The Financial Times Guide to Options: The Plain and Simple Guide to Successful Strategies
Transcript of The Financial Times Guide to Options: The Plain and Simple Guide to Successful Strategies
Contents
PrefaceAboutthisbookAbouttheauthorAcknowledgementsIntroduction
PART1OPTIONSFUNDAMENTALSIntroduction1Thebasicsofcalls2Thebasicsofputs3Pricingandbehaviour4Volatilityandpricingmodels5TheGreeksandriskassessment:delta6Gammaandtheta7Vega
PART2OPTIONSSPREADSIntroduction8Callspreadsandputspreads,oronebyonedirectionalspreads9Onebytwodirectionalspreads10Combosandhybridspreadsformarketdirection11Volatilityspreads12Ironbutterfliesandironcondors:combiningstraddlesandstranglesforreducedrisk13Butterfliesandcondors:combiningcallspreadsandputspreads
14Thecoveredwrite,thecalendarspreadandthediagonalspread
PART3THINKINGABOUTOPTIONSIntroduction15TheinteractionoftheGreeks16ThecostoftheGreeks17Optionstalk1:technicalanalysisandtheVix18Optionstalk2:tradingoptions19Optionstalk3:troubleshootingandcommonproblems20Volatilityskews
PART4BASICNON-ESSENTIALSIntroduction21Futures,syntheticsandput–callparity22Conversions,reversals,boxesandoptionsarbitrage23Conclusions
QuestionsandanswersGlossaryFurtherreadingIndex
Thisbookisdedicatedtothememoryofmyparents
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.
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.
Whileitisimpossibletocoachaninvestoratadistance,itispossibletorecountmanyofthesituationsthatoftenariseinthemarketplace,andtodiscusswaysofapproachingthem.InthisneweditionIhaveaddedmanyexamplesofpracticalapplications,orasitwere,scenariosoranecdotes.
Themathematicsinthisbookinvolveonlyaddition,subtraction,multiplicationanddivision.Thesefourfunctionsplusapricingmodelareallthatweprofessionalsuseinordertotrademostoftheoptionsproductsonthemajorexchanges.
Thefocusofthisbookisoptions:itisnotacomprehensiveguidetotrading.Asprofessionaltradersknow,tradingtechniqueisonlygainedthroughexperience.Forthis,youshouldengageaprofessionaladvisertohelpyoutodecidethebeststrategiestouse.Orbetteryet,[email protected].
Abouttheauthor
LennyJordanhastrainedcountlesstradersintheoptionsmarketsofChicagoandLondon.Hewasamarket-makerattheChicagoBoardofTrade(CBOT)andattheLondonInternationalFinancialFuturesandOptionsExchange(LIFFE).HenowlecturesforLondon-basedexchangesandinternationalbanks.Hecanbecontactedatlenny@lennyjordan.com.
Acknowledgements
Theauthorwouldliketothankthefollowingfortheirassistance:
TheChicagoBoardofTradeandtheChicagoMercantileExchange(CBOTandCME)TheChicagoBoardOptionsExchange(CBOE)TheLondonInternationalFinancialFuturesandOptionsExchange(LIFFE)EurexandDeutscheBorsePMPublishingwebsite(pmpublishing.com).MartyO’Connell,oneofthegreattrainers
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.
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.
part1
Optionsfundamentals
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
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
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.
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.
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.
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
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
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).
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
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
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.
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.
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
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.
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.
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
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
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.
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.
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
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
reasonably,thetimeuntilexpiration.Along-termhedgewillcostmorethanashort-termhedge.Timedecay,however,isnotlinear.Figure3.1illustratesthatanoptionlosesitsvalueatanacceleratingrateasitapproachesexpiration.
Figure3.1Valueofoptionwithrespecttotime
Anotherwayofstatingthisisthattheproportionofanoption’sdailytimedecaytoitsvalueincreasestowardexpiration.UsingtwooptionsbasedonCornfutures,Table3.2illustratesthisinpercentageterms.
Table3.2DecemberCorncalls2
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
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
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
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
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
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
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
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.
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.
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
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
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
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:
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
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
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.
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
volatilitycananticipateanincreaseinthehistoricalvolatility.
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,
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
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
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%
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
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(–)
isusedtorefertoaputdelta.Thispracticeconfusestheprocessofcalculatinganetdeltaposition;itisnotusedinthisbook.
3Buy,orgolong,threeunderlyingcontracts.
