.34,andselloneAugust45putat0.82inthesametransactionforanetdebitof0.29.Theprofitrangeis5pointsatacostof0.29.ComparethistotheAugust55–60spread,whichhasthesameprofitrangeatacostof1.11.Thethree-waymustaccountforthenakedshortput,however.Here,yourtechnicalanalysistellsyouthatthereissupportat45.
Theupsideofthisspreadbehaveslikealong55–60callspreadpurchasedforacostof0.29.Thebreak-evenlevelatexpirationisthelowerstrikeplusthecostofthespread,or55+0.29=55.29.
Themaximumupsideprofitisthedifferencebetweenthecallstrikesminusthecostofthespread,or(60–55)–0.29=4.71.
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Thedownsideofthisspreadbehaveslikeashort45puttradedforadebitof0.29.Ifthestockclosesbelow45atexpiration,youwillbeassignedontheshortput,andyouwillbeobligatedtopay45forthestock.Becauseyourspreadwastradedforadebitof0.29youreffectivepurchasepricewillbethestrikepriceoftheputplusthecostofthespread,or95+0.29=95.29.Nomatterhowfarthestockdeclinesbelow95,youwillstillbeobligatedtopurchaseitforaneffectivecostof95.29.Becauseofthenakedshortput,thepotentiallossisgreat.
Ifatexpirationthestockclosesbetweenthemiddlestrikesofthespread,or45–55,alossistakenequaltothecostofthespread,or0.29.Asummaryoftheprofit/lossatexpirationfollows.
DebitfromlongAugust55call:
–1.45
CreditfromshortAugust60call:
0.34
CreditfromshortAugust45put:
0.82
Totaldebit:
–0.29
Upsidebreak-evenlevel:lowercallstrikepluscostofspread:55+0.29=55.29Maximumupsideprofit:differencebetweenstrikesminuscostofspread:(60–55)–0.29=4.71Potentialdownsidepurchaseprice:putstrikepluscostofspread:45+0.29=45.29Maximumdownsideloss:fullextentofthestock’sdeclinebelow45.29Profit/lossifstockclosesbetweenthemiddletwostrikes(55–60)isthecostofthespread,or0.29loss
Likethecombo,thisthree-wayisoccasionallytradedatthebeginningofbullmarketsincommodities,whenlong-termsupportlevelsarewellestablished.Therearemanyotherhybridswhicharetradedlessoften.Themoresophisticatedtradersarecontinuallyinventingnewwaystospreadoptions.
____________1Thecreditearnedfromthisspreadispossiblebecauseofthepositiveputvolatilityskew.Thisisoftenthecase.Butbewareoftakingtoomuchcreditfromthisspread.
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2I'veevenheardofthisspreadreferredtoasthe‘collar’.Again,omitthejargon.Insteadsay‘Iwanttobuy[this]optionandsell[that]optionasaspread.’
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11
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Volatilityspreads
MarketvolatilityOptionsdifferfrommostotherinvestmentproductsbecausetheyaddressmarketvolatility.1Volatilityisafunctionofabsolutepricemovement,i.e.pricefluctuationsineitherdirection.Optionscanbetradedtoprofitfromeitherincreasingordecreasingabsolutemovement.Oftenthepricetrendofanunderlyingismoredifficulttoassessthanitsvolatilitytrend.Whenthisisthecase,volatilityspreadsarepreferable.
Ifthevolatilityisincreasing,wecanoftenassumethattheunderlyingisexpandingitsrange,andthatitwillbesignificantlyhigherorloweratexpirationthanitisatpresent.Theriskofourassumptionisthattheunderlyingmayincreaseitsrangebutthatatexpirationitmaysettleatthemidpoint.
Ifthevolatilityisdecreasing,wecanoftenassumethattheunderlyingwillbewithinitsrecentrangeatexpiration.Theriskofourassumptionisthattheunderlyingmaydecreaseitsrangebutthatbyexpirationtherangeitselfmayshifttoahigherorlowerlevel.
Ifwewishtotradevolatility,wecantakepositionsthatprofitfromeitherincreasingordecreasingabsolutemovement.Inmoreconventionalterms,wesaythatwecantakepositionstoprofitfromeithervolatileorstationarymarkets.Byconvention,theword‘volatile’meanshighvolatility,andbyconvention,theword‘stationary’meanslowvolatility.Theseconventionaltermsmaynotbeprecise,butnowthatweknowtheirlimitations,wecanusethem.Therefore,forourpurposewecansetoutthefollowingdefinitions:
Volatile means increasing absolute price movement, high absolute pricemovement, increasinghistorical and impliedvolatility, andhighhistoricalandimpliedvolatility.Stationarymeansdecreasingabsolutepricemovement,lowabsolutepricemovement, decreasing historical and implied volatility, and lowhistoricalandimpliedvolatility.
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Spreadsforvolatilemarkets,suchasthelongstraddle,profitfromincreasedvolatility,bothhistoricalandimplied.Theyincuracostfromtimedecay.Theymayormaynotbenetlongoptions.Theyhavenetpositivevega,positivegammaandnegativetheta.Thesespreadsarebestopenedwhenthemarketisquiet,oremergingfromquietconditions,andwhenabsolutemovementisexpectedtoincrease.
Spreadsforstationarymarkets,suchasthelongat-the-moneybutterfly,profitfromdecreasedvolatility,bothhistoricalandimplied.Theyprofitfromtimedecay.Theymayormaynotbenetshortoptions.Theyhavenetnegativevega,negativegammaandpositivetheta.Thesespreadsarebestopenedwhenthemarkethasbeenactive,andwhenabsolutemovementhasstartedtodecrease.
Thesamespreadcanoftenbetradedineithervolatileorstationarymarkets,dependingonwhetheritisboughtorsold.Practicallyspeaking,someofthesespreadsaremoresuitableforthefirstorthesecondtypeofmarket,andsomehavemoreinherentrisks.Allbeginnersshouldtradethespreadswiththeleastrisk,andthesearemarkedwithanasterisk(*).
Atsomepoint,youmaybenefitfromreviewingthisintroduction.
LongstraddleForvolatilemarketsThelongstraddleisasimultaneouspurchaseoftheat-the-moneycallandput.Thisspreadprofitswhentheunderlying,atexpiration,hasincreasedordecreasedtoalevelthatmorethancompensatesforitscost.IfXYZisat100,youcouldbuythe100callandthe100putinthesametransaction.Themaximumriskofthespreadisitscost,andthepotentialreturnisthefullamountthattheunderlyingincreasesordecreasesabovetheupside,orbelowthedownside,break-evenlevels.
ConsiderthefollowingApriloptionsonMarksandSpencer:
MarksandSpencerat350.6030daysuntilAprilexpiryContractmultiplieris£1,000
Table11.1MarksandSpencerApriloptions
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SettlementpricescourtesyofNYSEEuronextLiffe.
Here,youcouldpurchasetheApril350straddlebypaying11.25pforthe350calland10.25pforthe350putinasingletransaction,foratotaldebitof21.50p(£215).Thisdebitisyourmaximumrisk.Withthisspreadyouhavetherighttobuythesharesat350;alsotherighttosellthesharesat350.
Atexpiry,theupsidebreak-evenlevelisthestrikepriceplusthecostofthespread,or350+21.50=371.50.Thedownsidebreak-evenlevelisthestrikepriceminusthecostofthespread,or350–21.50=328.50.
Above371.50thespreadprofitspointforpointwithanincreaseinthestockprice,andthemaximumreturnispotentiallyunlimited.Below328.50thespreadprofitspointforpointwithadeclineinthestockprice,andthemaximumreturnisthefullextentoftheshares’decline.(ThereareprobablybuyersforMarksandSpencerbeforeitgetstozero.)
Betweenthebreak-evenlevels,apartiallossistaken.Ontheupside,thisequalstheshareprice,minusthestrikeprice,minusthecostofthespread.
Inthiscase,ifthesharesatexpirycloseat370,thelosswouldbe(370–350)–21.50=–1.50.Onthedownside,thepartiallossequalsthestrikeprice,minustheshareprice,minusthecostofthespread.Inthiscase,ifthesharescloseat330,thelosswouldbe(350–330)–21.50=–1.50.
Theexpiryprofit/lossissummarisedasfollows:
DebitfromlongApril350call:
–11.25
DebitfromlongApril350put:
–10.25
Totaldebit:
–21.50
Upsidebreak-evenlevel:strikepricepluscostofspread:350+21.50=371.50Downsidebreak-evenlevel:strikepriceminuscostofspread:350–21.50=328.50
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Maximumupsideprofit:potentiallyunlimitedMaximumdownsideprofit:amountthatstockdeclinesbelowlowerbreak-evenlevel:328.50Maximumrisk:costofspread:21.50
Inordertodeterminetherisk/returnpotentialofthisspread,youmustconsiderthecostofthespreadversusthepotentialforabsolutepricemovementofthestock.Intabularform,theexpirationprofit/lossisasinTable11.2.
Table11.2MarksandSpencerlongApril350straddle
Aprofit/lossgraphofthisspreadatexpiryisasshowninFigure11.1.
Figure11.1Expirationprofit/lossrelatingtoTable11.2
Thelongstraddlehasthetotalpositivevegaofthecallplustheput.Itisextremelysensitivetoachangeintheimpliedvolatility.Iftheunderlyingstarts
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tomove,andtheimpliedvolatilitystartstoincrease,thisspreadprofitsontwoaccounts:directionandincreasedimplied.
Thisspreadhasdoublethegammaofasingleat-the-moneycallorput.Ifthemarketrallies,theincreaseofthecalldeltaaccelerates,thedecreaseoftheputdeltaaccelerates,andthespreadgetslongerquickly.Ifthemarketbreaks,thespreadgetsshorterquicklyfortheoppositereasons.
Therisk,orthetrade-off,ofthelongstraddleisthatthemarketmaystayinitspresentrange,andthattheimpliedvolatilitymaydecreasewhiletimedecaydepreciatestheinvestment.Rememberthatwithat-the-moneyoptionstimedecayacceleratesintheperiodof60–30daysuntilexpiration.Theriskhereisdoublethatofasingleat-the-moneyoption,andevengreaterthanwithanout-of-the-moneyoption.Itisthereforeadvisabletotakealongstraddlepositionthatishalfthesizeofyourusualposition.
Thelongstraddleisthemostexpensiveoptionsspread,andsoitrequiresagreatdealofmarketmovementinordertoprofit.Itcanpayoffhandsomely,oritcanresultinabiglet-down.
Manytradersbuystraddlesinanticipationofashort-termspikeinvolatility–forexample,ifaneventisforeseen.Thenabitofmarketmovementisabonus.Theyselltheirstraddlequicklyaftertheevent,beforetimedecayreducestheirprofit.
Inthisexample,timedecayisseverewith30daysuntilexpiry,soinordertobuythisstraddle,youwouldneedtobeconfidentthatMarksandSpencerisdueforabigmove,andthattheoptionsweredueforanincreaseinimpliedvolatility.
Aspreadthatprofitsfromvolatilemarketsbutthathaslessriskthanthelongstraddleisthelongironbutterfly(discussedinChapter12).
ShortstraddleForstationarymarketsTheshortstraddleistheoppositepositionofthelongstraddle,i.e.asimultaneoussaleoftheat-the-moneycallandput.IfXYZisat100,youcouldsellboththe100callandthe100put.Therisk/returncharacteristicsarealsooppositetothelongstraddle.Themaximumreturnistheamountofthepremiumcollected;thepotentiallossisunlimited.Inordertosellthestraddle,youmustbeconvincedthattheunderlyingwillnotexceedtherangecoveredbythe
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premiumincome,orthebreak-evenlevels,atexpiration.Youmustalsobepreparedtomeetlargemargincallsifthepositiongoesagainstyou.Becausethepotentialriskisunlimiteditisnotadvisabletosellthestraddleuntilyouareanexperiencedoptionstrader.
Becausethestraddleisthemostexpensiveoptionsspread,itisoftenatemptingsale,anditisoftenprofitable.Itisjustifiableonlywhenprobabilityisontheseller’sside.Assessingprobabilityisdifficult,butthevolatilitytrendsarethemosthelpfulguides.
Theexpiryprofit/lossfortheshortstraddlecanbesummarisedbymakingtheoppositecalculationsofthepreviouslongstraddle.Thissummaryisasfollows:
CreditfromlongApril350call:
11.25
CreditfromlongApril350put:
10.25
Totalcredit:
21.50
Upsidebreak-evenlevel:strikepricepluscreditfromspread:350+21.50=371.50Downsidebreak-evenlevel:strikepriceminuscreditfromspread:350–21.50=328.50Maximumupsideloss:potentiallyunlimitedMaximumdownsideloss:amountthatstockdeclinesbelowlowerbreak-evenlevel:328.50Maximumprofit:incomefromspread:21.50
Therisk/returnpotentialofthisspreadmustbeevaluatedintermsofitsincomeversusalossthatispotentiallyunlimited.Intabularform,theexpiryprofit/lossisasshowninTable11.3.
Table11.3MarksandSpencershortApril350straddle
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Ingraphicform,theexpiryprofit/lossisasshowninFigure11.2.
Figure11.2Expirationprofit/lossrelatingtoTable11.3
Again,manytraderssellthestraddletoprofitfromashort-termdeclineinvolatility.Theirviewisthataforthcomingeventwillbeanon-event.Forexample,iftheUSnon-farmpayrollsarereportedasexpected,thenvolatilitymaygetcrushed,andthestraddlesellersquicklybuytheirstraddlesback.
Twosimilarspreadsthatprofitfromstationarymarketsbutthathavelimitedriskarethelongat-the-moneybutterfly(discussedinChapter13)andtheshortironbutterfly(discussedinChapter12).Theyareamongthespreadsrecommendedforstationarymarkets.
LongstrangleForabsolutemarketmovement
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Thelongstrangleisthesimultaneouspurchaseofanout-of-the-moneycallandput.Boththeoptionsareequidistantfromtheunderlying.IfXYZisat100,youcouldbuythe90putandbuythe110callinthesametransaction.Thisspreadissimilartothelongstraddlebutcostsless.Thebreak-evenlevelsaremoredistantfromtheunderlying,andwhilethereislesspotentialprofit,thereisalsolessrisk.
UsingtheprecedingsetofMarksandSpencerApriloptions,youcouldpay6.75forone360callandpay6.25forone340putinthesametransactionforatotaldebitof13p(£130)Thisdebitisyourmaximumrisk.
Atexpiry,theupsidebreak-evenlevelisthehigherstrikepriceplusthecostofthespread,or360+13=373.Thedownsidebreak-evenlevelisthelowerstrikepriceminusthecostofthespread,or340–13=327.
Likethelongstraddle,thisspreadprofitsthefullamountthatthestockclosesoutsidethebreak-evenlevelsatexpiration.Ifthestockclosesbetweenthestrikeprices,thecostofthespreadistakenasaloss.Betweenthestrikepricesandthebreak-evenlevels,apartiallossistaken.
Theexpiryprofit/lossforthisspreadissummarisedasfollows:
DebitfromlongApril360call:
–6.75
DebitfromlongApril340put:
–6.25
Totaldebit:
–13.00
Upsidebreak-evenlevel:upperstrikepricepluscostofspread:360+13+373Downsidebreak-evenlevel:lowerstrikepriceminuscostofspread:340–13=327Maximumupsideprofit:potentiallyunlimitedMaximumdownsideprofit:amountofstockdeclinebelowlowerbreak-evenlevel:327Maximumrisk:costofspread:13
Inordertodeterminetherisk/returnpotentialofthisspread,youmustweighitscostagainstthepotentialforthesharestomoveoutsidethebreak-evenlevels.Theexpiryprofit/lossisasshowninTable11.4.
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Table11.4MarksandSpencerlongApril340–360strangle
Theexpiryprofit/lossisshowninFigure11.3.
Figure11.3Expirationprofit/lossrelatingtoTable11.4
Asaspreadforvolatilemarkets,thelongstranglecanbeplacedatanydistancefromtheunderlying.Thecloserbothstrikesaretotheunderlying,themorethisspreadbehaveslikealongstraddle,withincreasedexposuretotimedecay(vianegativetheta),andincreasedexposuretoadeclineinimpliedvolatility(viapositivevega).Becausethemaximumriskofthisspreadisknownattheoutset,itisnotinadvisabletotradeit,butbecauseofthepremiumexposure,andbecauseonlyoneofthestrikesislikelytoprofit,theriskmaybeunjustifiableforsomeinvestors.Asimilarspreadwithlesspremiumriskisthelongironcondor,discussedinChapter12.
Thelongstrangleispreferableasatradetoprofitfromincreasingimpliedvolatility.Ifthecurrentimpliedislowand/orincreasing,thisspreadhasanadditionalreturnscenario.Itisthereforejustifiableinitself,regardlessof
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direction,andthewings,oreachstrike,canbeplacedfar-out-of-the-money.Aswithalllongvolatilitypositions,thedaysuntilexpirationshouldbemorethan60.
ShortstrangleForstationarymarketsThestrangleismoreoftenusedasashortspreadtoprofitfromdecreasingimpliedvolatility.Theshortstrangleistoooftentradedsimplytogainincomefromtimedecay,whichisadangerousmisapplication,aswehavealreadyseen.
Theshortstranglehas,liketheshortstraddle,theoreticallyunlimitedrisk,butbecausethetwostrikesareatgreaterdistancesfromtheunderlying,itismoremanageablestrategy.Thepositivetheta,orthedailyincomefromtimedecay,isnotasgreat,butthenegativevega,orexposuretoincreasedimpliedvolatility,isalsonotasgreat.
Becauseofthetwoshort,nakedoptions,itisadvisablenottotradethisspreaduntilyouhavegainedexperience.Asimilarspreadforstationarymarketswithlessriskistheshortironcondor,whichisalsodiscussedinChapter12.
UsingthesetofMarksandSpencerApriloptions,atypicalshortstranglewouldbeasaleofthe330putat3.75andasaleofthe370callat3.75inthesametransaction,foratotalcreditof7.50(£75).
Atexpiry,theupsidebreak-evenlevelistheupperstrikepriceplustheincomefromthespread,or370+7.50=377.50.Abovethislevelthepotentiallossisunlimited.Thedownsidebreak-evenlevelisthelowerstrikepriceminustheincomefromthespread,or330–7.50=322.50.Belowthislevelthepotentiallossisthefullvalueofthestock.Theexpiryprofit/lossissummarisedasfollows:
CreditfromApril370call:
3.75
CreditfromApril330put:
3.75
Totalcredit:
7.50
Upsidebreak-evenlevel:higherstrikeplusincomefromspread:370+7.50=377.50
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Downsidebreak-evenlevel:lowerstrikeminusincomefromspread:330–7.50=322.50Maximumloss:potentiallyunlimitedMaximumprofit:incomefromspread:7.50
Theexpiryprofit/lossisshowninTable11.5.
Table11.5MarksandSpencershortApril330–370strangle
Figure11.4isagraphoftheprofit/lossatexpiry.
Figure11.4Expirationprofit/lossrelatingtoTable11.5
____________1ThischaptershouldbereadinconjunctionwithChapter4,‘Volatilityandpricingmodels’.
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12
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Ironbutterfliesandironcondors:combiningstraddlesandstranglesforreducedrisk
Oftentheriskofunlimitedlossfrombeingshorttwonakedoptionscannotbejustified.Thisisespeciallytruefornewtraders.Occasionally,theriskofpremiumlossfrombeinglongtwooptionscannotbejustified.Bycombiningstraddlesandstrangles,youcantakethesameapproachestovolatileorstationarymarkets,butyoucanquantifyandlimityourrisks.Yourpotentialreturnsmaynotbeasgreat,butyoucansleepmoresoundly,andyou’llbeeasiertolivewith.Thefollowingspreadsallhavemoremanageablerisk.
Again,allthesespreadscanbetradedinonetransactiononmostexchanges.Theirbid–askmarketshouldbemarginallygreaterthanthatofasingleoption.
*LongironbutterflyForabsolutemarketmovementAlongstraddlecanbefinancedbythesaleofastrangle.IfXYZisat100,youcouldbuythe100straddleandsimultaneouslysellthe90–110strangleinordertocreatethelongironbutterfly.Youcanalsothinkofthisspreadasalongat-the-moneycallspreadatthe100and110strikes,plusalongat-the-moneyputspreadatthe100and90strikes.
Comparedtothelongstraddle,thisspreadhasreducedpremiumexposure,butitalsohasreducedpotentialreturn.
UsingtheprevioussetofMarksandSpencerApriloptions:
M&Sat350.6030daysuntilAprilexpiry
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Here,youcouldpay21.50forthe350straddle,andsellthe330–370strangleat7.50,foranetdebitof14.Thisissimilartopaying7.5forthe350–370callspreadpluspaying6.5forthe350-330putspread.
Likethelongcallspreadandthelongputspread,thedistancebetweenstrikesofthelongironbutterflycanbevariedinordertoadjusttherisk/returnpotential.Practicallyspeaking,underlyingsdonotmovetozeroorinfinitywithinthelifeofanoptionscontract;therearealwayslevelsofsupportandresistance.Itisrealistictoplacetheshortwingsofthisspreadattheselevels.Theabovechoiceofstrikesviewssupport/resistanceatapproximately6percentbeloworabovethecurrentprice.ThisisalargebutverypossiblemoveforMarksandSpencer.Ifyouchoosethisstrategyinthefirstplace,thenyouareexpectingsomethingoutoftheordinarytohappen.
Notethattheabovestrikesarewidelyseparated,andasaresultthestraddlecomponenthasalargeexposuretotheGreeks.Thisspreadhasabetterreturnpotentialwhentheimpliedisincreasing.Aprofit/losssummaryatexpiryisasfollows:
DebitfromApril350straddle:
–21.50
CreditfromApril330–370strangle:
7.50
Totaldebit:
14.00
Upsidebreak-evenlevel:straddlestrikeplusspreaddebit:350+14=364
Downsidebreak-evenlevel:straddlestrikeminusspreaddebit:350–14=336
Maximumupsideprofit:higheststrikeminusmiddlestrikeminusspreaddebit:370–350–14=6
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Maximumdownsideprofit:middlestrikeminusloweststrikeminusspreaddebit:350–330–14=6
Maximumloss:costofspread:14
Therisk/returnratioofthisspreadis14/6,or2.3/1,or£2.30potentialriskforeachpotentialreturnof£1.Admittedly,thisisnotanoptimumrisk/returnratio,butitisbetterthanthatofthelong350straddleifyouexpectthestocktorangeatamaximumof6percent.
Andwhenarisk/returnratiolooksthisunfavourable,thenyouneedtoconsiderdoingtheoppositesideofthetrade(seebelow).
Theexpiryprofit/lossforthisspreadisshowninTable12.1.
Table12.1MarksandSpencerlongApril330–350–370ironbutterfly
Ingraphicform,theprofit/lossatexpiryisasshowninFigure12.1.
Figure12.1Expirationprofit/lossrelatingtoTable12.1
Supposeyouthinkthattheupsidepotentialforthestockisgreaterthanitsdownsidepotential.YoumightcreatealongbrokenironbutterflybysubstitutingashortApril380callat2fortheshortApril370callat3.75.Yourspreaddebitincreasesto15.75,butyourprofitpotentialisnow8.25greater.
Alternatively,youmightcreateathree-wayspreadbypaying21.5fortheApril350straddle,andsellingonlytheApril340putat6.25foratotaldebitof15.25.
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Here,yourupsideprofitpotentialisunlimited.
*ShortironbutterflyForstationarymarketsSupposepremiumlevelsarehighandtrendingdownward.Youwouldliketosellastraddlebutyoudon’twanttheriskofunlimitedloss.Instead,youcouldselltheaboveironbutterfly.YouarethenshorttheApril350straddleandgolongtheApril330–370strangle,whichactsastwostop-lossordersatguaranteedlevels.Youareeffectivelyshortthe350–370callspreadandshortthe350–330putspread.Theprofit/losssummaryandtableatexpiryforthisspreadareexactlyoppositetothoseoftheabove,whiletheexpirygraphistheinverse.
CreditfromApril350straddle:
21.50
DebitfromApril330–370strangle:
7.50
Totalcredit:
14.00
Upsidebreak-evenlevel:straddlestrikeplusspreadcredit:350+14=364
Downsidebreak-evenlevel:straddlestrikeminusspreadcredit:350–14=336
Maximumprofit:creditfromspread:14
Maximumupsideloss:(higheststrikeminusmiddlestrike)minusspreadcredit:(370–350)–14=6
Maximumdownsideloss:(middlestrikeminusloweststrike)minusspreadcredit:(350–330)–14=6
Notethattherisk/returnratioisalsooppositetotheformerspread,at1/2.3.Thisisapreferredratio,providedvolatilityisdeclining.Theprofit/losstableatexpiryisshowninTable12.2.
Table12.2MarksandSpencershortApril330–350–37ironbutterfly
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Theprofit/lossatexpiryisshowninFigure12.2.
Figure12.2Expirationprofit/lossrelatingtoTable12.2
Lookingahead(forthosewhoalreadyknowthefundamentals)wewilllearnthattheprofit/losscharacteristicsofthisspreadareidenticaltothelongApril330–350–370callorputbutterfly.Personally,Iwouldrathertradetheabovespreadbecausetheout-of-the-moneycallandputareusuallymoreliquidthaneitherthecorrespondingin-the-moneyputandcallofthestraightbutterfly.InotherwordstheApril370callisprobablymoreliquidthantheApril370put.Thisusuallyresultsinatighterbid–askmarketforthespreadasawhole.
Lastly,thereiseveryreasontovarythewingsoftheshortorlongironbutterflydependingonyouroutlook.Forexample,youmayselltheApril350straddleat21.50andinsteadpay13fortheApril340–360strangle,resultinginanetcreditandmaximumprofitofonly8.5.Yourbreak-evenlevelsarethen358.5and341.5.Yourmaximumlossisonly1.5,bringingyourrisk/returnratiodownto1/5.6.Thetrade-offisthatyourprofitrangeisreducedfrom28points(twicethecreditfromthespread)to17points.
*ShortironcondorForstationarymarketsTherisksoftheshortstranglecanbelimitedbybuyingalongstrangleatstrikesthatarefurtherout-of-the-money.IfXYZisat100,youcouldsellthe90–110
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strangle,andbuythe85–115strangleinthesametransaction.Youmightthinkofthisfour-wayspreadasashortout-of-the-moneycallspreadat110–115,plusashortout-of-the-moneyputspreadat90–85.Thisspreadisknownastheshortironcondor.
Themaximumprofithereisthecombinedcreditfromtheshortcallandputspreads.Liketheshortcallandputspread,themaximumlosshereisquantifiableandlimitedattheoutset.Likeallpremiumsellingstrategies,thisspreadismostprofitablewhenusedwithacceleratedtimedecay.Decliningimpliedandhistoricalvolatilitiesarealsoprofitablescenariosforthisspread.Ifyouroutlookcallsforlowermarketvolatility,thisspreadisoneofthebestchoices.
UsingtheprevioussetofMarksandSpenceroptions,youcouldselltheApril340–360strangleat13,andpay7.5fortheApril330–370strangle,foranetcreditof5.5.
Ontheupside,thisspreadbehaveslikeashort360–370callspreadforwhichyouhavecollected5.5.Atexpiry,theupsidebreak-evenlevelisthestrikepriceofthelowercallplusthetotalincomefromthespread,or360+5.5=365.5.Themaximumupsidelossisthedifferencebetweencallstrikesminustheincomefromthespread,or(370–360)–5.5=4.5.
Onthedownside,thisspreadbehaveslikeashort340–330putspreadforwhichyouhavecollected5.5.Atexpiry,thedownsidebreak-evenlevelisthestrikepriceofthehigherputminusthetotalincomefromthespread,or340–5.5=334.5.Themaximumdownsidelossisthedifferencebetweenputstrikesminustheincomefromthespread,or(340–330)–5.5=4.5.Theprofit/lossatexpirationissummarisedasfollows:
CreditfromshortApril340put:
6.25
CreditfromshortApril360call:
6.75
DebitfromlongApril330put:
–3.75
DebitfromlongApril370call:
–3.75
Totalcredit:
5.50
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Maximumprofit:incomefromspread:5.5
Upsidebreak-evenlevel:lowercallstrikeplusspreadcredit:360+5.5=365.5
Downsidebreak-evenlevel:higherputstrikeminusspreadcredit:340–5.5=334.5
Maximumupsideloss:differencebetweencallstrikesminusspreadcredit:(370–360)–5.5=4.5
Maximumdownsideloss:differencebetweenputstrikesminusspreadcredit:(340–330)–5.5=4.5
Therisk/returnratioforthisspreadismaximumlossdividedbymaximumprofit,or4.5/5.5=0.82or0.82atriskforeachpotentialreturnof1.1Althoughtheprofitpotentialofthisspreadisnotspectacular,neitheristhemaximumloss.Alsoconsiderthattheprofitrangeis365.5–334.5=31points.Thestockwouldneedtosettlemorethan+/–4.4percentatexpirybeforealosswouldresult.Remember,youaretradingthisspreadbecauseyouexpectthestocktorange,andforvolatilitytocomedown.
Theexpiryprofit/lossisshowninTable12.3.
Table12.3MarksandSpencershortApril330–340–360–370ironcondor
Theexpirationprofit/lossisgraphedasinFigure12.3.
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Figure12.3Expirationprofit/lossrelatingtoTable12.3
Again,thereareasymmetricpossibilities.Ifyouarerange-bullish,youmightsellthe350–340putspreadat4andsellthe360–380callspreadat4.75foratotalcreditof8.75.Here,yourmaximumlossis1.25onthedownsideand11.25ontheupside.Yourbreak-evenlevelsare341.25and368.75,withaprofitrangeof27.5points.
*LongironcondorForvolatilemarketsTheoppositeformoftheabovefour-wayspreadisoccasionallyusedasawayoffinancingthelongstrangle.IfXYZisat100,youcouldbuythe95–105strangleandsellthe90–110strangleinonetransaction.Youmightthinkofthisasalongout-of-the-moneycallspreadat105–110,plusalongout-of-the-moneyputspreadat100–95.Thisspreadisknownasthelongironcondor.Aswithlongcallandputspreads,thelongoptionsherecanbeplacedclosertotheunderlyingbecausetheyarefinancedbyshortoptionsthatarefurtherout-of-the-money.Thereislesspotentialreturnthanwiththelongstrangle,butthereisalsolesscostandlesspremiumrisk.
WiththeprevioussetofMarksandSpenceroptions,youcouldtradethisspreadwithnon-adjacentstrikesonboththecallandputsidesinordertoextendtheprofitrange.Youcouldpay13fortheApril340–360strangle,andselltheApril330–370strangleat7.5,foranetdebitof5.5.
Ontheupside,thisspreadbehaveslikealongApril360–370callspreadforwhichyouhavepaid5.5.Atexpiration,theupsidebreak-evenlevelisthelowercallstrikeplusthecostofthespread,or360+5.5=365.5.Themaximumupsideprofitisthedifferencebetweencallstrikesminusthecostofthespread,or(370–360)–5.5=4.5.Themaximumriskisthecostofthespread,or5.5.
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Onthedownside,thisspreadbehaveslikealongApril340–330putspreadforwhichyouhavepaid5.5.Atexpiration,thedownsidebreak-evenlevelisthehigherputstrikeminusthecostofthespread,or340–5.5=334.5.Themaximumdownsideprofitisthedifferencebetweenputstrikesminusthecostofthespread,or(340–330)–5.5=4.5.Themaximumriskisagainthecostofthespread,or5.5.Theexpirationprofit/lossissummarisedasfollows:
DebitfromlongApril360call:
–6.75
DebitfromlongApril340put:
–6.25
CreditfromshortApril370call:
3.75
CreditfromshortApril330put:
3.75
Totaldebit:
–5.50
Upsidebreak-evenlevel:lowercallstrikeplusspreaddebit:360+5.5=365.5
Downsidebreak-evenlevel:higherputstrikeminusspreaddebit:340–5.5=334.5
Maximumupsideprofit:differencebetweencallstrikesminusspreaddebit:(370–360)–5.5=4.5
Maximumdownsideprofit:differencebetweenputstrikesminusspreaddebit:(340–330)–5.5=4.5
Maximumloss:costofspread:5.5
Therisk/returnpotentialismaximumloss/maximumprofit:5.5/4.5=1.2atriskforeachpotentialprofitof1.2Table12.4showstheexpirationprofit/loss.
Table12.4MarksandSpencerlongApril330–340–360–370ironcondor
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Agraphoftheexpirationprofit/lossisshowninFigure12.4.
Figure12.4Expirationprofit/lossrelatingtoTable12.4
____________1Itcanbeeasiertothinkintermsoftheriskasthenumber1.Here,youcouldcalculatetheR/Rratioas5.5/4.5=1.22,orrisking1tomake1.22.
2Theoppositesideofthistradeispreferable.
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13
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Butterfliesandcondors:combiningcallspreadsandputspreads
Thespreadsinthischapterareusedmostoftentoprofitfromstationaryorrange-boundmarkets.Allcombinealongonebyonespreadwithashortonebyonespreadthatisfurtherout-of-the-money.Foroneexample,ifXYZisat100,youcouldbuythe95–100callspreadandsellthe100–105callspreadtocreatealongcallbutterfly.
Allthesespreadshavefourcomponents.Theyaremostcommonlybought,andtheyareusedtoprofitfromdecliningvolatilityand/orpremiumerosion.Therearedirectionalusesaswell,whichwewilldiscuss.
Allthesespreadsareabletobetradedinonetransactiononmost,ifnotall,exchanges.Theirbid–askmarketsareonlymarginallygreaterthanthoseofsingleoptions.Whenpurchased,theyhaveminimalrisk,andarethereforerecommendedfornewtraders.
*Longat-the-moneycallbutterflyForstationarymarketsThelongat-the-moneycallbutterflyismosteasytounderstandasthecombinationofalongcallspreadwhosehigherstrikeisatthemoney,plusashortcallspreadwhoselowerstrikeisalsoatthemoney.Forexample,ifXYZisat100,thelongat-the-moneycallbutterflywouldbealong95–100callspreadplusashort100–105callspread.Thecombinedspreadislongone95call,shorttwo100calls,andlongone105call.
Thespreadisdoneforadebit,usuallysmall,andthedebitisthemaximumpotentialloss.Theprofit/lossgraphatexpirationresemblesabutterfly.Ifthefollowingdiscussionseemscomplicated,keepinmindthatthisspreadisbasicallytwocallspreadscombined.
Thereturnscenarioisfortheunderlyingtocloseatthemiddlestrikeatexpiration.There,thelong,lowercallspreadisworthitsmaximum,orthedifferencebetweenthelowertwostrikes,andtheshort,uppercallspreadexpires
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worthless.Takingtheexampleabove,ifXYZclosesat100,thenthe95–100callspreadisworth5,andthe100–105callspreadisworthzero.Thecostofthebutterflyisthensubtractedfrom5tocalculatetheprofit.
