CBOE Put-Call Ratio Statistical Analysis: A Useful Greed ...

In 20% of all observations the CBOE put-call ratio was below 0.81 and above 1.06 (showing moderate levels of greed and fear). According to the ... WSCResearch277FollowersFollowSummaryOnaverage,optiontradersloseabout90%ofthetime.Thus,theputtocallratioisoftenusedascontrarianindicatorwhenreachingextremelevels.Inthisarticle,wewillanalyzetheeffectivenessoftheput-callratioascontrarianindicatortoexploitextremelevelsofgreedandfearwithintheoptionmarket.Toreducethesubjectivityofinterpretationinthetermextremegreedandfearlevels,wewillusedescriptivestatistics.Afterward,weanalyzetheseentry-andexitpointsbasedontheiraverageforward-lookingreturnsontheS&P500andtestthemforstatisticalsignificance.Finally,weintroduceanewwayonhowtoimprovethetradingresultsbyapplyingthez-scorestatisticstotheput-callratios.Pgiam/iStockviaGettyImagesIntroduction:Whatistheput-callratio?Theput-callratioiscalculatedbydividingthedailyvolumeoftradedputoptionsbythedailyvolumeoftradedcalloptions.Acalloptionisgivingtheownertheright(butnottheobligation)tobuyacertainamountofanunderlyingsecurityataspecifiedpricewithinaspecifiedtime(whereastheputoption,incontrast,grantstheholdertherighttosellataspecifiedpricewithinaspecifiedtime).Whatisthetheorybehindtheput-callratioascontrarianindicator?Aholderofacalloptionwillpocketaprofitiftheunderlyingsecurityriseswithinapre-definedperiodaboveacertainlimitprice(whereasthereverseistrueforholdersofaputoption).Asaresult,bothformsarehardcashbetsonthefuturedirectionoftheunderlyingsecurity.Theaggregatedvolumeofallequityoptionsisexpressedasput-callratioandcanbethenusedtogaugeinvestorssentiment.Forexample,aputtocallratioof1showsthatthevolumeofputoptionsexactlymatchesthevolumeofcalloptionsonthatgivenday.Extremeratioswithintheput-callratiooccurwhenmostoptiontradersarebettingonthesamedirectionoftheunderlyingsecurity.Giventhefactthat,onaverage,90%ofoptiontraderslosemoney,suchstrongimbalancesintheput-callratioshouldtheoreticallybeagoodindicatortopinpointtrendreversals.Howtousetheput-callratiofortrading?Atafirstglance,extremevaluesintheCBOEput-callratiohave,indeed,oftenoccurrednearoratmajorinflectionpointsintheS&P500(SPY).Especially,strongerspikesintheCBOEput-callratiolookliketheyoccurredquiteregularlynearoratmarketbottoms.Lowput-callratiosincontrast,alsolooksomehowrelevantalthoughtheyseemtoappearlesssignificantinidentifyingmarkettops.Chart1:CBOEPut-CallRatiovs.S&P500(wallstreetcourier.com)StatisticalAnalysisoftheCBOEPut-CallRatio:Toevaluateifatradingstrategybasedontheput-callratioprovidesanyvaluetoinvestors,wewillfirstusedescriptivestatisticstoderiveextremeslevelsofgreedandfear.Thisensuresarationalapproachinidentifyingrelevantbuyandsellthresholdswhensentimenthitscontrarianlevels.Afterwards,wewillcalculatetheforward-lookingreturnsoftheseentry-andexitpointsandcompareitwiththeaveragereturnsofthebroadmarket.Thisisawidespreadpracticeandallowsstatementsaboutthestatisticalsignificanceofthegeneratedsignals.Theforward-lookingreturnsaretheaveragereturnsforacertainperiodafteraspecificsignaloccurred.Themoretheydifferfromtheaveragereturnsoftheunderlyingmarket,thehigherthechancesthatthesesignalsaresignificantfromastatisticalpointofview.Identifyingcontrariangreedandfearlevelsintheput-callratio:Todefineextremevalues,wesorttheput-callratio(ofallCBOEoptions)rangingfromJanuary2007untilJune2022,fromthehighesttothelowestvalue.Afterwards,wecalculatethemeanandthethresholdvalueswhichrepresentthetopandbottom5%,10%and20%ofallobservations