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-
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
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
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:
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
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
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
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.
Vega
Ofteninanoptionsmarketcircumstancesarisethatcausethevolatilityoftheunderlyingtoincreaseordecreasesuddenly.Thismaybetheresultoftheinceptionorconclusionofanunforseenmarketevent.Duringsuchcircumstancestheimpliedvolatilityofeachoptionscontractmonthreactstoadifferentdegree,andthisinturnaffectsthepriceofeachoptionofeachcontractmonthtoadifferentdegree.Undertheseaswellasmoreusualcircumstancesthereisaneedtoquantifytheeffectofachangeinimpliedvolatilityonthepriceofaparticularoption.Vegaistheamountthatanoptionchangesiftheimpliedvolatilitychangesbyonepercentagepoint.
Vegaitselfcanbeexpressedineitheroptionsticksorinanactualcurrencyamount.Table7.1showsasetofoptionswiththeirvegasforonecontractmonth.Thevegasareexpressedindollarsthenroundedintoticks.
30daysuntilexpirationImpliedvolatilityat30percentInterestrateat3percent.
Anincreaseinimpliedvolatilityleadstoanincreaseinoptionspremiums,whileadecreaseinimpliedvolatilityhastheoppositeeffect.Ifthecurrentimpliedvolatilityincreasesfrom30percentto31percent,thevalueoftheDecember380callincreasesfrom12½to13.Iftheimpliedvolatilitydecreasesfrom30percentto29percent,thevalueoftheDecember380calldecreasesfrom12½to12.
Table7.1DecemberCornat$3.80×5,000bushels
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
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
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.
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.
Belowisanindexofthemajorspreads.Itwillserveasaquickreferenceinselectingstrategies.Inafewcasesthetermsthatareappliedtothesespreadsvary,butthesewillbenoted.Ifyouarefirststartingtotrade,orifthisisyourfirstreading,focusonthespreadsmarkedwithanasterisk(*),becausetheyhavetheleast,andmostmanageable,risk.
Indexofspreads
ATM=at-the-money;OTM=out-of-the-money.
Termstousewhenplacingspreadorders
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.
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.
Second,ifyouarenewtotradingoptions,donottakeapositionthatisnetshortanoptionoroptions.Therearemanywaystotradefromtheshortsidewithouttakingunlimited,orpracticallyunlimited,risk.Theyallinvolvethepurchaseofoneormorerisklimitingoptions.Eachshortoptionshouldbecoveredbyalongoption.
Itishelpfultodiscusstheprofit/losspotentialofspreadsintermsoftheirvalueatexpiration.Practicallyspeaking,however,youwillmostoftencloseaspreadbeforeexpirationbecauseyouwillnotwanttoexerciseorbeassignedtoanunderlyingcontract.Youalsodonotwantpinrisk.
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
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:
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.
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
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
*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
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
*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
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
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.
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’.
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
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.
Table9.1Coca-ColalongAugust55-60onebytwocallspread
Ingraphicform,theexpirationprofit/lossofthisspreadisasshowninFigure9.1.
Figure9.1Expirationprofit/lossrelatingtoTable9.1
LongonebytwocallspreadforacreditBearishtoslightlybullishstrategyWithadjacentstrikes,orstrikesthatareclosetoeachother,thelongonebytwocallspreadcanoftenbedoneforacredit.Effectively,then,thereisnolowerbreak-evenlevel,andthespreadwillprofitfromadownsidemarketmove.The
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):
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
Therisk/returnpotentialofthisspreadmustconsiderthatthepotentiallossisthefullamountthatthestockmaydeclinebelowthelowerbreak-evenlevel.
Intabularform,theexpirationprofit/lossisasshowninTable9.2.
Table9.2Coca-ColalongAugust50–45onebytwoputspread:Coca-Colaat52.67,100daysuntilexpiration
Ingraphicform,theexpirationprofit/lossofthisspreadisshowninFigure9.2.
Figure9.2Expirationprofit/lossrelatingtoTable9.2
Howtomanagetheriskofthelongonebytwospreads
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
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
Figure9.3isagraphofthisspreadatexpiration.
Figure9.3Expirationprofit/lossrelatingtoTable9.3
Youcancomparethisladdertothe55–60onebytwo.Itwouldcost0.75,andthebreak-evenlevelsare55.75and64.25.Themaximumprofitofthe1×2is4.25,butthisprofitlevelis60.00.Thisladderisafairalternativeintermsofrisk/return.
