RFS-使用机器学习和大数据预测期权价格

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OptionReturnPredictabilitywithMachineLearningandBigData

TuranG.Bali

GeorgetownUniversity,USA

HeinerBeckmeyer

UniversityofMünster,Germany

MathisMörke

UniversityofSt.Gallen,Switzerland

FlorianWeigert

UniversityofNeuchâtel,Switzerland

Drawinguponmorethan12millionobservationsovertheperiodfrom1996to2020,wefindthatallowingfornonlinearitiessignificantlyincreasestheout-of-sampleperformanceofoptionandstockcharacteristicsinpredictingfutureoptionreturns.Thenonlinearmachinelearningmodelsgeneratestatisticallyandeconomicallysizableprofitsinthelong-shortportfoliosofequityoptionsevenafteraccountingfortransactioncosts.Althoughoption-basedcharacteristicsarethemostimportantstandalonepredictors,stock-basedmeasuresoffersubstantialincrementalpredictivepowerwhenconsideredalongsideoption-basedcharacteristics.Finally,weprovidecompellingevidencethatoptionreturnpredictabilityisdrivenbyinformationalfrictionsandoptionmispricing.(JELG10,G12,G13,G14)

ReceivedNovember8,2021;editorialdecisionJanuary19,2023byEditorStefanoGiglio.AuthorshavefurnishedanInternetAppendix,whichisavailableontheOxfordUniversityPressWebsitenexttothelinktothefinalpublishedpaperonline.

Wearegratefultotheeditor,StefanoGiglio,andtwoanonymousrefereesfortheirconstructiveandinsightfulcomments.WealsobenefitedfromdiscussionswithManuelAmmann,NicoleBranger,JieCao,JeromeDetemple,IliasFilippou,AmitGoyal,AlexanderKempf,SebastianoManzan,AndreasNeuhierl,SethPruitt,AlbertoRossi,PaulSöderlind,SebastianStöckl,YinanSu,AllanTimmermann,MartinWallmeier,GuofuZhou,andseminarparticipantsattheVirtualDerivativesPhDWorkshoporganizedbytheUniversityofIllinoisUrbana-ChampaignandMichiganStateUniversity,the14thAnnualHedgeFundConferenceatImperialCollege,theannualmeetingoftheGermanAcademicAssociationofBusinessResearch2022,theSFIResearchDays2022,aninternalseminaratGoldmanSachs,aninternalseminaratHullTacticalAssetAllocation,theBVI-CFR2021seminar,theFederalReserveBoard,GeorgetownUniversity,theUniversityofFribourg,theUniversityofLiechtenstein,theUniversityofMinnesota,andtheUniversityofMuenster.FlorianWeigertisalsoaffiliatedwiththeCentreofFinancialResearch(CFR)Cologneandthankfulfortheircontinuoussupport.

Supplementary

datacanbefoundonTheReviewofFinancialStudieswebsite.SendcorrespondencetoTuranG.Bali,McDonoughSchoolofBusiness,GeorgetownUniversity,37thandOStreetsNW,Washington,DC20057,USA;telephone:(202)687-5388;e-mail:turan.bali@.

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©TheAuthor(s)2023.PublishedbyOxfordUniversityPressonbehalfofTheSocietyforFinancialStudies.

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/10.1093/rfs/hhad017AdvanceAccesspublicationFebruary24

,2023

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1

Theimportanceofoptionmarketshasgainedmomentumoverthepastdecade.AccordingtodatafromtheFuturesIndustryAssociation’s(FIA)annualstatisticalreview,optionstradingonexchangesworldwidehasincreasedfrom$9.42billioncontractsin2013to$21.22billioncontractsin2020,agrowthrateofmorethan125%.Approximately60%ofthesecontractsarewrittenonindividualstocksandstockindices,makingequitythemostpopularunderlyingassetoffinancialmarketparticipants.Giventhehighpopularityofoptionstradingbyinvestors,thequestionariseswhetherindividualoptionreturnsarepredictableand,ifyes,whichcharacteristicscangiverisetosuchpredictability.Ourpaperisdevotedtoansweringthesequestions.