.Topthresholdvaluesshouldcoincidewithextremeleveloffearandbottomthresholdvalueswithhighcomplacentwithintheoptionmarket.Table1:Extremegreedandfearlevelsoftheput-callratio(wallstreetcourier.com)Asshowninthetableabove,theaveragevalueoftheCBOEput-callratiosince2007is0.94(andnot1).Thismakessensesincethemarkettendtoriseinmostofthecases.Therefore,therearenormallyslightlymoreinvestorsbuyingcalloptionsthanbuyingputoptions.In5%ofthetime,theCBOEput-callratiowasbelow0.72(representingextremelevelsofgreed)orabove1.23(representingextremelevelsoffear).In10%ofallcasestheCBOEput-callratiowasbelow0.76orabove1.15(indicatinghighlevelsofgreedandfear).In20%ofallobservationstheCBOEput-callratiowasbelow0.81andabove1.06(showingmoderatelevelsofgreedandfear).Accordingtothecontrariantheory,investorsshouldbuyiftheputtocallratiopassestheextremefearthreshold,andtheyshouldsellifmarketsentimentshowsextremegreedwithintheoptionmarket.AnalyzingForward-LookingReturns:Thebestwaytobacktestacontrarianputtocalltradingstrategyistoanalyzetheaverageforward-lookingreturnoftherelevantentry-andexitsignals(andcompareitwiththeaveragereturnsofthebroadmarket).Thisisawidespreadpracticeandallowsstatementsaboutthestatisticalsignificanceoftheusedsignals.Asinputparameters,wewillusethe5%ofextremeput-callratiosshownintable1,tocalculatetheaverageforward-lookingreturnsforthenext5,10,30,60,90,180and360tradingdays(aftertheentrysignaloccurred).Afterwards,wewillcomparethesereturnswiththeaveragereturnsfortheS&P500inthesameperiod.Weareawarethatidentifyingthresholdsonpastdataincludessomehowalook-aheadbias,butgiventhestationarityofthedata,theimpactshouldbelimited.Historically,entrysignalsbasedonhighput-callratioshave,indeed,shownstrongersignsofstatisticalsignificanceingeneratingaboveaveragemarketreturns.Theaverageforward-lookingreturnsofthetop5%ofallput-callratioshaveoutperformedtheaveragereturnsoftheS&P500byalargerextendbetweenthefollowing30and60days(withp-valuesbelow5%ascriticalstatisticalthreshold).Wehavenotfoundstatisticalsignificanceforthefollowing5,10and90days,althoughthesesignalshavealsogeneratedaboveaveragemarketreturns.Table2:Averageforward-lookingreturnsofthetop5%oftheput-callratios(wallstreetcourier.com)Thebottom5%oftheput-callratioshavegeneratedbelowaveragewithinthenext60daysthesellsignaloccurred.Althoughtheseresultslookquitepromising,thisunderperformancewasnotsignificantfromapurelystatisticalpointofview(asthep-valueisabovethecritical5%threshold).Thus,lowput-callratioscanbeconsideredasusefulinformationbutshouldnotbetakentooseriously,whenitcomestoimplementacontrariandriveninvestmentstrategy.Table3:Averageforward-lookingreturnsofthebottom5%oftheput-callratios(wallstreetcourier.com)Summaryandcriticalreview:Extremelyhighput-callratioswerehistorically,indeed,abletoidentifyattractiveentrypoints.Especially,thecompellingaboveaveragereturnsafter30and60dayshaveshownhighstatisticalsignificance.Thus,theput-callratiocanbeaquiteusefulcontrarianindicatortolookatwhenmarketsentimenthitsextremenegativelevels.Ontheotherside,theabilitytogeneratereliablesellsignalsislimited.Although,marketreturnswerebelowaveragewithinthefollowing60daysaftertheput-callratiodroppedtogreedylevels,wehavenotfoundstrongerstatisticalevidencefortheseresults.Sincelowput-callratiosmostlyoccurduringstrongbullmarkets,itcouldbepossiblethathighoptimismwithintheoptionmarketmightonlycauseconsolidationsandnomajortrendbreakswithinapositivemarketregime.Althoughtheseresultslookquitepromising,thebiggestdrawbackoftheput-callratioisitslimitednumberoftradingsignals.Additionally,mostoftherelevantsignalsoccurincluster,makingithardtoexploitanystatisticalsignificanceonaregularbasis.Additionally,identifyinggreedandfearbasedonthefullhistoryoftheput-callratiomightnotreflectstrongerandrapidshiftswithinnormalranges.Excursus:ApplyingtheZ-ScoretoImproveResultsfromthePut-CallRatioToovercometheshortcomingofrareandnon-adaptivesignalsbasedonfixedthresholds,wealsopublishanadvancedversionoftheput-callratioindicatoronourwebsite.There,weusearollingz-scoreapproachtonormalizetheput-callvalues,whichmakesiteasiertoidentifyextremevalueswithinthegivenlookbackperiod.Thez-scoremeasureshowmanystandarddeviationsthelatestobservationisbeloworabovethemeanvalue.Forexample,az-scoreof2showsthatthelatestput-callratiois2standarddeviationsaboveitsmean.Assuminganormaldistribution,only2.3%ofallobservationsshouldfallintothatbucket.Thus,valuesabove2orbelow-2shouldconsideredtobeextreme.Iftheput-callratioisthesameasitsmeanwithinthegivenlookbackperiod,thez-scorewillshowa0.Chart2:Z-ScoreCBOEPut-CallIndicator(wallstreetcourier.com)Apartfromitsstandardizationmechanism,themainadvantageisthatsuchanapproachderivesflexibleentry-andexitpointsbasedonstrongershiftswithinthegivenlookbackperiod.Forexample,astrongerincreaseafteranextendedperiodoflowput-callratioswillautomaticallyresultinahighz-score.Thisleadstoanincreasednumberofsignalssincetheyautomaticallyadapttotheprevailingmarketregime.Mostimportantly,thisapproachalsoincreasesthestatisticalsignificanceasshowninthetablesbelow.Thereyoucanseethattheaverageforward-lookingreturnofz-scorevaluesequalorgreaterthan2(oftheput-callratio)arestronglyoutperformingthebroadermarketupuntil180daysthebuysignalwastriggered.Between10and90days,thisstrongoutperformanceishighlystatisticallysignificant.Thus,thez-scorenormalizationimprovestheresultsofthestandardput-callratiobasedonfixedthresholdsconsiderably.Table4:Averageforward-lookingreturnsofz-scores(oftheput-callratios)>=2(wallstreetcourier.com)Asshownintheablebelow,thez-scoreapproachalsoleadstoasignificantboostinthequalityofexitsignals.Therewecanseethatz-scoresequalorbelow-2ledtostatisticallysignificantbelowaveragemarketreturnsona5,10and60daysbasis.Thisisaquitestrongimprovementcomparedtothesellsignalsgeneratedbythefixedthresholdsapproach.Table5:Averageforward-lookingreturnsofz-scores(oftheput-callratios)<=-2(wallstreetcourier.com)Conclusion:Theput-callratioisindeedaveryusefulcontrarianindicatortogaugemarketsentimentand,thus,toidentifyattractivetradeopportunities.Especially,thez-scorenormalizationshouldbepartofthe"mustdailyscreenindicators"ofactiveinvestors.Althoughthez-scoreput-callratioindicatorshowedstatisticalsignificanceinidentifyingattractiveentry-andexitpoints,marketsentimentindicatorsshouldjustbeaninputparameterandnotamajorcomponentofasoundinvestmentprocess.ThisarticlewaswrittenbyWSCResearch277FollowersFollowWallstreetCourier.com-IdentifyingMarketRegimes&Shifts-ActionableRegime-BasedResearchFollowDisclosure:I/wehaveabeneficialshortpositioninthesharesofSPYeitherthroughstockownership,options,orotherderivatives.Iwrotethisarticlemyself,anditexpressesmyownopinions.Iamnotreceivingcompensationforit.Ihavenobusinessrelationshipwithanycompanywhosestockismentionedinthisarticle.2Likes3CommentsRecommendedForYouComments(3)NewestToensurethisdoesn’thappeninthefuture,pleaseenableJavascriptandcookiesinyourbrowser.Isthishappeningtoyoufrequently?Pleasereportitonourfeedbackforum.Ifyouhaveanad-blockerenabledyoumaybeblockedfromproceeding.Pleasedisableyourad-blockerandrefresh.