Longputladder(UK),orlongputChristmastree
(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
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.
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
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
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
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.
10
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
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
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.
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
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
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.
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.
2I'veevenheardofthisspreadreferredtoasthe‘collar’.Again,omitthejargon.Insteadsay‘Iwanttobuy[this]optionandsell[that]optionasaspread.’
11
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.
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
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
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
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
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
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
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.
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
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
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’.
12
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
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
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.
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
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
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
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.
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.
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
Agraphoftheexpirationprofit/lossisshowninFigure12.4.
Figure12.4Expirationprofit/lossrelatingtoTable12.4
____________1Itcanbeeasiertothinkintermsoftheriskasthenumber1.Here,youcouldcalculatetheR/Rratioas5.5/4.5=1.22,orrisking1tomake1.22.
2Theoppositesideofthistradeispreferable.
13
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
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
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
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.
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
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.
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.
*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
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
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
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.
*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
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
*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
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
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.
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
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
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
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
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.
14
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.
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
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.)
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
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
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
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
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
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
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.
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.
part3
Thinkingaboutoptions
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.
15
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
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
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.
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
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
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
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.
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
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
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.
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.
16
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
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
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
Again,thelargestpercentagetrade-offiswiththe3050calls.Theymayincreaseordecrease15.2percentoftheirvaluewitha1percentchangeintheimplied.
Forthepurposeofcomparison,thesametableoffiguresisgiveninTable16.4,butwith30DTE.
Table16.4EurostoxxJuneoptions,30DTE,Junefutureat2831
Aswemightexpectwithtimepassing,mostofthedelta/priceratios,theta/priceratiosandvega/priceratioshaveincreasedforalltheoptionsthatcontaintimepremium.Notethatthevega/priceratiofortheATMcallremainsat
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.
17
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
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
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.
18
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
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
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.
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.
OnetipIcangiveyouistokeepyourcostslow–andthatincludespersonalexpenses.Thenyou’llhavemorepatiencebecauseyou’llworrylessaboutmeetingyourmonthlyexpenses.
19
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
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.
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
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
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
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.
20
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
Source:Datacourtesyofpmpublishing.com.
InFigure20.1,thedottedlineistheactualplotoftheimpliedsfromstriketostrike,whilethesolidlinehasbeengeneratedwithanalgorithm.Sometradersusetheequationtodetermineifanoptionisundervaluedorovervalued.Thediscrepanciesasyoucanseeareverysmall.
TheATMimpliedvolatilityisthatofthe128strike,at9.44percent.Notethattheimpliedvolatilityofthe136callis9.84percent,whiletheimpliedofthe120putis10.38percent,andthatboththesestrikesareequidistantfromthe
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
money.Notealsothattheimpliedofthe500strikeis34.46percent,oralmostdoublethatoftheATMimplied.
Heretheputskewispositivewhilethecallskew,withdecreasingimplieds,isnegative.Thistypeofskewisfoundinotherstockindexoptions,suchastheFTSE.
(Personally,Irefertothistypeofskewasa‘linear’skew.Itissimplymorelinearthanaparabolicskew.Notethatthetailofthecallskewflattensout.)
Table20.2OEXDecemberoptions
Source:Datacourtesyofpmpublishing.com.
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.
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
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
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).
Figure20.6JanuaryT-BondoptionsskewSource:pmpublishing.com.
Table20.4JanuaryTreasuryBondoptions
Source:pmpublishing.com.
Skews’shiftwithunderlyingSkewsmostoftenshifthorizontallywiththepriceoftheirunderlyingcontracts.Ifanunderlyingdriftsbackandforthinarange,theskewwillmostoftenrangeaswell.Thefocalpointclingstotheat-the-moneystrike,withlittlechangetotheATMimplied.Thiseffectivelychangestheimpliedofeachstrike.
Forexample,iftheaboveMarchT-Bondcontractroseto129.01thentheimpliedsofallthestrikeswouldbelikelytoshifttothenextstrikeupward.TheJanuary129callswouldhaveanimpliedof8.14,andtheJanuary123putswouldhaveanimpliedof10.42,etc.
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
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).
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.
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
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.
part4
Basicnon-essentials
Introduction
Mostofuswon’tspendouroptionscareerstradingarbitrage,butwhentheopportunityarises,asitdoesfromtimetotime,it’sanalmostrisk-freewaytomakemoney.Soifyoulearnaboutthearb,thenyou’repreparedtotakeadvantageofitwhenyouseeit.