Whileclassicaloptionpricingmodelsassumethatoptionsareredundant

assets(BlackandScholes

1973

),morerecentresearchrejectsthisideaandshowsthatoptionpricesdependonrisksotherthantheunderlying’sexposure

(BuraschiandJackwerth

2001

;

Garleanu,Pedersen,andPoteshman

2009

).Asanexample,

GoyalandSaretto

(2009

)documentthatthecrosssectionofoptionreturnsreflectsapremiumforvariancerisk,computedasthedifferencebetweenhistoricalrealizedvolatilityandat-the-moneyimpliedvolatility.Inthispaper,wefollowtheideaofcharacteristic-basedassetpricingandlinkfuturedelta-hedgedoptionreturnstoex-antecharacteristicsdrawnfrombothoptionsandstocks.Asweeliminatethedirectionalimpactofstockpricesthroughourhedgingprocedure,wefocusonrisksthatareinherentlynonlinearandarelikelytointeractwitheachotherincomplexways.Hence,thedescribedsetupisideallysuitedfortheapplicationofmachinelearningmodelsthatarenotonlyabletocapturetheimpactofnonlinearitiesandinteractionsbetweenalargesetofoptionandstockcharacteristics,butalsomitigatetheriskofin-samplemodeloverfitting.

WestudythecrosssectionofindividualU.S.equityoptionreturnsusingdatafromOptionMetricsIvyDBovertheperiodfromJanuary1996toDecember2020.Toabstractfromthedirectionalexposuretotheunderlying,wefollow

BakshiandKapadia

(2003

)andperformdailydelta-hedgesforeachoptionasthemarketcloses.Ourmainvariableofinterestisthemonthlyexcessdelta-hedgedoptionreturn.Afteraccountingfordifferentfilteringtechniques,ourdatasetconsistsofmorethan12millionoption-monthreturnobservationsofcallsandputs,allwrittenonindividualU.S.stocks.

Topredictfutureoptionreturns,weuseatotalof273variablescom-posedof80option-basedcharacteristics(e.g.,optionilliquidity,time-to-maturity,andtheimpliedshortingfee)and193stock-basedcharacteristics

.1

Thestockcharacteristicsincludethe94predictorvariablesproposedby

Optioncharacteristicsoperateonthreedifferentlevels:First,theycanbethesameforalloptionsonthesameunderlyingstock(e.g.,thevarianceriskpremiumby

GoyalandSaretto

[2009

]).Second,theycanbeclassifiedontheindividualoptioncontractlevel(e.g.,theoptionsmaturity).Third,theycanbecategorizedonabucket

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Green,Hand,andZhang

(2017

)topredictthecrosssectionofstockreturns,90industrydummies,andadditionalcharacteristicsthathavebeenshowntobesignificantlyassociatedwithfuturestockreturns(suchasthebearbetaproposedby

LuandMurray

[2019

],defaultriskof

VasquezandXiao

[2021

],

andtheunderlying’sclosepricefollowing

Eisdorfer,Goyal,and

Zhdanov[2022

]).Inthesamefashionas

Gu,Kelly,andXiu

(2020

),weapplydifferentlinearandnonlinearmachinelearningmodelstoformoptimalpredictionsbasedontheseoption-andstock-basedcharacteristics.Linearmodelsincludedarepenalizedregressionmodels(Ridge,Lasso,andElastic-Net)anddimensionalityreductionregressions(principalcomponentandpartialleastsquares).Nonlinearmodelscomprisegradient-boostedregressiontreeswithandwithoutdropout,randomforests,andfully-connectedfeed-forwardneuralnetworks.Wealsocomputeequal-weightedensemblesofalllinearandallnonlinearmodelstocombinetheinformationalcontentoftheindividualmodels.

Toassessthepredictivepowerofthedifferentmodelsforindividualoptionreturns,wefollow

Gu,Kelly,andXiu

(2020

)andusetheout-of-sampleR2-statistic,whichbenchmarkstheR2againstaforecastofzeroexcessreturns

.2

Tomakepairwisecomparisonsoftheforecastaccuracyofdifferentmachinelearningmodels,weutilizethemodel-free

DieboldandMariano

(1995

)teststatistic.

Ourempiricalresultsadvancetheknowledgeonpredictabilityofthecrosssectionofindividualoptionreturnsinvariousdimensions:First,weshowthatcomplexityofthepredictionmodelmatters.Whilenoneofthelinearmodelsmanagestoproducepositiveout-of-sampleR2sfortheentiretestingsample,allnonlinearmodelsdo.Ourresultsrevealthatthebest-performingmodelsaregradient-boostedregressiontreeswithandwithoutdropout(GBRandDart)producingout-of-sampleR2sof2.26%and1.96%

.3

Moreover,theequal-weightedensembleofallnonlinearmodels(denotedN-En)outperformstheensembleofalllinearmodels(denotedL-En)bymorethan1.7%inout-of-sampleR2predictionpower.Ourresultsareconfirmedwhenwecomparepairwiseforecastaccuracyusing

DieboldandMariano

(1995

)tests:Theensembleofallnonlinearmodelsbeatsallothermodelsandmostothermodelswithstatisticalsignificanceatthe5%level(theonlyexceptionstothisfindingareGBR,Dart,andfeed-forwardneuralnetworks,whichallproduceforecastshighlycorrelatedwiththenonlinearensemblemodel(correlationsamountto

level(e.g.,theoptionbucket’stradingvolume),wherebucketsareformedbasedonthemoneynessandtime-to-maturityoftheoption.

