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,contactmeatlenny@lennyjordan.com.

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.

Optionsfundamentals

Introduction

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

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

400 5⅜ 0.28 25¼ 0.72

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:

Gammacanbethoughtofastheheatofanoption.Ittellsushowfastouroption’sdelta,orourequivalentunderlyingposition,ischanging.

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.

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.

Ofteninanoptionsmarketcircumstancesarisethatcausethevolatilityoftheunderlyingtoincreaseordecreasesuddenly.Thismaybetheresultoftheinceptionorconclusionofanunforseenmarketevent.Duringsuchcircumstancestheimpliedvolatilityofeachoptionscontractmonthreactstoadifferentdegree,andthisinturnaffectsthepriceofeachoptionofeachcontractmonthtoadifferentdegree.Undertheseaswellasmoreusualcircumstancesthereisaneedtoquantifytheeffectofachangeinimpliedvolatilityonthepriceofaparticularoption.Vegaistheamountthatanoptionchangesiftheimpliedvolatilitychangesbyonepercentagepoint.

Vegaitselfcanbeexpressedineitheroptionsticksorinanactualcurrencyamount.Table7.1showsasetofoptionswiththeirvegasforonecontractmonth.Thevegasareexpressedindollarsthenroundedintoticks.

30daysuntilexpirationImpliedvolatilityat30percentInterestrateat3percent.

Anincreaseinimpliedvolatilityleadstoanincreaseinoptionspremiums,whileadecreaseinimpliedvolatilityhastheoppositeeffect.Ifthecurrentimpliedvolatilityincreasesfrom30percentto31percent,thevalueoftheDecember380callincreasesfrom12½to13.Iftheimpliedvolatilitydecreasesfrom30percentto29percent,thevalueoftheDecember380calldecreasesfrom12½to12.

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.

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.

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:

Hi,IwanttoplaceanoptionsspreadorderinIBM.

Broker:

Goahead.

Onaspreadbuy5July130calls,andsell5July135callsforanetdebitof1.27times5.Totaldebitis6.35.[Youshouldknowthat6.35equals$635.00.]

Broker:

Checking,inIBMoptionsyouarebuying5July130calls,andselling5July135callsasaspread,foradebitof1.27times5.Yourtotaldebitis6.35.

Yes,that’scorrect.

Broker:

Working,I’llcallyouback.

Whenyourbrokercallsyoubacktoconfirm,heorsheshouldspecifyalloftheaboveplusthepricesofeachoption.

Broker:

Hi,you’refilledonyourspread.

Good,readitoff.

Broker:

OnaspreadinIBMyoubought5July130calls,andsold5July135callsforadebitof1.27times5.Yourtotaldebitis6.35.Youpaid2.87for5oftheJuly130calls,andyousold5oftheJuly135callsat1.60.

Yes,that’scorrect.

Broker:

Checking,youpaid1.27for5July130–135callspreads.

Yes,Ipaid1.27togolong(tobuy)5July130–135callspreads.

Broker:

Canyouconfirmthatagain?

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:

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.

*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:

DebitfromlongJune119call:

–1.70

Totalcredit:

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.

*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

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.

*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:

DebitfromlongJune111put:

–2.60

Totalcreditfromspread:

Maximumprofit:creditfromspread:

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.

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:

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.

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=

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.

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:

CreditfromshortAugust60.00call:

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.

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:

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.

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.

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:

Totalcredit:

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.

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:

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.

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:

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.’

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.

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:

CreditfromlongApril350put:

Totalcredit:

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.

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:

–6.75

–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.

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:

CreditfromApril330put:

Totalcredit:

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.

____________1ThischaptershouldbereadinconjunctionwithChapter4,‘Volatilityandpricingmodels’.

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:

Totaldebit:

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.

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:

DebitfromApril330–370strangle:

Totalcredit:

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.

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:

CreditfromshortApril360call:

–3.75

Totalcredit:

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.

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:

–6.75

–6.25

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

Therisk/returnpotentialismaximumloss/maximumprofit:5.5/4.5=1.2atriskforeachpotentialprofitof1.2Table12.4showstheexpirationprofit/loss.

Table12.4MarksandSpencerlongApril330–340–360–370ironcondor

Agraphoftheexpirationprofit/lossisshowninFigure12.4.