Therearetwocommonriskscenarios.
Thefirst is thatatexpiration theunderlyingclosesatorbelowthe loweststrike,leavingalloptionsout-of-the-moneyandworthless.IfXYZclosesat93,thenalltheaboveoptionswillsettleatzero.Thecostofthebutterflyisthentakenasaloss.The second risk scenario is that at expiration the underlying closes at orabove thehighest strike.There, both call spreads expire at full and equalvalue,makingtheirsumzero.Forexample,withthelong95–100–105callbutterflyabove, ifXYZclosesat108,bothcall spreadsareworth5.Theprofitonthelong95–100callspreadpairsoffagainstthelossontheshort100–105 call spread. The butterfly is thenworthless, and the cost of thebutterflyistakenasaloss.
Thereareother,lesscommonrisks,andtheyarediscussedattheendofthesectiononbutterflies.
Alongat-the-moneybutterflyincreasesinvalueasitapproachesexpirationandwhentheunderlyingremainsbetweentheoutermoststrikes.Becauseitisapremiumsellingstrategy,itisbestopenedwhentheoptionscontracthas60daysorlesstillexpiration.Becausethereisminimumrisktothebutterfly,itcanbeopenedclosetoexpiration,forexample,under30days,anditcanbehelduntilseveraldaysbeforeanoptionscontractexpires.Theriskremainsmimimalprovidedthespreadremainsatthemoney,i.e.withnoshortstrikedeeplyinthemoneyandthereforesubjecttoearlyassignment.
TakingagainthesetofMarksandSpenceroptions:
M&Sat350.6040daysuntilAprilexpiry
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Here,youcouldpay17foroneApril340call,selltwoApril350callsat11.25andpay6.75fortheApril360callforanetdebitof1.25YouarethenlongtheApril340–350–360callbutterfly.Thepremiumoutlayissmall,butsoisthepossibilityofthesharesclosingat350,30daysfromnow.Ontheotherhand,thepotentialprofitis8.75,andtheprofitrangeis8.75×2=17.5points.Thevalueofthespreadgrowsasexpiryapproachesandasthesharesremaincentredatapproximately350.
Atexpiration,themaximumprofitoccursifthesharescloseat350.There,thelowercallspreadisworthitsmaximum,10,andtheuppercallspreadisworthitsminimum,0.Theprofitiscalculatedasthedifferencebetweenthelowertwostrikesminusthecostofthebutterfly,or(350–340)–1.25=8.75.Themaximumlossisthecostofthebutterfly,or1.25.
Atexpiry,therearetwobreak-evenlevelswiththecallbutterfly.Thelowerleveliswherethevalueofthelongcallspreadpaysforthecostofthebutterfly.Thisiscalculatedastheloweststrikepriceplusthespreaddebit,or340+1.25=341.25.
Thehigherbreak-evenleveliswheretheprofitonthelongcallspreadequalsthelossontheshortcallspread.Thiscouldbecalculatedasthedifferencebetweenthelowertwostrikes,minusthebutterflydebit,plusthemiddlestrike,or(350–340)–1.25+350=358.75.However,itismoreeasilycalculatedasthehigheststrikeminusthebutterflydebit,or360–1.25=358.75.Atthislevel,thevalueofthe340–350callspreadat10,lessthebutterflydebitof1.25,equalsthevalueofthe350–360callspreadat8.75.
Theprofitrangeofthisbutterflyisthen358.75–341.25=17.50.Itisimportanttothinkaboutprofitrangeswhentradingvolatilitybecause,inessence,wearetradingarangeofprobableoutcomesfortheunderlyingatexpiry.
Theexpiryprofit/lossissummarisedasfollows:
DebitfromonelongApril340call:
–17.00
DebitfromonelongApril360call:
–6.75
CreditfromtwoshortApril350calls:2×11.25=
22.50
Totaldebit:
–1.25
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Downsidebreak-evenlevel:loweststrikepluscostofbutterfly:340+1.25=341.25
Upsidebreak-evenlevel:higheststrikeminuscostofbutterfly:360–1.25=358.75
Maximumprofit:differencebetweenlowertwostrikesminuscostofbutterfly:(350–340)–1.25=8.75
Levelofmaximumprofit:middlestrike:350
Maximumloss:costofbutterfly:1.25
Therisk/returnratioforthisspread,atexpiry,is1.25/8.75,or0.14atriskforeachpotentialprofitof1,or1atriskforareturnof7.1Thislowratioistheparticularadvantageofthelongbutterfly.
Youdon’twanttoholdthisspreaduntilexpiry,however.Insteadyouwanttotakeyourprofitafterareasonableamountoftimedecay.Begladifyoudoubleyourmoney.
Theexpiryprofit/lossisshowninTable13.1
Table13.1MarksandSpencerlongApril340–350–360callbutterfly
Thegraphoftheexpiryprofit/lossisasshowninFigure13.1.
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Figure13.1Expirationprofit/lossrelatingtoTable13.1
*Longat-the-moneyputbutterflyForstationarymarketsThelongat-the-moneyputbutterflyhastheidenticalprofit/losscharacterisiticsofalongat-the-moneycallbutterfly.(Thisfortunateoccurrencehasbroughtrelieftomanyoptionstrainers.)Ifbothspreadsareat-the-money,theircostisnearlythesame.Thesamestrikesareused,butwithputsinsteadofcalls.Forexample,ifXYZisat100,youcouldbuyone105put,selltwo100puts,andbuyone95puttocreatethebutterfly.Youcanthinkofthisspreadasalongin-the-moneyputspreadatthe105and100strikes,plusashortat-the-moneyputspreadatthe100and95strikes.
Atexpirationthemaximumprofitoccursiftheunderlyingclosesatthemiddlestrike.Themaximumlossisthecostofthespread.
WiththeaboveMarksandSpenceroptions,youcouldpay16.25fortheApril360put,selltwoApril350putsat10.75,andpay6.25fortheApril340putordertogolongtheApril340–350–360putbutterfly.Yourtotaldebitis1.00,2andthisisyourmaximumpotentialloss.
Atexpiration,theupsidebreak-evenlevelisthehigheststrikeminusthecostofthebutterfly,or360–1=359.Thedownsidebreak-evenlevelistheloweststrikeplusthecostofthebutterfly,or340+1=341.Notethattheprofitrangeis359–341=18.
Themaximumprofitisthedifferencebetweenthetwohigherstrikesminusthecostofthespread,or(360–350)–1=9Theexpirationprofit/lossissummarisedasfollows:
DebitfromonelongApril360put:
–16.25
DebitfromonelongApril340put:
–6.25
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CreditfromtwoshortApril350puts:2×10.75=
21.50
Totaldebit:
–1.00
Maximumprofit:differencebetweentwohigherstrikesminusspreaddebit:(360–350)–1=9
Levelofmaximumprofit:middlestrike:350
Upsidebreak-evenlevel:higheststrikeminuscostofspread:360–1=359
Downsidebreak-evenlevel:loweststrikepluscostofspread:340+1=341
Maximumloss:costofspread:1
Therisk/returnratioofthisspreadismaximumloss÷maximumprofit,or1/9.Intabularformtheexpiryprofit/lossissummarisedinTable13.2.
Table13.2MarksandSpencer340–350–360longputbutterfly
Thegraphoftheexpirationprofit/loss(seeFigure13.2)isalmostidenticaltotheoneshowninFigure13.1forthecallbutterfly.
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Figure13.2Expirationprofit/lossrelatingtoTable13.2
Shortat-the-moneycallandputbutterfliesForvolatilemarketsForeachspreadtradedtherearetwoopposingoutlooks.Intseadofbuyinganat-the-moneybutterflyinordertoprofitfromastationarymarket,atradermaysellthesamebutterflybecausehisoutlookcallsfortheunderlyingtobeoutsidethespread’srangeatexpiration.Thisisusuallynotdonebyinvestorsbecausetherisk/returnratiosareunfavourable.
Forexample,insteadofbuying,youcouldselltheaboveputbutterflyat1.Thisisyourmaximumprofitatexpiryifthestockclosesatorbelow340,oratorabove360.Practicallyspreaking,this1pincomeissmall,butinavolatilemarketsoistheriskofthestockexpiringwithinthebutterfly’srange.YourpositionwouldbeshortoneApril340call,longtwoApril350calls,andshortoneApril360call.Yourriskis9p,however,ifthesharessettleat350attheoptions’expiry.
Figure13.3belowillustratestherisk/returnprofile.
Figure13.3Therisk/returnprofile
Youcanseewhyonlyamarket-makerwillsellyouthisbutterfly,sodon’tbegrudgehimonetickwhileherisksnine.
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*Longout-of-the-moneycallbutterflyForupsidedirectionfollowedbystationarymarketAbutterflycanbeusedwithadirectionaloutlook.Supposeyouthinkthatastockhasrecentlybecomeoversoldbecauseofanunfavourableanalyst’sreport,orbecauseoflessthanexpectedearnings.Youknow,however,thestockisfundamentallysound,anditwillmostlikelyrallybacktoitsformerlevel.Inordertoprofitfromyouroutlook,youcouldbuyanout-of-the-moneycallbutterfly.Thisspreadcostslessthananat-the-moneybutterfly,anditspricewillincreaseasthestockentersitsrange.Allthebetteriftherallyisslowandtimeconsuming,becausethebutterfly,whenitfinallybecomesat-the-money,willbeworthmorethroughtimedecay.
Forexample,ifyouexpectMarksandSpencertoincreasefromitscurrentpriceof350.60intothe360range,youcouldpay1fortheApril350–360–370callbutterfly.Youdothisbypaying11.25forone350call,sellingtwo360callsat7,andpaying3.75forone370call.3Ifthesharesincreaseto360in40days’timeyourbutterflywillbeworth3.25.YouknowthisbecausethecurrentMarchat-the-moneybutterfly,the340–350–360,with10daystogo,isworth3.25.Ifthesharesthensettleintoarangecentredon360,youhaveaprofitableandlow-riskoptionsposition.Youmaydecidetotakeyourprofitatthispoint.
Theexpirationprofit/lossforthisbutterflyisasfollows.
DebitfromonelongApril350call:
–11.25
DebitfromoneApril370call:
–3.75
CreditfromtwoshortApril360calls:2×7=
14.00
Totaldebit:
–1.00
Maximumprofit:differencebetweentwolowerstrikesminusspreaddebit:(360–350)–1=9
Levelofmaximumprofit:middlestrikeofspread:360
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Lowerbreak-evenlevel:loweststrikepriceplusspreaddebit:350+1=351
Upperbreak-evenlevel:higheststrikepriceminusspreaddebit:370–1=369
Profitrange:369–351=18
Maximumloss:costofspread:1
Therisk/returnratiois1/9.
Throughknowingthebasicsofbutterflies,thetableandgraphoftheprofit/lossatexpirationcanbeconstructed.
*Longout-of-the-moneyputbutterflyFordownsidedirectionfollowedbystationarymarketJustasthelongout-of-the-moneycallbutterflycanprofitfromoversoldconditions,thelongout-of-the-moneyputbutterflycanprofitfromoverboughtconditions.Thissituationoftenoccursincommodities,butitiscommontoallmarkets,especiallybearmarkets.
Forexample,ifyouexpectMarksandSpencertoretraceto330,youcouldpay0.75fortheApril320–330–340putbutterfly.Youdothisbypaying6.25forthe340put,sellingtwo30putsat3.75,andpaying2.00forone320put.Iftheshareseventuallysettleintoarangecentredat330,thenyouhavealow-riskprofitopportunity.Theexpiryprofit/lossissummarisedasfollows.
DebitfromoneApril340put:
–6.25
DebitfromoneApril320put:
–2.00
CreditfromtwoApril330puts:2×3.75=
7.50
Totaldebit:
–0.75
Maximumprofit:differencebetweentwohigherstrikesminusspread
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debit:(340–330)–0.75=9.25
Levelofmaximumprofit:middlestrike:330
Upperbreak-evenlevel:higheststrikeminusspreaddebit:340–0.75=339.25
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:320+0.75=320.75
Profitrange:339.25–320.75=18.5
Maximumloss:costofspread:0.75
Therisk/returnratioofthisbutterflyis0.75/9.25=0.08atriskforeachpotentialprofitof1.(1/0.08=12.5,or1atriskforareturnof12.5).Again,notetheexcellentrisk/returnratiosforthisgroupofspreads.
AstoryaboutOTMfliesOneofoutclientswasheadoffixedincomeataLondonmajor.Hewasaveryastutetrader,havingtradedsuccessfullyovertheyears.
Onthisoccasion,hethoughtthattheEuriborwasdueforarallyduringthenextfewweeks,andthentorangeatahigherlevel.HeboughtanOTMcallflybeforetravellingtoameetinginTokyo.
Whilehewasontheplane,themarketsuddenlyrallied,andhedoubledhismoney.Asusual,hewasright.
ButwhenhearrivedinTokyoheunfortunatelydecidedtoholdhisflyinthehopeofgettingtimedecaythroughastationarymarket.Afterall,hisviewcalledfortheEuribortorange.Tobefair,histradingsensewasprobablydistractedbyhisadminduties.
Thequestionforthetraderwas,hadthemarketmadeitsmovetoanewlevelearlierthanexpected,orhadthemarketsimplymadeatemporaryupwardspike?Eitherway,heknewthatwiththebutterflyhismaximumriskwashisoutlay.
WhenbackinLondon,hefoundthatnewinformationhadhitthemarket,anditretracedtoitsformerlevel.Hewasbacktobreak-even.Wisely,hesoldhisfly
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withoutaloss.
Ihavemadethismistakemanytimesinmycareer,andthelessonis:takeagift.
AdditionalriskswiththebutterflyThereareotherriskswiththebutterfly.Thefirstispinrisk,whichisunlikely,butpossible.Thetwoshortstrikesmayexpireat-the-money.Itisbesttoclosethebutterflyseveraldaysbeforeexpiration.YoumayrefertothesectiononpinriskinPart1.
AnotherriskisthatofearlyexercisewithAmerican-styleoptionssuchastheOEX,andmostoptionsonindividualstocksintheUSandUK.Ifyourshortstrikebecomesdeepin-the-moneyclosetoexpiration,youmaybeassignedtocashintheindexes,thereforeleavingyourlongoptionsunhedged.Withalongcallbutterflyinstocks,youmaybeassignedanunwantedshortstockposition,andwithalongputbutterflyinstocks,youmaybeassignedanunwantedlongstockposition.Inallthesecases,ifyourbutterflybecomesdeepin-the-moneyclosetoexpiration,itwillhavelostitsvalue,andyoushouldclosetheposition.
Ifyouholdthelongbutterflyuntilexpirationtherearetwoadditionalrisks.Foracallbutterfly,iftheunderlyingsettlesbetweenthetwohigherstrikes,thenyouwillbeassignedonemoreshortunderlyingcontractthantheonetowhichyouwillexercise.Mostlikelyyouwillnotwantthisposition.
Second,iftheunderlyingsettlesbetweenthetwolowerstrikes,thenyouoryourclearingfirmwillexercisetoonelongunderlyingcontract,whichyoumaynotwant.
Forthelongputbutterfly,iftheunderlyingsettlesbetweenthetwolowerstrikes,thenyouwillbeassignedonemorelongunderlyingcontractthantheonetowhichyouwillexercise.Iftheunderlyingsettlesbetweenthetwohigherstrikes,thenyouoryourclearingfirmwillexerciseoneshortunderlyingcontract.
Thereisanadditionalriskinthatthedeepin-the-moneyputsonstocksandAmerican-stylestockindexesgenerallyhavemoreearlyexercisepremiums,andaremorefrequentlysubjecttoearlyexerciseandassignment.Perhapsforthisreasontheat-the-moneycallbutterflyismoreoftentradedthantheputbutterfly,especiallyinstocks.
Themostprudentwaytoavoidtheserisksistocloseyourbutterflypositionifitbecomesdeeplyin-the-money,orcloseitseveraldaysbeforeexpiration.
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*Longout-of-themoneycallcondorForupsidedirectionfollowedbystationarymarketIftheexpectedupsiderangeofanunderlyingistoodifficulttoassessfortheuseofanout-of-the-moneycallbutterfly,thenyoucanincreasetherangeofthespreadbyshiftingtheshortcallspreadtothenexttwohigherstrikesthatareoutofthemoney.Thiscreatesalongout-of-the-moneycallcondor.Forexample,ifXYZisat100youcouldbuyone105call,sellone110call,sellone115call,andbuyone120call.Whilethemaximumprofitisthesameaswiththebutterfly,theprofitrangeisextendedbyfivepoints.Thisspreadcostsmore,butithasanincreasedprobabilityofprofit.ItissimilartothelongcallladderorChristmastree,butithastheprotectionoftheextralongcallatthehigheststrike.
Forexample,inMarksandSpenceroptionsyoucouldpay11.25forone350call,sellone360callat6.75,sellone370callat3.75,andpay2.00forone380call.Yourdebitis2.75.Here,themaximumprofitistakenifthesharesarebetween360and370atexpiry.Thebreak-evenlevelsare352.75and377.25.Theprofit/losscalculationsarepracticallythesameaswiththecallbutterfly.Theexpirationprofit/lossforthiscondorissummarisedasfollows:
DebitfromonelongApril350call:
–11.25
DebitfromonelongApril380call:
–2.00
CreditfromoneshortApril360call:
6.75
CreditfromoneshortApril370call:
3.75
Totaldebit:
2.75
Maximumprofit:differencebetweenlowesttwostrikesminusspreaddebit:(360–350)–2.75=7.25
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:350+2.75=352.75
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Upperbreak-evenlevel:higheststrikeminusspreaddebit:380–2.75=377.25
Profitrange:377.25–352.75=24.50
Maximumloss:costofspread:2.75
Therisk/returnratioofthislongcallironbutterflyis2.75/7.25=0.38atriskforeachpotentialprofitof1.Atableoftheprofit/lossatexpirationisshowninTable13.4.
Table13.4MarksandSpencerlongApril350–360–370–380callcondor
Aprofit/lossgraphofthiscondoratexpirationappearsinFigure13.4.
Figure13.4Expirationprofit/lossrelatingtoTable13.4
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*Longat-the-moneycallcondorForstationarymarketsLikethebutterfly,thecallcondorcanbeplacedatmanydifferentstrikes,dependingonyouroutlookforthepricerangeoftheunderlying.Ifyouthinkthattheunderlyinghasmadeitsmoveforthenearfuture,thenyoumighttradetheat-the-moneycallcondor.Forexample,ifXYZisat100,youcouldbuyone95call,sellone100call,sellone105call,andbuyone110call.Thisspreadcostsmorethantheat-the-moneybutterfly,andconsequentlyitsmaximumprofitislessthantheat-the-moneybutterfly,butitsprofitrangeisgreater.
UsingournowfamiliarsetofMarksandSpencerApriloptions,youcouldpay17forone340call,sellone350callat11.25,sellone360callat6.75,andpay4.00forone370call.Yournetdebitis3.00.Theexpirationprofit/lossissummarisedasfollows:
DebitfromoneApril340call:
–17.00
DebitfromoneApril370call:
–4.00
CreditfromoneApril350call:
11.25
CreditfromoneApril360call:
6.75
Totaldebit:
–3.00
Maximumprofit:differencebetweentwoloweststrikesminusspreaddebit:(350–340)–3.00=7.00
Rangeofmaximumprofit:350–360
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:340+3.00=343.00
Upperbreak-evenlevel:higheststrikeminusspreaddebit:370–3.00=367.00
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Profitrange:367.00–343.00
Maximumloss:costofspread:3.00
Therisk/returnratioforthisspreadis3/7=0.43for1,or1/2.64.Byknowinghowthecondorworks,youcandeviseatableandagraphoftheprofit/lossatexpiry.
*Longout-of-the-moneyputcondorFordownsidedirectionfollowedbystationarymarketIftheprofitrangeofanout-of-the-moneyputbutterflyistoolimited,itcanbeextendedbyshiftingtheshortputspreadtothenexttwolowerstrikes.IfXYZisat100,youcouldbuyone100put,sellone95put,sellone90put,andbuyone85put.Theresultingspreadisthelongout-of-the-moneyputcondor.Thisspreadcostsmorethanthebutterflyanditsmaximumprofitisconsequentlyless,butitsprofitrangeisgreater.ItissimilartothelongputladderorlongputChristmastree,butithastheprotectionofthelongputattheloweststrike.
Forexample,inMarksandSpencerApriloptionsyoucouldpay10.25forone350put,sellone340putat6.25,sellone330putat3.75,andpay2.00forone320put.Yourtotaldebitis2.25.
Theexpirationprofit/lossforthisputcondorissummarisedasfollows.
DebitfromlongApril350put:
–10.25
DebitfromlongApril320put:
–2.00
CreditfromshortApril340put:
6.25
CreditfromshortApril330put:
3.75
Totaldebit:
–2.25
Maximumprofit:differencebetweenhighesttwostrikesminusspreaddebit:(350–340)–2.25=7.75
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Rangeofmaximumprofit:340–330
Upperbreak-evenlevel:higheststrikeminusspreaddebit:350–2.25=347.75
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:320+2.25=322.25
Profitrange:347.75–322.25=25.50
Maximumloss:costofspread:2.25
Therisk/returnratioisagainfavourableat2.25/7.75=0.29for1,or1/3.44.Theprofit/lossatexpirationisshowninTable13.5.
Table13.5MarksandSpencerlongApril320–330–340–350putcondor
Thegraphoftheprofit/lossatexpirationisshowninFigure13.5.
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Figure13.5Expirationprofit/lossrelatingtoTable13.5
*Longat-the-moneyputcondorForstationarymarketsPutcondors,likecallcondors,canbeplacedatmanydifferentstrikes,dependingonyournear-termoutlookfortheunderlying.Ifyouroutlookcallsforastationarymarket,butyouwishtoleaveroomforerroronthedownside,youcansubstitutethelongat-the-moneyputcondorfortheat-the-moneyputbutterfly.Youmight,forexample,buytheaboveApril360–350–340–330putcondorforadebitof3.5ThedownsideprofitpotentialofthisspreadisthesameastheupsideprofitpotentialofthelongApril340–350–360–370callcondor.Theprofit/lossatexpirationissummarisedasfollows:
DebitfromlongApril360put:
–16.25
DebitfromlongApril330put:
–3.75
CreditfromshortApril350put:
10.25
CreditfromshortApril340put:
6.25
Totaldebit:
–3.50
Maximumprofit:differencebetweenhighesttwostrikesminusspreaddebit:(360–350)–3.5=6.5
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Rangeofmaximumprofit:350–340
Upperbreak-evenlevel:higheststrikeminusspreaddebit:360–3.5=356.5
Lowerbreak-evenlevel:loweststrikeplusspreaddebit:330+3.5=333.5
Profitrange:356.5–333.5=23
Maximumloss:costofspread:3.5
Therisk/returnratioisagainfavourableat3.5/6.5=0.54for1,or1/1.85.
Bynowyoushouldbeanexpertattabulatingandgraphingtheexpirationprofit/losslevelsofcondorsandbutterflies.
*Shortat-the-moneyputcondorForvolatilemarketsLikethebutterfly,thecondorcanbesoldinordertoprofitfromavolatileortrendingmarket.Althoughthisismoreofamarket-maker’strade,youmightconsidertradingitduringvolatilemarkets.Forexample,youcouldselltheaboveApril360–350–340–330putcondorat3.5.IfMarksandSpencerclosesabove360orbelow330atexpiration,youearnthecreditfromthespread.Inthiscaseyouaretakingaslightlybullishposition.
Theprofit/lossfiguresareexactlytheoppositeoftheabovelongputcondor.
*Shortat-the-moneycallcondorforvolatilemarketsIfinsteadyouroutlookisforvolatileconditionsandyouareslightlybearish,youmightselltheApril340–350–360–370callcondorat2.75.(Don’tbesurprisedifyouearnyourprofitontheupside.)IfatexpirationMarksandSpencerclosesbelow340orabove370,thenyouearnthecreditfromthespread.Again,thisisamarket-maker’strade,butyoumightlearnaboutittoincreaseyourmarketawareness.Yourprofit/losssummaryisasfollows.
CreditfromshortApril340call:
17.00
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CreditfromshortApril370call:
3.75
DebitfromlongApril350call:
–11.25
DebitfromlongApril360call:
–6.75
Totalcredit:
2.75
Maximumprofit:spreadcredit:2.75
Rangeofmaximumprofit:below340andabove370
Lowerbreak-evenlevel:loweststrikeplusspreadcredit:340+2.75=342.75
Upperbreak-evenlevel:higheststrikeminusspreadcredit:370–2.75=367.25
Maximumloss:differencebetweenlowesttwostrikesminusspreadcredit:(350–340–2.75=7.25
Pricerangeofsharesforpotentialloss:367.25–342.75=24.5points
Therisk/returnratiois7.25/2.75=2.64to1.
*Butterfliesandcondorswithnon-adjacentstrikesButterfliesareflexiblespreadswhichcanprofitfromavarietyoftradingranges.Youcanextendtheprofitrangeofabutterflybyextendingthedistanceofthestrikes.IfXYZisat100,andyouexpectittorallyintoarangeofbetween105and115,thenyoucanbuythe100–110–120callbutterfly.Thisspreadcostsmorethantheadjacentstrike,105–110–115callbutterfly,butithasagreaterprofitrange.
UsingthesetofMarksandSpencerApriloptions,youcouldpay11.25forthe350call,selltwo370callsat3.75,andpay1forthe390call,foranetdebitof4.75.Yourprofitrangeisthen354.75to385.25,or30.5points,or8.7percentof
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theshare’svalue.
Condorscanalsoincreasetheirprofitrangesbyincreasingthedistanceofthestrikes.Thisisespeciallyfeasiblewhilethatstockindexesand,asaresult,optionspremiums,areathighlevels.ConsiderthesetofFTSEoptionsbelow.
JuneFTSE-100options
JuneFutureat62504
106daysuntilexpiry
ATMimpliedat26percent
Ifyoudiscernthatthepathofleastresistanceisup,orifyou’resimplybullish,youmaywishtotakealongcallpositionintheUKmarket.Butifthethoughtofspending£2,000to£3,000foroneoptionscontractgivesyoupause,thenyoumayinsteadconsiderfinancingyourcallpurchasewithaspread.
For£470,the6325–6525–6725–6925callcondorcanbepurchasedwithouttakingoutasecondmortgage.Themaximumprofitis200–47=153ticks.Thebreak-evenlevels,at6372and6878,provideaprofitrangeof506points.Therisk/returnforthisspreadisfavourable,at47/153=0.31.
Thetrade-offwiththisspreadisthatiftheFTSEralliesquickly,thenthespreadwillshowonlyamodestprofit.Likeallbutterfliesandcondors,thisspreadneedstimedecaytoworkforit.
Non-adjacentstrikebutterfliesandcondorsarepreferredalternativesintheOEXorSPXandSPY(SPDRS)aswell.Theyaresensiblewaysofreducingpremiumexposurewhileminimisingrisk.Someexchangeshavereducedtheticksizeofthesecontractsinordertoaccommodatetheindividualinvestor,andtoimproveliquidityandpricediscovery.
Volatility,daysuntilexpiration,andbutterfliesand
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condorsLikewisewhenvolatilitiesarehigh,youcanoftenfindinexpensiveadjacentstrikebutterfliesandcondors,suchasintheaboveFTSEexample.Thisisbecausetheunderlyingistradinginawiderange,andtheprobabilityofitsettlingnearaparticularstrikeatexpirationissmall.Thesamefactorsapplytothesespreadswhentherearemanydaysuntilexpiration.Attimeslikethese,itispreferabletotradebutterfliesandcondorswithnon-adjacentstrikes.
TheadvantagesInthischapterwehavecoveredbutterfliesandcondorsindepth.Thereasonsforthisaretwofold:whenpurchased,thesespreadshavelowrisk/returnratios;also,theycaneasilybeopenedandclosedinonetransaction.Theyarethereforejustifiabletradingstrategiesundermanymarketconditions.Itisworthlearninghowtousethem.
____________18.75/1.25=7/1,andflipitover.2BearinmindthatthepricesinTable13.1abovearesettlements,andsettlementpricescanoccuronorbetweenthebidandtheoffer.YouwouldexpecttopaylessforanATMputflythatisfurtherfromthemoneythantheATMcallfly.
3Thesepricesarerealistic.4IfandwhentheFTSEreachesthislevelagain.Thepointistousebutterfliesandcondorswhenoptionspremiumsareexpensive.
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14
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Thecoveredwrite,thecalendarspreadandthediagonalspread
ThediagonalspreadfortrendingmarketsTherearetwoadditionalspreadsthatprofitfromstationarymarkets.Thecoveredwriteinvolvessellingacallagainstalongunderlyingposition,andthecalendarortimespreadinvolvessellinganear-termat-the-moneyoption,usuallyacall,andbuyingafurther-termat-the-moneyoption,againusuallyacall.Bothspreadsprofitfromtimedecay.
Thecoveredwriteorthebuy-writeIfaninvestorownsorislonganunderlyingcontract,hemaysellorwriteacallonittoearnadditionalincome.Thisstrategyisknownasthecoveredwriteanditisoftenusedbylong-termholdersofstocksthataretemporarilyunderperforming.Itisoftentradedinbearmarkets.
Whentheunderlyingisboughtandthecallissoldinthesametransaction,thisspreadisalsoknownasthebuy-write.
Forexample,ifyouownXYZatapriceof100,orhopefullyless,youmaysellone105callat3.Themaximumprofitisthepremiumearnedfromthesaleofthecallplustheamountthattheunderlyingappreciatestothestrikepriceofthecall.Here,thiswouldbe5+3=8.Thedownsidebreak-evenlevelisthepriceoftheunderlyingatthetimeofthecallsalelessthecallincome.Here,thiswouldbe100–3=97.
Therearetworisks:
Thefirstisthattheunderlyingmaydeclinebelowthedownsidebreak-evenlevel,andthatyouwilltakealossonthetotalposition.Thesecondisthattheunderlyingmayadvanceabovethecallstrikeprice,theunderlyingwillbecalledaway,andyouwillrelinquishtheupsideprofitfromtheunderlying.
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Thisspreadisbestusedbyinvestorswhohavepurchasedtheunderlyingatsignificantlylowerlevels,whothinkthatthereislittleornoupsidepotential,andwhocantolerateshort-termdeclinesintheunderlying.
ConsiderCoca-Colaat52.67;Augustoptionswith60daysuntilexpiration:
Forexample,Coca-Colaiscurrentlytradingat52.67,andtheAugust60calls,with60daysuntilexpiration,arepricedat0.34.Youmaysellonecalloneach100Coca-Colasharesthatyouown.Alternatively,youmaypay52.67for100shares,whilesellingthecall,asaspread.
Atexpiration,themaximumprofitforyourspreadoccursatthestrikepriceofthecall.There,yougainthepriceappreciationofthestockplusthefullincomefromthecall.Themaximumprofitiscalculatedasthestrikepriceminusthepurchasepriceofthestockplustheincomefromthecall,or(60–52.67)+0.34=7.67.
Abovethecallstrikeprice,theprofitfromthestockisoffsetbythelossonthecall,onapointforpointbasis.Themaxiumprofitisearned,nomore,noless.Thestockwillbecalledawayfromyouatexpiration.
Thelowerbreak-evenlevelforyourpositionisthepriceatwhichthecallincomeequalsthedeclineinthestockprice.Thisiscalculatedasthepriceofthestockminustheincomefromthecall,or52.67–0.34=52.33.Belowthislevelthespreadlosespointforpointwiththestock.
Theexpirationprofit/lossforthiscoveredwriteissummarisedasfollows.
Maximumprofit:strikepriceminusstockprice,plusincomefromcall:(60–52.67)+0.34=7.67
Themaximumprofitoccursatorabovethestrikepriceofthecall
Break-evenlevel:stockpriceminusincomefromcall:52.67–0.34=52.33
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Maximumloss:fullamountofstockpricedeclinebelowbreak-evenlevel:52.33
Theexpirationprofit/lossissummarisedinTable14.1.
Table14.1Coca-Colacoveredwrite:withCoca-Colaat52.67,sellAugust60callat0.34
Theexpirationprofit/lossisshowninFigure14.1.
Figure14.1Expirationprofit/lossforCoca-Cola
TwocommentsFirst,ifthischartlookslikeanakedshortput,thenyou’reabsolutelyright.Thebuywriteisnomorethanasyntheticshortput.(RefertoChapter21onsynthetics.)
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Sowhybotherwiththecomplications?Makeitsimple:ifyouwanttobuystockandwritethecall,andiftherearenodividendsinvolved,andifyou’reashort-terminvestor,thenjustselltheinthemoneyputandsaveyourselfcommissions.You’llhavethesameriskprofile.(Obviously,I’mnotafanofsellingnakedputs.)
Second,andmoreimportantly,thereiscurrentlyalotofcommonadvicewhichtellsyoutoinitiatebuy-writesfortemptingyields.Well-meaningadvisersusuallytellyouthatyoucouldpay52.67forCoca-ColaandselltheAugust55callat1.45.Yourannualisedreturnwouldbe1.45/52.67×360/60=16.5%Butthisyieldprojectsthatthestockstayswhereitisforayearwhileyouwritemorecalls.
True,ifCoca-Colaralliesthenyou’vemadeabit,butthenyou’remakingtheclassicmistakeoftradingonhope.Instead,ifCoca-Coladeclinespast52.67–1.45=51.22thenyou’realoser.ThisiswhyIdon’trecommendthebuy-writeasaninitiatingtrade.
Ontheotherhand,ifyou’veinheritedthestockfromyourfather,whoboughtitfor$20orthereabouts,andwe’reatthestartofabearmarket,ormaybewe’reinabullmarket,andCoca-Colaislookingtoppy,andyoucan’taffordtosellitbecauseyou’llpaycapitalgainstax,then,ineitherofthesecasesyoumightconsiderwritingacall.
Butonlydoitonceortwice.
AndastorySeveralyearsago,IgavealectureatamajorLondonbank.Duringtheinterval,atraderconfidedtomethattheyhadrecentlydoneverywellwithabuy-writeonshares.Healsostatedthattheyweredisappointedbecausetheshareshadralliedpastthecut-offlevel,ortheshortcalllevel,andthattheyhadmissedoutonagooddealofprofit.
Knowingwhattheyhaddone,Isuggestedthattherewerebetterwaysofcapturingtheupside.TheseareoutlinedintheexamplesattheendofChapters1and2,andtheyarecalledsubstitutiontrades.
Ifyoureallylikethe‘stuff’(aswecalleditattheChicagoBoardofTrade),andbythisImeansoybeans,wheat,bonds,orwhatever,thenjustbuyitwithasellstoporder.Youdon’tneedoptions.