2Inaddition,weapplythe

Hanetal.

(2021

)cross-sectionalout-of-sampleR2,whichfocusesonhowwellamodelpredictscross-sectionaloptionreturnspreads.

3NotethatthemagnitudeoftheseR2sisconsiderablyhigherthanthecorrespondingnumbersforthecrosssectionofstockreturns,forexample,

Gu,Kelly,andXiu

(2020

)findanout-sampleR2ofapproximately0.6%fornonlinearmachinelearningmodels.Thisdiscrepancymaybedrivenbythedifferent(andshorter)sampleperiodthatweconsider,whichisrestrictedbytheavailabilityofinformationonsingleequityoptions.

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0.95,0.93,and0.77,respectively).Theoutperformanceofnonlinearmodelscomparedtolinearmodelsisstableovertimewithahigherpredictabilityforfutureoptionreturnsin69.8%ofthemonthsinoursample(86.0%whenconsideringthecross-sectionalout-of-sampleR2).Notably,wealsofindbetterpredictionsforthenonlinearmodelsduringtheDecember2019–December2020period,inwhichtheCOVID-19pandemicshookfinancialmarkets

worldwide.4

Thehigherpredictabilityofnonlinearmodelsnotonlyholdsforthecompletesetofoptionsinvestigatedinoursample,butalsofordifferentoptionbuckets,suchasoptionssortedbymaturity(i.e.,short-termandlong-termoptions)andmoneyness(i.e.,out-of-themoney,at-the-money,andin-the-moneyoptions).

Second,weinspectwhetherpredictabilityofoptionreturnsthroughmachinelearningmodelscanbeexploitedinaneconomicallyprofitabletradingstrategy.Ourresultsindicatethatthelong-shortportfoliosbasedonL-En’sandN-En’sforecastsofexpectedreturnsgenerateeconomicallysignificantreturnspreadsof1.30%and2.04%permonth,respectively,bothstatisticallysignificantatthe1%level

.5

Thelong-shortreturnspreadofthenonlinearensembleoutperformsthereturnspreadofthelinearensemblebyastatisticallysignificant0.74%permonth,stressingtheimportanceofnonlinearities.Thisresultholdsalsoforthesubsetofcallandputoptionsseparately,doesnotdependonearningsannouncements,andpersistsovertime.Moreover,theprofitabilityofthelong-shortreturnspreadofthenonlinearensembleexceedsexistingandnewlyproposedmeasuresofexpectedreturnbenchmarksandisrobusttoriskadjustmentsofestablishedassetpricingmodels,accountingfortime-varyingleverage,aswellaschangesinthelengthofthetrainingwindow,return

frequency,anddifferentsamplesofbigandliquidstocksonwhichoptionscanbetraded.Theresultsalsoremainsignificantacrossdifferentstatesoftheeconomy.

Diggingdeeperintothecompositionsofthedifferentspreadportfolios,wefindthattheshortlegcontainsmoreputsandshort-termoptionsthanthelongleg.Interestingly,theshortlegofthespreadportfolioalsodisplaysstrongdifferencesfromtheotherportfoliosintermsofcomplexityofthecharacteristicsthatdeterminetheallocationofoptionsintoportfolios.Inthissense,optionsthatareselectedintheshortlegaredeterminedbytheleastnumberofcharacteristics,buthavethehighestnumberofnonlinearitiesand

interactioneffectsamongthesecharacteristics.

Ofek,Richardson,andWhitelaw(2004

)showthattransactioncostsin

theoptionsmarketarehighandthatthesecostscansubstantiallyreduceeconomicprofitsofoption-basedtradingstrategies.Hence,tounderstand

4

Dew-BeckerandGiglio

(2020

)showthattheCOVID-19epidemicismarkedbyanextraordinarilyhighlevelofcross-sectionaluncertainty,asmeasuredbystockoptionsonindividualfirms.Similarlevelsofcross-sectionaluncertaintyhaveonlybeenwitnessedduringthetechboomandthefinancialcrisis.

5TherespectivemonthlySharperatiosamountto1.03and1.28.