____________1Itcanbeeasiertothinkintermsoftheriskasthenumber1.Here,youcouldcalculatetheR/Rratioas5.5/4.5=1.22,orrisking1tomake1.22.

2Theoppositesideofthistradeispreferable.

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

–6.75

CreditfromtwoshortApril350calls:2×11.25=

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.

*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=

Totaldebit:

–1.00

Maximumprofit:differencebetweentwohigherstrikesminusspreaddebit:(360–350)–1=9

Upsidebreak-evenlevel:higheststrikeminuscostofspread:360–1=359

Downsidebreak-evenlevel:loweststrikepluscostofspread:340+1=341

Therisk/returnratioofthisspreadismaximumloss÷maximumprofit,or1/9.Intabularformtheexpiryprofit/lossissummarisedinTable13.2.

Table13.2MarksandSpencer340–350–360longputbutterfly

Thegraphoftheexpirationprofit/loss(seeFigure13.2)isalmostidenticaltotheoneshowninFigure13.1forthecallbutterfly.

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.

–11.25

DebitfromoneApril370call:

–3.75

CreditfromtwoshortApril360calls:2×7=

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

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=

Totaldebit:

–0.75

Maximumprofit:differencebetweentwohigherstrikesminusspread

debit:(340–330)–0.75=9.25

Upperbreak-evenlevel:higheststrikeminusspreaddebit:340–0.75=339.25

Lowerbreak-evenlevel:loweststrikeplusspreaddebit:320+0.75=320.75

Profitrange:339.25–320.75=18.5

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:

–11.25

–2.00

CreditfromoneshortApril360call:

CreditfromoneshortApril370call:

Totaldebit:

Maximumprofit:differencebetweenlowesttwostrikesminusspreaddebit:(360–350)–2.75=7.25

Profitrange:377.25–352.75=24.50

Therisk/returnratioofthislongcallironbutterflyis2.75/7.25=0.38atriskforeachpotentialprofitof1.Atableoftheprofit/lossatexpirationisshowninTable13.4.

Table13.4MarksandSpencerlongApril350–360–370–380callcondor

Aprofit/lossgraphofthiscondoratexpirationappearsinFigure13.4.

*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:

–17.00

–4.00

CreditfromoneApril350call:

CreditfromoneApril360call:

Totaldebit:

–3.00

Maximumprofit:differencebetweentwoloweststrikesminusspreaddebit:(350–340)–3.00=7.00

Rangeofmaximumprofit:350–360

Profitrange:367.00–343.00

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.

–10.25

–2.00

Totaldebit:

–2.25

Maximumprofit:differencebetweenhighesttwostrikesminusspreaddebit:(350–340)–2.25=7.75

Profitrange:347.75–322.25=25.50

Therisk/returnratioisagainfavourableat2.25/7.75=0.29for1,or1/3.44.Theprofit/lossatexpirationisshowninTable13.5.

Table13.5MarksandSpencerlongApril320–330–340–350putcondor

Thegraphoftheprofit/lossatexpirationisshowninFigure13.5.

*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:

–16.25

–3.75

Totaldebit:

–3.50

Maximumprofit:differencebetweenhighesttwostrikesminusspreaddebit:(360–350)–3.5=6.5

Profitrange:356.5–333.5=23

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.

–11.25

–6.75

Totalcredit:

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.

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:

Purchaseof60call:

–1.45

Saleof65call:

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.

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.

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

December420calls

December400calls

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:

Theta $5.20 Theta $11.50

$15.00

$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.

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(%)

185.40

149.40

116.80

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.

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.

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(lenny@lennyjordan.com).

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.

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.

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.

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.

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.

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

Maycalls

Mayputs

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.

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,Iwouldliketoknow.Feelfreetocontactmeatlenny@lennyjordan.com.I’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)

Answer2g

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)

Answer4g

(h)Futurespriceatexpirationminusstrikepriceofcallequals590–575=15,orexpirationvalueofcallTradedpriceofcallminusexpirationvalueofcall,22.75–15=7.757.75×contractmultiplierof$50=$387.50profit for seller, loss for

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)

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)

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

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

Decembercalls

Decemberputs

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

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.

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

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