Ontheotherhand,ifyouhaveeverbeenstoppedouttwoorthreetimesinone
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trade,thenoptionsarethewayforwardforyou.
HowtomanagetheriskofthecoveredwriteThecoveredwriteisbestsuitedtolong-termstockholderswhocantolerateadeclineinthestockpricebelowthecurrentprice.
Therearetwosolutionstotheupsiderisk.Usingtheabovespread,firstnotethatwithCoca-Colaat52.67,theAugust55callsarepricedat1.45.Let’sassumethatCoca-Colaimmediatelyrallies$5,to57.67.Atthispoint,yourshort60callswillbeworthapproximately1.45,andyoumaysimplybuythemback.Yourprofit/lossisasfollows:
Saleof60call:
0.34credit
Purchaseof60call:
1.45debit
Profitonstock:
5credit
Profit/loss:
3.89credit
Withthissolutionyouhaverevisedyouroutlook.YouhaveconcludedthatthereissignificantupsidepotentialforCoca-Cola.
Thesecondsolutionistomaintainyouroutlook.YouconcludethatyouhaveerredinyourestimateforCoca-Cola’supsidepotential,butthatthestock’snewlevelisthetopforthetimebeing.Yourstrategyistowritecallsforthenexttwoexpirations,andyouexpecttoprofitintheend.
WithCoca-Colaat57.67,thevalueofthe60callwillbe,aswesaid,approximately1.45.The65callwillthenbeapproximately0.34.The60–65callspreadwillbeapproximately1.45–0.34=1.11.Youcanthenbuythisspread,andbydoingso,rollyourshortcalltothe65strike.
Theoptionssummaryisasfollows:
Saleof60call:
0.34
Purchaseof60call:
–1.45
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Saleof65call:
0.34
Totaloptionsdebit:
–0.77
Here,theprofitequalsthefivepointsappreciationonthestockminusthetotaloptionsdebit,or5–0.77=4.23.
Thetotalprofit/losssummaryatexpirationisasfollows:
Maximumprofit:newstrikepriceminusstockpurchaseprice,minusdebitfromcallposition:(65–52.67)–0.77=11.56
Themaximumprofitoccursatorabovethestrikeprice,65,oftheopenAugustcall
Break-evenlevel:stockpurchasepriceplustotaloptionsdebit:52.67+0.77=53.44.Notethatthislevelis1.11pointsabovetheformerbreak-evenlevel,whichwas52.44.
Maximumloss:fullamountofstockpricedeclinebelowbreak-evenlevel:53.44
Theriskhereisthatatthenewpricelevel,57.67,Coca-Colacontainsfivepointsofdownsidelosspotentialforwhichyouhavereceivedacreditofonly4.23.Thepotentialreturn,ofcourse,isimproved.
Theexpirationprofit/lossissummarisedinTable14.2.
Table14.2Expirationprofit/lossforCoca-Cola
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AstoryandabitofadviceWiththecoveredwrite,itisimportantnottothinkintermsoftheshortcallas‘downsideprotection’.Remember’portfolioinsurance’?Aformofthisnowdiscreditedstrategywasavariationofthecoveredwrite.Duringthe1980sportfolioinsurancewassoldtoinvestorsasameansof‘downsideprotection’,inotherwords,callswerewrittenagainstastockportfolioinordertocompensateforapricedecline,andinthemeantime,toearnincome.
Haveyoueverheardofaninsurancepolicythatpaidyoutobeinsured?On19October1987,noamountofcallssoldprotectedstockholdersfromtheenormouslossoftheirassets’values.Withoptions,theonlyformoffulldownsideprotectionisthepurchaseofaput.
ThelongcalendarspreadorlongtimespreadCalendarspreadsinparticularcanbecomplicated,andtheirreturnpotentialscaninmanycasesbeduplicatedbyotherstationarymarketspreads.However,learningaboutthemisanexcellentwaytoimproveyourunderstandingofoptions,andtoimproveyourriskawareness.
Becauseanoption’sdecayaccelerateswithtimeitispossibletosellanear-termoptionandbuyafurther-termoptionatthesamestrikeinordertoprofitfromthedifferentratesofdecay.Theresultingpositionistermedeitherthelongcalendarspreadorthelongtimespread.Usuallythisspreadistradedwithbothoptions
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at-the-money.Forexample,ifXYZisat100,youcouldselloneJune100callandbuyoneSeptember100callinthesametransaction.Apartfromextraordinarycircumstances,thisspreadisdoneforadebit.Youroutlookshouldcallforastationarymarketwithbothoptionsremainingat-the-money.
Thisspreadisbestopenedwhenthenear-termoptionhasbetween60to30daystillexpiration.Thetimedistancebetweenthetwooptionscanvary.Agreaterdistanceincreasesthecostofthespread,andreducesthehedgevalueofthefurther-termoption,whileashorterdistancereducesthedifferenceinratesofdecay,whichinturnlowerstheprofitpotential.Optimally,thereshouldbe30to90daysbetweenoptions.Thisspreadshouldbeclosedbeforethenear-termoptionexpires.
Apreferableopportunityiswhentherelationshipbetweenthenear-termimpliedvolatilityandthefurther-termvolatilityisatadiscrepancy,i.e.thenear-termvolatilityisatahigherlevelthanusualincomparisontothefurther-termvolatility.Thisoftenoccurswhentheunderlyinghasreactedsuddenlytoaneventthatisofshort-termsignificance,orperhapswhenthelonger-termsignificanceofaneventisnotfullyaccountedfor.Theunderlyinghasmovedtoalevelatwhichitisexpectedtoremainforthenearterm.
ConsiderthefollowingsetofoptionsonRolls-Royce:
Rolls-Royceat223.5Novemberoptionswithninedaysuntilexpiry,Novemberimpliedat52percentFebruaryoptionswith98daysuntilexpiry,Februaryimpliedat46percent(Feb–Nov=89days)Mayoptionswith188daysuntilexpiry,Mayimpliedat44percent(May–Feb=90days)
Thevaluesofthecalendarspreadsaregiveninparentheses(CS).NotethatthecalendarspreadwiththemostvalueistheFebruary–November220callcalendar
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spread.Therethecharacteristicofat-the-money,acceleratedtimedecayismostinevidence.BycomparingtheFebruary–November220callcalendarspreadtotheFebruary–November180and260callcalendarspreadsitcanbeseenthatastheunderlyingmovesawayfromthestrikes,thecalendarspreadshavelessvalue.
Becauseofthislatterfact,manytradersbuycalendarspreadsthatareoutofthemoney.Theiroutlookcallsfortheunderlyingtoapproachthestrikeofthespreadasthefrontmonthoptionreaches30orfewerdaysuntilexpiration.Forexample,youcouldpay6.5fortheMay–February260callcalendar,andifthestockrisesto260atthepointwhenFebruaryhasninedaysuntilexpiration,thenthespreadwillbeworthapproximately17,orthepresentvalueoftheFebruary–November220callcalendar.
Togetanaccurateprofit/lossassessmentatexpirationrequiressimulationbycomputer,whichcandeterminethevalueofthecalendaratvariouspointsintimeandatvariouspricelevelsoftheunderlying.Theabovesetofoptions,however,indicatethebasicprofit/lossbehaviourofthisspread.
Exceptunderunusualcircumstances,themaximumlossisthedebitofthespread.
RisksofcalendarspreadsBecausethecalendarspreadincludesoptionsontwocontractmonthsthereareseveralriskscenarios,andthesearedifferentforoptionsonstocks,interestratecontractsandcommodities.Calendarspreadsmustoftenbeevaluatedastwoseparatepositions,andthereforeaproperrisk/returnprofilecanonlybeobtainedwiththeaidofariskanalysisprogram.However,themajorriskscanbenoted.
Oneriskcommontoallisthattheimpliedvolatilitymayincreasemorefortheshort,near-termoptionthanforthelong,further-termoption,causingthespreadtoloseitsvalue.Thisisusuallyduetoanunforeseenevent.Theunderlyingmaythenmoveawayfromthestrikesbeforeprofitismadefromtimedecay.
Anotherpossibleriskisthatthehistoricalvolatilityoftheunderlyingmaydecrease,bringingtheimpliedvolatilitiesofalltheoptionscontractsdownwithit.Becausethelong,further-termcontracthasthegreatervega,thespreadwillloseitsvalue.
Ifastockmakesalargeupsidemove,bothcallsmaygotoparity,andthespreadwillbecomeworthless.Ifastockmakesalargedownsidemove,bothcalls,and
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thespread,willbecomeworthless.
Withstocksandstockindexes,takeovers,changesindividendsorachangeinthecurrentlevelofinterestratescanaffectthedeltaspreadbetweenthetwooptionscontracts.
Short-terminterestrateandotherinterestratecontractshavetheirownrisks.Acentralbankmayunexpectedlyannounceachangeininterestrates,orthechangemaybegreaterorlessthanexpected.Economicindicatorsmaychangethemarket’sassessmentoftheinterestrateoutlook.Thiswillcausethespreadsbetweentheunderlyingfuturescontracts,andconsequentlytheoptionsspreads,tochange.Cautionmustbeexercisedwhenspreadingoptionsbetweencontractswithdifferentdeliverymonths.
Thereissignificantriskinspreadingagriculturalcommoditiesfromoldcroptonewcrop.Forexample,withCBOTcornearlyinthegrowingseasonyoushouldavoidsellingSeptembercallsagainstDecembercalls.ThisisbecauseashortagemaydevelopinSeptemberwhichwillcauseitsunderlyingfuturescontracttorallywhiletheDecemberunderlyingremainspracticallyunchanged.Manycommoditieshaveseasonalvolatilitytrendswhichshouldbestudied.
Mostcalendarstradedarecallcalendars,butthereisnoreasonnottotradeputcalendars.Theprofit/losscharacteristicsarepracticallyidentical,exceptintheOEXandotherAmericanstyledcontracts,wherethecallsandputshavedifferentbehaviourduetoearlyexercise.Putsonstocksaremorelikelytobeexercisedearlyiftradingatparity,becauseaputistherighttosellthestockandraisecash.
Becausetherearemorevariableswithacalendarspread,itissimplertobuyabutterflyorcondorifyouroutlookcallsfordecreasedvolatilityandfortheunderlyingtoclosenearaparticularstrike.Abetterreasontotradethelongcalendarasopposedtothelongbutterflyistoprofitfromadiscrepancyintheimpliedvolatilitiesfrommonthtomonth.
LongdiagonalcallspreadforabullishmarketfollowedbyastationarymarketItispossibletoalterthestrikesofthecalendarspread.Themostcommonvariationistosellanear-term,out-of-the-moneycallandbuyafar-termat-the-moneycall.Forexample,youmightpay32.5fortheMay220callabove,whilesellingtheFebruary260callat10.5,foranetdebitof22.
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Thereturnscenarioforthisspreadisforthesharestorallygraduallyto260towardsFebruaryexpiration.AtninedaysuntilFebruaryexpiration,thevalueofthespreadwouldbesimilartothecurrentFebruary180–November220callcalendar,at42.5.Thediagonalcalendarisacombinationofthelong,far-term,at-the-moneycallspreadplusthelong,out-of-the-moneycallcalendarspread:
(longMay220call+shortMay260call)+(longMay260call+shortFebruary260call)=longMay220call+shortFebruary260call
Diagonalspreadsmayalsobetradedwithputs.Here,youcanbuyafar-termputandsellanear-termputthatisatastrikefurtherout-of-the-money.
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part3
Thinkingaboutoptions
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Introduction
Part3describesthefinesseofoptions.There’salotinvolvedhereandittakesyouwaypast1×1s.
ThispartguidesyouthroughadvancedtopicssuchashowtheGreeksinteract.BearinmindthattheGreekshavenon-linearvariables,andsoyouneedtoreadaboutthemandworkwiththem.Inotherwords,readingthispartwillgiveyouaheadstartonexperience.
Part3alsodiscussesvolatilityskews.Ittalksaboutwhya10percentout-of-the-moneyputcostsmorethata10percentOTMcallinthefinancials.Itdiscussescommonproblemsintradingoptions,suchasleverage(gearing),aswellaspracticalissuessuchasliquidity.
Oneofthesedaysyou’llaskyouselfwhysuchandsuchhappened,anditwillprobablybebecauseofatopiccoveredinPart3.So,readorskimthispartonceeachyearIdo.
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15
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TheinteractionoftheGreeks
TheGreeks,thetimeuntilexpirationandtheimpliedvolatilityinteractwitheachotherinwaysthatworktogetherandinwaysthattradeoff.Theyworkdifferentlyforeachoptionsposition.Byknowinghowtheyinteractyoucantestyourpositionformarketscenarios.Youcananticipatewhatmayhappenunderthebest,orreturn,scenario,orundertheworst,orrisk,scenario.Youcanknowwhattoexpect.
ThischaptersummariseswhatyouhavepreviouslylearnedabouttheGreeks.Itplacesthemallintoperspectiveanddescribestheirinteraction.
Comparingoptions1:theGreeksandtimeLet’slookagainatDecemberCornoptions.Tables15.1and15.2showtwosetsofoptionswithdifferentdaysuntilexpiration,andwiththecorrespondingdeltas,gammas,thetasandvegas.Thepriceoftheunderlyingisheldconstant.
Youmaycomparetheeffectoftimeonoptionswiththesamestrike,andonoptionswithdifferentstrikes.Note,forexample,the400call,atwo-strikeout-of-the-moneyoption.Asitapproachesexpiration,itsdeltabecomessmaller,itsgammabecomesgreater,itsthetabecomesgreateranditsvegabecomessmaller.Notethe340put,whosedelta,thetaandvegabecomeless,butwhosegammaremainspracticallythesame.Notethatwithtimepassingthegammaoftheat-the-moneyoptionincreasessignificantlymorethantheout-ofandthein-the-moneyoptions.Theseareallconsequencesofthecharacteristicsdiscussedinpreviouschapters.
Table15.1DecemberCornoptions,90daysuntilexpiration
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DecemberCorn at $3.80;90daysuntil expiration; impliedvolatility at 30percent;novolatilityskews;interestrateat3percent;optionsmultiplierat$50,somultiplycallandputvaluestimes$50aThe380callisactually22×$50=$1,100.bNotethatthe440callispricedhigherthanthe320puteventhoughtheyareequallyout-of-the-money.ThisisbecausethemodelassumesthatCorncanrallyfurtherthanitcanbreak.
Table15.2DecemberCornoptions,30daysuntilexpiration
December Corn at $3.80 × 5,000 bushels; 30 days until expiration; implied
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volatilityat30percent;novolatilityskews; interestrateat3percent;optionsmultiplierat$50
Table15.3isageneralisedsummaryoftheeffectoftimeontheGreeks.Again,theunderlyingisheldconstant.Theterms‘in-the-money’(ITM),‘at-the-money’(ATM)and‘out-of-the-money’(OTM)areusedinabbreviatedform.
Table15.3TheeffectoftimepassingontheGreeks
Theserelationshipsholdtrueforalloptions,buttheybecomemoreexaggeratedastheunderlyinghaslessvalue,andlessimpliedvolatility,withlesstimeuntilexpiration,andwithstrikepricesthataremorewidelyseparated.Conversely,theybecomelessexaggeratedif,asthestrikepricesnarrow,theunderlyingincreasesinvalue,andtimeandtheimpliedincreases.
Imagineastockindexat4000andanimpliedat50percent.(I’veseenit.)TheGreeksbetweenthe4000and4050strikeswillbeverysimilar.WhenCornwasat$2.20perbushel(forthoseofuswithamemory),andwith60daysuntilexpiration,theGreeksbetweenthe220and180strikeswereverydifferent.
TheexceptionstoTable15.3arethedeepin-the-moneyandfarout-of-the-moneyoptions,suchastheDecember320callsandputs,andtheDecember440callsandputs.Whentheseoptionshave30DTE,mostoftheirtimepremiumhasbeenexpended,andchangesintheGreeksareoflittleconsequence(exceptwhenyou’reshortthem).
Rememberthatalongoptionspositionhaspositivegamma,negativethetaandpositivevega.Astimepasses,itbenefitsmorefrompricemovement,itcostsmoreintimedecay,anditbenefitslessfromanincreaseinimpliedvolatility.AshortoptionspositionhastheoppositeprofilewithrespecttotheGreeks.
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ByknowinghowtheGreeksinteract,wecanevaluateapositionfromjusttwovariables.Tradersoftendothiswithdeltaandthenumberofdaysuntilexpiration.‘I’mlongahundred,twenty-deltacallswiththirtydaysout’,hasaverydifferentmeaningfrom‘I’mlongahundred,twenty-deltacallswithninetydaysout’.Theformercallpositionhasastrikepricethatisclosertothemoney,higher(positive)gamma,greater(negative)thetaandsmaller(positive)vega(seeTable15.4).Itindicatesthatthetraderislookingforalargemoveintheunderlying,soon.Thelatterpositionindicatesthatthetraderislookingforalargeeventualmoveand/oranincreaseinimpliedvolatility.
Table15.4DecemberCornoptionswithapprox0.28deltas
DecemberCornat380
90DTE
December420calls
30DTE
December400calls
Delta
0.27
Delta
0.28
Gamma
0.006
Gamma
0.011
Theta
$5.5
Theta
$10.0
Vega
$25.0
Vega
$21.5
Understandably,tradersseldomdiscusstheirpositionsexceptwiththeirriskmanagers.ConsiderthecharacteristicsoftheGreeksandtheoutlookofthetraderswhohavepositionsoppositetothoseabove.
Comparingoptions2:deltaversusgamma,thetaandvegaTheabovetablesalsosummarisewhatwealreadyknowabouttherelationshipbetweendeltaandtheotherGreeks.Gamma,thetaandvegaareallgreatestwith0.50deltaoptions.Therefore,astheunderlyingmoves,theGreeksofalloptionsincreaseordecreasetogether,althoughnotatthesamerate.Thissimplifiesthe
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risk/returnanalysisofgamma,thetaandvegawithrespecttodelta,ortheunderlyingpricemovement.
Tradersoftenspeakofgamma,thetaandvegawhendiscussinghowtheirpositionshavefaredwithachangeintheunderlying.‘Everythingwasfineuntilmygammasstartedkickingin,andnowvol’sgettingpumped’,meanstheoppositeof‘Iwasgettinghammeredontimedecaybutnowmygammasandvegasarehelpingmeout’.(Tradersarefondofcomplaining,evenwhiletheyaremakingmoney.)
Thefirsttraderhaspositivethetaandhehasbeencollectingtimedecay.Hehasbeenshortout-of-the-moneyoptionsthathavenowbecomeat-the-moneyoptions.Hisdeltasarechangingrapidlybecauseofhisnegativegamma,makinghispositiondifficulttomanage.Inaddition,hehasnegativevegaandtheimpliedvolatilityisincreasing.
Thesecondtraderhasbeenlongout-of-the-moneyoptionsandhisnegativethetahascosthimintimedecay.Nowhisoptionsareat-the-money.Hispositivegammahascausedhisdeltas,andthereforethevalueofhisoptions,toincreaserapidly.Becausetheimpliedisincreasing,hispositivevegaispayingoff.
Inbothcases,themarkethasbehavedthesame.Itwasformerlyquiet,itrecentlymovedtoanewpricerange,andnowitismorevolatile.ThischangeofunderlyinglevelandcorrespondingchangeofoptionscharacteristicsisillustratedinTable15.5.Ithappenseverydaywithalloptionscontractstoagreaterorlesserdegree.
Table15.5DecemberCornwith30DTE,position:December420calls
Position:December420calls
Positionthen
Decembercornat380December420calls:
Positionnow
Decembercornat420December420calls:
Delta
0.12
Delta
0.51
Gamma
0.006
Gamma
0.013
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Theta $5.20 Theta $11.50
Vega
$15.00
Vega
$21.00
Theeasiestwaytoknowhowanoptionbehaveswhenthemarketmovesistocomparetwooptionsatdifferentstrikes.Here,wecansaythatifCornralliesfrom380to420,thenthe420callswillresemblethe380calls.
ButifCornmakesasuddenmoveupward,thenmostlikelytheimpliedvolatilitywillincrease.Readon.
Comparingoptions3:impliedvolatilityversustheGreeksBecausetheimpliedvolatilityoftentrends,oroccasionallymakesasuddenchange,itisessentialtoknowhowanoptionspositioncanchangeaccordingly.TheinteractionbetweenimpliedvolatilityandtheGreekshassomeunusualcharacteristicswhichtaketimetofullyunderstand.Toknowhowthedeltaschangeisthepriority,becauseachangeintheimpliedoftenchangestheoptionspositionwithrespecttotheunderlying.
Table15.6isournowfamiliarsetofDecemberCornoptions.Theunderlyingisagainat380andthereare90daysuntilexpiration.Theimpliedvolatility,however,isincreasedto40percent.ThistableshouldbecomparedwithTable15.1onpage166,wheretheimpliedis30percent.
Table15.6DecemberCornoptionswith90DTE
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Withanincreaseintheimpliedvolatility,wecanmakethefollowingobservations.
Thedeltasofout-ofthe-moneyoptionsincreasewhilethedeltasofin-the-moneyoptionsdecrease.Thereasonisthatwithanincreaseinimpliedvolatility,out-of-the-moneyoptionshaveagreaterprobabilityofbecomingin-the-money,whilein-the-moneyoptionshavelessofaprobabilityofstayingin-the-money.Similarchangesoccurwhenoptionshavemoredaysuntilexpiration.
Gammasdecrease.Notethatwithincreasedvolatility,thedifferencebetweenthedeltasfromstriketostrikeisdecreased.Thisindicatesthattheunderlyingpassesthroughstrikesmorereadilyand,asaconsequence,thedeltasofthesestrikeschangelessradically.Theircorrespondinggammasarethereforelowered.Thisoccurrenceisalsosimilarinoptionswithmoredaysuntilexpiration.
Thereisaseriousexceptiontotheabove.Farout-of-andin-the-moneyoptions,suchasthe$3.00putsand$4.60callsincreasetheirgamma.Theyhavelowgammastobeginwithbecausetheirdeltaschangeverylittlewhentheunderlyingisatalowvolatility.Butifvolalititysuddenlyincreases,theywakeup.Thischaracteristicbecomesmorepronouncedwithapproximately30daysuntilexpiration.Manytradershavegonebustbynotunderstandingthis.
Thetasincrease.Becauseoptionspremiumsincreasewhilethetimeuntilexpirationcontinuestodecrease,thereisincreasedtimedecayperday.Thetaisthereforegreater.
Thevegasoftheout-of-the-moneyandthein-the-moneyoptionsincrease.
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Astheunderlyingincreasesitsrange,theseoptionsaremorelikelytobecomeat-the-money.Theirvegasapproachthatoftheat-the-moneyoptions,andtheybecomemoresensitivetoachangeintheimpliedvolatility.
Theprinciplehereisthatanincreasedimpliedsignifiesthattheunderlyingisincreasingitsrange.Thismakesthedistinctionsbetweenstrikesless,andthereforetheGreeksbecomemorealike.
Table15.7isageneralisedsummaryoftheeffectofincreasedimpliedvolatilityontheGreeks.
Table15.7EffectofincreasedimpliedvolatilityontheGreeks
Likeallgeneralisations,theabovearesubjecttomodifications.NotethesetofoptionsshowninTable15.8with30DTEat30percentimplied.YoumaycomparethisdatawiththatshowninTable15.2whichhastheDecemberCornimpliedat20percent.
Theexceptionstothegeneralisedsummaryarethatnowthegammasatthe320and440strikesareincreased.Thisisafunctionofthewake-upeffectdiscussedabove.Withvolatilityat30percentand30DTEthesestrikesweremarginallyinplay,butnowwithvolatilityat40percenttheyareshowingsignsoflife.Supposeit’smid-Octoberandthenewcropisplentifulandonitsway,whatcouldpossiblygowrong?
Table15.8DecemberCornoptionswith30DTE,impliedat40percent
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AfewpracticalobservationsonhowimpliedvolatilitychangesMostofthetimeanincreaseintheimpliedvolatilityistheresultofanincreaseinthehistoricalvolatility,butoftenitisnot.Shortlybeforethepublicationofgovernmenteconomicreports,cropforecasts,earningsannouncementsandtheresultsofcentralbankmeetings,thepricesofoptionsoftenriseinanticipationofmarketmovement.TheresultingchangestotheGreekschangetheexposureofaposition,andthereforechangetherisk/returnprofile.
Occasionally,theimpliedincreasesbecausetheoptionsmarketsuspectsthatthereistroublebrewing,andthissituationofexpectancycanlastformonths,eventhoughthereisnosignificantchangeintheunderlying’sdailypriceaction.
Occasionally,anunderlyingmayincreaseitsvolatilityoverthecourseofoneortwodaysafterapublishedearningsreportorotherevent,buttheimpliedwillexhibitlittlechange.Thisisbecausetheoptionsmarketviewstheeventasfallingwithintherangeofexpectations,andhavingnosignificancebeyondafewtradingsessions.
Moretroublesome,andatthesametimepotentiallyrewarding,isachangeofimpliedvolatiltyduetoanunexpectedevent.Forexample,atradermaybecomfortablyshortout-of-the-moneycallsinstocksorastockindexwhenacentralbanksuddenlylowersitsovernightlendingrate.Hispositionissimilarto
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thatinTable15.5.
Ifthestockmarketrallies,asitusuallydoeswithanunexpectedratecut,thispositionbecomesshorterindeltasnotonlybecauseitistrendingtowardsthemoneybutalsobecausethedeltasarebeinggivenanaddedpushbytheincreaseintheimplied.Inaddition,thistrader’sformerlymanageable,negativevegapositionsuddenlygrowswiththeimplied.Thepriceof,andlosson,hisshortcallsisthereforeincreasingbythreefactors:
theincreasingdeltastheincreasingimpliedvolatilitytheincreasingvegas.
Theoptionsaregrowingteeth.
Meanwhile,thetraderwhohaspatientlyheldtheoppositeposition,payingtimedecayforhislongcalls,isrewardedmanifoldly.
Anout-of-the-moneyputpositionbehavesinasimilarmannerifthemarkettakesasuddenhitonthedownside.Supposethecentralbanksuddenlyraisesitsrate.Ifthemarketbreaksdownward,andif,asusual,theimpliedincreases,whatistheeffectontheout-of-the-moneyputs?
TheotherGreeksThereareadditionalGreekswhichsometradingfirmsusetomonitortheirpositions.Theyareallbasedonthefourthatwehavediscussed,andaremoreusefulinassessingtheriskoflargehedgefundsorinstitutionalportfolios.Oneoftheseisrhowhichisthechangeofanoption’svaluewithrespecttoachangeintheinterestrate.Withthecurrentlowlevelsofinterestratesthisisnotasignificantfactorunlessyouhaveaverylargeportfolio.Itwillbecomesignificantif,inthefuture,interestratesreach5percentormore.
TheGreeks,impliedvolatilityandtheoptionscalculatorYoucancalculatetheGreeksofmostoptionsbyusinganoptionscalculator.Withthisdeviceyouinputthestrikeprice,priceoftheunderlying,timeuntilexpiration,volatility,interestrate,anddividendsifapplicable,anditusesthepricingmodeltocalculatethetheoreticalvalueoftheoptionwiththeGreeks.
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Theoptionscalculatorisaninvaluabledevice,especiallyforbeginners.Itisadvisabletospendatleastafewhourswithit.
Withtheoptionscalculatoryoucanalsodeterminetheimpliedvolatilityofanoptionfromtheoption’sprice.Supposeyou’rereadingtheclosingoptionspricesovertheinternet.Theclosingpricesoftheoptionsandtheunderlyingsareoftenlisted.Thenear-termeurodollarorshortsterlinginterestratecanbeused.IntheUS,theamountanddateofthedividendsareconsistantandwidelyreported,butintheUKthisrequiresmoreofanestimate.Thedaysuntilexpirationarealsooftenlistedand,whennot,youcancheckthemontheexchangewebsite.ForstocksyoucangenerallyusethethirdFridayoftheexpirationmonth.Thestrikepriceyouknow.
Ifyouplugthesefivevariablesintotheoptionscalculator,itproducestheimpliedvolatilityoftheoption.
Nowadays,optionscalculatorsareeasytofindwithasearchengine.Manyoptionswebsitesandsomeexchangewebsiteshaveoptionscalculators.DatavendorsincludetheGreekswiththeirpricereports,andmostbrokeragefirmssubscribetooneormoredataservices.Manybrokerageandtradingfirmsalsohaveoptionscalculatorsontheirwebsites.
AstoryabouttheGreeksIoncehadadiscussionwithaquant(someonewhopractisesquantitativeanalysisofthefinancialmarkets)aboutdeltas.Veryauthoritatively,hetoldmethathewasworkingonanewmodeltocalculatedeltas.IrepliedthatItotallyapprovedbecauseofmyexperienceasamarket-maker.
IsaidthatwhenIwastradinginafastmarket,theunderlyingwouldgapupordown,volatilitywouldexplode,theskewswouldtakeoffandtheskewcruxwouldshift,andmydeltahedgewouldbepracticallyuseless.ThenIcouldonlyrelyonmyexperience.(Whichpaidoff.)
Itoldhimthatwhattradersreallyneededwasareal-timedeltamodel.
Helookedatmewithablankstare,mutteredsomethingIcan’tremember,andthenwalkedaway.WhenInextmethim,hewasn’tveryfriendly.
ThelessonisthattheGreekscanreactincomplicatedways,sostudythemandworkwiththemuntilyougetanintuitivefeelforhowtheywork.Thenyou’llhaveanedge.
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ThecostoftheGreeks
Sofar,wehavediscussedanumberofdifferentwaysofanalysingstraightoptionsandoptionsspreads.Wecantakethisastepfurtherbyexaminingwhichoptionsarepreferablechoicesgivenaspecificamounttoinvest.Inthischapterwelookatagroupofstraightoptionsandcomparetheirrisk-returnpotentialstotheirprice.WecandothiswiththehelpoftheGreeks.
Delta/priceratioThecostoftradingpricemovementAnotherwaytothinkofdeltaisthatitindicatesthepotentialforpricechangeintheoption.Ifyoucomparethedeltatothepriceoftheoptionitself,youcandeterminetheoption’spotentialpricechangegiventheamountthatyouwishtoinvest.Table16.1showsasetofDowJonesEurostoxx50optionsat57DTEwiththeirdeltas.Let’sassumethatwehaveanupsidedirectionaloutlook;onlythecallsarelisted.
Inthelastcolumnthedeltaofeachoptionisdividedbyitsprice.Theratioisthenexpressedasapercentage.Mytermforthisfigureisthedelta/priceratio.Iftheindexmovesplusorminusonepoint,thenthe2700callincreasesordecreasesbyplusorminus0.70ofapoint.0.70is0.38percentof185.40,theamountinvested.
DowJonesEurostoxx50Junefuture283157daysuntilexpirationInterestrate1percent
Table16.1JuneDJEurostoxxoptions,withdelta/priceratio
Strike
Callvalue
Calldelta
D/P(%)
2700
185.40
0.70
0.38
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2750
149.40
0.64
0.43
2800
116.80
0.56
0.48
2850
88.10
0.48
0.54
2900
63.80
0.40
0.63
2950
44.20
0.32
0.72
3000
29.20
0.24
0.82
3050
18.40
0.17
0.92
Bycomparingthedelta/priceratioswefindthattheout-of-the-moneyoptionshavethegreatestpotentialforpricemovementperamountinvested.Notethatthispotentialisforincreasedaswellasdecreasedpricemovement.Here,bothriskandreturnincrease.Butbecausetheamountinvestedislessthanwithin-orat-the-moneyoptions,investorsoftenfindthisriskworthtaking.
Thetrade-offiswithtimedecay.Thedelta/priceratioincreasesasoptionsmoveclosertoexpiration,buteventuallyanout-of-the-moneyoptionhasverylittleprobabilityofprofitingfromunderlyingpricemovement.(Butitcancauseseriousdamageifyousellit.)
Theoption’sdeltaandthenumberofdaysuntilexpirationarethebestguidestothistrade-off.Ashort-term,0.30deltaoptionoflessthan30days,forexample,hasagreaterdelta/priceratiothana0.30deltaoptionofmorethan100days,buttheformerisinarapiddecaytimeperiod.
Theta/priceratioThecostoftradingtimeWehavepreviouslydiscussedthetimedecayvariable,ortheta.Wesaidthatanoption’stimedecayacceleratesasexpirationapproaches.Beforeyoudecidewhichoptiontobuyorsell,itisimportanttoknowthetimedecayoftheoption
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asapercentageoftheoption’svalue.Youcanthenbetterchoosethestriketotrade.Table16.2showsoursetofEurostoxxoptions,eachfollowedbyitstheta/priceratioexpressedinpercentageterms.
Here,thepriceofthe3050is18.40.Thedailydecayofthisoptionis0.46,makingthethetapriceratio0.46/18.40×100=2.50%.Inpercentagetermsthe3050callisthemostexpensivetohold,whileinabsolutetermsitistheleastexpensive.
Table16.2JuneEurosroxxoptionswiththeta/priceratios
Vega/priceratioThecostoftradingvolatilityInChapter7wediscussedimpliedvolatilityanditsrelationtovega,andwenotedthatanoption’svegaincreaseswithmoredaysuntilexpiration.Table16.3comparesthevegaofanoptiontoitspriceinordertodeterminehowaninvestmentmayperforminpercentagetermsduetoa1percentchangeintheimplied.Thevega/priceratio,asapercentage,islistedinthelastcolumn.
Table16.3JuneEurostoxxoptionswithvega/priceratios
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Again,thelargestpercentagetrade-offiswiththe3050calls.Theymayincreaseordecrease15.2percentoftheirvaluewitha1percentchangeintheimplied.
Forthepurposeofcomparison,thesametableoffiguresisgiveninTable16.4,butwith30DTE.
Table16.4EurostoxxJuneoptions,30DTE,Junefutureat2831
Aswemightexpectwithtimepassing,mostofthedelta/priceratios,theta/priceratiosandvega/priceratioshaveincreasedforalltheoptionsthatcontaintimepremium.Notethatthevega/priceratiofortheATMcallremainsat
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approximately5percent.Therisk/returntrade-offwithalltheotheroptionsisclear.
TwoapproachesInthischapterwehaveexaminedriskandreturnintermsofdelta/price,theta/priceandvega/priceratios.Wehavefoundthatboththeriskandreturnperamountinvestedincreaseastheoptionbecomesfurtherout-of-the-moneyandastheoptionapproachesexpiration.Theseratiosvarywithoptionsoneachunderlyingcontract,andyouwillneedtoexaminethemforthecontractsthatyouwishtotrade.