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6

7

8

howfarthemachinelearningtradingstrategybasedonthenonlinearensembleisimplementable,weexamineitsprofitabilityafteraccountingfortransactioncosts.SinceactualtransactioncostsoftradesarenotobservableintheOptionMetricsIvyDBdatabase,weassumethatinvestorshavetopay25%–100%ofthequotedbidandaskspread,whichwedenoteastheeffective

spread(Eisdorfer,Goyal,andZhdanov

2022

).Inaddition,weincorporatethecostsoftradingwiththedelta-hedgingprocedurebyaccountingforasimilar

percentageoftheunderlying’squotedspread.6

Ourresultsshowthatthereturnsofthenonlinearmachinelearningtradingstrategyremainsizable(0.67%permonth)evenifinvestorshavetopaythefulleffectivespreadfortransactionsanddelta-

hedgingonalloptions.7

Marginsareanimportantconsiderationwheninvestingintheoptionsmarket.Ontopofthetransactioncostsarisingfrombid-askspreads,wealsoincludedifferentmarginrequirementsforsettinguphedgedlongandshortoptionpositions.RealizedreturnsandSharperatiosofthepredictionsmadebythenonlinearensembledecrease,butonlyturninsignificantiftheinvestorhadtopay100%ofthequotedspreadforeachoptionanddelta-hedge.Importantly,thepredictionsbythenonlinearensemblesignificantlyoutperformthosebyitslinearcounterpartinallcases.

Asourthirdmainempiricalresult,wequantifytherelativeimportanceofdifferentcharacteristicsforthepredictionofoptionreturns.Wefollowrecent

advancesincomputerscienceandestimateSHAPvalues(LundbergandLee

2017

),whichapproximatechangesinthemodelpredictionshadweexcludedcertaincharacteristicsinitsestimation.Todoso,weclassifyour273optionandstockpredictorvariablesinto12subgroups:Accruals,Industry,Investment,Profitability,Quality,Value,Contract,Frictions,Illiquidity,InformedTrading,PastPrices,andRisk.Ourresultsrevealthatthecontractgroupcontainsthemostimportantpredictors,whichincludeinformationabouttheoption’slocationontheunderlying’simpliedvolatilitysurface.Illiquidityandriskmeasuresfollowasthesecondandthirdmostimportantvariablegroup,respectively.Withrespecttotherelativeimportanceofsinglecharacteristics,wefindthatimpliedvolatilityplaysbyfarthemostimportantrole,followedbythebid-askspreadoftheunderlyingstockandindustrymomentum.Ifweassessthefunctionalformoftheimpactofthethreemostimportantsinglecharacteristicsonthemodel-predicteddelta-hedgedreturn,ourresultsrevealthathigherimpliedvolatilitynegativelyaffectsreturns,whereashigherbid-ask

spreadsandindustrymomentumpredictreturnspositively.8

Tosimulatearealisticinvestmentprocess,weaddanestimateofthetransactioncostsatthetimeofthetradeinitiationtothereturnpredictionandthensortoptionsintodecileportfolios.

Itisimportanttonotethatinthiscase(i.e.,100%effectivespreadfortransactioncostsanddelta-hedging),wedonotobserveanoutperformanceofthetradingstrategybasedonlinearmachinelearningmodelsanymore.Thisagainillustratestheimportanceofincorporatingnonlinearitiesandinteractionswhenformingoptionportfolios.

Investigatingthisfunctionalformrevealsthateachofthe10mostimportantcharacteristicsaffectsreturnsinanonlinearfashion.

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Ourempiricalsettingenablesustoanswerwhetheroptionorstockcharacteristicsaremoreimportanttoaccuratelypredictfutureoptionreturns.Hence,wereestimatethemachinelearningmodelsusingonly(i)option-basedcharacteristics,(ii)stock-basedcharacteristics,aswellas(iii)option-basedcharacteristicsthatoperateonthebucketorcontractlevel,andcomparetheout-of-sampleforecastingresultswiththefullinformationsetofalloptionand

stockcharacteristics.9

Weobservethatthemodelsonlybasedonasubsetofinformationshowseverelylowerout-of-sampleR2scomparedtothosethatincorporatealloptionandstockcharacteristics.Whencomparingdifferentsubsetsofinformation,ourresultsindicatethatrestrictinginformationtoonlyoption-basedcharacteristicsyieldssubstantiallyhigherpredictiveR2sthaninformationononlystock-basedcharacteristics.However,thebenefitofaddingstock-basedtooption-basedcharacteristicsissubstantialandhelpstoobtainmoreaccurateforecastsforfutureoptionreturns.