ReadPart4atleastonce.Thinkaboutitfromtimetotime.Whenyou’rescanningthemarkets,askyourself,‘Isthereanarbitragehere?CanIlockinaprofitwiththistradeuntilexpiration?’Ifyoukeepthisinmind,thensomedayyou’llfindyourselfmakingalotofmoneyinaveryshorttime.
Ifyou’reprepared.
21
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
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.
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.
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.
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.
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
Table21.2Profit/lossofSPZDecember1140syntheticcallatexpiration
SyntheticshortcallpositionIfinsteadXYZissoldat100,andatthesametimea100putissold,asyntheticshort100callresults.Below100theprofitontheshortunderlyingpositionandthelossontheshortputoffseteachother.Above100,alossistakenontheshortunderlyingposition.Let’sassumethattheputwassoldforfree.ThegraphatexpirationwouldbeasshowninFigure21.5.
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
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.
Figure21.7SyntheticshortXYZ100put
ReturningtoourSPZexample,iftheDecember1140callissoldat34.40,andalongpositionistakenintheunderlyingat1140.70,theresultisasyntheticshortputsoldat33.70.Theprofit/lossistheoppositeoftheabovelongsyntheticput(seeTable21.6).
Table21.6Profit/lossofshortSPZDecember1140syntheticputatexpiration
Thecomplexproblemofput–callparityTheaboveareillustrationsofput–callparity,whichtellsusthatbyknowingthevalueoftheunderlying,thestrikeprice,andeitherthecallorput,thepriceoftheunknowncallorputcanbedetermined.Theformulasfordeterminingthe
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.
22
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
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
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
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
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.
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.
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
cent,willtradeat20–(20×0.01×75/365)=19.96.
Thesaleofaboxthroughcash-tradedEuropean-styleoptionsisoftenusedasameansofshort-termfinance.Ifatradinghousewantedtoborrowmoneythenitcouldselltheabove20-pointboxat19.96.Cashwouldbecreditedtotheiraccountuntilexpiration,andthenthehousewouldpay20toclosetheposition.Commissionsandexchangefeeswouldeffectivelyraisetheborrowingratetomorethan1percent.Onlyfirmsthattradeinlargesizeandthatbenefitfromlowcostscantakeadvantageofthisopportunity,andmostoftentheyprefertoborrowandlendinthecashmarkets.
23
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
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.
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
thatsponsoredday-tradersinfuturescontactsonEuribor,Bund,FTSE,etc.Ialsogavetraininglectures.Oneofournewtraderswasafemalegraduatewhowasveryastute.Afteroneofmylecturesshewalkeduptomeandasked,‘C’monnowLenny,what’sittaketobeagoodtrader?’Ianswered,‘Supposeyourdadgaveyouahundredpounds.CouldyouwalkinandoutofHarrodswithoutspendingapenny?’Shegavemeadefiantstareandsaid,‘Mydaddygivesmetwohundredpounds!’Thischarmingyoungwomandidnotmakeitasatrader.
Mayprobabilitybeonyourside.
Questionsandanswers
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.
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.
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?
Chapter1answers
1. (a)19.18(b)unlimited(c)0.18(d)19.18,0.18,unlimited(e)$18(f)
(g)
Answer2g
(h)
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
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
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
buyer
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
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
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?
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
(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
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.
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
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?
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
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.
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?
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.)
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
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.
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?
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?
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
–1.50–2.70–1.40–3.05Totaldeltaposition.
(a)Shortthreefuturescontracts.(b)Buy,orgolong,threefuturescontracts.
11. 75percent.
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?
6. (a)ReferringtoTables6.3and6.4,whatisthepercentageincreaseingammaoftheDecember380callfrom90to30DTE?(b) What is thepercentage increase in theta for thisoptionover thesametimeperiod?
7. Whatisthecorrelationbetweengammaandtheta?8. Isitpossibletohavepositivegammaandpositivetheta?Whyisthis?
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.
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?
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.
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.
(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?
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?
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)
Answer2f
(g)
Answer2g
3. (a)193–154=39p;0.39×£1,000=£390(b)5400–39=5361(c)[5400–5300]–39=61
(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
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
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
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?
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
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
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
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?
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
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?
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?
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.
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
(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?
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
vi)4.26
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
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.