Therearetwoapproachestoconsider:
Thefirstisobviouslytolimityourriskbylimitingthenumberofcontractsyouwishtotrade.Theremaybeagreateramountatriskbypaying88.10foroneJune2850callwith57DTEthanthereisbypaying11.50foroneJune3000call,butthelatterhasgreaterpercentagerisk.Perhapsyouareanatural risk-taker, often taking long odds. Then the 3000 call has theadvantageofgreaterpotentialreturn,and11.50isthesmallerlosstotakeifyourinvestmentfailstosucceed.The second approach is to limit the amount you wish to invest. Forexample, If you have €88 to invest (times the multiplier) you may pay88.10foroneofthe2850calls,oryoumaypay80.50forsevenofthe3000calls.Inthiscasethepercentageriskisgreaterwiththe3000callposition.
Givenafixedamounttoinvest,wecandrawthefollowingconclusions:
Ifthemarketisacceleratingtotheupside,thenyourbestchoiceistheD/Pratioofthe3000s.If themarket is trending up, but volatility is stable or perhaps declining,thenyou’llpreferthelowerV/Pratioofthe2850s.Ifvolatilityisincreasingbutit’sgettingclosetoexpiration,youmayprefertheT/Pratioofthe2900sor2950s.You might also use the above tables to evaluate risk/return for sellingoptions.Inallcases,beclearaboutyourmarketassessmentandyourgoals.
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Optionstalk1:technicalanalysisandtheVix
Chapters17through19aremoreinformalthanthosepreviously;theirpurposeistoprovideageneralinsight.Asstatedintheintroductiontothisbook,itmaybeimpossibletocoachyouvialongdistance,butthemoreknowledgeyouhave,themoreresourcesyou’llhave.Whatfollowsisnotgospel,butitisbasedonagooddealofexperience.
AnalysisofatradeInpreviouschapterswehavereferredtotheuseoftechnicalanalysiswhentradingoptions.Here,wehaveanexampleofonetrade.Thiswasarealtrade,withalotofrealmoneybehindit.Imadethistraderecommendationwiththehelpofourbrokers,anditwastradedbyoneofourclients.
Atonepoint,itcameclosetolosing,butintheenditwentreallyright.Becauseitwasagoodtrade.
EndofSep06DecSchatzat104.12Schatz104.00–103.90–103.80putladderPay1tick(0.01)Maximumprofit:(104–103.90)–0.01=0.09(9ticks)Upperbreak-evenlevel:104–0.01=103.99Lowerbreak-evenlevel:103.80–0.09=103.71Technicalsupportat103.80Schatzputladder
EndSep06
DecSchatz104.12
Dec104.00–103.90–103.80putladderpay1tick
riskbelow103.71butweseesupportat103.80
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EndOct06 DecSchatzat103.80sellat8.5
BackgroundOurclientwascash-flowtraderatoneoftheLondonmajors.ShewasthinkingthattheSchatzhadmadeashort-termlow.Weagreed.Themarkethadbouncedoffthetechnicallowsat103.80,butwethoughtthatthelowswouldholdunlesstheEuropeanCentralBankdidsomethingfunny,likeraiseinterestrates.Ourviewoftheeconomicreportstoldusthattheywouldn’t.
Ianalysedthistradeforward,back,andupsidedown.IestimatedthattheGreeksandthetechnicalsmadethisagoodtrade.Beinganex-riskmanager,Ipreferredtosellthenaked103.70putinsteadofthe103.80put,butthatwouldhaveincreasedthecostofthespreadto4ticks.
Anyway,Iagreedtosellthe103.80sifweallagreedonacoveringplan,whichwastobuythe103.70sifthemarketbrokesupportat103.80.Wewouldthenturntheputladderintoacondorandcutourrisk.Allagreed.
Severalweekslaterthemarketretracedtothe103.80area.Thiswasadifficultrideforthetraderbecausethe103.80swereinplay.Still,wegavehertheconfidencetoknowthatherbreak-evenlevellayat103.71,andthatwehadaplantocover.
Wefiguredthatwewereseeingatwo-testsupportscenario,whichiscommoninthetechnicals.Wewereconcernedthatifthemarkettestedthelowonceagain,thenitwouldbreakthrough.
Thetraderhadaprofit,soweadvisedhertoclosethetrade,whichshedidfor8.5ticks.Sowepaid1forthespreadandsolditat8.5.Notabadrateofreturn.
Althoughwecameclosetobeingforcedtocover,wewereneverindangeroftakingabighit.Butifyouwanttoknowwhatcangoseriouslywrongwiththistrade,thenrefertothestoryonpage98.
Toconclude,letmereiteratewhatI’vesaiditbefore.Newtradersshouldnotsellnakedshortoptions.ButasItellmyson:
Youshouldn’tdoitButyouprob’lywilldoitSobeforeyoudoit
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Takesomeadvice.
TheVixTheVixisaverystraightforwardidea.It’stheprojectedvolatilityoftheS&P500.Actually,it’stheimpliedvolatilityofthenear-term,at-the-moneyandonestrikeaboveandbelowtheat-the-moneyoptionsontheS&P500.ItisaproductoftheChicagoBoardOptionsExchange(CBOE).
Rememberthatoptionstellyouwhatinvestorsthinkthatthemarketwilldo.Optionstrytoanticipate.Optionsareindicators.AndtheVixisanexcellentindicatorofmarketsentiment.
Lately,withtheaidofthequants,theCBOEhasrevisedtheVix,andsonowtherearetwoVix’s:theoldandthenew.Butifyou’reusingtheVixasanindicator,there’snotmuchdifferencebetweenthem.
Personally,Ithinkthattherearemoreprofitablewaysoftradingvolatilitythanasafuturescontract.Youcouldtradestraddles,strangles,butterfliesandcondors.ButiftradingtheVixsuitsyourstyle,thengoforit.
Still,theVixisaveryusefulindicator.Ittellsyouhowvolatilitycanhibernateforalongtime,butthatwhenitwakesup,itrearsupandroarslikeagrizzlybear.Forexample,youdon’tsellvolatilitywiththeVixat10percent.Don’teventhinkaboutit.
Tradevolatilityjustlikeyoutradeanyotherunderlyingcontract.Followthetrends,usetechnicalanalysis,don’ttrytocatchafallingknife,etc.AsweusedtosayinChicago:tradethestuff.
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Optionstalk2:tradingoptions
TradingdeltaandtimedecayByknowingthatdeltaindicatestheprobabilityofanoptionexpiringin-the-money,youcanassesstheeffectoftimedecayonprobability.Thiscanhelpyoudecidewhethertoopenorcloseaposition,andwhichstrikepricestoconsidertradinginthefirstplace.
BuyinganoptionForexample,ifyouroutlookisforalarge,directionalmove,youmightconsiderbuyinga0.30deltaoption,callorput,with90to120daysuntilexpiration.Youknowthatiftimepassesandtheunderlyingremainsstable,thedeltadecreases.Thisimpliesthatthelargemoveyouarelookingforbecomeslessprobableaswell.Rememberthatanoption’stimedecayacceleratesasitapproachesexpiration.Youmayconsider,atsomepointbetween60and30daysuntilexpiration,rollingyourpositionintoacontractmonthwithmoretimeuntilexpiration,eventhoughitmaycostmore.Alonger-termoptiongivesyoumoretimetoberight.
A0.30deltaoptionwith30daysuntilexpirationwillcostlessthana0.30deltaoptionwith90daysuntilexpiration,butifyouroutlookisnotsoonrealised,itwillsoonbecomea0.10deltaoption,anditwillhavecostyouintimedecay.
Anear-term,0.10deltaoptionisaffordable,andifthemarketsuddenlymovesinitsdirection,itwillprofithandsomely,butitshouldbeboughtorheldbythosewhofeelcomfortablemakingashort-termtradeagainst10to1odds.Amoreprudentuseofthisoptionistohedgeanotherposition.
Don’tmakethemistakeofbuyinganoptionjustbecauseitischeap.Alow-priced,farout-of-the-moneyoptionalsohasalowprobabilityofexpiringin-the-money.Italsohashigherdelta,thetaandvegapriceratios.Ifyouwanttoreducethecostofyourcallorput,youcandothisbyspreading.
Supposeyouhaveboughta0.30deltaoption,andasaresultofmarketmovement,itnowhasa0.60delta,andyouhaveaprofit.Thisoftenhappenssoonerthanyouexpect.Didyouroriginaloutlookcallforthisoptionhavea0.80
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delta?Don’tkidyourself;ifthemarketmovehasmetyourexpectations,thentheoptionhasdoneitswork.Ratherthanriskexposuretotheta,youshouldclosetheposition.
SellinganoptionOptionssellersshouldhavedecliningvolatilityontheirside,whichmeansthattheprobabilityofsmallerinter-andintradaypricemovementisincreasing.
Itisalsoadvisableforoptionssellerstotakeadvantageoftimedecaywheneverpossiblebytakingashortpositionclosetoexpiration.Howclosedependsonthedeltaoftheoptionandtheriskthatisjustifiable.AsillustratedinPart1,thefurtherthestrikeisfromtheunderlying,themoredaysuntilexpirationitsdailytimedecayaccelerates.
Iftheunderlyingmakesasudden,unforeseenmovethatresultsinaloss,youmusthavesufficientcapitaltomaintainyourshortstrategyinordertotakeadvantageofareturntostablemarketconditions.Inanycase,itisprudenttorollyourshortpositiontoafurthercontractwhenyourcurrentcontracthas30DTEorless.Aprobabilityassessmentleastaccountsforshort-termpricefluctuations,andanunexpectedmovewhentheunderlyingisclosetoexpirationcanseverelydamageyourprofit.
Shouldyouwishtotakeadvantageofdecreasingprobability,youmaywishtosella0.20deltaoptionthatisnear-term,approximately60DTE.Thisoptionhaslessthetathana0.30or0.50deltaoption,butitsdeltaindicatesthatithasagreaterprobability(80percent)ofremainingout-of-the-money,andthereforehaslesspotentialrisk.
Ifthisoption’sdeltaeventuallybecomes0.05,eitherthroughanunderlyingpricemovementorthroughtimedecay,thenyouhaveaprofit.Youmaynowbetemptedtoholdthispositioninordertocontinuetocollectasmallamountoftheta,butinsteadyoushouldaskyourselfifyourpreviousoutlookfortheunderlyinghasbeenrealised.Ifso,itisbettertocloseyourpositionthantoriskexposuretoanincreaseddelta,i.e.anunderlyingmoveinthedirectionofyourshortcallorput.
Butsupposeourshort0.20deltaoptionbecomesa0.50deltaoptionthroughanadversemarketmove.Clearlyyouroutlookdidnotleadtosuccess,andyouhaveincurredaloss.Youmayhopeforamarketretracement,andyoumayfearacontinuedadversemarketmove,butinsteadyoushoulduseallavailablemeanstoformulateanewoutlook.Youmayevenuseyouroldoutlookasastarting
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point;itmayhavebeenflawedinsomerespects,butitmayhavebeenaccurateinothers.
Ifyournewoutlookcallsforastablemarketinthenearterm,thenyour0.50deltaoptionpresentsanopportunitytorecoupsomeandpossiblyallofyourlossthroughgreatertheta,andyoushouldretainyourposition.Again,don’tkidyourself;ifyouareuncertain,ortoounsettledtoformulateanewoutlook,thenyoushouldcloseyourposition.
Themajorriskofanakedshortcallpositionisasudden,unforeseenincreaseinthepriceoftheunderlying.Likewisethemajorriskofanakedshortputpositionisasudden,unforeseendecreaseinthepriceoftheunderlying.Bothoftheseriskscanandshouldbelimitedbyspreading.
TradingvolatilitytrendsWhentradingvega,andthereforevolatility,itisimportanttotakeadvantageof,andnottofight,thevolatilitytrend.Volatilitycanincreaseanddecreaseforlongperiodsoftime,justasstock,bondandcommoditymarketshavetheirbullandbeartrends.
Itmayseemobvious,butitisalwayspreferabletobuyoptionswhenvolatilityisincreasingandtoselloptionswhenitisdecreasing.Manyoptionstradersignorethetrend,perhapsbecausetheyareaccustomedto,orsimplybetterat,buyingorsellingpremium.Thismakesforfrustratinganddifficulttrading.
Tobefair,itisoftendifficulttotradevolatilitybecause,likeanyothermarkettrend,itcanbeerratic.Whenthisisthecase,youarefullyjustifiedtostayoutofthemarket.
Rememberthatthevegaofanout-of-the-moneyoptionincreasesordecreasesastheimpliedvolatilitychanges,whereasthevegaofanat-the-moneyoptionremainsunchanged.Thereneedstobeagammaofthevegacalculationintheoptionsbusiness.Perhapsyoumightresearchthistopic,andcontactmewithyourfindings([email protected]).
DurationaloutlookAproperoutlooktellsyounotonlywhentoopenaposition,butalsowhentocloseaposition,eitherbytakingaprofitorbycuttingalosswithastoporder.Therearemanyexcellentbooksthatdescribehowtotradethevarioustypesofmarkets;thisguideteachesyouhowtobemoreflexibleinyourapproach.
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Whentradingoptionsyoushouldalwayshaveadurationforyouroutlookbecauseoptionsworkforalimitedtime.Inallcaseskeepyourdurationinmind,andwhenithasended,eithercloseyourpositionorformulatearevisedoutlook.Arevisedoutlookcanbeformulatedbyaskingyourselfthefollowingquestion:IfIwantedtoenterthemarketnow,isthisthepositionIwouldtake?Iftheanswerisno,thencloseyourposition.Otherwise,youarepayingtohope.
OptionsvsbasispointsAnannualisedreturnprojectionisnotthewaytothinkaboutoptions.Ortrading,forthatmatter.Youwon’tbemakingmoneydaybyday.It’snotlikereceivingacouponorgettingamonthlypaycheck.
Still,fundmanagerspressuretheirtradersforweeklyormonthlyresults.Thisleadstotraderstryingtomeetshort-termtargets,andthentoover-trading,andthentorackingupcommissions,andthentotakingunduerisk,andthensometimestoablowout.
Thisisbecauseaweeklyormonthlyreturnanalysisfavourscollectingmoneyfromtimedecay.Incomefromtimedecayisthemostnumb-nutwayoftradingoptions.AttheChicagoBoardOptionsExchange,wecalledit‘sellin’premo’.Soonerorlateritblowsupinyourface.
Anannualisedreturnshouldbeevaluatedattheendofeachquarter(barringanextraordinaryevent).Butthebestwaytoanalyseatrader’sperformanceistoreviewhimafterayear.Thereasonisthatthebesttradesarefewandfarbetween.
ThebesttradersIhaveknownarethosewhoarecapableofpatience.Patiencerequiresexperienceandcapital.
Sometradersmakeonlythreeorfourtradesperyear.Thatmeansthattheyonlyexecutesixtoeighttimesperyearapartfromadjustmenttrades.Mostofthetimetheylookforopportunitiesortheymanagetheirposition.
Thisisadifficultapproachtosellunderthefixedincomemodelbecausethetradingfirmhasmonthlyexpenses.Thefirmneedsmonthlyrevenue.
IrememberoneproptradingfirmbasedinChicagothatwasdoingverywell,butwhosoldouttoagroupofwell-capitalisedinvestorswhodidn’tunderstandtrading.Withinayearthepropfirmwasoutofbusiness.Ofcourse,wehiredafewoftheirtraders.
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OnetipIcangiveyouistokeepyourcostslow–andthatincludespersonalexpenses.Thenyou’llhavemorepatiencebecauseyou’llworrylessaboutmeetingyourmonthlyexpenses.
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Optionstalk3:troubleshootingandcommonproblems
InvestingwithleverageOptionsareleveragedinvestments:therisk/returnpotentialisfargreaterperamountinvestedthanwithstandardinvestmentstrategies.Itisthereforeadvisabletoapportionlesscapitalthanwithstandardinvestments,unlessyouareveryconfidentofyouroutlook.
Oneofthemostprudentoptionsstrategiesfortradingastraightcallorputpositionistodeterminetheamountofstockorsharesthatyouarecomfortablyabletoafford,thenbuythenumberofcalloptionsthatleveragethesamenumberofsharesandnomore.Therestofyourcapitalisthenplacedinacashdeposit.
Forexample,supposeyouarebullishonastock,andyouareconsideringpaying$95for500shares.Youcouldinsteadpay10for5,April95callswith180DTE,andplacetheremainderinasix-monthcashdeposit.Yourexpenditureandcashdepositbreakdownaccordingly:
Amounttoinvest:$95×500=$47,500Costofoptions:$10×100×5=$5,000AmountdepositedinCD:$85×500=$42,500
Ofcourse,investorsfrequentlyleveragetoagreaterdegree.Thepointtokeepinmindisthatacallcanpotentiallyexpireworthless,andifitdoes,thenyouhavestillriskednomorecapitalthanyoucanafford.
Theaboveguidetoleverageisessentialforthosewhosellcallsnaked.Ifyouaretheselleroftheabove5,April95calls,youincurthepotentialobligationtobuy500sharesinordertotransferthemtothelongcallholder.Youshouldhaveatleasttheamountofthebreak-evenleveltimesthenumberofsharesleveragedondepositinordertomeettheobligationofyourshortcalls:
Shortcallbreak-evenlevel:$10+$95=$105Multipliedbynumberofshares:$105×500=$52,500ondeposit
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Ashortcallspreadfacesthesamepotentialcapitalrequirement,althoughtheriskislimited.
Coveredcallwritingassumesthattheshortcallholderhasalreadypurchasedsharestodeliver,andsothecapitalrequirementisalreadyondeposit.
Thesellerofanakedputincursthepotentialobligationtobuystockatthebreak-evenlevel.Therefore,thislevelofcapitalshouldbeondeposit.Forexample,ifyouarebullishinastockyoumight,ifcompelledbythedeviltosellpremium,sell5,April95putsat10.Youmayalsowishtobuythestockonapricedeclinebut,ineithercase,yourprudentcapitalrequirementwouldbeasfollows:
Shortputbreak-evenlevel:$95–$10=$85Multipliedbynumberofshares:$85×500=$42,500
Theputbuyerisinanadvantageouspositionintermsofcapitalrequirement.Hehasthepotentialrighttosellthestockatahigherlevelthanthemarketpriceatexpiration.
Notethatclearingfirmsoftenrequirelesscapitalondepositthanwehavementioned.Theabovearemerelyprudentsuggestions.Theywillalsoleadtomoredisciplinedtrading.
ContractliquidityandmarketmakingGenerallyspeaking,themoreliquidanoptionscontract,thetighteristhebid–askspreadforanoption’sprice.Thegreaterthebid–askspread,thegreateristhecostofopeningandclosingaposition.Thisspreadisoftensimplycalled‘themarket’fortheoption.Eurodollaroptions,forexample,havemarketsthatarehalftoonetickwide,or$12.50to$25.00.Themarketsforoptionsonthinlytradedstockscanbethreeormoretickswide,or$300+.
Thewidthofabid–askspreadisaproductoftheopportunitiesforspreadingrisk,eitherwiththeunderlyingorwithotheroptions.Iftheunderlyingortheotheroptionscontractsarenotliquid,thentheoptionsmarket-makerscannothedgethepositionsthatretailcustomerswantthemtoassume.Theymaybeforcedtocarrythepositionsintheirinventoryforperiodsofweeksormonths,andduringthistimetheyareexposedtorisk.Inordertocovertheirrisk,themarket-makersneedtowidentheirbid–askspreads.Underthesecircumstances,toaskthemarket-makerstotightentheirspreadsistoaskthemtoputtheirjobsinjeopardy.Nosensibletrader,includingyourself,willdothis.
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Bid–askspreadsalsowidenduringhighlyvolatilemarkets.Iftheunderlyingisleapingwildly,thentheoptionsmarket-makerscannothedge.Inordertocovertheirrisk,theyneedtowidentheirmarketstocorrespondtothewiderangeoftheunderlying’sprices.Youwoulddothesame.
CommonproblemswithstraightcallorputpositionsThissectionoffersobservationsonwhatmayhappentoastraightcallorputposition.Thecircumstancesherepresentedarenotthosethatnecessarilywillhappen.Theseobservationsaregivenincasesimilarcircumstancesoccurtoyou.Thepurposeissimplyforyoutohaveabasisforunderstandingthebehaviourofyouroptionspositionifoneofthesesituationsarises.
Stocksup,callspracticallyunchangedorunderperformingOccasionallywhenastockorstockindexrallies,purchasedout-of-the-moneycallsunderperform.Thiscanoccurwhentheimpliedvolatilityhasbeenextremelyhigh,afterasell-off,andlongcallpositionshavebeenseeneitherasdefensivealternativestobuyingthestockorassyntheticputs.ThisisdiscussedinPart4.Asthemarketrallies,thedownsideprotectionthatthecallsaffordisneededless,andthemarketprobablythinksthatthepotentialupsideislimited.Asaresulttheimpliedvolatilityofthecallsdeclines,andpremiumlevelsfall.Theoptionsstillgaininvaluebecausetheyaretrendingtowardsthemoney,butprofitsarenotoptimum.
Underthesecircumstances,analternativestrategywouldbethelongcallspread.Withthisstrategythelongcallposition’sexposuretodecliningvolatilityisoffsetbythatoftheshort,furtherout-of-the-moneycall.RefertoChapter8onthisspread.
Stocksdown,callspracticallyunchangedordownslightly(theoppositeoftheabove)Sometimeswhenanunderlyingbreaks,shortout-of-the-moneycallsinstocksorstockindexesstubbornlyclingtotheirvalue.Thiscanbeduetoageneralriseintheimpliedvolatilityastradersseekdownsideprotectionfrombothcallsandputs.Thecallsarelosingvaluebecausethestockismovingawayfromthem,buttheyaregainingvalueastheincreasingimpliedvolatilityincreasestheirpremium.Thereisincreaseddemandforthembecausetheyarealternativestoa
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stockpurchaseandbecausetheycanbeconvertedintosyntheticputs.ThisalsodiscussedinPart4.
Whenthisoccurs,itisadvisablesimplytoholdthepositionuntilthemarketstabilises.Thisrequiresstrongnerves,butkeepinmindthatthestock’spricedirectionandtimedecayareonyourside.Ifthestockrebounds,theimpliedvolatilityoftendecreases,andifso,thecalls’premiumswillalsodecrease.Thepotentialproblemisthatthestockmaysuddenlyreboundtoahigherlevelthanwhereyousoldthecalls.Bereadywithabuy-stoporder.Themoreprudentstrategyistheshortcallspread.
Stocksdown,putspracticallyunchangedorunderperformingOccasionallyastockorstockindexsellsoff,andlong,out-of-the-moneyputsunderperform.Thisisoftenduetothefactthatthestockhasretracedtothelowerendofitstradingrange,andthemarketthinksthatitwillremainsupportedatitspresentlevel.Theimpliedremainsstable,ordecreasessomewhat,becausethestockdeclinehasmetexpectations.Thisproblemmayalsobeduetoadecreaseintheimpliedvolatilityoftheputbecauseofashiftinthevolatilityskew,andforthis,youshouldconsultChapter9onvolatilityskews.
Analternativestrategyisthecallsale,above,ifproperlymanaged.Thelongputspreadisabetteralternativebecauseanydeclineintheimplied,viatheskeworotherwise,affectsboththelongandshortputstrikes.Youarethentakingadvantageofdownsidepricemovementwithlittleexposuretoachangeintheimplied.RefertoChapter8onthelongputspread.
Personally,Ihaveadifferentapproachtobuyingastraightput.Iusetechnicalanalysistonotethesupportlevelofthestockorindex.IfIthinkthatthestockismorelikelytobreaksupportthanthemarketisindicating,Ibuyputsbelowthelevelofsupport.Notonlyaretheseputscheaperbut,moreimportantly,ifthestockdoesbreaksupport,theimpliedoftenincreasesbecausethemarketisthenuncertainoftheextentofthedownsidepotential.IfIamuncertainthatthestockwillbreaksupport,whichIammostoften,Iusethelongputspread.
Stocksup,putsdownslightlyorunchangedOftenwhenthestockmarketrallies,putsloseverylittleoftheirpremium.Thisoccurswhenthemarketfearsaretracement.Arallyinthestocksmaybeseenasaputbuyingopportunity,anddemandremainsstrong.Thiscanbenerve-racking
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forputsellers,andtheyfeellikesittingducks.Oftenthemarketretracesandstabilises,andtimedecaybeginstoeatawayattheputs,butbythentheputsellersareonlytoogladtoclosetheirpositionsatabreak-evenlevel.
Anotherreasonforthisoccurrenceisthatwitharally,theputskewoftenshiftshorizontallywiththeunderlying,causingtheimpliedsoftheputstoincrease.RefertoChapter19onvolatilityskews.
Asensiblealternativetobeingshortputsistheshortputspread.Thisspreadlimitsdownsideriskwhilestillpreservingtheopportunityforincomethroughtimedecay.Theexposuretochangesintheimplied,viatheskeworotherwise,isalsolimited.Aswesaidbefore,youshouldn’tsellnakedputsunlessyouwanttobuythestockorotherunderlying.
StraightcallsandputswithcommoditiesAlthoughitisdifficulttogeneralise,withcommoditiesyoucanoftensubstitutecallstrategiesfortheaboveanomalieswithputstrategies,andputstrategiesfortheaboveanomalieswithcallstrategies.Incommodities,callsareoftenkingbecauseofpotentialsupplyshortages.Theyoftenhavepositivecallskewsinsteadofpositiveputskews.Thisistrueforstockswithlargecommodityexposureaswell.Generallyspeaking,withcommoditiesthestrategywiththemostriskistheshortcall.
MisconceptionstoclearupaboutstraightcallandputpositionsRemember,therearetwoadvantagestoacallpurchase.Theymustbothbeseenasalternativestobuyingastockorotherunderlying.
Thefirstistotakeadvantageofmarketgains.Thesecondistolimitexposuretocapitalrisk.
Itisinaccurateandmisleadingtothinkofacallassimply‘achancetowin’,whenitisequallyachancenottolose.Furthermore,ifyouthinkofanoptionasa‘chance’,youwillmostlikelybecomepreytothosetraderswhostrivetominimisechancefromtheirdealings.
Anotheradvantageofacallpurchaseisthatastheunderlyingadvances,thecallbecomesagreaterpercentageoftheunderlyinguntileventuallyittradesatparity
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withtheunderlying.Thealternativeadvantageisthatastheunderlyingdeclines,thepurchasedcallbecomeslessapercentageoftheunderlyinguntiliteventuallylosesitscorrelationwiththeunderlying.
Likewise,forstockholders,longputsofferthedualbenefitofdownsideprotectionwhilepreservingpotentialupsidegains.Putsarenotsimplyadownsidechance.Asthestockorunderlyingdeclines,thelongputpositionbecomesagreaterpercentageofasaleatthestrikepriceuntiliteventuallytradesatparity,orthefullamountoftheunderlying’sdecline.Butastheunderlyingincreasesinprice,thelongputgraduallylosesitscorrelationwiththestockorunderlying,andtheupsideprofitismaintained.
Itisnocoincidencethatat-the-moneycallsandputsarepricedthesame.Theybothofferthesameamountofupsideanddownsidevolatilitycoverage.Thisamount,orprice,istheexpectedrangeoftheunderlyingthroughexpiration.
Inotherwords,ifXYZistradingat100,boththe100callandthe100puthavethesameprice,perhapsfour,becausethemarketexpectsXYZtoclosebetween96and104atexpiration.IfyoubuythecallinsteadofbuyingXYZ,youhave96pointsofpotentialsavings,andunlimitedprofitpotentialabove104.IfyoubuytheputinsteadofsellingXYZthatyouown,youhave96pointsofpotentialsavings,andunlimitedprofitpotentialabove104.
Theaboverelationshipbetweencallsandputsisthebasisofsyntheticoptionspositions,orput–callparity.ThiswillbediscussedinPart4.
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20
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Volatilityskews
Wehavepreviouslydiscussedtherelationshipbetweenimpliedvolatilityandhistoricalvolatility.Wementionedthattheimpliedcanhavealifeofitsownbasedonexpectationsforfuturechangesinthehistorical.Thisconditionoftencreatesvariationsinimpliedvolatilityfromstriketostrike.Thesevariationsoftenfallintopatternswhichcanbeplottedonagraph,andforwhichequationscanbefoundtomatch.Suchpatternsinimpliedvolatilityareknownasvolatilityskews.
Inthischapterwewillseehowskewsaffecttheprofit/lossofstraightoptionspositions.Wewillalsoseethatunlessyouareaskewwizard,yourbestwaytoreduceskewriskistospread.
Observingskews:bondsFigure20.1showsagraphofthevolatilityskewforoptionsonMarchTreasuryBonds.Belowthat,Table20.1givesthedatacontainingtheimpliedvolatilitiesusedtoplottheskew.
Figure20.1Optionsvolatilityskew:MarchTreasuryBond,underlyingfuturescontractat128.01Source:pmpublishing.com.
Table20.1MarchTreasuryBondoptions,87daysuntilexpiration,Marchfuturesat128.01
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Source:Datacourtesyofpmpublishing.com.
InFigure20.1,thedottedlineistheactualplotoftheimpliedsfromstriketostrike,whilethesolidlinehasbeengeneratedwithanalgorithm.Sometradersusetheequationtodetermineifanoptionisundervaluedorovervalued.Thediscrepanciesasyoucanseeareverysmall.
TheATMimpliedvolatilityisthatofthe128strike,at9.44percent.Notethattheimpliedvolatilityofthe136callis9.84percent,whiletheimpliedofthe120putis10.38percent,andthatboththesestrikesareequidistantfromthe
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money.
Callsandputsofthestrikepricesascendingfromtheat-the-moneystrikearesaidtobeonthecallskew,whilecallsandputsofthestrikepricesdescendingfromtheat-the-moneystrikearesaidtobeontheputskew.Here,boththecallandputskewshaveincreasedimplieds,andsotheyaresaidtobepositive.Thistypeofskewisoftenfoundinlonger-termdebtmarketssuchasbonds,giltsandbunds.
(Personally,Irefertothistypeofskewasa‘parabolic’skew,becauseofitsobviousresemblancetoaparabola.)
Observingskews:stocksandstockindexesFigure20.2showsagraphofthevolatilityskewforDecemberoptionsontheOEX.Table20.2givesthedatacontainingtheimpliedvolatilitiesusedtoplottheskew.
Figure20.2Optionsvolatilityskew:DecemberOEX,underlyingindexat587.18,Decembersyntheticfutureat590.00Source:pmpublishing.com.
Again,thedottedlineistheactualplotoftheimpliedsfromstriketostrike,whilethesolidlinehasbeengeneratedwithanalgorithm.Theclosematch-upmayseemarbitrary,butbecauseskewscontinuetoexhibitregularpatternsovertheyears,theyarecalculable.
TheATMimpliedvolatilityisthatofthe590strike,at17.82percent.Notethattheimpliedvolatilityofthe610callis15.12percent,whiletheimpliedofthe570putis20.56percent,andthatboththesestrikesareequidistantfromthe
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money.Notealsothattheimpliedofthe500strikeis34.46percent,oralmostdoublethatoftheATMimplied.
Heretheputskewispositivewhilethecallskew,withdecreasingimplieds,isnegative.Thistypeofskewisfoundinotherstockindexoptions,suchastheFTSE.
(Personally,Irefertothistypeofskewasa‘linear’skew.Itissimplymorelinearthanaparabolicskew.Notethatthetailofthecallskewflattensout.)
Table20.2OEXDecemberoptions
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VolatilityskewsonindividualstocksSkewsonindividualstockshavebasicallythesamecharacteristicsasskewsontheindexes.Figure20.3showsarecentskewofJuneoptionsonMarksandSpencer.
Onthisday,M&Ssettledat375.80.1
Figure20.3RecentskewofJuneoptionsonMarksandSpencer
Observingskews:CommoditiesVolatilityskewsincommoditieshavetheirownspecialproperties.Asanexample,wecanexaminetheskewforDecember2010Corn(seeFigure20.4).
Figure20.4SkewforDecember2010CornwithCornat$3.80perbushell
Here,wehaveatypicalcommoditiesvolatilityskew.Thecallsideispositivebecauseproducersandconsumerswishtohedgeshortageofsupply.Theybuycalls.
ThenewskewRecentlywehaveseenachangeincommodities’skews.HavealookatthecrudeoilchartinFigure20.5.
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Figure20.5Crudeoilskew
Herewehaveapositiveputskew.Itresemblestheskewinstocksandbonds,notcommodities.Sowhat’sgoingon?Here’smyopinion.
Oilisnowbeingtradedbythebanksandhedgefunds.Ifyoucanthinkbackafewyears,thenyou’llrememberthatcommoditieswereanichemarket.Theyweretradedbyconsumersandproducers.Thisisnolongerthecase.Commoditiesarenowanassetclass,supposedly.
Theresultisthatthecurrentopeninterestinderivativescontractsoverwhelmstheavailablesupply.Thelongsoutnumbertheshorts,andtheyhavemoremoney.Priceisthereforesupported.Butinordertohedgetheirasset,thefundsbuyputs.That’swhythere’sapositiveputskewinoil.So,intheend,what’sgoingtohappen?Ablowout.Nofirm,noone,nobodyisbiggerthatthemarket.ThinkoftheHuntbrotherswhotriedtocornersilverinthe1970s.
Soonerorlater,traders–andImeanbigones–willgetwisetotheweaknessofthelongsandtheywillshortthem.Thenthelongswillberouted.Inthemeantime,youmightaskyourbankmanagerifhisfirmhasexposuretocommodities.
TradingskewsSohowtotradetheskews?Ifthereisapositiveskew,onesuggestionistoneutraliseyourexposurebybuyingthe1×1callspreadorputspread.You’rethenfinancingyourlongoptionwithashortoptionthatismoreexpensiveintermsofimpliedvolatility.You’refinancingoptionisvalueformoney.Thereis
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moreonthistopicbelow.
Volatilityskewsversustheat-the-moneyimpliedvolatilityRegardlessofthenatureoftheskews,theimpliedvolatilityofanyoptionscontract,i.e.theimpliedthatcorrespondsmostcloselytothecurrentvolatilityoftheunderlying,isalwaystheimpliedthatisat-the-money.Onecansaythattheat-the-moneystrike,howeverthatmaychange,isalwaysthefocalpointofboththecallandputskews.
WhythereareskewsThereisnoagreementastowhythereareskews,apartfromtheobviousreasonofsupplyanddemandfortheoptions.Weknow,however,bystudyinghistoricaldatathatlargepricechangesinmanyunderlyingsoccurwithgreaterfrequencythanareaccountedforbynormaldistribution.Atleastonceinagenerationanasteroidhitsthestockmarket.Skewsmightseemirrational,butthensodomanymarketevents.
