Forecasting Market Returns Using the Put-Call Pari

ForecastingMarketReturnsusingthePut-CallParityBiasofTransactionsLevelOptionsDataCameronRookleyDepartmentofFinanceUniversityofArizonaApril,1998(2ndDraft)Severalmethodscurrentlyexistforextractingsomeoftheinformationembeddedinoptionprices.Todate,mostofthesemethodshavefocusedonthesecondorhighermomentsoftheunderlyingasset’sinstantaneousreturnorvalueatexpiration.Incontrasttothesemethods,Ipresentamethodherewhichexploitstransactionsleveloptionsdatatohelpforecastthefirstmomentofleadreturnsintheunderlyingasset.ThisisaccomplishedbyconstructingasignalfromwhatIcallthe“put-call-paritybias”ofoptionquotes.Althoughput-call-parityintrinsicallytiestogetherthepriceofaputandcallwiththesamestrikeandexpiration,inthepresenceoftransactioncostsitispossibletoobservebullishandbearishpressurebasedontherelativevaluesofthebidandaskquotesfortheput,call,indexandriskfreebond.Insteadofworkingwiththesebidandaskpricesdirectlythough,Imapthesepriceintoasetof4impliedvolatilityvaluestoformindividualsignals,andaggregatesuchsignalsusinglocalpolynomialregression;theseaggregatesignalsarethenusedtoforecastmarketreturns.ForthecaseofS&P500indexoptions,theseaggregatesignalsareshowntoberelatedtorecentandcontemporaneousmarketperformance,andmoreimportantlyappeartopossessinformationalcontentforforecastingleadindexreturns.I.IntroductionOptionsbythereverynatureareforwardlookinginstruments.Forthisreason,manymethodshavebeensuggestedasameansofexploitingtheinformationcontentofoptionprices.Mostofthesemethodsfocusonthesecondandhighermomentsoftheunderlyingasset’sinstantaneousreturnorvalueatexpiration.LamarouxandLastrapes(1993)forexample,showhowimpliedvolatilitycanbeusedtohelpimprovevolatilityforecastsbasedonhistoricaldataalone.Severalmethodsalsoexistforestimatingtheriskneutraldensityoftheunderlyingassetatexpiration,suchasShimko(1993),Rubinstein(1994),Ait-SahaliaandLo(1997),JackwerthandRubinstein(1997),Rookley(1997).Unfortunately,inanon-BlackScholesworld,therelationshipoftheriskneutraldensitytotheactualdensityremainsarelativelyopenquestion.InfactLongstaff(1994)evensuggeststhereisempiricalevidencetorejectthemartingalerestrictionalltogether,implyingcertainoptionsmaynotevenbepricedintheriskneutralmeasure.Incontrasttotheseotherstudies,verylittleresearchhasbeendoneontheuseofoptionstoforecastthefirstmomentoftheunderlyingasset’sinstantaneousreturnorvalueatexpiration;thisistobeexpectedgiventhedominantparadigmofriskneutralpricing.Ifoptionsarepricedintheriskneutralmeasure,withoutknowledgeoftheactualexpectedreturntotheunderlyingasset,allwereallyknowwithconfidenceisthatadelta-hedgedportfolioshouldearnaninstantaneousexpectedreturnequaltotheriskfreerate.Infact,bymakinguseofput-callparityoptionpricesareoftenusedtoestimateimpliedriskfreerates.Furthermore,althoughcallownershipisingeneralaratherbullishstrategy,whileputownershipisingeneralabearishstrategy,itisdifficult-althoughnotimpossibleasweshallseeinthispaper-toextractfirstmomentinformationbasedupontherelativepricesofcallsandputsasthesepricesareintrinsicallytiedtogetherbyput-callparity.Althoughlittleresearchhasbeendoneontheuseofoptionpricestoinferfirstmomentpropertiesoftheunderlyingasset,theabilitytodosoisofobviousinteresttoportfoliomanagersandindividualswhoimplementactiveassetallocationmodels.TwostudieswhichattempttouseoptionsdatatoforecastmarketreturnsareBillingsleyandChance(1988),andChance(1990).Inbothcasestheauthorsfocusontherelativevolumeofputandcalloptionsandsuggestusingput-callvolumeratiosasacontrarianindicatorforinvestingintheunderlyingindex,orrebalancinganactivelymanagedportfolio.Theauthorsfindsomeevidencethatahighput-callvolumeratio,usingOEXortotalCBOEoptionvolume,positivelyeffectstheconditionalreturnsoftheS&P500index.Schaeffer(1997)advocatesmonitoringcommonlyobservedvaluesfromtheoptionsmarketssuchasvolumeandopeninterest,inordertoextractcontrarianmarketsignals.Althoughhepresentsverylittlesystematicevidencetosuggestsuchanapproachisfruitful,hedoesintroducealotofanecdotalevidencetosupportoneofthemajorthemesinhisbook:calloptionbuyerstendtobeoverlyenthusiasticduringmarkettopsandputbuyerstendtobeoverlypessimisticregardingtheunderlyingassetduringmarketbottoms.Inthispaper,Imovebeyondreadilyobservedstatisticsfromtheoptionsmarketssuchasvolumeandopeninterestandconstructasignalusingtransactionsleveloptionsdata.ThissignalisbaseduponwhatIcallthe“put-call-paritybias”ofoptionprices.Unlikethefewpreviousstudiesinthisarea,Ihavenoa-prioribeliefastowhetherthesignalIconstructwillbecontrarianinnature,oractuallyindicateforesightonthepartofoptionsmarketparticipants.ForEuropeanoptions,put-call-parityisoftenpresentedasafunctionalidentity,howeverinthepresenceoftransactionscostsweknowthatput-call-parityshouldonlyholdapproximately.Ifweexplicitlyusethebidandaskpricesforallfourassetsinvolved(thecall,theput,theunderlyingandabond),put-call-parityimpliesasetoftwoinequalitieswhichmustholdtoruleoutstaticarbitrageopportunities.Withintheboundsoftransactionscosts,itisthenpossibleforaputandcalloptionwiththesamestrikeandexpirationtorevealupwardordownwardpressurewit