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
iv)2650+7.3=2657.3v)2842.7–2657.3=185.4pointsvi)7.3(c)Thecondorhasagrossprofitrangethatis185.4–92.4=93pointsgreateratanadditionalcostof3.5.
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
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?
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.
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
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?
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?
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.
(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.
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
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
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
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?
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.
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.
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.
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.
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.
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.
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.
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.
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
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
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
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
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
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
FTSEEuropean-styleoptionscontract,2ndFTSE-100,2nd,3rdfuturescontractexampleinitialmarginsyntheticseeseparateentryvaluationformulavariationmarginfuturesoptionsearlyexercisepremiumexerciseandassignmentmarginvscashpaymentpinrisk,2nd
gamma,2nd,3rddefinitionandexamplesdeltaversusimpliedvolatilityvslongstraddle,2ndpositiveandnegative,2ndshortstraddlestrangle,2ndtimeandvolatilitytradingGreeksdeltaseeseparateentrydeltavsgamma,thetaandvegagammaseeseparateentryimpliedvolatilitychangesimpliedvolatilityvslongironbutterflyoptionscalculatorotherrho,2ndspreads,2nd,3rd,4ththetaseeseparateentrytimeand
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
laddersasymmetricorbrokencomparingcallspreads,1x2sanddifferentstrikepriceslongcalllongputriskmanagementleverage,2ndLIFFEEuropean-styleoption,2ndmarginonfuturesoptionstermsusedforspreadslong1×2callspread,2nd,3rdcallspreadforacredit,2nd,3rdputspread,2ndlongat-the-moneycallbutterflycallcondorputbutterflyputcondorlongbox,2ndlongcalendar/timespread,2ndriskslongcallbutterflylongcallcondorlongcallladder/Christmastreeasymmetricorbrokenladdercomparingcallspreads,1×2sandladdersdifferentstrikepricesriskmanagementlongcallspread,2nd1×1sandvolatilityskewsbullishstrategyshortvslongstrikeslongdiagonalcallspreadlongironbutterfly,2nd,3rdlongironcondor,2nd
longout-of-the-moneyadditionalrisksofbutterflycallbutterflycallcondorputbutterflyputcondortakeagift:butterflylongposition,2nd,3rdlongputbutterflylongputcondorlongputladder/Christmastreeasymmetricorbrokenladdercomparingcallspreads,1×2sandladdersdifferentstrikepricesriskmanagementlongputspread,2nd,3rd1×1sandvolatilityskewsbearishstrategyshortvslongstrikeslongstraddle,2ndlongstrangle
marginfuturescontracts:initialandvariationinterestrates,dividendsandcashpaymentvsmarketdirectionlongandshortmarket-makerscontractliquiditydeltaneutral,2ndputs,2ndshortat-the-moneybutterfliesshortat-the-moneyputcondorssyntheticpositionstradingboxesmisconceptionscallandputpositions
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
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
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
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
shortironbutterfly,2ndshortironcondorshortputspreadshortstraddle,2ndtimedecay,2ndvolatility,2nd
seasonalvolatilitytrendssellstopordershortat-the-moneycallcondorcallandputbutterfliesputcondorshortbox,2ndshortcallspread,2ndlongvsshortneutraltobearishstrategystrikesshortironbutterfly,2ndshortironcondor,2ndshortposition,2nd,3rdshortputspread,2ndlongvsshortneutraltobullishstrategystrikesshortsterlingcontracts,2ndshortstraddle,2ndshortstrangleSPDR(‘Spider’),2ndspreadingrisk,2ndlistofspreadstermstouseSPXoptions,2nd,3rd,4thstartingtotradeadvice,2ndlistofspreadsspreadingriskstationary
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
syntheticfuturescontractlongcallpositionlongputpositionput–callparityputs,2nd,3rd,4thshortcallpositionshortputposition,2ndstockoptions
takeoverstechnicalanalysis,2ndtermstouseplacingspreadorderstheta,2nd,3rddefinitionandexamplesdeltaversusimpliedvolatilityvslongstranglepriceratio,2ndshortstrangletimeanduseandabuseoftimedecay,2nddelta,2ndgamma,2ndshortstrangletheta,2nd,3rdtimepremium,2nd,3rdtimespread,2nd,3rdriskstradingoptionsbuyinganoptiondurationaloutlook,2ndoptionsvsbasispointssellinganoptiontermstousetradingdeltaandtimedecay
tradingvolatilitytrendsvolatilityskews,2nd
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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
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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