Don’tmakethemistakeofthinkingthatskewsexistbecausebrokersliketobuyorsellout-of-the-moneyoptions,orbecauseaparticularhouseorgroupofhousesalwaysbuysorsellscertainoptions.Onemightaswellsaythatshort-terminterestratesareattheircurrentlevelsbecausethecentralbanksholdthemhere.2Marketsdon’toperateinthisway;theyaremorepowerfulthantheparticipants.
Forwhateverreasons,skewscontinuetoappearinmostoptionscontractsyearafteryear,andtheycontinuetodisplaysimilarpatternsineachcontract.Mostofusbynowhavelearnedtotreatthemwithrespect.
Ihavepersonalopinionsonthereasonsforvolatilityskews.Askewisafunctionofvariationsinimpliedvolatility.Liketheimplied,itindicatesmarketexpectationsforthenear-termlevelofthehistoricalvolatility.Itthereforeindicateswhatthemarketexpectsthehistoricalvolatilitywillbeiftheunderlyingsuddenlyshiftstoanewlevelinthedirectionoftheskew.Thisisaformofdiscounting,whichallmarketsdo.
Further,aparabolic-shaped,positiveskewindicatesthattheimpliedislikelytoremainrelativelystablewhentheunderlyingremainsinthecurrenttradingrange.Thebellyoftheskewaccountsforthis.Theincreasingslopesofthe
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parabolicskewindicatethattheimpliedislikelytoincreaseexponentiallyiftheunderlyingsuddenlymovestowardsthewingsoftheskewandbreaksthroughthecurrenttradingrange.Again,thisisaformofdiscountingbythemarket.
Moststockindexandlong-terminterestratecontractshavepositiveputskewsbecausethesemarkets,moreoftenthannot,becomemorevolatileastheybreak.Thereisalsoperennialdemandforputsinthesemarketstoprotectagainstlossofassetvalue.
Manycommoditieshavepositivecallskews.Commoditiesbecomemorevolatileaspricesincrease,whichtheysuddenlydowhenfacedwithsupplyshortages.Cornandsoybeanshavehadpositivecallskewsforyears.Ifdroughtconditionsoccur,graindealersfinditdifficulttohonourforwardcommitments.Cashandfuturesprices,alongwiththeimpliedvolatilitiesofoptions,soar.
Aflatornegativeskewindicatesthatthevolatilityofanunderlyingisexpectedtobestable,ortodeclineslightlyiftheunderlyingmovesinitsdirection.Bondsspendlongperiodsoftimewithflattoslightlypositivecallskewsduringperiodsofinterestratestability.Commoditiesoftenhavenegativeputskewsbecauseslackeningdemandresultsintheirgrindinglower.Negativecallskewsinstockindexesindicatethatastheirmarketsmovesteadilyhigherandthevalueoftheirindexesincreases,anequivalentpricechangecalculatestoalowerhistoricalvolatility.
SkewbehaviourtowardsexpirationSkewscanchangetheirdegreeofpositivenessornegativeness.Positiveskewsmostoftenbecomemorepositiveastheyapproachexpiration.
TheunderlyingcontractforthisJanuarysetofT-BondoptionsisthesameasforthepreviousMarchsetofT-Bondoptions;itistheMarchfuturescontract.Here,theimpliedoftheATMcallatthe128strikeislower,at8.14(seeTable20.4).TheimpliedoftheJanuary122putisgreater,at10.42,thantheMarch122putat10.01.TheJanuary134callhasanimpliedof9.19,whiletheMarch134callhasanimpliedof9.58.WhilebothJanuaryskewsareincreased,theputskewexhibitsthemoreradicalchange.Youmaycomparetheimpliedvolatilitiesstrikebystrike(seeFigure20.6).
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Figure20.6JanuaryT-BondoptionsskewSource:pmpublishing.com.
Table20.4JanuaryTreasuryBondoptions
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Source:pmpublishing.com.
Skews’shiftwithunderlyingSkewsmostoftenshifthorizontallywiththepriceoftheirunderlyingcontracts.Ifanunderlyingdriftsbackandforthinarange,theskewwillmostoftenrangeaswell.Thefocalpointclingstotheat-the-moneystrike,withlittlechangetotheATMimplied.Thiseffectivelychangestheimpliedofeachstrike.
Forexample,iftheaboveMarchT-Bondcontractroseto129.01thentheimpliedsofallthestrikeswouldbelikelytoshifttothenextstrikeupward.TheJanuary129callswouldhaveanimpliedof8.14,andtheJanuary123putswouldhaveanimpliedof10.42,etc.
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ThisoccurrencepresupposesnochangeinthehistoricalorATMimpliedvolatility.Heretheunderlyingismostoftentradinginarange.Sometimestheunderlyingmovesbutthefocalpointoftheskewclingstoastrike;thisoccurswhenthemarketexpectsaretracement.
Skews’changeofdegreeAskewoftenbecomesmorepositiveiftheunderlyingmakesasuddenmove,orthreatenstomakeasuddenmove,initsdirection.Abondmarketputskewmaybecomemorepositiveifaninflationreportisrevealedtobeworsethanexpected.Severaldaysinadvance,theputskewmaybehaveinthesamemannerifthereportisexpectedtobeworsethanexpected.
Underthesecircumstances,theskewbecomesmorelikeaskewwithfewerdaysuntilexpiration.Ifandwhenthemarket’sapprehensionsubsides,theskewmayreturntoitsformerlevel.
AcallskewinastockindexmaybecomelessnegativetoflatinanticipationofaChristmasorJanuaryrally,oranimminentcutininterestrates.Eventually,theskewwillreverttoitsformerposition.
Skews’verticalshiftIftheATMimpliedincreasesordecreases,thentheskewmostoftenshiftsverticallyupwardordownward.Thiseffectivelyraisesorlowerstheimpliedofallstrikesbecausetheskewretainsitsshape.ThefocalpointoftheskewremainsattheATMstrike(seeFigure20.7).
Figure20.7Skewverticalshift
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CautionDonotassumethatskewsforetelldirectionalmovesorchangesinvolatility.Sometimestheydo,butoftentheydonot.Astock’sputskewmaybebidbecauseearningsareexpectedtobebad.Whentheearningsarereported,theymaybenoworsethanexpected,theputskewmayfall,thestockmayrallyandvolatilitymaydecline.Likewise,aflatcallskewinabondmarketisnoindicatorthateventswillcontinuetobedullandroutine.Ifashockhitsthestockmarket,aflighttoqualityandsoaflighttobondsmayresult,rapidlyforcingtheircallimplieds,andtheircallskews,higher.
TradingwithskewsVolatilityskewspresentadditionalopportunitiesforprofitaswellasadditionalrisks.Theyareadditionalvariableswhichshouldbeconsideredwhentradingoptions,especiallystraightlongorshortcallsandputs.Theirrisksarelessenedthroughspreading.Thefollowingparagraphsofferguidelinesonhowtodealwithsomeofthemorecommon,butbynomeansall,marketsituations.Skewbehaviourvariesasmuchasmarketbehaviour.
Asyoumightexpect,therearetwobasicpossibilitiestoskewtrading:
buyingorsellingout-of-themoneyoptionsonapositiveskewbuyingorsellingout-of-the-moneyoptionsonanegativeskew.
TradingoptionsonapositiveskewThepurchaseofanout-of-the-moneyoptiononapositiveskew,likethepurchaseofanyoption,profitsiftheunderlyingmovesinitsdirectionand/oriftheimpliedincreases.Iftheunderlyingmovesintheoption’sdirection,butmeetsasupportorresistancelevel,theoptionprofitsfromdirectionbutoftenunderperforms.Thisisbecausethefocalpointoftheskewshiftshorizontallytotheat-the-moneystrike,causingtheimpliedoftheoptioneffectivelytodecrease(seeFigure20.8).
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Figure20.8Positiveskew,righthorizontalshift
WithXYZat100,the105callispurchasedatanimpliedthatisabovetheat-the-moneylevel,andastheunderlyingmovestothe105strike,theoption’simpliedeffectivelydecreasesfrom28percentto20percent.Thenetresultisstillaprofitiftimedecayhasnotbeentoocostly.Notethattheimpliedofthe100callandputbothincreasefrom20percentto28percent.
Forexample,supposeyoupay25(25/64)fortheT-BondJanuary130callfromthesetinTable20.4.Youmightestimatetheprofitpotentialforatwo-pointrallyinbondsbymultiplyingtwopoints(128optionsticks)bytheaveragedeltaofthecalloverthecourseofthemove.Thisaveragedeltaisdeterminedbythedeltaofthe129call,at0.36:128×0.36=46ticksprofit.Yourestimatednewvalueofthe130callwithbondsat130is46+25=71/64,or1.07.
Bylookingatthe128callwithbondsat128,younotethatthecurrentATMcallhasavalueofonly1.05.IftheATMimpliedremainsstable,thenthemarketistellingyouthata130callwithbondsat130willhaveavalueof1.05.
Effectivelythen,foratwo-pointrally,your130callmayunderperformbytwoticks.Inpractice,thisoftenhappens.Thereasonforthisisthatyouhavepurchasedacallatanimpliedof8.40whichwillbereducedto8.14byahorizontalshiftinthevolatilityskew.
Inthiscase,theunderperformanceisnotagreatamount.Butifthecallwerepurchasedfurtheruptheskew(atahigherstrike),andiftheskewweremorepositive,thenthereductionduetoadecreaseinimpliedvolatilitywouldbegreater.
Inordertominimisethisskewrisk,youmightinsteadpurchaseanout-of-the-moneycallspread.Here,youcouldbuythe130callandsellthe132call.Astheskewshifts,bothimpliedsdecrease.
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Anotherapproachissimplytopay1.05(69/64)forthe128call.Here,asthemarketrallies,theshiftintheskewcausestheimpliedofyourcalltoincrease.Usingthedeltaofthe127callat0.65,yourexpectedprofitforatwo-pointrallywouldbe0.65×128=83.Thenewvalueofyourcallisestimatedat83+69=152/64,or2.24.
Younotethatthecurrent126callhasavalueof2.26.Thisistheexpectedvalueofyour128callifbondsrallytwopoints.Becausetheimpliedofyourcallincreasesfrom8.14to8.59,your128callmay,andoftenwill,outperformbytwoticks.
Stillanotherapproachistobuythe128–130callspread.Here,yourspread’slongstrikeprofitsfromincreasedvolatility,andyourspread’sshortstrikeprofitsfromdecreasedvolatility.
Youcanusetheprecedingdatatocalculatetheeffectofaskewshiftontheimpliedsandvaluesofselectedputs.Iftheunderlyingbreaks,putsonapositiveskewmayunderperformduetoadecreaseintheirimplieds.
TradingoptionsonalinearskewAlongout-of-the-moneyoptiononalinearskew,oraskewthatiscallnegativeandputpositive,presentsacoupleofpossibilities.Astheunderlyingrallies,youmightexpecttheskewtoshifthorizontally,resultinginanincreaseinalltheimplieds.Oftenthishappens.
InFigure20.9,asXYZralliesfrom100to105,allthecallsandputsincreasetheirimpliedvolatility.Notethatthereversesituationoftenoccurs:anunderlyingbreaks,usuallyonaretracement,andtheskewshiftstotheleft,resultinginadecreaseinalltheimplieds.
Figure20.9Horizontalskewshift,negativecallskew,positiveputskew
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Frequently,however,onarallytheskewcanremaininplace,andtheimpliedsofallstrikesareunchanged.Effectively,theimpliedvolatilitydecreasesbecausethefocalpointoftheskewmovestothenewat-the-moneystrike.ThesolidlineofFigure20.9illustratesthis:XYZralliesfrom100to105,andthenewATMimplied,nowatthe105strike,islessthanthatoftheformer100strike.
Thissituationoftenoccurswithskewsinstockindexesastheyrallytoformerlevels.Theoptionsmarketisunfazedbytheupsideretracement.Thisalsooccursincommoditiesthathavenegativeputskewsasthecommoditiesretracefromarally;therethegraphisthemirrorimageofFigure20.9.
Anotherpossibilityisthatonabreak,theskewcanremaininplace.Effectively,theimpliedvolatilityincreasesbecausethefocalpointoftheskewmovestothenewat-the-moneystrike.ThedottedlineofFigure20.9illustratesthis:XYZbreaksfrom105to100,andthenewATMimplied,nowatthe100strike,isgreaterthanthatoftheformer105strike.
Thislattersituationoftenoccurswithskewsinstockindexesastheybreak.Theoptionsmarketisfearfulthatthisisthebigone.Whenitreallyisthebigone,thentheentireskewwillshiftverticallyupward,andtheputwingwillbecomemorepositive.
AnoteonmarketsentimentInallcaseswhereastraightlongorshortoptionischosenforadirectionalstrategy,skewriskcanbeminimisedbytradingthelongorshortcallorputspread.
Volatilityskewsareindicatorsofmarketsentiment.Positiveskewsindicatefear,whilenegativeskewsindicatecomplacence.Sentiment,asweknow,canoftenbewrong,butitcannotbeignored.
____________1FigurescourtesyoftheLondonInternationalFinancialFuturesandOptionsExchange,LIFFE.2True,centralbankshaveinthepastresistedmonetarytrends,butonlybyplacingtheirnations’economiesatrisk.
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part4
Basicnon-essentials
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Introduction
Mostofuswon’tspendouroptionscareerstradingarbitrage,butwhentheopportunityarises,asitdoesfromtimetotime,it’sanalmostrisk-freewaytomakemoney.Soifyoulearnaboutthearb,thenyou’repreparedtotakeadvantageofitwhenyouseeit.
ReadPart4atleastonce.Thinkaboutitfromtimetotime.Whenyou’rescanningthemarkets,askyourself,‘Isthereanarbitragehere?CanIlockinaprofitwiththistradeuntilexpiration?’Ifyoukeepthisinmind,thensomedayyou’llfindyourselfmakingalotofmoneyinaveryshorttime.
Ifyou’reprepared.
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21
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Futures,syntheticsandput–callparity
Itispossibletocombineoptionsandunderlyingpositionsinwaysthatsimulatestraightcallorputpositions.Anunderlyingitselfmaybesimulatedwithacombinationofoptions.Asanexampleoftheformer,alongat-the-moneycallplusashortunderlyingpositionhasthesamerisk/returnprofileasalongat-the-moneyput,andisthereforeknownasasyntheticput.
Syntheticpositionsareusedprimarilybyprofessionalmarket-makerstosimplifytheviewoftheiroptionsinventoryinordertomanageriskbetter.Theyareoflittlepracticalusetotraderswhotakeoptionspositionsbasedonmarketoutlooks,buttheycanbestudiedinordertounderstandhowoptionsmarketswork.
Inordertounderstandsynthetics,itisbestifyouunderstandwhytheyexist.Likealloptionspositions,theyarebasedonarelationtoanunderlyingcontract,whichmaybeacashinvestmentorafuturescontract.Ifwebrieflytakethissubjectstepbystep,thenwewillavoidfuturedisorientation.
WhatafuturescontractisAfuturescontractissimplyanagreementtotradeacommodity,stock,bondorcurrencyataspecifiedpriceataspecifiedfuturedate.Becausenocashisexchangedforthetimebeing,thefuturebuyerissaidtohavealongposition,andthefuturesellerissaidtohaveashortposition.Asaresult,theholderofthelongpositionprofitsasthemarketmovesupandtakesalossasthemarketmovesdown.Theholderoftheshortpositionhastheoppositeprofit/loss.
Ifshortsellingwerenotpossible,investorswouldonlybeabletobuyfromthosewhowantedtosellphysicalholdings;liquiditywouldsufferandmarketvolatilitywouldincrease.Mostexchangesrequireasecuritydepositinordertoopenafuturescontract,andthisdepositisknownasinitialmargin.Thevalueofthecontractastradedontheexchangeinvariablyfluctuates,andsoresultsinaprofittoonepartyandalosstotheother.Thepartywhohasalossisthenrequiredtodeposittheamountoftheloss,andthisadditionaldepositisknownasvariationmargin.Marginmaybeintheformofcash,oritmaybeintheformofliquidsecuritiessuchastreasurybillsorgilts,forwhichthedepositor
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stillcollectsinterest.Meanwhilethepartywhohastheprofitiscreditedwithvariationmargin,andhereceivesinterestonthebalance.
Futurescontractshavetraditionallybeenusedincommoditiesmarketsinordertohedgesupplyshortagesandsurpluses.Theyarenowusedinstocks,stockindexes,bondsandcurrencies.Manyexcellentbooksdescribehowtheseformsoffuturescontractsoperate.
AnexampleofafuturescontractConsiderthefollowingexampleofaclosingpriceoftheS&P500indexwiththesettlementpriceoftheDecemberfuturescontractandthesettlementpricesoftheat-the-moneycallandputonthefuturescontract.
S&Pindex:1133.68Decemberfuture:1140.70December1140call:34.40December1140put:33.70
Here,theS&Pfuturescontractmultiplieris$250.AninvestorwhotradesoneoftheaboveDecembercontractsishedging1140.70×$250=$285,175worthofstocksthattracktheindex.Theoptionscontractmultiplieris$25.
WeknowthattheDecemberfuture,herewithapproximatelysixweeksuntilexpiration,tradesatapremiumtothecash.Thisisbecausetakingalongpositioninthefuturescontractinsteadofbuyingallthestocksintheindexrequiresamargindepositonly.Theholderofthefuturespositionthereforehastheuseofhiscashforthenextsixweeks.Thevalueofthefuturescontractisincreasedbythecostofcarryingonthestocks.
Ontheotherhand,theholderofthelongfuturespositionforgoesthedividendspayableforthenextsixweeks,andthereforethevalueoftheDecemberfutureisdecreasedbythatamount.Theformulaforthevalueofthefuturescontractisapproximatedasfollows:
Futurescontract=cashvalueofindex+interestorcostofcarryonindexuntilexpiration–dividendspayableuntilexpiration
Inpractice,theformulaismorecomplicatedbecauseannualisedratesofcarryanddividendyieldsareused.Here,wearesimplyconcernedwithwhytheabovefuturetradesaboveorbelowthecash.
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Untilrecentlyshort-terminterestratespaidmorethandividendyields,andsostockindexfuturestradedatapremiumtotheirunderlyingindexes.Thesituationisnowreversed,anditissimilartothe1950s,wheredividendyieldspaidmorethanshort-terminterestratesinordertocompensatefortheriskofowningstock.Thiswasaholdoverfromthecrashof1929,whenmanystockholders’investmentswerewipedout.Thereasonnow,however,isthataftertherecentbankingcrisis,thecentralbanksaretryingtomaintainliquiditybykeepinginterestrateslow.
Occasionally,shortlybeforeexpiration,theremaybealargeamountofdividendspayableinastockorstockindex.Thenthedividendoutweighstheinterestamountandthefuturetradesatadiscounttotheindex.Oncethedividendordividendsarepaid,thenthefuturetradesabovethecash.
Inanyevent,thefuturescontractandthecashindexconvergeatexpirationbecausethenthereisnoremainingdifferentialbetweencostofcarryandpayabledividends.Thefuturescontractsimplyexpirestothecurrentcashvalueoftheindex.
There,theholderofthelongfuturescontractpaysthecashvalueofallthestocksintheindex.Theholderoftheshortfuturescontractreceivesthecashvalueofallthestocksintheindex.Theultimateamountexchangedisdeterminedbythevalueoftheindexatexpirationtimesthecontractmultiplier.
Inthecaseofaphysicalcommoditysuchascornorcrudeoil,thefuturescontractisdeliverabletothequantityofthecommodityspecifiedinthecontractatthesettlementprice.
SyntheticfuturescontractAswealreadyknow,alongXYZ100call,byvirtueofitsrighttobuy,equalsalongXYZpositionwhenXYZisabove100atexpiration.WealsoknowthatashortXYZ100put,byvirtueofitsobligationtobuy,equalsalongXYZpositionwhenXYZisbelow100atexpiration.Thesumofthesetwooptionspositions,therefore,equalsasyntheticlongXYZpositionwithastrikepriceof100.Thisisaresultofthecombinedrightandobligation.ConsidertheexampleinFigure21.1.
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Figure21.1LongXYZsynthetic
WealsoknowthatashortXYZ100call,byvirtueofitsobligationtosell,equalsashortXYZpositionwhenXYZisabove100atexpiration.AlongXYZ100put,byvirtueofitsrighttosell,equalsashortXYZpositionwhenXYZisbelow100atexpiration.Thesumoftheseoptionspositions,therefore,equalsasyntheticshortpositionwithastrikepriceof100.Thisagainisaresultofthecombinedrightandobligation.ConsidertheexampleinFigure21.2.
Figure21.2ShortXYZsynthetic
Assumingthatinterestrateswilleventuallyrise,thentheS&P500exampleaboveistypicalofthemodernera.AlongDecember1140callplusashortDecember1140putequalsasyntheticlongfuturescontractvaluedat1140.Ifyoupay34.40forthecall,andselltheputat33.70,thenyouhavepaidanet0.70forthesyntheticat1140.Inotherwords,youhavepaid0.70togolongthefutureat1140.Youhavepaid1140.70forthesyntheticlongfuture.
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NotethattheactualDecemberfutureisvaluedat1140.70.Yoursyntheticoptionspositionisvaluedthesame,andalwayswillbe,asafuturescontract.
If,ontheotherhand,yousellthecallat34.40andpay33.70fortheput,thenyouhavesoldthesyntheticfutureat1140.70.Here,youhavetheobligationtosellthefutureabove1140,andtherighttosellthefuturebelow1140.
Theprofit/lossofthetwosyntheticsisgraphedinFigure21.3.
Figure21.3SyntheticlongDecemberSPZfuturescontract+syntheticshortDecemberSPZfuturescontract
SyntheticsonindividualstocksInthecaseofindividualstocks,therearealsoasyntheticfuturesposition,becausetheholderofalongcallplusshortputpositionatanystrikecontrolsalongstockpositionwithouthavingtopayforthestock.ThesituationisthesameaswiththeS&Pexampleabove,butoftenthereisnounderlyingfutureforcomparison.Still,thesyntheticfutureexists.Inthestockoptionsthesyntheticfutureisoftenspokenofsimplyasthesynthetic,oroccasionally,thecombo.
SyntheticlongcallpositionWhenalongXYZ100putiscombinedwithalongunderlyingposition,theprofit/loss’softheputandtheunderlyingcanceleachotherbelow100,leavingtheupside,profit-makinglegoftheunderlying.Thesumequalsasyntheticlongcall.Forthepurposeofillustration,let’sassumethatthecallwaspurchasedforfree.Atexpiration,thesyntheticpositionwouldbeasshowninFigure21.4.
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Figure21.4Syntheticlong100call
Nowlet’sreturntotheexamplebasedontheS&P500futuresandoptionsonthefutures:
S&P500Decemberfuture:1140.70December1140call:34.40December1140put:33.70
Supposeyoutakealongpositioninthefuturescontractat1140.70andatthesametimeyoupay33.70fortheDecember1140put.Youknowthatbelow1140theprofit/lossoftheputandthefuturescontractoffseteachotherbecausebelow1140youhavetherighttosellwhatyouownatthepriceatwhichitwaspurchasedlessthecostoftheput.Above1140youaresimplylongthefuturescontract.Beingnetlongafuturescontractabove1140isthesameasowningaDecember1140call.Thecostofyoursyntheticcallbreaksdownasfollows.
Thefuturescontractcosts1140.70,andtherighttosellitat1140costs33.70.Withyourfuturescontractyouhavepaid0.70moreforwhatyouownthanforyourpotentialsellingprice.Withyourputyourtotalcostis0.70+33.70=34.40,orthepriceoftheDecember1140call.Comparetheprofit/losstablesforthe1140call(Table21.1)andthe1140syntheticcall(Table21.2).
Table21.1Profit/lossofSPZDecember1140callatexpiration
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Table21.2Profit/lossofSPZDecember1140syntheticcallatexpiration
SyntheticshortcallpositionIfinsteadXYZissoldat100,andatthesametimea100putissold,asyntheticshort100callresults.Below100theprofitontheshortunderlyingpositionandthelossontheshortputoffseteachother.Above100,alossistakenontheshortunderlyingposition.Let’sassumethattheputwassoldforfree.ThegraphatexpirationwouldbeasshowninFigure21.5.
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Figure21.5SyntheticshortXYZcall
ReturningtoourSPZexample,supposetheaboveDecember1140putissoldfor33.70andashortpositionistakeninthefuturescontractat1140.70,theresultisasyntheticshortcall.Theprofit/lossistheoppositetotheabovelongsyntheticlongcall(seeTable21.3).
Table21.3Profit/lossofsyntheticshortSPZDecember1140callatexpiration
SyntheticlongputpositionWhenalongXYZ100calliscombinedwithashortunderlyingposition,theprofit/lossofthecallandtheunderlyingcanceleachotherabove100,leavingthedownside,profit-makinglegoftheunderlying.Thesumequalsasyntheticlongput.We’llassumethattheputistradedforfree.Atexpiration,theprofit/lossgraphisshowninFigure21.6.
Figure21.6SyntheticlongXYZput
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ReturningtoourSPZexample,supposetheDecember1140callispurchasedfor34.40,andashortpositioninthefuturescontractistakenat1140.70.Theresultisasyntheticlongputpurchasedfor33.70.Tables21.4and21.5showacomparisonoftheprofit/lossofthesyntheticandthestraightput.
Table21.4Profit/lossoflongSPZDecember1140putatexpiration
Table21.5Profit/lossoflongSPZDecember1140syntheticputatexpiration
SyntheticshortputpositionWhenashortXYZ100calliscombinedwithalongunderlyingposition,theprofit/lossofthecallandtheunderlyingcanceleachotherabove100,leavingthedownside,loss-takinglegoftheunderlying.Thesumequalsasyntheticshortput.Again,we’llassumethattheputistradedforfree.Atexpiration,theprofit/lossgraphisshowninFigure21.7.
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Figure21.7SyntheticshortXYZ100put
ReturningtoourSPZexample,iftheDecember1140callissoldat34.40,andalongpositionistakenintheunderlyingat1140.70,theresultisasyntheticshortputsoldat33.70.Theprofit/lossistheoppositeoftheabovelongsyntheticput(seeTable21.6).
Table21.6Profit/lossofshortSPZDecember1140syntheticputatexpiration
Thecomplexproblemofput–callparityTheaboveareillustrationsofput–callparity,whichtellsusthatbyknowingthevalueoftheunderlying,thestrikeprice,andeitherthecallorput,thepriceoftheunknowncallorputcanbedetermined.Theformulasfordeterminingthe
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valueofacorrespondingcallorputataparticularstrikeareasfollows.
Call–put=futures–strikeprice(34.40–33.70=1140.70–1140),thereforeCall=futures–strikeprice+put(34.40=1140.75–1140+33.70),orPut=call–futures+strikeprice(33.70=34.40–1140.70+1140)
Thisequationcanalsobesolvedfortheothertwovariables.
Futures=call–put+strikeprice(1140.70=34.40–33.70+1140),andStrikeprice=futures+put–call(1140=1140.70+33.70–34.40)
Allthisreallytellsusisthatacallandaputatthesamestrikehavethesameamountoftimepremium,orvolatilitycoverage.Ifyou’vereadthisbookwithopeneyes,you’vealreadyarrivedatthesameconclusion,atleastintuitively.Themysteriousandcomplexworldofput–callparityisnowexposedasatrifle.You,theintelligentreader,havemoreimportantthingstothinkabout,suchaschoosingyoursocksinthemorning.
Therealproblemofput–callparityisthatformanyoptionscontractsitdoesn’tapply.Itassumesthatin-the-moneyoptionshavenoearlyexercisepremium,whichisonlytrueofEuropean-styleoptions.Put–callparityworkswithastraightBlack–Scholesmodelonly,andonlywhendeepin-the-moneyoptionswiththeircarryingcostsarenotinvolved.
IftheaboveS&P500optionsweredeepinthemoney,therewouldbesmalldiscrepenciesintheput–callparityvalues.Iftheput–callparityformulawereappliedtooptionsontheOEXorotherAmerican-styleindexoptions,largediscrepencieswouldresultduetoearlyexercisepremium.SignificantdiscrepanciesalsoresultwithAmerican-styleoptionsonindividualstocks,i.e.moststockoptions.
Put–callparitycanbeahelpfulwayofpricingoptions,butitslimitationsmustbeconsidered.
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22
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Conversions,reversals,boxesandoptionsarbitrage
Conversions,reversals,andboxesareusedalmostexclusivelybymarket-makersandriskmanagerstoneutralisetheriskoflargeoptionsportfolios.Atonetime,theyweretradedinordertoprofitfromsmallpricediscrepanciesinsyntheticpositions,butnowmostmatureoptionsmarketshaveeliminatedthisopportunity.
Ashortsyntheticunderlyingpositioncanbecombinedwithanactuallongunderlyingpositiontoyieldaforwardconversion,orconversion.Likewise,alongsyntheticpositioncanbecombinedwithanactualshortunderlyingpositiontoyieldareverseconversion,orreversal.Theprofit/lossofthesepositionsdoesnotchangeregardlessofmarketmovement,andtheironlypracticalrisksarethoseofpinriskandearlyassignment.
Alongboxisthepurchaseofasyntheticunderlyingatalowerstrikeandthesaleofasyntheticunderlyingatahigherstrike.Ashortboxistheoppositeposition.Becausetheboxisbothlongandshorttheunderlying,itsprofit/lossdoesnotchangeregardlessofmarketmovement.Again,theonlypracticalrisksarepinriskandearlyassignment.
ConversionAconversionisalongunderlyingplusashortcallandalongputatthesamestrike.
IfXYZisat100,youcouldsellone100call,buyone100put,andbuyorgolongXYZtocreateaconversion.Becausethesumofthepositionisshortthesyntheticandlongtheunderlyingthereisnoprofit/losschangeregardlessofunderlyingpricemovement.Atexpiration,thesyntheticpairsoffagainsttheunderlyingtoleavenoposition.
ConsideragaintheexamplefromS&P500futures,andoptionsonfutures.
DecemberS&P500futureat1140.70December1140callat34.40
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December1140putat33.70
Here,youcouldsellthecallat34.40,pay33.70fortheput,andpay1140.70forthefuture.Youhavethensoldthesyntheticat1140.70andyouhaveboughtthefutureatthesameprice.Thereisnoprofitorlosstothisposition,norwillitchangeforthelifeoftheoptionscontract.Atexpirationtheshortsyntheticpairsoffagainstthelongfuture,andtheresultisnoposition.Thereisminimalrisk.Figure22.1showsisagraphoftheconversion.
Figure22.1SPZ1140conversion
Occasionally,thereisasmallamountofprofittobemadebytradingthecomponentsofaconversionseparately.Forexample,atradermightbeabletoselltheabovecallat34.50,therebymaking0.10profitonthewholeposition.This0.10issecureuntilexpirationwhenallthecomponentspairoff.Sometradersspendthebestpartoftheiryouthtryingtotradethesesmallpricediscrepancies,anditisgoodfortherestofusthattheydoso.Theirformoftradingiscalledarbitrage.
Bykeepingtheconversionsinline,thearbitrageurs,orarbs,helptomaintainefficientpricinginthemarket.Asaresult,webenefitbygettingafairpriceforouroptions.
Reverseconversion,orreversalAreversalisashortunderlyingplusalongcallandashortputatthesamestrike.
IfXYZisat100,youcouldbuyone100call,sellone100put,andsellorgoshortoneXYZtocreateareversal.Becausethesumofthepositionislongthe
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syntheticandshorttheunderlying,thereisnoprofit/losschangeregardlessofunderlyingpricemovement.Atexpiration,thesyntheticpairsoffagainsttheunderlyingtoleavenoposition.
WiththeS&Pexample,youcouldpay34.40forthecall,selltheputat33.70,andsellthefutureat1140.70.Hereyouhavepaid1140.70forthesyntheticandsoldthefutureatthesameprice.Figure22.2showsagraphoftheentireposition.
Figure22.2SPZ1140reversal
Again,thearbsexploitthesmallestpricediscrepancywithanyofthecomponentsofthereversal.Here,theymightpay34.30forthecall,orselltheputat33.80,orpay1140.60forthefuture.Rarelyismorethanonecomponentoutoflineatonetime.
ConversionandreversalsonindividualstocksandonotherstockindexesTheconversionandreversalmarketsonstocksoperateinbasicallythesamemanner.Rememberthatwithstockstherearenofuturescontracts,butthattheoptionscombinetoformsyntheticfuturescontracts.ThesituationissimilartotheS&P500cash–futures–optionsrelationshipgiveninChapter20:
S&P500cashindexat1133.68Decemberfutureat1140.70December1140callat34.40
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December1140putat33.70
Ifthefuturescontractwereeliminated,andtheoptionswereexercisableinsteadtocash,thentherelationshipwouldbethesameasbetweenstocksandstockoptions.
TheOEXoptionsaretradedinthismanner,withoutanunderlyingfuturescontract;theyareAmericanstyle.Becausethereisnounderlyingcashinstrument,apartfromanunwieldybasketofstocks,thereisnoconversionorreversaltradableintheOEX.
TheSPXoptionsontheS&P500index,tradedattheCBOE,arealsobasedsolelyontheunderlyingindex;theyareEuropeanstyle.TradersheresometimesusedtheS&P500futurescontractattheCMEinordertocreateaconversionorreversal.
TheFTSE-100contractisahybrid.TheoptionsareassignedtocashatmonthlyexpirationsliketheOEX.Thereisafuturescontractaswell,liketheS&P500,whichtradesintheMarch–June–September–Decembercycle.Duringthesefourmonths,expirationforoptionsandfuturescoincidesat10:30onthethirdFriday,makingconversionspossible.
AnexampleofaconversioninstocksisfoundinthefollowingsetofMarksandSpenceroptions:
M&Sat350.60Mayoptions,75DTEMay350call:15.75May350put:14.75
Here,youcouldsellthe350syntheticat1.00andpay350.60forthesharestocreatetheconversion.AtMayexpirytheshortsyntheticconvertstoashortsharespositionwhichpairsoffagainstthelongsharesposition.Youhaveeffectivelysoldthesyntheticat351foranetcreditof0.40onthetotalposition.Thiscreditequalsyourcostofcarryonthesharesforthenext75daysasdeterminedbytheprevailingshort-terminterestrate(0.50percent).(Whereapplicable,dividendsareanegativecomponentinthelongsyntheticjustastheyarewithafuturescontract.Inthisexample,therewerenodividendsthroughexpiry.)Duringthenext75daysthedifferencebetweenthesyntheticandthestockwillconvergefrom0.40tozero.
Longbox
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Theboxisanotherspreadthatisoccasionallyemployedbyarbitrageursinordertoprofitfromsmallpricediscrepanciesintheoptionsmarkets.Again,itcontainsminimalrisk.
IfXYZisat100,youwouldgolongthe100–105boxbygoinglongthe100syntheticandbygoingshortthe105synthetic.Youwouldbuyone100call,sellone100put,sellone105call,andbuyone105put.Theboxitselfalwaystradesforapricethatnearlyequalsthedifferencebetweenthestrikeprices,inthiscase,adebitoffive.Yourpurchaseholdsitsvalueuntilexpiration,atwhichtimethesyntheticspairoffandyouarecreditedwiththedifferencebetweenthestrikeprices.
Asanexample,considerthefollowingsetofMay,MarksandSpenceroptions,with75DTE:
MarksandSpencerat350.60Mayoptionswith75daysuntilexpiry
Table22.1MarksandSpencerMayoptions
Strike
340
350
360
Maycalls
21.25
15.75
11.00
Mayputs
10.25
14.75
20.00
Here,thelong340–360boxiscalculatedasthe340callminusthe340put,minusthe360callplusthe360put,or(21.25–10.25)–(11.00–20.00)=20.00.Untilexpirythisdebitisyourtotalprofit/loss.
Atexpiration,thelong340synthetic,throughexerciseorassignment,becomesasharespurchaseatapriceof340.Theshort360synthetic,throughexerciseorassignment,becomesasharessaleatapriceof360.Youraccountisthencreditedwith20ticksandyourprofit/lossistheoreticallyzero.
Inpractice,however,thevalueoftheboxismostoftenmodifiedbytimeuntilexpiration,earlyexercise,andinterestratefactors;thesearediscussedbelow.
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Atexpiration,yourprofit/losssummaryisasshowninTable22.2.
Table22.2Profit/lossoflongM&SMay340–360boxatexpiry
Theprofit/lossgraphshowninFigure22.3issimplyanoverlayofthetwosyntheticsatexpiration.Thecallsyntheticgoesfromlowerlefttoupperright.Theputsyntheticgoesfromlowerrighttoupperleft.
Figure22.3MarksandSpencer340–360box
Atanypricelevel,thecallplustheputcomboequals20.Forexample,at350the340callisworth10,andthe360putisworth10.You’relongthemboth.Meanwhile,the340putandthe360callareworthless.
At330you’relongthe360put,whichisworth30,andyou’reshortthe340putwhichisworth10.Yournetisstill+20.
Ifyouconnectthefourdotsat340and360thenthepicturelookslikeabox.
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ShortboxIfXYZisat100,youcouldsellone100call,buyone100put,buyone105call,andsellone105puttocreateashortbox.Here,youareshortthe100syntheticandlongthe105syntheticforacreditoffive.Yoursaleholdsitsvalueuntilexpiry,atwhichtimethesyntheticspairoff,andyoupaythevalueoftheboxtothecounterparty.
Foranexample,simplyreversethelongboxtransactioninM&S,above.Sellthe340syntheticandbuythe360syntheticforacreditof20.Atexpirythiscreditreturnstothecounterparty.
TradingboxesBoxesareseldomtradedexceptasclosingpositionsbetweenmarket-makers;wetradethemclosetoexpirationinordertoclearoptionsoffourbooksandtoavoidpinrisk.Butthenagain,thearbstrytopay19.75fortheabovebox,andtheytrytosellitat20.25.Theyoftendothisbytradingthecomponentsquicklyandseparately.Theydothisinlargevolume,sotheircostsarelow.Theirunitprofitmightbesmall,butoncethepositionison,itisalmostriskfree.
Withcontractsthathaveearlyexercise,in-the-moneyboxesoftentradeformorethanthedifferencebetweenthestrikeprices.Theoptionsthatarein-the-moneyhaveearlyexercisepremium,andtheoptionthatisdeeperin-the-moneyhasmore.Mostoften,thein-themoneyputwillhaveextravaluebecauseitcontainstherighttoexercisetocash.
EarlyexercisepremiumraisesthevalueoftheboxesintheOEXandotherAmerican-styleoptionsaswell.
Oncontractsthatarepaidforupfront,andwherethereisnoearlyexercise,thepurchaseofaboxresultsincashtiedup.Theboxthereforetradesatadiscountequaltothedifferencebetweenstrikesminusthecostofcarrythroughexpiration.Atexpirationthevalueoftheboxistransferredatexactlythedifferencebetweenstrikes.ExamplesofthisareFTSEoptionscontract,andtheSPXEuropean-styleoptionsontheS&P500whicharetradedattheCBOE.
CostofcarryonboxesTobeprecise,aboxthathasnoearlyexercisepremiumwillalwaystradeatadiscountequaltoitscostofcarry.Forexample,anat-the-money20-pointboxinMarksandSpencerabove,with75DTE,atashort-terminterestrateof1per
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cent,willtradeat20–(20×0.01×75/365)=19.96.
Thesaleofaboxthroughcash-tradedEuropean-styleoptionsisoftenusedasameansofshort-termfinance.Ifatradinghousewantedtoborrowmoneythenitcouldselltheabove20-pointboxat19.96.Cashwouldbecreditedtotheiraccountuntilexpiration,andthenthehousewouldpay20toclosetheposition.Commissionsandexchangefeeswouldeffectivelyraisetheborrowingratetomorethan1percent.Onlyfirmsthattradeinlargesizeandthatbenefitfromlowcostscantakeadvantageofthisopportunity,andmostoftentheyprefertoborrowandlendinthecashmarkets.
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23
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Conclusions
RecentproblemsRecentproblemsinamajorUSinsurancefirm,amajorBritishoilcompanyandaUKbankhavehighlightedthelackofunderstandingofriskatthehighestlevels.Ifyouhavereadthebookassiduously,thenyouprobablyhavemoreriskawarenessthantheirCEOs.
Inthecaseoftheinsurancefirmitappears–andIcan’tsayforcertain–thattheyincreasedthevolumeoftheirderivativesexposureinordertomaintaintheirprofitlevel.Fairenough.Buttheyalsoincreasedtheirleverage.Theytriedtoapplythemanufacturingmodeltoderivatives.Adisasterwaitingtohappen.
Inthecaseoftheoilcompany,itappearsthatinordertocutcosts,theyoutsourcedtoawelldrillingfirmthatgavethemthecheapestbid.Theoutsourcingfirmcouldonlygivethecheapestbidbecausetheywouldnotexpendonphysicalriskprovisions,i.e.hardwaretocontrolawellblow-up.Anotherdisasterwaitingtohappen.
Inthecaseofthebank,theCEOhadhadaprevioussuccessintakingoveranotherbank.Thisgavehimthefalseconfidencetoattemptatakeoverofsecondbank.Buthewasincompetitionwithathirdbank.Theybothtriedtooutbideachother.Herewasaclassictrader’smistake:hubris…TheCEO’segobecameinflatedbyhisprevioussuccess.Hethenassumedthathecoulddonowrong.Butwhenconfrontedbyhisriskmanager,whohadconcernsaboutduediligence,whatdidhedo?Hefiredhisriskmanager.Hethenoutbidhisrivaland,loandbehold,itturnsoutthatheboughtatoxicasset.Itwassoonrevealedthatthetakeoverbankhadacorruptbalancesheet.Unabletofinancethetakeoverbank’sliabilities,theCEO’sbankwasbroughttobankruptcy.
Intheend,thecentralgovernment,withitspoweroftaxation,rescuedhimandhisfirm.
Thelessonisthatthemarketpunisheshubris.Sobewareofreadingthisbook:itmayleadtoyoubeingfired.
Onethingtheyallhadincommon:theycutcostswhileincreasingrisk.Inotherwords,theydidn’tbuytheput,orworse,theysoldtheput.Thesefirms,like
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manyothers,seemtothinkthatyoucansavemoneybysqueezingoutprecautions.TheymadethesamemistakesthatwemadewhenoptionswerefirstlistedattheChicagoBoardofTrademanyyearsago.
Theseareclassicriskproblemsandclassicoptionsproblems,andunlessfutureplayersunderstandthetrade-offbetweenlong-termriskandshort-termprofit,theywillhappenagainandagain.
CongratulationsIfyouhavereadthisbookinitsentirety,Iofferyoumycongratulations.Youarewillingtomaketheeffortneededtobecomeaserioustrader.Younowknowwhatoptionsareandwhattheydo.Youalsoknowhowtocreatespreads,andyouhaveabasicunderstandingofvolatility.Mostimportantly,youhaveanunderstandingofrisk.Youunderstandhowthevariablesinteractandhowtoemploythosevariablesthatsuityouroutlook.Beforeyouplaceyourhard-earnedcapitalatrisk,hereissomeadvice:
Learn the fundamentals cold. Even those of us who have been in thebusinessawhilearesometimessurprisedbyoptionsbehaviourbecausenotwomarkets,andtheireffectsonoptions,arealike.Neverstop increasingyourknowledge.Paper trade before you place capital at risk. Take a position based onclosingpricesandfollowitdailyorweekly.Dothiswithstraightcallsandputs,anddoitwithspreads.Begintradingwith1×1s,butterfliesandcondors,inordertominimiseskewandimpliedvolatilityrisk.When you first start to trade, keep your size to amimimum, even if thismakes your commision rates high. If this annoys your broker, offer toincrease your sizewhen your trading becomes profitable, or find anotherbroker.Whenyou first start to trade,donot sellmoreoptionscontracts thanyouarelong.Sellingnakedoptionscantakeyoutothedoorofthepoorhouse.Tradeoptionsonunderlyingsthatyouknow,andimproveyourknowledgebystudyingthehistoryoftheunderlyingsandtheoptionsonthem.Manydatavendors,includingallexchanges,havepricehistory.Afteryouhavetradedthebasicspreads,studyvolatility.Thisistheelusivevariable,andintheendthisiswhatoptionsarereallyabout.Volatilitydataisalsoavailablefromdatavendorsandexchanges.
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Tradeoptionswithadurationaloutlook;whenthedurationhasended,takeyourprofitsorcutyourlosses.Likewise,tradewithapriceobjective;whenthe objective is reached (it often happens sooner than you expect), closeyour position and don’t hope for unrealistic profits. Before you open aposition,establishastop-losslevel.With straight calls and puts, discipline yourself by basing your optionsinvestmentonthevalueoftheunderlyingcontrolled,notontheamountofpremiumboughtorsold.Analyseyourtrades,bothgoodandbad.Whatwasyouroutlookatthetimeyou opened the trade? How did the market change while the trade wasoutstanding?Whatwereyourreasonsforclosingthetrade?Analyseyourreactionstotrading.Howdidyourespondwhenthetradewasgoingyourwayorgoingagainstyou?Didyoumakereasonabledecisions,ordidyoumakedecisionsbasedonhopeorfear?Themajorbenefitoftradingoptionsisthatyoucanlimityourrisk.Usethisbenefit by choosing a risk-limiting strategy. You will then trade withconfidence.
Thereisobviouslymuchmoretobesaidaboutoptionsintermsoftheoryandintermsoftrading.TheFinancialTimesGuidetoOptions,anditsprecursor,OptionsPlainandSimple,areintendedtobeapracticalguidetothemostcommonstrategiestradableunderthemostcommonmarketcircumstances.Markets,ofcourse,defycommonality,buttheirmanyvariationsoccuragainandagain.
Thisbookshouldbeconsideredbasic;inotherwords,abletoimpartfundamentalawareness,notsimplytransmitrules.Youmaywishtoreadmuchofthisbookagain.OneheadofoptionsataLondonspread-bettingfirmhasreadOptionsPlainandSimple,threetimes.Byrereadingthisbook,discussingitsideaswithyourfinancialadviserandfollowingmarkets,thebehaviourofoptionswillbecomesecondnaturetoyou.Thiswillbethebasisofsoundandprofitabletrading.
Ifyouhaveanycommentsorquestions,[email protected]’lltrytoincludeyourfeedbackinthenexteditionofthisbook.
AfinalwordontradingAndsowhat’stradinglike?AfewyearsagoIwasatrainerforaLondonfirm
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thatsponsoredday-tradersinfuturescontactsonEuribor,Bund,FTSE,etc.Ialsogavetraininglectures.Oneofournewtraderswasafemalegraduatewhowasveryastute.Afteroneofmylecturesshewalkeduptomeandasked,‘C’monnowLenny,what’sittaketobeagoodtrader?’Ianswered,‘Supposeyourdadgaveyouahundredpounds.CouldyouwalkinandoutofHarrodswithoutspendingapenny?’Shegavemeadefiantstareandsaid,‘Mydaddygivesmetwohundredpounds!’Thischarmingyoungwomandidnotmakeitasatrader.
Mayprobabilitybeonyourside.
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Questionsandanswers
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Chapter1questions
Hereareafewquestionsoncallcontracts.Don’texpecttoknowalltheanswers.Theanswersaregiven,soyoushouldtreatthequestionsasadditionalexamplesfromwhichtolearn.
1. GEiscurrentlytradingat18.03,andtheApril19callsaretradingat0.18.(a) Ifyoubuyoneof thesecallsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthiscall.(e) The multiplier for this options contract is $100, or 100 shares.Whatisthecashvalueofthiscall?(f)Writeaprofit/losstableforabuyofthiscallatexpiration.(g)Graphtheprofit/lossforabuyofthiscallatexpiration.(h)Answerquestionsf–gforasaleofthiscall(i)IfatAprilexpiration,GEclosesat19.00whatistheprofit/lossforthecallbuyerandforthecallseller?(j)IfatAprilexpiration,GEclosesat19.10whatistheprofit/lossforthecallbuyerandforthecallseller?
2. Thisisaquestiontogetyouthinkingaboutriskandreturn.Unileveriscurrentlytradingat553p(£5.53)1,andtheMarch550callsaretradingat74p(£0.74).Thisyear,Unilevershareshaverangedfrom346.75to 741. You foresee a continued volatile market and you think that foodproducerswillattractbuyinginterestasdefensiveinvestments.Becauseofmarket volatility you hesitate to risk an outright purchase of shares, andyouwouldliketocomparetheriskofacallpurchase.
(a) Ifyoubuyoneof thesecallsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthiscall.(e)Themultiplierforthisoptionscontractis£1,000,or1,000shares.
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Whatisthecashvalueofoneofthesecalls?(f) IfatMarchexpiryUnileverclosesat650,what is theprofit/lossforthecallbuyer,andforthecallseller?(g)Whatistheamountofcapitalatriskforthecallbuyerversusthebuyerof1,000shares?Calculatethedifference.(h) IfbyMarchUnileverhasretracedtoitsformerlow,whatwouldbe the amount lost on buying the shares versus buying the call?Calculatethedifference.Calculatetherisk/riskratio.(i) If byMarchofnextyearUnileverhas rallied to its formerhigh,whatwouldbetheamountgainedonbuyingthesharesversusbuyingthecall?Calculatethedifference.Calculatethereturn/returnratio.(j) Looking at the above risk scenario h), and the above returnscenarioi),comparetherisk/returnratiosofthesharespositionversusthecallposition.Thisisjustonemethodofaccessingrisk/return.Thepointisthatyoudoneedtohaveamethod.
3. IntheUK,theFTSE-100shareindexiscurrentlytradingat5133,andtheDecember 5300 call is trading at 253. Assume that you are a large unittrust,andifyoumissayear-endrally,yourinvestorswillbedisappointed.Youcouldbuyabasketofallthestocksintheindexforacostof£51,330,or you could take a long futures position with an exposure of £51,330.Lately the market has been volatile, however, and you don’t want thedownsiderisk.
(a) Ifyoubuyoneof thesecallsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthiscall.(e) Themultiplier for this options contract is £10.What is the cashvalueofoneofthesecalls?(f) This year, the trading range of the FTSE-100 index has been4648.7to6179.Ifthemarketretracespartofitsrecentgains,atwhatlevelwouldtheretracementequalthecostofthecall?(g) Writeaprofit/loss tableatexpiry forasaleof thiscallwith theFTSEinarangeof5000to6000atintervalsof100.(h) WriteagraphatexpiryforasaleofthiscallwiththeFTSEinarangeof5000to6000atintervalsof100.
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4. March soybeansare currently tradingat573.75and theMarch575callsaretradingat22.75.
(a) Ifyoubuyoneof thesecallsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthiscall.(e) Themultiplier for this options contract is $50.What is the cashvalueofoneofthesecalls?(f)Writeaprofit/losstableforabuyofthiscallatexpiration,whichwillbeinFebruary.(g)Graphtheexpirationprofit/lossforabuyofthiscall.(h) If atMarch expiration,which is in February, theMarch futurescontractsettlesat590,whatistheprofit/lossforthecallbuyerandthecallseller?
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Chapter1answers
1. (a)19.18(b)unlimited(c)0.18(d)19.18,0.18,unlimited(e)$18(f)
(g)
Answer2g
(h)
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Answer2h
(i)Thecallexpiresworthless:0.18lossforthebuyer;0.18profitfortheseller.(j)Valueofcallispriceofstockminusstrikepriceminuscostofcall,or19.10–19.00–0.18=–0.08:Lossforbuyer;profitforseller.
2. (a)624(b)unlimited(c)74(d)624,74,unlimited(e)740(f)Priceofstockatexpirationminusstrikeprice,650–550=100,orexpirationvalueofcall100minustradedvalueofcallat74=260.26×contractmultiplierof£1,000=£260profit forbuyer, loss forseller(g)£740versus£5,530,oradifferenceof£4,790(h) 553–346.75=206.25lossfortheshares,versus74lossforthecall206.25–74=132.25greaterlossfortheshares206.25÷74=2.79,orriskof2.79withsharespurchaseper1.00riskwithcallpurchase(i)741–553=188gainfortheshares,versus741–624=117gainforthecall
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188–117=71greatergainfortheshares188÷117=1.61orreturnof1.61sharesper1.00returnwithcall(j)Sharesrisk/return=206.25÷188=1.10=riskof1.10toreturnof1.00.Callrisk/return=74÷117=0.63toreturnof1.00
3. (a)5553(b)unlimited(c)253(d)5553,253,unlimited(e)£2,530(f)5133–253=4880(g)Answer3g
(h)Seeanswer3honnextpage
Answer3h
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4. (a)597.75(b)unlimited(c)22.75(d)597.75,22.75,unlimited(e)$1,137,50(f)
(g)
Answer4g
(h)Futurespriceatexpirationminusstrikepriceofcallequals590–575=15,orexpirationvalueofcallTradedpriceofcallminusexpirationvalueofcall,22.75–15=7.757.75×contractmultiplierof$50=$387.50profit for seller, loss for
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buyer
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Chapter2questions
Herearesomequestionsonputs,andonthedifferencebetweencallsandputs.Again,don’texpecttoknowalltheanswers.
1. Whatisthesimilarityanddifferencebetween:(a)alongcallandashortput?(b)alongputandashortcall?
2. Alongcallprovidesdownsideprotection,whilealongputprovidesupsideprotection.Trueorfalse?Whyorwhynot?
3. Suppose your outlook calls for amore extensive decline inGE.With thestockat18.03,theApril17.00putsareofferedat0.21.
(a) Ifyoubuyoneof theseputsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthisput.(e)Ifyouselloneoftheseputsatthecurrentmarketprice,whatisthepotentialeffectivepurchasepriceofthestockatexpiration?(f) Themultiplierfor thisoptionscontract is$100.What is thecashvalueofoneoftheseputs?(g)IfatAprilexpirationGEclosesat16.50,whatistheprofitfortheputbuyer,andwhatisthelossfortheputseller?(h)Writeaprofit/losstableforasaleofthisputatexpiration.(i)Drawagraphoftheexpirationprofit/lossforasalethisput.
4. Boeingiscurrentlytradingat74.16,andtheJune70.00putsaretradingat1.51.
(a) Ifyoubuyoneof theseputsat thecurrentmarketprice,what isyourbreak-evenlevel?(b)Whatisthemaximumamountthatyoucangain?(c)Whatisthemaximumamountthatyoucanlose?(d)Answerquestionsa–cforasaleofthisput.(e)Ifyouselloneoftheseputsatthecurrentmarketprice,whatisthe
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potentialeffectivepurchasepriceofthestockatexpiration?(f) Themultiplierfor thisoptionscontract is$100.What is thecashvalueofoneoftheseputs?(g)IfatMayexpirationBoeingclosesat30,whatistheprofitfortheputbuyer,andwhatisthelossfortheputseller?(h)Writeaprofit/losstableforasaleofthisputatexpiration.(i)Drawagraphoftheexpirationprofit/lossforasalethisput.
5. ThisquestioninvolvesputoptionsontheChicagoBoardofTrade(CBOT)TreasuryBond futures contract.The futures contract trades in ticksof32perfullfuturespoint,i.e.1.00=32/32.Theoptionscontract,however,tradesin ticks of 64 per full futures point, i.e. 1.00 = 64/64. An options tick issimplyhalf thevalueofa futures tick.Bothcontractshaveamultiplierof$1,000,therefore1/32=$31.25,andofcourse,1/64=$15.625.December Bonds are currently trading at 129.26 (12926/32), and theDecember129putsare currently tradingat0.58 (58/64). (A129price forbondsispossibleduringaflighttoquality.)
(a)WhatisthevalueoftheDecember129put?(b) Ifyoubuyoneof theseputsat thecurrentmarketprice,what isyour break-even level? [The formula is the same for all put options,i.e.break-even=strikepriceminuspriceofput.Here,youmustfirstconvert the futures strike price from a decimal listing into theequivalent number of options ticks. Next you subtract the put pricefrom the converted strike price. Then you reconvert the break-evenlevelintoadecimallisting.Theprocessistediousbutnotdifficult.](c)Whatisthemaximumamountthatyoucangain?(d)Whatisthemaximumamountthatyoucanlose?(e)Answerquestionsa–cforasaleofthisput.(f)Ifyouselloneoftheseputsatthecurrentmarketprice,whatisthepotentialeffectivepurchasepriceoftheDecemberfuturescontractatexpiration?
6. AtEuronextLIFFE,BritishAirwaysiscurrentlytradingat233.5p(£2.335),and theJune220putsare tradingat9.75 (0.0975).Thecontractsare for1,000shares,sothecashoutlayforthemwouldbe£2335and£97.5.Thisyear’s range for British Airways is 174 to 255.5. The airlines sector iscurrentlyunderpressurebecause theglobal ecomomy is sluggishand the
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priceofoilisrising.Theeconomicindicatorsarelookingpositive,however,and you think that BA would be a profitable medium-term investment.However, the sharesare ina zoneof technical resistanceandanoutrightpurchase risks a short-term decline. You want to compare a purchase ofsharestoasaleoftheJune220put.
(a)Ifyouselltheput,whatisyourpotentialpurchaseprice?(b)Ifyouboughtthesharesat233.50,atwhatlevelwouldanincreaseintheirpricebyAprilequaltheincomefromtheput?(c) Suppose you sell the put instead of buying the shares.ConsiderthatifBAreaches280thatwouldsignalatechnicalbreakout.Whatisthepotentialsavingsfromapurchaseofsharesifassignedontheputcompared to the potential opportunity cost of not buying the shares,shouldBAreach280,byJuneexpiry?(d)Supposeyouselltheputandplaceastopordertobuythesharesat280.BA rallies to 280 and you are filled on your stop order at thatprice. Your put eventually expires worthless. What is the effectivepurchasepriceoftheshares?(e) Ifyoubuy1,000sharesat thecurrentmarketpriceof233.5andyou sell one June 220 put at 9.75, what is your average cost if thesharesdeclineandyouareassignedontheput?
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Chapter2answers
1. (a)Bothareapotentialpurchaseorapotentiallongposition.Thelongcallhastheright,whiletheshortputhastheobligation.(b)Bothareapotentialsaleorapotentialshortposition.Thelongputhastheright,whiletheshortcallhastheobligation.
2. True,becausealongcallisalimitedriskalternativetothepurchaseofanunderlying,whilea longput isa limitedriskalternative to thesaleofanunderlying.
3. (a)17.00–0.21=16.79(b)16.79minusthevalueofthestockatexpiration(intheory,16.79)(c)0.21(d)16.79,0.21,16.79(e)17.00–0.21=16.79(f)0.21×$100=$21(g)17.00–16.50–0.21=0.29(h)
(i)
Answer3i
4. (a)68.49
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(b)68.49(c)1.51(d)68.49,1.51,68.49(e)Obligationtobuystockatthestrikepriceminusincomefromput:70.00–1.51=68.49(f)$151(g)Strikepriceminuspriceofstockatexpirationminusvalueofput:70.00–65.00–1.51=3.49(h)
(i)
Answer4i
5. (a)58/64×$1,000=$906.25
(b) 129.00 = 12832/32 = 12864/64, or strike price in options ticks12864/64–58/64=1286/64=1283/32=128.03,orbreak-evenlevel(c)128.03(d)0.58(e)128.03,0.58,128.03(f) Obligation to buy futures contract at strike price minus incomefromput,or129.00–0.58=1286/64=128.03futuresprice
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6. (a)Strikepriceminusincomefromput:220–9.75=210.25(b) Shares purchase price plus income from put: 233.5 + 9.75 =243.25(c) 233.5 – 210.25 = 23.25 potential savings: 280 – 233.5 = 46.5potentialopportunitycost(d)Costofsharesminusincomefromput:280–9.75=270.25.Butrememberthatbeforeexpiryyourputcontractisstilloutstanding,andifBAretracestobelow220,youwillbeobligatedtobuy1,000shares.Ifyoudon’twanttomakeanadditionalpurchase,thenbuybackyourput as soon as you buy your shares. This will raise the effectivepurchasepriceofyourshares.(e)Costofpurchaseviaputisstrikepriceminusincomefromput,or220–9.75=210.25.Averagecostofsharesis(233.5+210.25)÷2=£221.875.
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Chapters3questions
1. IfGEistradingat18.03,the17.00putsandthe19.00callsarebothout-of-the-money.Trueorfalse?
2. AttheNYSE-LIFFE,BritishAirwaysistradingat233.5.TheJune235callsarequotedat12.75,andtheJune235putsarequotedat16.75.Whataretheintrinsicandtimevaluesoftheoptions?
3. Parityoptions containapproximately equal amountsof intrinsicand timepremiums.Trueorfalse?
4. Whydoat-the-moneyoptionscontainthemosttimepremium?5. Which option or options have the most accelerated time decay as theyapproachexpiration?
(a)In-the-moneyoption(b)At-the-moneyoption(c)Out-of-the-moneyoption
6. Whichoptionsalwaysrequiremargin?(a)Longputs(b)Shortcalls(c)Shortputs(d)Longcalls
7. Concerningoptionsonstocksorshares,whichofthesestatementsaretrue?(a)Theshort-terminterestrateisaddedtothepriceofacall.(b)Thedividendsuntilexpirationareaddedtothepriceofacall.(c) Thedividendsuntilexpirationaresubtracted fromthepriceofaput.(d)Theshort-terminterestrateissubtractedfromthepriceofaput.
8. Which positions are potentially long the underlying, and which positionsarepotentiallyshorttheunderlying?
(a)Longcalls(b)Shortputs(c)Longputs(d)Shortcalls
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9. YouareshortoneGE19.00putatexpiration,andGEhasclosedat17.50.Doyouexercise,orwillyoubeassigned?What isyourresultingpositionandatwhatprice?
10. ItisthethirdweekinNovember,andtheDecemberCornoptionscontractshave expired. You are short one December 280 Corn call, and theDecember futurescontracthas settledat284.25.Doyouexercise,orwillyoubeassigned?Whatisyourresultingposition,ifany,andatwhatprice?
11. YouarelongoneOEX520callatexpirationandtheclosingindexpriceis529.45.Doyouexercise,orwill youbeassigned?What is your resultingposition,ifany,andatwhatprice?
12. AtNYSE-LIFFE, youare short oneFTSE5525put at expiration and theclosing index price is 5479.6.Do you exercise, or will you be assigned?Whatisyourresultingposition,ifany,andatwhatprice?
13. Youhavepreviouslysoldnaked(beware!)oneXYZMay80callat3.35.Itisnowthreeweeksuntilexpirationandthecallisworth0.28.Thestockisat74.16, and it has been ranging from 72.50 to 77.00 during the past twoweeks,andyouexpectittocontinuetodosofortheforeseeablefuture.Youwouldliketocontinuetocollecttimedecay.Whatdoyoudo?
14. AEuropeanstyledcallcanonlybeexercisedwhenitisin-the-money.Trueorfalse?
15. Earlyexercisepremiumisaminorcomponentofallin-the-moneyAmericanstyledputoptions.Trueorfalse?
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Chapter3answers
1. True.2. Call,no intrinsic; timevalue is12.75.Put intrinsic is235–233.5=1.5;timevalueis16.75–1.5=15.25.
3. False;parityoptionscontainonlyintrinsicvalueorpremium.4. Because they are the only options that hedge the underlying for equalamountsofupsideanddownsidemovement.
5. All have accelerated time decay, but the at-the-money options acceleratemorequicklybecausetheycontainthemostamountoftimepremium.
6. bandc,allshortoptionsrequiremargin.7. (a)True
(b)False(c)False(d)True
8. (a)Long(b)Long(c)Short(d)Short
9. Youwillbeassignedapurchaseof100sharesat19.0010. YouwillbeassignedoneshortDecemberfuturescontractat280.11. Your clearing firm will exercise for you, and you will receive the cash
differential between the index price and the strike price of the option:529.45 – 520 = 9.45. You have no remaining position. Remember thecontractmultiplieris$100,thereforeyoureceive$945.
12. You will be assigned, and you will pay the cash differential between thestrike price and the index price: 5525 – 5479.6 = 45.4. You have noremainingposition.Rememberthatthemultiplieris£10,thereforeyoupay£454.
13. Youhaveaprofit.Youdon’twanttheriskofalarge,unforeseenmovebythestock to the upside, which could result in a loss and an unwantedassignment toashortstockposition.Youalsowant toavoidpinrisk.Youshould soon buy this call back. If youwant to continuewith a short callposition, you could sell the November–December or November–January
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time spread, thereby rolling your short call position to a more distantmonth.
14. False;thereisnoearlyexercisepossibleforEuropeanoptions.15. False;stockandstock indexputshavesignificantlygreaterearlyexercise
premium than puts on futures contracts because they can be exercised togaincashand,therefore,interest.
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Chapter4questions
1. Whatisthedifferencebetweenthehistoricalandtheimpliedvolatility?2. Suppose that the S&P 500 index has just made a 5 per cent downsidecorrection. If the implied volatility of the near-termat-the-money put hasincreased,thentheimpliedvolatilityofthenear-termat-the-moneycallhasdecreased.Trueorfalse?
3. The implied volatility always adjusts to the 20-day historical volatilitywithinseveraldays.Trueorfalse?
4. (a)Afive-dayhistoricalvolatilitygivesamoreaccurateindicationofan underlying contract’s volatility than a 30-day historical volatility.Trueorfalse?(b)Whatdothesedifferentreadingstellyou?
5. The December US 30-Year Treasury Bond Futures contract is currentlytradingat129.01.TheDecember129.00calls,with60daystillexpiration,aretradingat1.43withanimpliedvolatilityof8percent.Bondssuddenlybreak to128.00on themonthly employment report, butgradually retracethroughoutthedaytosettleat129.01.ThesettlementpriceoftheDecember129callsis1.49.Whathashappenedtotheimpliedvolatility,andwhatdoesthistellyouaboutthehistoricalvolatility?Whatmarketexplanationcouldyougiveforthis?
6. Referring to question 5, above, if an options trader expects the impliedvolatility trend tocontinue,hewillmost likelydowhichof the following?Why?
(a)Buycallsandsellputs.(b)Buyputs.(c)Sellcallsandbuyputs.(d)Buycallsandbuyputs.
7. TheS&P500 indexhas closedat 1085.93, up17.84.What is a layman’sestimatefortheday’sannualisedvolatilityoftheindex?
8. Younotethatthedailyvolatilityinquestion4,above,isaboutaverageforthe past five days. You also note that the current, at-the-money impliedvolatilityis35percent.Whatarethesefigurestellingyou?
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9. Duringthecourseofseveralweeks,theaverageday-to-daypricerangeofShellTransporthasbeen increasing. Is the ten-dayhistorical volatilityofShellTransportincreasingordecreasing?
10. Lastnight theFTSE-100indexsettledat4800,andthismorning,afteranovernightfallintheUSmarket,ithasopenedat4400.Thefront-monthat-the-moneyoptionsarebidwithanimpliedvolatilityof70percent(October1997).Areyouaseller?(Hint:First,estimatethevolatilityoftheindexattheopening,thencompareittotheimpliedvolatilityoftheoptions.)
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Chapter4answers
1. The historical volatility is an average of a set of daily annualisedvolatilitiesoftheunderlying,whiletheimpliedvolatilityisanindication,bythe price of an option, of the historical volatility expected throughexpiration.
2. False.Bothimpliedshaveincreasedthesameamountbecausetheyareatthe same strike price. Both options hedge the same expected range ofunderlyingpricemovement.
3. False.Thetwovolatilitiescandifferformonthsattime.4. (a)False.Thefive-dayvolatilityonlygivesamorerecentindication.
A30-dayvolatilitygivesabetterindicationofthevolatilitytrend.(b)Thefive-daycanleadthe30-dayiftheshort-termtrendcontinues.Butifthefive-dayisashort-termaberrationbasedonaspecialeventthat has no long-termconsequences, then thevolatilitywill revert tothe30-day.
5. Theimpliedhasincreased(to8.25percent),whichindicatesthatthenear-termhistorical volatility is expected to increase. The optionsmarketmayindicate that there are components in the employment report that willcontinuetounsettlethefuturesmarket.
6. Thetrader is likely todobord, i.e.anycombinationofbuyingcallsandputs. He is buying the volatility trend, which is increasing. This iscomparable to a trader in the stockmarket who buys stocks because hisoutlookisforincreasedprices.
7. 1085.93–17.84=1068.09wasyesterday’sclosingprice17.84/1068.09=0.0167,or1.67%1.67×16=26.72%estimateofday’sannualisedvolatility
8. Onepossibilityisthattheoptionshaveyettoaccountforadecreaseinthehistoricalvolatility,andthattheymaybeovervalued.Anotherpossibilityisthat the options are anticipating a near-term increase in the historicalvolatility,andifso,theyarecorrectlyvalued.
9. Ten-dayhistoricalvolatilityisincreasing4800–4400=400pointschangeatopening400/4800=0.0833,or8.33%pricechange8.33%×16=133%volatilityofindex
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Theoptions,at70percent,areextremelyundervalued.Ontheotherhand,the impliedvolatility isatanexceptionallyhigh leveland itmayaveragedown during the next few days. You may not want to buy these optionsbecauseoftheirhighcost,butyoucertainlywouldn’tgoshortthemunlessyouarewellcapitalised.
10. It’syourchoice.
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Chapter5questions
1. State whether the following positions are equivalent to a long or shortunderlyingposition.
(a)shortcall(b)longput(c)shortput(d)longcall
2. A0.20deltaputdecreasesat80percentoftheunderlyingiftheunderlyingmovesup.Trueorfalse?
3. Forasmallupwardmoveintheunderlyinga0.50deltacallchangesmorethana0.50deltaput,butforasmalldownwardmoveintheunderlyinga0.50deltaputchangesmorethana0.50deltacall.Trueorfalse?Whyorwhynot?
4. Giventhefollowingsetofoptionswiththeirdeltas,whatisthenewpriceofeachoptioniftheunderlyingmovesupbyonepoint?
5. Giventhefollowingsetofoptionswiththeirdeltas,whatisthenewpriceofeachoptioniftheunderlyingmovesdownbyonepoint?
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6. A0.50deltaoptionhasthesamecorrelationwiththeunderlyingfrom50to10daysuntilexpiration.Trueorfalse?Whyorwhynot?
7. Fivelong0.20deltacallshavethesamedeltaequivalenceasfive(longorshort?)0.20deltaputs.
8. A delta neutral hedge can be createdwith 20 short, 0.30 delta calls andhowmanylongorshortunderlyingcontracts?
9. Astimepasses,thedeltasofout-of-the-moneycallsandin-the-moneyputsbothdecrease.Trueorfalse?
10. GiventhefollowingpositioninMarchUSTreasuryBondoptions,calculatethetotaldeltafortheposition.(Figurescourtesyofpmpublishing.com.)
(a)Whatistheequivalentfuturesposition?(b)Howwouldyoucreateadeltaneutralhedgefortheaboveoptionsposition?
11. FortheaboveexampleinUST-Bondoptions,theMarchfuturescontractiscurrently at 128.01 with 87 days until expiration. Suppose you are shorttwo,March124calls.What is theprobabilityof yourbeingassigned twoshortfuturescontractsatexpiration?
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Chapter5answers
1. (a)shortunderlying(b)shortunderlying(c)longunderlying(d)longunderlying
2. False, a 0.20 delta put decreases in price by 20 per cent for a smallupwardsmoveintheunderlying.
3. False, theybothchangethesameamount ineithercase.If theunderlyingmoves up, the 0.50 delta call increases in value at half the rate of theunderlying,while the0.50deltaputdecreases invalueathalf the rateoftheunderlying.Iftheunderlyingmovesdown,thecalldecreaseswhiletheputincreases.
4. Newprice9.25(rounded)39.255⅝12.00
5. Newprice200934.002.251.10
6. True, a 0.50 delta, at-the-money option correlates the same with theunderlyingbecauseitsdeltaisnotaffectedbytime.
7. Short.8. A delta neutral hedge is here created with six long underlying contractsassuming, as inmost cases, that the options contract and the underlyingcontracthavethesamemultiplier.
9. False.Astimepasses,thedeltasofout-of-the-moneycallsdecreasebecausetheyhavelessprobabilityofbecomingin-the-money,whilethedeltasofin-the-moneyputsincreasebecausetheyhavemoreprobabilityofstayingin-the-money.
10. Deltasperstrike+2.55
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–1.50–2.70–1.40–3.05Totaldeltaposition.
(a)Shortthreefuturescontracts.(b)Buy,orgolong,threefuturescontracts.
11. 75percent.
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Chapter6questions
1. 50deltaoptions in thesamecontractmonthhavemoregammaand thetathan0.80deltaoptions.Trueorfalse?Why?
2. Given the following options with their deltas and gammas, what is theapproximatenewdeltaiftheunderlyingmovesupbyonepoint?
3. Given the following options with their deltas and gammas, what is theapproximatenewdeltaiftheunderlyingmovesdownbyonepoint?
4. Given the following options, which are expressed in ticks and whosemultiplier is $50, and given their thetas expressed in dollars and cents,calculate theapproximatenewvalueof theoptionsafter sevendays’ timedecay.Bothoptionshave30DTE.
5. High thetaoptionshaveagreaterprobabilityofmakingaprofit than lowthetaoptions.Trueorfalse?Why?
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6. (a)ReferringtoTables6.3and6.4,whatisthepercentageincreaseingammaoftheDecember380callfrom90to30DTE?(b) What is thepercentage increase in theta for thisoptionover thesametimeperiod?
7. Whatisthecorrelationbetweengammaandtheta?8. Isitpossibletohavepositivegammaandpositivetheta?Whyisthis?
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Chapter6answers
1. True, because at-the-money options always have the largest gamma andthetainanycontractmonth.
2. Newdelta0.660.060.410.59
3. Newdelta0.750.490.600.40
4. NewvalueForthe380call:(12½×$50)–(7×$11.5)=$544.50Forthe400call:(5⅜×$50)–(7×10)=$198.75
5. False,because there isnocorrelationbetween thetaandprofit/loss.Highthetaoptions,thosewith0.50deltasaremorelikelytoexpirein-the-moneythanlowthetaoptionswith0.20deltas,buttheirgreatertimepremium,andthereforetheirgreatertheta,isafairexchangeforthis.
6. (a)(0.013–0.008)/0.013=38%(b)(11.5–6.65)/6.65=73%
7. Increasedgammacorrelatestoincreasedtheta.8. Not possible, because positive gamma indicates that the options positionprofits from market movement, while positive theta indicates that theoptionspositionprofitsfrommarketstasis.
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Chapter7questions
1. Ashortcallpositionhasnegativevega,andthereforeittakesalossfromanincreaseintheimpliedvolatility.Trueorfalse?
2. (a) Given the following OEX options, which have a contractmultiplierof$100,whatistheirnewvaluebothindollarsandroundedinto ticks if the implied increases by 3 percentage points? TheDecember OEX is currently at 590.00, and the January OEX iscurrentlyat592.75.
(b)Iftheimpliedincreasesby3percentagepoints,whichoftheaboveoptionsgainsthemostinpercentageterms?
3. Increasedimpliedvolatilityleadstoincreasedvegas.Trueorfalse?Why?4. Intheexampleinquestion2,theJanuaryat-the-moneyimpliedvolatilityis20 per cent, and the range of theOEX implied volatility during the pastyear is 18 per cent to 25 per cent. In dollar terms, what is the vegarisk/returnratioforapositionthatisshorttenoftheJanuary590callsiftheimpliedremainswithinitsrangeduringthenextweek?
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Chapter7answers
1. True for both short calls and puts, because negative vega profits fromdecreased implied volatilities, while positive vega profits from increasedimplieds.
2. (a)Newvalue12.3,$12303.6,$36021.8,$218011.2,$1120(b)December610callincreases0.40×3/2.4=50percent.
3. False,becauseonlyvegasofout-of-andin-the-moneyoptionsincreasewithan increase in the implied.At-the-moneyoptionsvegasremainpracticallyunchanged.
4. The simple answer is a vega risk of = 5/2 2.5. An answer that bettercommunicatestheamountatriskisasfollows:vegaequals0.90,or$90;2×$90=$180reductioninoneoption’svalueiftheimplieddecreasesfrom20percentto18percent;10×$180=$1,800totalpotentialvegareturn.5×$90=$450increaseinoneoption’svalueiftheimpliedincreasesfrom20percent to25percent;10×$450=$4,500 totalpotentialvegarisk.R/R=$4,500/$1,800=$2.50potentialriskforeachpotentialreturnof$1.
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Chapter8questions
1. Refer again to the Spider options prices in Table 8.1. Suppose you arebearishonthestockfortheshortterm,andyouwishtobuytheJune111–109putspread.
(a)Whatisthenetdebitinticksandindollarsforthisspread?(b)Whatisthemaximumprofit?(c)Whatisthemaximumloss?(d)Whatisthebreak-evenlevel?(e)Whatistherisk/returnratio?(f)TheSPDRiscurrentlyat115.22.Inpercentageterms,howmuchwouldtheindexneedtoretraceinorderforthespreadtobreakeven?(g)Constructatableanddrawagraphoftheexpirationprofit/loss.
2. AttheLIFFE,Sainsburyiscurrentlypricedat323p.TheJune330callsarepricedat7.75p,and theJune340callsarepricedat4.75p.Thereare30daysuntilexpiry.Rememberthatthecontractmultiplierhereis£1,000,sothevalueofthe330callsis0.0775×£1,000=£77.50,andthatofthe340callsis0.0475×£1,000,or£47.50.
(a)WhatisthecostofagoinglongoneJune330–340callspread?(b)Whatisthebreak-evenlevelofthespread?(c)Whatisthemaximumprofit?(d)Whatisthemaximumloss?(e)Whatistherisk/returnratio?(f)Constructatableanddrawagraphoftheprofit/lossatexpiry.(g)Nowsupposeyou’reabear.ConstructatableanddrawagraphoftheP/Latexpiryforasellofthiscallspread.
3. In London, the FTSE-100 index is currently trading at 5422. Supposeyou’re bearish for the next several weeks, with a target of 5300 byDecember expiry. Youwould like to buy oneDecember 5400put, but thecostof193p(£1,930) is toogreat,especiallywithaccelerated timedecay.Younotethatthe5300putsarepricedat154p,andyoudecidetobuythisputspread.Thecontractmultiplieris£1,000.
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(a) What is the cost of buying this spread, in ticks and in actualpoundssterling?(b)Whatisthebreak-evenlevel?(c)Whatisthemaximumprofit?(d)Whatisthemaximumloss?(e)Whatistherisk/returnratio?
4. ThefollowingoptionsontheDowJonesIndustrialAveragetradeatCBOE.Here,thevalueof theDowJonesIndexisdividedby100inordertogivethevalueoftheindex,knownasDJX,onwhichtheoptionsarebased.Forexample,iftheDowclosesat9056,theDJXsettlesat90.56.Youmaythinkof the index as a stock with a price of 90.56, etc. The options contractmultiplieris$100,sotheDecember91callat1.90isworth1.90×$100,or$190.DJXat90.5630daysuntilDecemberexpiration
(a) What is the break-even level for a purchase of one straightDecember91call?WhatvalueoftheDowwouldthisbreak-evenlevelcorrespondto?Whatisthebreak-evenlevelforapurchaseofonestraightDecember90put?WhatvalueoftheDowwouldthisbreak-evenlevelcorrespondto?(b)SupposeyouthinkthattheDowhastoppedoutforthetimebeing,andyouanticipateaChristmasbreak,i.e.acorrectionof3percentbyDecemberexpiration.Whatindexlevelwouldthiscorrespondto?(c) Whichout-of-the-moneyputspreadwouldcompletelycover thisrange?(d) If you buy, or go long, this spread, what is your net debit inoptionsticks?(e)Whatisyourmaximumprofit?Whatisyourmaximumloss?
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Whatisyourbreak-evenlevelWhatisyourrisk/returnratio?(f) Suppose you believe in theChristmas rally.Your chart analysis,however, tells you that there is resistance at 9300 in theDow.Whatout-of-the-moneycallspreadcouldyoubuy?(g)Whatisyourdebitforthisspread?Whatisthemaximumprofit?Whatisthebreak-evenlevel?Whatisthemaximumloss?Whatistherisk/returnratio?
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Chapter8answers
1. (a)2.60–2.15=0.45ticks;0.45×$100=$45(b)111–109–0.45=1.55(c)0.45(d)111–0.45=110.55(e)0.45/1.55=$29atriskforeachpotentialreturnof$1.00,or1/3(f)115.22–110.55=4.67;4.67/115.22=4%(g)
Answer1g
2. (a)7.75p–4.75p=3p;0.03×£1,000=£30(b)330+3=333(c)[340–330]–3=7(d)3(e)3/7=43patriskforeach£1ofpotentialreturn(risking1tomake2.33)(f)
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Answer2f
(g)
Answer2g
3. (a)193–154=39p;0.39×£1,000=£390(b)5400–39=5361(c)[5400–5300]–39=61
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(d)39(e)39÷61=64patriskforeachpotentialreturnof£1(£1atriskforeachreturnof£1.56)
4. (a)91+1.9=92.90;9290;90–1.80=88.20;8820(b)90.56×0.03=2.72;90.56–2.72=87.84(c)LongDecember90–87putspread(d)1.8–1=0.8(e)3–0.8=2.2=$220;$80;90–0.8=89.20;0.8/2.2=0.36for1(2.8/1)(f)December91–93callspread(g)1.9–1.1=0.8=$80;2–0.8=1.2=$120;91+0.8=91.8;$80;80/120=0.67for1,or1.5for1
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Chapter9questions
1. It’s now the third week in November, and the global stock markets haveovercome theirannualOctobernervousnessandhavebegun to rally.YouwanttotakeabullishpositionbecauseyouexpecttherallytocontinueuntilChristmas.TheS&P500index iscurrentlyat1152.61,butyour technicalanalysistellsyouthatthereisresistancebetween1180and1200.Youthinkthat the indexwill eventuallymeet resistance and settle at approximately1200forDecemberexpiration.Youwanttogiveyourassessmentatry,butyoudon’twanttorisktoomuch.AttheCBOEthefollowingSPXoptionsontheS&P500aretradingatthe followingprices.Thecontractmultiplier is$100.This isaEuropean-styleoption,sothereisnoearlyexercise.S&Pindexat1152.61Decemberoptionswith30daysuntilexpirationStrike117512001225Callprices177.52.5
(a)i)WhatisthecostoftheDecember1175–1200,onebytwocallspreadinticksandindollars?ii)Whatisthelowerbreak-evenlevel? iii) At December expiration, what index level will give themaximumprofit?iv)Whatisthemaximumprofit?v)Whatistheupperbreak-evenlevel?vi)Whatisthemaximumloss?vii)Whatisyourprofit/lossiftheindexsettlesat1212? viii) If, one week after you open this position, i.e. withapproximatelythreeweekstillexpiration,theindexreaches1200,howcanyoumanagetherisk?(b) Suppose instead you want to pay more for your spread inexchangeforlessupsiderisk.i)WhatisthecostoftheDecember1175–1200–1225callladder
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inticksandindollars?ii)Whatisthelowerbreak-evenlevel? iii) At December expiration, what index level will give themaximumprofit?iv)Whatisthemaximumprofit?v)Whatistheupperbreak-evenlevel?vi)Whatisthemaximumloss?vii)Whatisyourprofit/lossiftheindexsettlesat1212?(c)Perhapsyouthinktheupsideriskoftheabovetwospreadsisstilltoo great, and you think the indexmight reach 1225 before settlingintoarange.Youarewillingtopaymoretoreduceyourexposure,andtoprofitmorefromtheupsidepotential.i)WhatisthecostoftheDecember1175–1225,onebytwocallspread?ii)Whatisthelowerbreak-evenlevel? iii) At December expiration, what index level will give themaximumprofit?iv)Whatisthemaximumprofit?v)Whatistheupperbreak-evenlevel?vi)Whatisthemaximumloss?vii)Whatisyourprofit/lossiftheindexsettlesat1212?
2. Because of perennial lawsuits in the US, you are bearish on BritishAmericanTobacco.Thecurrentpriceofthesharesis479.5p(£4.795).2Youthink that the shares are well supported below 400p, and you note thepricesofthefollowingJanuaryputs.(Remember,thecontractmultiplieris£1,000.)BritishAmericanTobaccoat479.5pJanuaryputswith70daysuntilexpiryStrike390420460Januaryputs4.51022.5
(a) i) What is the cost of the January 460 – 390, one by two putspreadinticksandinsterling?ii)Whatistheupperbreak-evenlevel?iii)AtJanuaryexpiry,whatpriceleveloftheshareswillgivethe
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maximumprofit?iv)Whatisthemaximumprofit?v)Whatisthelowerbreak-evenlevel?vi)Whatisthemaximumloss?vii)Atexpiry,whatisyourprofit/lossifthesharescloseat370?(b) Supposeyoudecidetobemoreeconomical,andyoudon’tmindraisingyourlowerbreak-evenlevel.i)WhatisthecostoftheJanuary460–420–390brokenputladderinticksandinsterling?ii)Whatistheupperbreak-evenlevel?iii)AtJanuaryexpiry,whatpriceleveloftheshareswillgivethemaximumprofit?iv)Whatisthemaximumprofit?v)Whatisthelowerbreak-evenlevel?vi)Whatisthemaximumloss?vii)Atexpiry,whatisyourprofit/lossifthesharescloseat370?(c)Ifinsteadyouthinkthatthemaximumdownsidepotentialfortheshares is approximately 420, youmight buy the January 460 – 420,onebytwoputspread.i)Whatisthecostofthisspreadinticksandinsterling?ii)Whatistheupperbreak-evenlevel?iii)AtJanuaryexpiry,whatpriceleveloftheshareswillgivethemaximumprofit?iv)Whatisthemaximumprofit?v)Whatisthelowerbreak-evenlevel?vi)Whatisthemaximumloss? vii) If, twoweeks after you open this position, the shares aretradingat420,howcanyoumanagetherisk?viii)Atexpiry,whatisyourprofit/lossifthesharescloseat370?(d) For a favourable price you are willing to buy shares in BritishAmericanTobacco.Thisyear’srangeforthesharesis584.5–329.5.You realise that by trading the above three spreads, you may beobligated to buy shares via your extra short put.Whatwould be theeffectivepurchasepriceofyourshareswithspreadsa,bandcabove?
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Chapter9answers
1. (a)i)17–[2×7.5]=2,or$200ii)1175+2=1177iii)1200iv)[1200–1175]–2=23v)1200+23=1223vi)potentiallyunlimitedvii)23–12=11profitviii)Buyeitherone1200call,orone1225call.(b)i)17–7.5–2.5=7,or$700ii)1175+7=1182iii)1200to1225iv)[1200–1175]–7=18v)1225+18=1243vi)potentiallyunlimitedvii)18profit(c)i)17–[2×2.5]=12,or$1200ii)1175+12=1187iii)1225iv)[1225–1175]–12=38v)1225+38=1263vi)potentiallyunlimitedvii)[1212–1175]–12=25profit
2. (a)i)22.5–[2×4.5]=13.5,or£135ii)460–13.5=446.5iii)390
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iv)[460–390]–13.5=56.5v)390–56.5=333.5vi)333.5,ifthesharesgotozerovii)56.5–[390–370]=36.5pprofit(b)i)22.5–10–4.5=8,or£80ii)460–8=452iii)420to390iv)[460–420]–8=32v)390–32=358vi)358,ifthesharesgotozerovii)32–[390–370]=12pprofit(c)i)22.5–[2×10]=2.5,or£25ii)460–2.5=457.5iii)420iv)[460–420]–2.5=37.5v)420–37.5=382.55vi)382.5,ifthesharesgotozerovii)Buyone420put,orbuyone390put.viii)37.5–[420–370]=12.5ploss(d)390–56.5=333.5;390–32=358;420–37.5=382.5
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Chapter10questions
1. Canyouseeafreighttraincoming?Thenyoucantradethegrainmarketsduringthegrowingseason.It’sonlyMay,andDecemberCornseemslikealongwayaway,butyouknowthatifitgetsafullheadofsteam,itcanrollover price levels. Besides, Corn, like other commodities, is now amainstreaminvestmentsupportedbyhedgefunds,andevenbanks.3Onthisday,DecemberCornsettlesat380,or$3.80perbushel,andyounote the following set of December options. These options expire on thethirdFridayofNovember,andtheyareexercisabletotheDecemberfuturescontract. (If you want a grain silo, then take delivery.) Their contractmultiplieris$50,whichmeansthatthe$4call,pricedat25,costs25×$50=$1,250.Cornoptionstradein1/8ths,so1=⅛,2=¼,3=⅜,etc.DecemberCornat380Decemberoptions,with176daysuntilexpiration.
(a)i)Whatisthecostofthelong$5call,short$3putcombointicksandindollars?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Whatisthemaximumupsideprofit?iv)WhatisthedownsidepriceofapotentiallongpositionintheDecemberfuturescontract?v)Whatisthepotentialdownsideloss?vi)Whatistheprofit/lossiftheDecemberfuturescontractsettlesbetween420and440attheexpirationoftheDecemberoptions?(b) Suppose, instead, your outlook for December Corn calls for amaximumpriceappreciationof$5.i)Whatisthecostofthelong$4.40–$5.00callspread,short$3.20
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put,three-wayspread?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Whatisthemaximumprofit?iv)WhatisthedownsidepriceofapotentiallongpositionintheDecemberfuturescontract?v)Whatisthepotentialdownsideloss?
2. TheCBOTDecemberTreasuryBondfuturescontractiscurrentlytradingat129.26 (12926/32), which corresponds to a yield of 5.08 per cent. Lately,Treasurieshaveattractedbuying interest througha flight toqualitybasedonproblemsinemergingmarkets.Youthinkthatthebullishnesshasrunitscourse, however, and you note the following December options. TheseoptionsexpireinthethirdweekofNovemberandtheyareexercisabletotheDecemberfuturescontract.Asspecifiedearlier,theytradein64ths,andthecontractmultiplier is$1,000,whichmeans that thecostof the132call is32/64×$1,000,or$500.DecemberT-Bondfuturesat129.26Decemberoptionswith22daysuntilexpiration
(a) Youdecide tobuy the129putandsell the132callasacombo.Whatisthecostofyourspreadinticksandindollars?(b)Atexpiration,whatisthedownsidebreak-evenlevel?(c)Whatisthemaximumdownsideprofit?(d)IftheDecemberfuturescontractrallies,whatisthepriceofyourpotentialshortposition?(e)Whatisyourpotentialupsideloss?(f) What is your profit/loss if the December futures contract isbetween129and132whentheDecemberoptionsexpire?
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Chapter10answers
1. (a)i)7⅞–3½=4⅜×$50=$218.75ii)500+4⅜=504⅜ iii) The full amount that theDecember futures contract ralliesabove504⅜.iv)300+4⅜=304⅜ v) Thefullamount that theDecember futurescontractdeclinesbelow300,plus4⅜.vi)4⅜loss(b)i)[15⅜–7⅞]–7½=zeroii)$4.40iii)[500–440]=60×$50=$3,000iv)$3.20perbushel v) Thefullamount that theDecember futurescontractdeclinesbelow320.
2. (a)0.58–0.32=0.26;26/64×$1,000=$406.25(b)26optionsticks=13futuresticks.Futurestradein32nds.129.00–0.13=128.32–0.13=128.19(c)ThefullamountthattheDecemberfuturescontractdeclinesbelow128.19.(d) Futures price of 132.00 – 0.26 options ticks = 131.32 – 0.13 =131.19(e) Thefullamount that theDecemberfuturescontract ralliesabove132,plusthespreaddebitof26optionsticks.(f)Lossofspreaddebit,26optionsticks
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Chapter11questions
1. Coca-Cola’searningsprospectsaregood,butthestockmarketasawholehas been bearish and volatile lately. The market could rally, or it couldretracetorecentlows,draggingCoca-Colaalongwithit.Thestockpriceis52.67, and the following August options are listed with 90 days untilexpiration:Coca-Colaat52.67Augustoptionswith90daysuntilexpiration:
(a)i)WhatisthecostoftheAugust52.50straddle?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumprofit?v)Whatisthemaximumloss? vi) What is the profit/loss if the stock closes at 57.50 atexpiration?(b)i)WhatisthecostofthelongAugust50–55strangle?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumprofit?v)Whatisthemaximumloss? vi) What is the profit/loss if the stock closes at 47.50 atexpiration?(c)Whyisthe50putpricedhigherthanthe55call?
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2. IntheUK,theoutlookforSainsburyduringthenextseveralmonthsisforcontinuedgood,butnotspectacular,trading,andyouexpectthesharestobestable.The impliedvolatility for theoptions is38percent,down fromover50percent.ItisNovember,andtheJanuaryoptionsareenteringtheiraccelerated time decay period. Sainsbury is trading at 537.5, and thefollowingoptionspricesarelisted:Sainsburyat537.5Januaryoptionswith70daysuntilexpiry:
i)WhatistheincomefromsellingtheJanuary500–600strangle?ii)Atexpiry,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumprofit?v)Whatisthemaximumloss?
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Chapter11answers
1. (a)i)2.52+2.90=5.42ii)52.50+5.42=57.92iii)52.50–5.42=47.08iv)upsideunlimited;downside,valueofthestockv)5.42vi)[57.50–55]–5.42=–2.92loss(b)i)2.05+1.45=3.50ii)55+3.50=58.35iii)50–3.5=46.5iv)upsideunlimited;downside50–3.5=46.5v)3.50vi)5–3.5=1.5(c)Becauseoftheputvolatilityskew.ThisexplainedinPart4.
2. i)17.5+17.5=35ii)600+35=635iii)500–35=465iv)35v)unlimitedupside,465onthedownside.
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Chapter12questions
1. RefertotheprevioussetofSainsburyJanuaryoptions:Sainsburyat537.5Januaryoptionswith70daysuntilexpiry
(a)i)WhatistheincomefromtheshortJanuary460–500–600–650ironcondor?Thisisanasymmetricspread.ii)Atexpiry,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumupsideloss?v)Whatisthemaximumdownsideloss?vi)Whatisthemaximumprofitfromthisspread?vii)Whatistheprofitrange?(b)i)WhatistheincomefromtheshortJanuary460–550–650ironbutterfly?Thisisalsoanasymmetricspread.ii)Atexpiry,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumupsideloss?v)Whatisthemaximumdownsideloss?vi)Whatisthemaximumprofit?vii)Whatistheprofitrange?
2. GiventheprevioussetofCoca-Colaoptions.Coca-Colaat90Augustoptionswith90daysuntilexpiration
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(a)i)WhatisthecostofthelongAugust45–50–55–60ironcondor?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumupsideprofit?v)Whatisthemaximumdownsideprofit?vi)Whatisthemaximumloss?(b)i)WhatisthecostofthelongAugust45–52.50–60ironbutterfly?ii)Atexpiration,whatistheupsidebreak-evenlevel?iii)Atexpiration,whatisthedownsidebreak-evenlevel?iv)Whatisthemaximumupsideprofit?v)Whatisthemaximumdownsideprofit?vi)Whatisthemaximumloss?
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Chapter12answers
1. (a)i)17.5+17.5–8–8=19creditii)600+19=619iii)500–19=481iv)[650–600]–19=31v)[500–460]–19=21vi)19vii)619–481=138(b)i)34+39.5–8–8.5=57.5creditii)550+57.5=607.5iii)550–57.5=492.5iv)[650–550]–57.5=42.5v)[550–460]–57.5=32.5vi)57.5vii)607.5–492.5=115
2. (a)i)2.05+1.45–0.82–0.34=2.34debitii)55+2.34=57.34iii)50–2.34=47.66iv)[60–55]–2.34=2.66v)[50–45]–2.34=2.66vi)2.34(b)i)2.52+2.90–0.82–0.34=4.26debitii)52.50+4.26=56.76iii)52.50–4.26=48.24iv)[60–52.50]–4.26=3.24v)[52.50–45]–4.26=3.24
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vi)4.26
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Chaper13Questions
1. IntheUK,theFTSE-100indexhasbeenbullishsincetheendofOctober,and you expect this trend to continue through the end of the year. TheDecember futures contract is currently at 5470.Using technical analysis,you determine that there is resistance at a former support area between5700 and 5800. You note the following European-style December calloptions:DecemberFTSEcontractat5470Decemberoptionswith40daysuntilexpiry
(a)i)Whatisthecostofthelong5675–5775–5875callbutterfly?ii)Atexpiry,whatisthemaximumprofitofthespread?iii)Whatisthelowerbreak-evenlevel?iv)Whatistheupperbreak-evenlevel?v)Whatistheprofitrange?vi)Whatisthemaximumloss?(b) i) What is the cost of the long 5625–5725–5825–5925 callcondor?ii)Atexpiry,whatisthemaximumprofitofthespread?iii)Whatisthelowerbreak-evenlevel?iv)Whatistheupperbreak-evenlevel?v)Whatistheprofitrange?vi)Whatisthemaximumloss?(c)Howdoyouaccountforthegreaterprofitrangeofthecondor?
2. BecauseofbudgetdeficitproblemsinWesterneconomiesthestockmarketshavebeenextremelyvolatile.However,bail-outpackageswiththeIMFandthemore solventnationshave finallybeenagreedupon.Theglobal stockmarkets have sold off, and you expect them to range for the next two
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months.DJEurostoxx50at2831Juneputswith57daysuntilexpiration
(a) i) What is the price of the long June 2850–2800–2750 putbutterfly?ii)Atexpiration,whatisthemaximumprofit?iii)Whatistheupperbreak-evenlevelforthisbutterfly?iv)Whatisthelowerbreak-evenlevel?v)Whatistheprofitrange?vi)Whatisthemaximumloss?(b)i)Supposeyouprefertoleaveyourselfamarginoferrorinyouroutlook.You are range bearish.What is the cost of the 2850–2800–2700–2650putcondor?ii)Atexpiration,whatisthemaximumprofit?iii)Whatistheupperbreak-evenlevel?iv)Whatisthelowerbreak-evenlevel?v)Whatistheprofitrange?vi)Whatisthemaximumloss?(c)Comparetheadvantagesanddisadvantagesoftheputbutterflytotheputcondor.
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Chapter13answers
1. (a)i)137.5+68–[2×97.5]=10.5ii)[5775–5675]–105=89.5iii)5675+10.5=5685.5iv)5875–10.5=5864.5v)5864.5–5685.5=179pointsvi)10.5=£105(b)i)159.5+57–117–81=18.5ii)[5725–5625]–18.5=81.5iii)5625+18.5=5643.5iv)5925–18.5=5906.5v)5906.5–5643.5=263pointsvi)18.5=£185(c)Thecondorhasagrossprofitrangethatis100pointsgreater.The8p extra cost reduces eight points of profit fromboth the lower andupperbreak-evenlevels.Thenetprofitrangeofthecondoristherefore84pgreater.
2. (a)i)107+68.40–(2×85.80)=3.8ii)(2850–2800)–3.8=46.2iii)2850–3.8=2846.2iv)2750+3.8=2753.8v)2846.2–2753.8=92.4pointsvi)3.8(b)i)107+54.5–85.8–68.4=7.3ii)(2850–2800)=42.7iii)2850–7.3=2842.7
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iv)2650+7.3=2657.3v)2842.7–2657.3=185.4pointsvi)7.3(c)Thecondorhasagrossprofitrangethatis185.4–92.4=93pointsgreateratanadditionalcostof3.5.
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Chapter14questions
1. Your shares in Intel have performed well in the past, but now, with thepossibilityofaglobalrecession,Intel’sordersaredown,andthestockisina trading range. You are looking to supplement your dividend bywritingone call on each 100 shares that you own. You realise that if the stockralliesabovethecallstrikeprice, itwillbecalledawayfromyou.Intel iscurrently trading at 21.42, and the July 24 calls, with 46 days untilexpiration,aretradingat0.21.Theyare12percentout-of-the-money.
(a)WhatisthemaximumprofitfromwritingoneJuly24call?(b)Whathappensifatexpirationthestockclosesabove24?(c)Whatisthebreak-evenlevel?(d) What isyourpercentage returnover thenext46dayswithyourstockvaluedat21.42?
2. Sainsbury’srangethispastyearisnolessthan370to588.5.Youhaveheldontoyourshares,ridingthemarket turbulence.Becausesupermarketsarecurrently cutting prices, you forsee reduced profit margins for the nearterm. Sainsburyiscurrently tradingat537.5.With70daysuntilexpiration,the January 550 calls are trading at 34, and the January 600 calls aretradingat17.5.Youwould like to selloneof theseasacoveredwriteon1,000sharesthatyouown.
(a)i)WhatisthemaximumprofitfromwritingoneJanuary550call?ii)Whathappensifatexpirythesharesclosesabove550?iii)Whatisthebreak-evenlevel?iv)Whatisyourpercentagereturnoverthenext70dayswithyoursharesvaluedat537.5?(b)i)WhatisthemaximumprofitfromwritingoneJanuary600call?ii)Whathappensifatexpirythesharesclosesabove600?iii)Whatisthebreak-evenlevel?iv)Whatisyourpercentagereturnoverthenext70dayswithyour
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sharesvaluedat537.5?3. ItislateNovember,andIBMiscurrentlytradingat159.75.YouexpectIBMtoremainatapproximately160forthenextmonth.Younotethefollowingpricesfor160calls.November160calls,withonedayuntilexpiration:0.69December160calls,with29daysuntilexpiration:5.13January160calls,with64daysuntilexpiration:7.5
(a)WhatisthecostoftheDecember–January160callcalendar?(b) Barring a special dividend or takeoverwithin the next 29 days,whatisthemaximumlossofyourcalendarspread?(c)i)Althoughthereare28daysbetweenNovemberandDecemberexpirations,and35daysbetweenDecemberandJanuaryexpirations,you would like to estimate the profit potential of the December–Januaryspread.WhatisyourestimateforthevalueofthisspreadwithIBMat160andonedayuntilDecemberexpiration? ii)WouldyouexpecttheDecember–JanuaryspreadtobeworthmoreorlessthantheNovember–Decemberspread?
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Chapter14answers
1. (a)[24–21.42]+0.21=2.79(b) Your stockwill be called away, or sold, but youwill still haveyourmaximumprofit.(c)21.42–0.21=21.21(d)0.21/21.42=1%
2. (a)i)[550–537.5]+34=46.5ii)Yourshareswillbecalledaway,orsold,butyouwillstillhaveyourmaximumprofit.iii)537.5–34=503.5iv)34/537.5=6.33%(b)i)[600–537.5]+17.5=80ii)Yourshareswillbecalledaway,orsold,butyouwillstillhaveyourmaximumprofit.iii)537.5–17.5=520iv)17.5/537.5=3.26%
3. (a)7.5–5.13=2.37(b)2.37(c)i)EstimatewouldequaltheNovember–Decemberspread’svalue,5.13–0.69=4.44.ii)More,becausethelongJanuarycallwillhavemoredaysuntilexpiration than the long December call. This doesn’t imply greaterprofit potential, however, because the November–December spreadwould have cost less to begin with. This analysis assumes that thethreeimpliedvolatilitiesareequalandwillremainconstant.
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Chapter15questions
1. Coca-Colaistradingat52.67FortheSeptember60callswith90daysuntilexpiration, note whether time passing causes the following Greeks toincrease,decreaseorremainunchanged.
(a)delta(b)gamma(c)vega(d)theta
2. AnswertheabovequestionsfortheSeptember52.50calls.(a)delta(b)gamma(c)vega(d)theta
3. (a)Ifthemanagerofyourpensionfundwantstohedgeaportfolioofstocks and Treasury Bills against a possible interest rate increaseduringthenexttwoweeks,whichoptionspositionorpositionsmightheemploy?(b)IntermsoftheGreeks,comparetheadvantagesanddisadvantagesthathemightconsiderbyemployingout-of-,orat-the-moneyoptions.i)deltaii)gammaiii)vegaiv)theta(c) Suppose he considers an at-the-money option. In terms of theGreeks,comparetheadvantagesofemployinga30-dayoptiontoa60-dayoption.i)deltaii)gammaiii)vegaiv)theta(d) Nowsupposeheconsidersanout-of-the-moneyoption. In terms
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oftheGreeks,comparetheadvantagesofemployinga30-dayoptiontoa60-dayoption,eachatthesamestrike.i)deltaii)gammaiii)vegaiv)theta(e) Gettingsettlementsfromexchangewebsites,chooseanoptionortwofromthemajorstockindexes:DJEurostoxx50,SPDRSorSPX,FTSE-100, CAC or DAX, etc. Follow the options for the next twoweeks.
4. TheDecemberFTSEfuturescontractiscurrentlyat5530andyouarelongone theDecember5575callwhich is currently tradingat 190.A rumourcirculates that a certain tabloid baron has dropped his opposition toEuropean monetary union because he has formed a partnership with anItalian media mogul, and the December futures contract rallies to 5620.Youknow thatyourcallpositionhasmadeaprofit,andwhileawaitingaprice quote (and a possible change in the tabloid’s editorial policy), youdecidetoevaluatetheeffectofthemarketmoveonyourcall’sGreeks.HowwilltheybeaffectedbythechangeintheDecemberfuturescontract?
(a)delta(b)gamma(c)vega(d)theta
5. Coca-Colaiscurrentlytradingat52.67.TheJanuaryoptionshave60daysuntilexpirationandtheDecemberoptionshave30daysuntilexpiration.Iseachofthefollowingstatementstrueorfalse?
(a) If the impliedvolatility increases, then thedeltaand thetaof theJanuary47.50putwillalsoincrease.(b)Iftheimpliedincreases,thenthegammaoftheJanuary57.50callwillincrease,andthevegawilldecrease.(c)Iftheimplieddecreases,thenthevegaoftheDecember52.50callwilldecrease.(d)Iftheimplieddecreases,thenthegammaanddeltaoftheJanuary47.50callwillincrease.
6. Underwhatcircumstancescananincreaseintheimpliedcauseanincreaseinanout-of-the-moneyoption’sgamma?
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7. SupposetheS&P500indexisat1030,andyouarelonganumberof975puts. The chairman of theUSFederal Reserve bank,who is liked by thefinancial markets, announces that he is to retire when his term expires.Whatmayhappentotheimpliedvolatilityofyourputoptions?
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Chapter15answers
1. (a)decrease(b)increase(c)decrease(d)increase
2. (a)practicallyunchanged(b)increase(c)decrease(d)increase
3. (a)Purchaseputsonastockindexand/oreurodollars.(b)i)ATMputsprovidemorecoverageperoption.ii)ATMputsrespondmoretomarketmovement.iii)ATMputsaremoresensitivetoanincreaseordecreaseintheimplied.iv)OTMputscostlessintimedecay.(c)i)Nodifference. ii) Near-term has greater gamma, it respondsmore tomarketmovement.iii)Not-so-nearismoresensitivetochangeintheimplied.iv)Near-termcostsmoreindailytimedecay.(d)i)60-dayhaslargerdelta,thereforemorecoverageperoption.ii)30-dayhasgreatergamma.iii)60-dayismoresensitivetochangeintheimplied.iv)30-daycostsmoreindailytimedecay.
4. (a)Increased.(b) Practicallyunchangedbecause the call is nowas equally far in-the-moneyasitwasformerlyout-of-themoney.
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(c)Unchanged,fortheabovereason.(d)Unchanged,fortheabovereason.
5. (a)True.(b)False,thegammawilldecreasebutthevegawillincrease.(c)False,itwillremainpracticallyunchanged.(d)True.
6. Iftheimpliedisincreasingfromaverylowlevelthenthegammasofthefarout-of-the-moneyoptionswillincrease.
7. If his retirement is unexpected, then the implied may increase due touncertainty; ifhis retirement isexpected, then the impliedwillmost likelyremainunchanged.
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Chapter21questions
1. Given the following set of FTSE December European-style options,calculate the price of the missing call or put using the put–call parityformulas.FTSEDecemberfuturescontractat5470
(a)December5325put(b)December5475call(c)December5525call(d)December5725put
2. Given the following May options on Marks and Spencer, determine thepriceofthesyntheticfuturescontractandthepricesofthemissingoptions.Bear in mind that these are settlements and that there can be smalldiscrepanciesbetweentheirvaluesandthesyntheticthattheyequal.M&Sat350.60Mayoptionswith75daysuntilexpiry
(a)Maysyntheticfuturescontract(b)Mayput(c)May340call(d)May360put(e)May370call
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Chapter21answers
1. (a)306.5–5470+5325=161.5(b)5470–5475+217=212(c)5470–5525+238.5=183.5(d)97.5–5470+5725=352.5
2. (a)15.75–14.75+350=351(b)28.50–351+330=7.50(c)351–340+10.00=21.00(d)11.00–351+360=20.00(e)351–370+26=7.00
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Chapter22questions
1. SupposethecurrentBankofEnglandinterestrateis3percent.(a) With37daysuntilexpirywhatisthepriceofaDecember1,000point box in the FTSE-100 European-style options? (Hint: the boxtradesatadiscount.)(b)Supposeyouwanttoborroworlendmoneyforthenext37daysattheabove rate in theFTSEoptionsmarket.What strategy,boughtorsold,wouldenableyoutotrademoneyatapproximately3percent?(c)TheDecemberFTSEfuturescontractistradingat5470,andthreelegsofthe4975–5975boxaretradingasindicatedbelow.Whatisthepriceofthefourthleg?FTSEDecemberfuturesat5470
Strike
4975.0
5975
Decembercalls
572.5
35.5
Decemberputs
81.0
?
2. The purpose of the following questions is to help you understand howconversions and reversals form the basis of bid–ask spreads, ormarkets,foroptions.M&Sat350.60Mayoptions,75daysuntilexpiryBankofEnglandrateat0.50percent
Strike
350.00
Januarycallstheoreticalvalue
15.75
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Januaryputstheoreticalvalue 14.75
(a) What is the value of theMay synthetic future, andwhy is it sovalued?(b)Toberealistic,thereisprobablyabid–askmarketforMarksandSpencer of 350–351 and the spread is certain to increase duringvolatilemarkets.InordertopricetheMay350conversion,themarketassumesthatthesharesareboughtat351.Atwhatpricemustthecallandputbetradedinordertobreakeven,ormakeasmallprofitonthecostofcarryontheshares?(c) Now determine themarket price ofMay 350 reversal.Here thesharesmust be sold at 350.Atwhat pricesmust the call and put betraded in order to break even, or make a small profit on the cashincomefromtheshares?(d)IfthepricesintheoptionsmarketscorrespondtothecurrentBankofEnglandrate,whatwouldbetheminumumbid–askmarketsfortheMay350callsandputs?
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Chapter22answers
1. (a)1000×0.03×37/360=3pointsdiscountfrom1,000.Theboxispricedat1,000–3=997.Themarket for thebox isprobably995–999.(b)PurchaseboxesintheFTSEtolend,sellboxestoborrow.(c)997=(572.5–81)–(35.5+?)?=997–572.5+81+35.5(d)?=541
2. (a)350+15.75–14.75=351.The£0.40priceabovetheshockisduetothecostofcarryontheshockfor75days:350.60+(350.60×0.005×75/365)=0.36,tradedat0.40.(b)Thesyntheticmustbesoldat£0.40overtheaskpriceofthestockinorder to recoup thecostofcarry.Bearing inmind that theoptionscontract trades in multiples of 0.25, the synthetic must be sold at351.50.This ispossible if thecall issoldat16.00,and14.50 ispaidfortheput.(c) Ifthereturnonasaleofthestockis0.50percent,thennomorethan £0.40 must be paid for the synthetic over the bid price of thestock.Bearinginmindthattheoptionscontracttradesinmultiplesof0.25, thesyntheticmustbe tradedat350.25.Therefore15.25willbepaidforthecall,whiletheputwillbesoldat15.00.(d)Callmarketis15.25–16.00Putmarketis14.50–15.00
____________1ArecentpriceofUnileveris1961p.Ifyouwish,youcansubstituteanothershareatthispricelevel.Exampleslikethisarewhythisbookisusedinuniversitycourses.
2Anothergreatexample.Overlooktheformerprices,orsubstituteothershares,andyou’lllearnagreatdeal.
3Asifyourmortgagelenderhasanybusinessspeculatingincommodities.
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Glossary
Thefollowingglossaryisbestusedasaquickreminderofbasicoptionsdefinitions.Alternatively,itmaybeusedasasourceofjargonforsmalltalkatwinebars.(Makesureyou’reoverheard.)Itisnosubstituteforproperlearning.
AmericanstyleAnAmerican-styleoptioncanbeexercisedatanydateduringthelifeoftheoption’scontract.
AsymmetricspreadAspreadwhosestrikesarenotequidistant.
At-the-money(ATM)Callsandputsclosesttotheunderlying.
BearcallspreadShortcallspread.
BearputspreadLongputspread.
BoxAlongboxisalongsyntheticplusashortsyntheticatahigherstrike.Ashortboxhastheoppositelong/shortposition.
BrokenspreadAnasymmetricspread.
BullcallspreadLongcallspread.
BullputspreadShortputspread.
ButterflyAlongcallbutterflyisalongonebytwocallspreadplusalongcallatathird,higherstrike.Allstrikesareequidistant.Alongputbutterflyisalongonebytwoputspreadplusalongputatathird,lowerstrike.Again,allstrikesareequidistant.Forshortsofthesespreads,reversethelong/shortpositions.
CalendarspreadAlongcalendarspreadisalongoptionplusashortoptionthatisclosertoexpiration.Bothoptionshavethesamestrike.
CallAcalloptionistherighttobuytheunderlyingassetataspecifiedpriceforaspecifiedtimeperiod.Thecallbuyerhastheright,butnottheobligation,tobuytheunderlying.Thecallsellerhastheobligationtoselltheunderlyingatthecallbuyer’sdiscretion.
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CallspreadAlongcallspreadisalongcallplusashortcallatahigherstrike.Ashortcallspreadistheopposite.
ChristmastreeSeeLadder.
ComboAlongout-of-the-moneycallplusashortout-of-the-moneyput,orviceversa.Thisisalsoknownasthecylinder.Theshortcall,longputversionisalsoknownasthefence.Occasionallythistermappliestothesyntheticunderlying.
CondorAlongcallcondorisalongcallspreadplusashortcallspreadathigherstrikes.Allstrikesareequidistant.Alongputcondorisalongputspreadplusashortputspreadatlowerstrikes.Again,allstrikesareequidistant.
ConversionAlongunderlyingplusashortsynthetic.
CoveredwriteAlongunderlyingplusashortout-of-the-moneycall.Thisisalsoknowasthebuy-write.
CylinderSeeCombo.
DeltaTherateofchangeofanoptionwithrespecttoachangeintheunderlying.
DeltaneutralAnycombinationofoptionsandanunderlyingpositionwhosedeltasumispracticallyzero.
Delta/priceratioThepercentthatanoption’svaluechangeswithrespecttoachangeintheunderlying.
DiagonalspreadAlongdiagonalisalongoptionplusashortoptionthatisclosertoexpirationandfurtherout-of-the-money.
EuropeanstyleAEuropean-styleoptioncanonlybeexercisedatexpiration.
ExtrinsicvalueSeeTimepremium.
FenceSeeCombo.
FutureAcontracttobuyorsellaphysicalassetataspecifiedpriceataspecifiedfuturedate.Thisassetcanbeacommodity,bondorstock.Inthecaseofastockindex,thecontractisforacashvalueofallthestocksthatcomprisetheindex.
GammaTherateofchangeofthedeltawithrespecttoachangeintheunderlying.
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HybridspreadAspreadcombinationthatisnotoneofthestandardspreads.
In-the-money(ITM)Apartfromat-the-moneyoptions,callsbelowtheunderlyingandputsabovetheunderlying.
IntrinsicvalueTheamountthatanoptionisinthemoney,ortheparitycomponentofanin-the-moneyoption.
IronbutterflyAlongironbutterflyisalongstraddleplusashortstranglewithallstrikesequidistant.Ashortironbutterflyhastheoppositelong/shortposition.
IroncondorAlongironcondorisalongstrangleplusashortstranglethatisfurtheroutofthemoney.Ashortironcondorhastheoppositelong/shortposition.
LadderAlongcallladderisalongcallspreadplusashortcallatathird,higherstrike.Usuallyallstrikesareequidistant.Alongputladderisalongputspreadplusashortputatathird,lowerstrike.Again,allstrikesareusuallyequidistant.AlsoknownastheChristmastree.
LeverageTherightorobligationtotradethefullvalueoftheunderlyingbytradingonlythevalueoftheoption.
LongTobelongistoown.Alongfuturescontractownsacashorphysicalassetwhenthecontractexpires.Alongoptionscontractownstherighttobuy,foracall,ortherighttosell,foraput.
LongdeltasAnycombinationoflongcalls,shortputsandlongunderlying.
MarginCashorliquidsecuritydepositedbyholdersoffuturesoroptionscontracts.
MultiplierPartofacontractspecification:thecashamountbywhichafuturesoroptionsvalueismultiplied.
NakedAshortoptionnotspreadwithalongoptionorunderlying.
OnebytwoAlongonebytwocallspreadisalongcallplustwoshortcallsatahigherstrike.Alongonebytwoputspreadisalongputplustwoshortputsatalowerstrike.
Out-of-the-money(OTM)Apartfromat-the-moneyoptions,callsabovetheunderlyingandputsbelowtheunderlying.
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ParityAnin-the-moneyoptionwithnotimepremiumthatconsequentlyhasa100percentcorrelationwiththeunderlying.
PinriskTheriskofanunderlyingclosingexactlyattheoptionsstrikepriceatexpiration.Theriskliesprimarilywiththeshortoptionholderbecauseheisuncertainofassignment.
PutAputoptionistherighttoselltheunderlyingassetataspecifiedpriceforaspecifiedtimeperiod.Theputbuyerhastheright,butnottheobligation,toselltheunderlying.Theputsellerhastheobligationtobuytheunderlyingattheputbuyer’sdiscretion.
PutspreadAlongputspreadisalongputplusashortputatalowerstrike.Ashortputspreadistheopposite.
ReversalShortunderlyingpluslongsynthetic.
RhoThechangeofanoption’svaluethroughachangeintheinterestrate.
ShortToshortistosell.Ashortfuturescontractsellsacashorphysicalassetwhenthecontractexpires.Ashortoptionscontractsellstherighttobuy,foracall,ortherighttosell,foraput.
ShortdeltasAnycombinationofshortcalls,longputsandshortunderlying.
StoporderAnordertobuyorsellatthemarketpricewhenamarketreachesapre-specifiedpricelevel.
StraddleAcallplusaputatthesamestrike,botheitherlongorshort.
StrangleAnout-of-the-moneycallplusanout-of-the-moneyput,botheitherlongorshort.
StrikepriceThepriceoftheunderlyingthatformsthebasisofanoptionscontract.
SyntheticcallAlongsyntheticcallisalongputplusalongunderlying.Ashortsyntheticcallisashortputplusashortunderlying.
SyntheticputAlongsyntheticputisalongcallplusashortunderlying.Ashortsyntheticputisashortcallplusalongunderlying.
SyntheticunderlyingAlongsyntheticisalongcallplusashortputatthesamestrike.Ashortsyntheticisashortcallplusalongputatthesamestrike.
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Sometimesreferredtoasthecombo.
ThetaTheamountthatanoptiondecaysinoneday.
Theta/priceratioThepercentofanoption’svaluediminishedbyoneday’stimedecay.
TimedecayThedeclineinanoption’svaluethroughalloraportionoftheoption’slife.Usuallyexpressedastheta.
TimepremiumThepremiumapartfromintrinsicvalueofanoption.Theamountofanoption’svaluethatcorrespondstovolatilitycoverage.
TimespreadSeeCalendarspread.
UnderlyingAnassetuponwhichanoption’svalueisbased.Thiscanbeastockorstockindex,bond,commodityorfuturescontract.
VegaTheamountthatanoptionchangesthrougha1percentchangeintheimpliedvolatility.
Vega/priceratioThepercentthatanoption’svaluechangesthrougha1percentchangeintheimpliedvolatility.
VerticalspreadAcallorputspread.
VolatilityAone-day,onestandarddeviationmove,annualised.
Volatility,historicalVolatilityaveragedoveratimeperiodsuchas10,20or30days.
Volatility,impliedThevolatilitythatisimpliedbyanoption’sprice.InthecaseofanATMoption,thisistheexpectedhistoricalvolatilityoftheunderlyingthroughexpiration.
VolatilityskewApatternofimpliedvolatilityvariationsexhibitedbyin-the-moneyandout-of-the-moneyoptions.
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Furtherreading
Therearenowmanyhelpfulbooksonoptions,andbelowareafewthatcanberecommended.Alsoincludedarebooksofamoregeneralinterestinordertohelpyoumaketradingdecisions.Theyallare,orwillbe,classics.Thelistislimitedbecauseyourtimeislimited,andyourpriorityistotaketheshortestroutetoamoreadvancedlevel.
TechnicalbooksOptionVolatilityandPricing(1994)bySheldonNatenberg,McGraw-Hill.Anexcellentnextstep
Options,FuturesandOtherDerivatives(2009)byJohnHull,PrenticeHall.Anotherclassic.Forthosewithanadvancedmathematicalbackground
PaulWilmottIntroducesQuantitativeFinance(2007)byPaulWilmott,JohnWiley&Sons.Heavyonthemaths,butreadable.Wilmottisasuper-quant.
TechnicalAnalysisoftheFinancialMarketsbyJohnJ.Murphy,NewYorkInstituteofFinance.Thoroughandreadable
AnIntroductiontotheGlobalFinancialMarkets(2010)byStephenValdez,andPhilipMolyneux,PalgraveMacmillan.Afirst-rateintrotothisbusiness.
OptionsPlainandSimple(2000)byLennyJordan,PrenticeHall.Aclassic,generallyagreed.Sometradershavereaditthreetimes.Justgetoverthefractions.
BooksabouttradingTheGamblerbyF.M.Dostoyevsky(variouseditions).Toknowthedifferencebetweentradingandgambling.
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ReminiscencesofaStockOperator(2004)byWilliamJ.O’NeilandEdwinLefevre,JohnWiley&Sons.Aclassic,formarketawarenessaboutstockmanipulators.
TheBigCon(2000)byDavidW.Maurer,Arrow/RandomHouse.Writteninthe1930s.AnyoneinvolvedintheBernieMadoffscandalcouldreadthisandweep.Therestofyoushouldreaditbeforeyoucontractafinancialadviser.
Traders’websitewww.nakedtrader.com
Mostlyaboutcashfuturestrading,butveryhelpfulwithtechnicalanalysis.Itwillalsobringyouintothemindofthetrader.
Andfinally…
TheMeditationsofMarcusAurelius(variouseditions).Advicefromabattle-hardenedemperor.Stoicismwillhelpyoumanageyourself.
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Index
Pagenumbersinboldindicateaglossaryentry.
agriculturalcommoditiesAmerican-styleoptions,2nd,3rd,4th,5th,6thboxes,tradingput–callparityanalysisofatradearbitrage,2nd,3rdasymmetricorbrokenladder,2ndlongironbutterflyat-the-money(ATM),2nd,3rd,4thboxes,tradingcalendarspread,2nd,3rddelta,2nd,3rd,4th,5thdeltapriceratios,2nddeltavsgamma,thetaandvegaearlyexercisepremiumgamma,2nd,3rdimpliedvolatilityvsGreekslongat-the-moneycallbutterfly,2ndlongat-the-moneycallcondorlongat-the-moneyputbutterflylongat-the-moneyputcondorlongdiagonalcallspreadlongironbutterflylongstraddle,2nd,3rdpinrisk,2nd,3rdshortat-the-moneycallandputbutterfliesshortstraddletheta,2nd,3rdtimedecay,2nd
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timepremium,2ndvega,2nd,3rd,4th,5thVIXvolatilityskews,2nd,3rd,4th,5th,6th,7th,8th
bearspreads,listofbear/longputspread,2nd,3rd,4th1×1sandvolatilityskewsshortvslongstrikesbear/shortcallspread,2nd,3rdlongvsshortstrikesbellcurve,2ndBlack-Scholesmodel,2nd,3rdbondsfuturescontractsvolatilityskews,2nd,3rd,4thboxescostofcarryonlong,2ndshort,2ndtradingbreak-evenlevelcalls,2ndcondorwithnon-adjacentstrikescoveredwrite,2nd,3rdhybridspreads,2nd,3rdlong1×2callspreadlong1×2callspreadforacreditlong1×2putspreadlongat-the-moneycallbutterflylongat-the-moneycallcondorlongat-the-moneyputbutterflylongat-the-moneyputcondorlongcall,shortputcombolongcallspreadlongironbutterfly
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longironcondor,2ndlongladder/Christmastree,2nd,3rd,4thlongout-of-the-moneycallbutterflylongout-of-the-moneycallcondorlongout-of-the-moneyputbutterflylongout-of-the-moneyputcondorlongput,shortcallcombo,2ndlongputspreadlongstraddle,2ndlongstrangleputs,2nd,3rd,4thshortat-the-moneycallcondorshortcallspreadshortironbutterfly,2ndshortironcondor,2ndshortputspreadshortstraddleshortstrangle,2ndbrokenorasymmetricladderlongironbutterflybullspreads,listofbull/longcallspread,2nd1x1sandvolatilityskewsshortvslongstrikesbull/shortputspread,2nd,3rdlongvsshortstrikesbutterfly,2nd,3rdadditionalriskswithadvantagesironseeseparateentrylongat-the-moneycalllongat-the-moneyputlongout-of-the-moneycalllongout-of-the-moneyputnon-adjacentstrikesshortat-the-moneycallandput
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takeagiftvolatility,datesuntilexpirationandbuy-stop,2nd,3rdbuy-writeriskmanagement
calendarspread,2nd,3rdriskscallsat-the-money,2nd,3rd,4thbuyingcommoncharacteristicsofputsandcomparisonofputsandeverydayexamplein-the-money,2nd,3rdlongpositionmisconceptionsnaked,2ndofferingout-of-the-money,2nd,3rdowningproblemssellingshortpositionsummarycashpaymentdividends,interestratesandmarginvsChicagoBoardOptionsExchange(CBOE)contractmultiplierEuropeanandAmericanstyle,2ndSPDR(‘Spider’),2ndSPXoptions,2nd,3rd,4thVixChicagoBoardofTrade(CBOT)exerciseandassignmenttermsusedforspreadsChristmastreesseeladderscollar
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combolongcall,shortputlongput,shortcallcommodities,2ndfuturescontracts,2ndproblemsvolatilityskews,2nd,3rd,4thcommonproblemswithcallandputpositionscondor,2nd,3rdadvantagesironseeseparateentrylongat-the-moneycalllongat-the-moneyputlongout-of-the-moneycalllongout-of-the-moneyputnon-adjacentstrikesshortat-the-moneycallshortat-the-moneyputvolatility,datesuntilexpirationandcontingencyplancontractliquidityandmarketmakingcontractmultiplier,2ndconversion,2ndreverse,2ndcostoftrading,2ndpricemovementtimevolatilitycoveredwrite,2ndriskmanagementcrises,2nd,3rdemergingmarket(1997)currenciesfuturescontractscylinderseecombo
delta,2nd
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calendarspread,2nddefinitionandexamplesequivalencetounderlyinghedgeratioimpliedvolatilitychangesimpliedvolatilityvslong1x2spreadslongstraddleneutral,2ndpriceratio,2ndprobabilitysummarytimeandtimedecay,2ndvsgamma,thetaandvegadiagonalcallspreaddirection,marketlongandshortdividends,2ndfuturescontractsmarginvscashpayment,interestratesanddurationaloutlook,2nd
earlyexercisepremium,2ndemergingmarketcrisis(1997)ESXoptionsEurodollars,2nd,3rdvolatilitycalculationEuropean-styleoptions,2nd,3rd,4th
fence,2ndfixedamounttoinvestconclusionsdeltapriceratio,2nd,3rdthetapriceratio,2nd,3rdtwoapproachesvegapriceratio,2nd
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FTSEEuropean-styleoptionscontract,2ndFTSE-100,2nd,3rdfuturescontractexampleinitialmarginsyntheticseeseparateentryvaluationformulavariationmarginfuturesoptionsearlyexercisepremiumexerciseandassignmentmarginvscashpaymentpinrisk,2nd
gamma,2nd,3rddefinitionandexamplesdeltaversusimpliedvolatilityvslongstraddle,2ndpositiveandnegative,2ndshortstraddlestrangle,2ndtimeandvolatilitytradingGreeksdeltaseeseparateentrydeltavsgamma,thetaandvegagammaseeseparateentryimpliedvolatilitychangesimpliedvolatilityvslongironbutterflyoptionscalculatorotherrho,2ndspreads,2nd,3rd,4ththetaseeseparateentrytimeand
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vegaseeseparateentry
hedgeratiohybridspreads,2ndin-the-money(ITM),2nd,3rdboxes,tradingbutterfly,2nd,3rdcostofcarrydiscountdelta,2nd,3rd,4th,5th,6thdeltapriceratios,2ndearlyexercisepremiumgamma,2nd,3rdimpliedvolatilityvsGreeks,2ndlongat-the-moneyputbutterflylongandshortspreads,2ndpremium,2ndput–callparitytheta,2nd,3rdtimedecay,2ndvega,2nd,3rdinterestratecontracts,long-terminterestratecontracts,short-termcashsettledcontracts,2nd,3rdvolatilitycalculationinterestratescalendarspreads,2ndimpliedvolatilitymarginvscashpayment,dividendsandrho,2ndintrinsicvalue,2ndironbutterfly,2ndlong,2nd,3rdlongbrokenshort,2ndironcondor,2ndlong,2ndshort,2nd
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laddersasymmetricorbrokencomparingcallspreads,1x2sanddifferentstrikepriceslongcalllongputriskmanagementleverage,2ndLIFFEEuropean-styleoption,2ndmarginonfuturesoptionstermsusedforspreadslong1×2callspread,2nd,3rdcallspreadforacredit,2nd,3rdputspread,2ndlongat-the-moneycallbutterflycallcondorputbutterflyputcondorlongbox,2ndlongcalendar/timespread,2ndriskslongcallbutterflylongcallcondorlongcallladder/Christmastreeasymmetricorbrokenladdercomparingcallspreads,1×2sandladdersdifferentstrikepricesriskmanagementlongcallspread,2nd1×1sandvolatilityskewsbullishstrategyshortvslongstrikeslongdiagonalcallspreadlongironbutterfly,2nd,3rdlongironcondor,2nd
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longout-of-the-moneyadditionalrisksofbutterflycallbutterflycallcondorputbutterflyputcondortakeagift:butterflylongposition,2nd,3rdlongputbutterflylongputcondorlongputladder/Christmastreeasymmetricorbrokenladdercomparingcallspreads,1×2sandladdersdifferentstrikepricesriskmanagementlongputspread,2nd,3rd1×1sandvolatilityskewsbearishstrategyshortvslongstrikeslongstraddle,2ndlongstrangle
marginfuturescontracts:initialandvariationinterestrates,dividendsandcashpaymentvsmarketdirectionlongandshortmarket-makerscontractliquiditydeltaneutral,2ndputs,2ndshortat-the-moneybutterfliesshortat-the-moneyputcondorssyntheticpositionstradingboxesmisconceptionscallandputpositions
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models,pricing,2ndvolatilityseeseparateentrymonthlyresultsmultiplier,2nd,3rd
nakedsellingcalls,2ndsellingputs
OEXboxes,tradingbutterflies,2nd,3rdcalendarspreads,2ndcashsettledcontractscondorsandbutterflieswithnon-adjacentstrikesconversionandreversalsearlyexercisepremiumput–callparityvolatilityskews,2ndonebyonedirectionalspreads,2ndcomparingcallspreads,1x2sandladdersonebytwodirectionalspreadscomparingcallspreads,1x2sandladderslong1×2call,2nd,3rdlong1×2callspreadforacredit,2nd,3rdlong1×2put,2ndlongcallladder/Christmastree,2ndlongputladder/Christmastreeriskmanagement,2ndoptionscalculatorout-of-the-money(OTM),2nd,3rd,4th,5thcalendarspread,2nddelta,2nd,3rddeltapriceratios,2nddeltavsgamma,thetaandvegaearlyexercisepremiumfixedamounttoinvest,2nd
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gamma,2nd,3rdimpliedvolatilitychangesimpliedvolatilityvsGreeks,2ndinterestratecomponentofpricelong1×2spreadslongat-the-moneycallbutterflylongcall,shortputcombolongdiagonalcallspreadlongironcondorlongladder/Christmastree,2ndlongout-of-the-moneycallbutterflylongout-of-the-moneycallcondorlongout-of-the-moneyputbutterflylongput,shortcallcombolongandshortspreads,2ndlongstrangleshortironbutterflyshortironcondortheta,2nd,3rdtimedecay,2ndtimepremium,2ndvega,2nd,3rd,4thvolatilityskews,2nd,3rdoutlook,durational,2nd
parity,2ndpatiencepinrisk,2nd,3rd,4th,5th,6thportfolioinsurancepremiumdeltaandtimedecayearlyexercise,2ndtimedecayseeseparateentrypricingandbehaviourBlack-Scholesmodel,2nd,3rdearlyexercisepremiumEuropeanvsAmericanstyleexerciseandassignment
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interestrates,dividendsandmarginvscashpaymentintrinsicvalue,2ndlongandshortoptionspositionsmodels,2ndpinrisk,2nd,3rd,4th,5th,6thpremium,2ndpricelevelsriskplantimepremium,2ndseealsodelta;gamma;theta;vega;volatilityandpricingmodelsprobabilitydeltaand,2ndthetaand,2ndproblemswithcallandputpositionsput–callparityputsat-the-money,2nd,3rdbuyingcommoncharacteristicsofcallsandcomparisonofcallsandeverydayexample3in-the-money,2ndlongpositionmisconceptionsout-of-the-money,2ndproblemssellingsellingnakedshortpositionshortputspreadstrategysummary
restingbuyordersellorderreversal,2nd,3rd,4th
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rho,2ndrisk/returnpotential,2nd,3rd,4th,5thbuyingacallbuyingaputcalendarspread,2ndcalls,2nd,3rdcondorwithnon-adjacentstrikescontingencyplancoveredwrite,2ndGreeksseeseparateentryhybridspreads,2ndlong1×2callspreadlong1×2putspreadlong1×2spreadslongat-the-moneycallbutterflylongat-the-moneycallcondorlongat-the-moneyputbutterflylongat-the-moneyputcondorlongcallladder/Christmastree,2ndlongcall,shortputcombolongcallspreadlongironbutterfly,2ndlongironcondorlongout-of-the-moneycallbutterflylongout-of-the-moneycallcondorlongout-of-the-moneyputbutterflylongout-of-the-moneyputcondorlongputladder/Christmastree95,longput,shortcallcombolongputspreadlongstraddlelongstrangleplantocoverrisk,2ndputs,2nd,3rdsellingacallsellingaputshortat-the-moneycallcondorshortat-the-moneycallandputbutterfliesshortcallspread
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shortironbutterfly,2ndshortironcondorshortputspreadshortstraddle,2ndtimedecay,2ndvolatility,2nd
seasonalvolatilitytrendssellstopordershortat-the-moneycallcondorcallandputbutterfliesputcondorshortbox,2ndshortcallspread,2ndlongvsshortneutraltobearishstrategystrikesshortironbutterfly,2ndshortironcondor,2ndshortposition,2nd,3rdshortputspread,2ndlongvsshortneutraltobullishstrategystrikesshortsterlingcontracts,2ndshortstraddle,2ndshortstrangleSPDR(‘Spider’),2ndspreadingrisk,2ndlistofspreadstermstouseSPXoptions,2nd,3rd,4thstartingtotradeadvice,2ndlistofspreadsspreadingriskstationary
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definitionoflistofspreadsstockindexesbutterfly,2ndcalendarspreads,2ndcashsettledcontracts,2nd,3rdcommonproblemsconversionandreversalsearlyexercisepremiumfuturescontracts,2ndinterestrates,dividendsandmarginvscashpaymentvolatilityskews,2nd,3rd,4th,5thstockoptionscalendarspreads,2ndcommonproblemsconversionandreversalsearlyexercisepremiumexerciseandassignmentinterestrates,dividendsandmarginvscashpaymentpinrisk,2ndput–callparitysynthetic/combovolatilityskews,2ndstop-losscalls,2ndlongput,shortcallcomboshortcallspread,2ndshortironbutterflyshortputspreadstraddlelong,2ndshort,2ndstrangle,2ndlongshortstrikeprices,2nd,3rdcallandputspreadsladdersatdifferentsubstitutiontrades
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syntheticfuturescontractlongcallpositionlongputpositionput–callparityputs,2nd,3rd,4thshortcallpositionshortputposition,2ndstockoptions
takeoverstechnicalanalysis,2ndtermstouseplacingspreadorderstheta,2nd,3rddefinitionandexamplesdeltaversusimpliedvolatilityvslongstranglepriceratio,2ndshortstrangletimeanduseandabuseoftimedecay,2nddelta,2ndgamma,2ndshortstrangletheta,2nd,3rdtimepremium,2nd,3rdtimespread,2nd,3rdriskstradingoptionsbuyinganoptiondurationaloutlook,2ndoptionsvsbasispointssellinganoptiontermstousetradingdeltaandtimedecay
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tradingvolatilitytrendsvolatilityskews,2nd
underlyingasset,2nd,3rd,4th
vega,2nd,3rd,4thcalendarspread,2nddefinitionandexamplesdeltaversusimpliedvolatilitychangesimpliedvolatilitytrendsimpliedvolatilityvslong1×2spreadslongstraddlelongstranglepositiveandnegativepriceratiorisk/returnofshortstrangletimeandverticalspreads,2ndVIXvolatilemarketspreads,listofvolatilityandpricingmodels,2ndbellcurve,2ndcomparinghistoricalandimpliedvolatilityconventionalusagehistoricalvolatilityofunderlying,2ndimpliedvolatility,2nd,3rdnuma.comvolatilityskews,2nd,3rd,4th,5th,6th1×1sand,2ndat-the-moneyimpliedvolatilityvsbonds,2nd,3rdcallskew,2nd,3rd,4thchangeofdegreecommodities,2nd,3rd,4th
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expiration,behaviourtowardsinterestratecontracts,long-termmarketsentimentputskew,2nd,3rd,4th,5threasonsforstockindexes,2nd,3rd,4thstockstrading,2ndtradingoptionsonlinearskewtradingoptionsonpositiveskewunderlying,shiftwithverticalshiftvolatilityspreads,2nd,3rddefinitionsofvolatileandstationarygamma,2nd,3rd,4thlongstraddle,2ndlongstranglemarketvolatilityshortstraddle,2ndshortstrangletheta,2nd,3rdvega,2nd,3rd,4thvolatilitytrendsseasonaltrading
weeklyormonthlyresults
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