Finally,wedeterminepossiblesourcesofoptionreturnpredictability.Wehypothesizethatoptionreturnpredictabilityoriginatespartlyasaresultofinformationalfrictions,suchthattheinformationimpliedfromstock-andoption-basedcharacteristicsisnotdirectlyincorporatedintooptionprices.Totestthisconjecture,wecreatedifferentindicesofinformationfrictionsbasedonstock-andoption-levelinformation.Inlinewithourprediction,wefindthatthepredictabilityofoptionreturnsincreaseswithhigherinformationalfrictions.Ourresultsrevealthattheout-of-sampleR2forthenonlinearensemblemodelequals5.32%(0%)foroptionswhoseunderlyingsfallwithinthehighest(lowest)quintileofstock-levelinformationfrictions.Optionsexhibitingthehighest(lowest)levelofinformationfrictionsshowanR2of4.00%(1.36%).Wealsoestimatethelevelofmispricingperoptioncontract,againusingacompositemispricingscore.Consistentwiththeintuitionthatmachinelearningmodelsmanagetoidentifymisvaluationintheoptionsmarket,overallpredictabilityisincreasinginthemispricingscore.

1.RelatedLiterature

Ourpapercontributestotheliteratureonpredictingandexplainingthecrosssectionofindividualoptionreturns.

DennisandMayhew

(2002

)documenttheimportanceofvariousfactors,suchasbeta,size,andtradingvolume,inexplainingtherisk-neutralvolatilityskewobservedinstockoptionprices,whereas

BollenandWhaley

(2004

)investigatetherelationbetweennetbuyingpressureandtheshapeoftheimpliedvolatilityfunctionofstockoptions.

Garleanu,Pedersen,andPoteshman

(2009

)theoreticallymodelandempiricallyinvestigatedemandpressureeffectsonoptionprices.Byexaminingvolatilityriskintheoptionsmarket,

GoyalandSaretto

(2009

)findthatoptions

9IncontrasttothefeatureimportancebymeansofSHAPvalues,thisapproachhasthebenefitofcorrectlyaccountingforinteractioneffectsbetweendifferentfeaturegroups.

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withalargepositivedifferencebetweenrealizedandimpliedvolatilityhavelowfuturedelta-hedgedreturns.

Roll,Schwartz,andSubrahmanyam

(2010

)examinetradingvolumeinoptionmarketsrelativetothevolumeinunderlyingstocksandrelateittocontemporaneousreturns.

CaoandHan

(2013

)showthatdelta-hedgedoptionreturnsdecreasemonotonicallywithanincreaseintheidiosyncraticvolatilityoftheunderlyingstock.

BaliandMurray

(2013

)findastrongnegativerelationbetweenrisk-neutralskewnessanddelta-andvega-neutralequityoptionreturns,consistentwithapositiveskewnesspreference.

Anetal.

(2014

)showthatthecrosssectionofstockreturnspredictsfuturechangesinoptionimpliedvolatilities.

ByunandKim

(2016

)findthatcalloptionswrittenonthemostlottery-likestocksunderperformotherwisesimilarcallo

ptionsontheleastlottery-likestocks.

Christoffersen,Fournier,and

Jacobs(2018

)showthatequityoptionsdisplayastrongfactorstructure,whichishighlycorrelatedtothevolatility,skew,andtermstructureofS&P500indexoptions.

Christoffersenetal.

(2018

)includeilliquiditypremiainoptionvaluationmodelsand

Kanne,Korn,andUhrig-Homburg

(2022

)findthatthesepremiaarenegative(positive)ifthereisnetbuying(selling)pressure.

RamachandranandTayal

(2021

)examinetheimpactofshort-saleconstraintsonthepricingofoptions.

Zhanetal.

(2021

)uncoverreturnpredictabilityinthecrosssectionofdelta-hedgedequityoptionsbasedonstock-basedinformation,suchasprices,profitmargins,andfirmprofitability.

Hestonetal.(Forthcoming

)investigatethephenomenonofoptionmomen-tumandreversal.Incontrasttotheirstudy,whichfocusesonextractingtradingsignalsfromtheinsightthatoptionsthatappreciatedoveracertainpasthorizontendtocontinuetodosointhefuture,weareagnosticaboutwhichcharacteristicsexplainfutureoptionreturnsandinsteadproposeawaytoextractinformationsimultaneouslyfrom273optionandstockcharacteristics.Finally,

GoyenkoandZhang

(2021

)applymachinelearningtechniquestoanalyzewhichcharacteristicsdriveoptionandstockreturns.

Wealsoextendtheliteratureontheusageofmachinelearningtechniquesinempiricalassetpricing.Sofar,themajorityofpapersapplymachinelearningmodelstopredictthecrosssectionofindividualstockreturns

.10

Rapach,Strauss,andZhou

(2013

)useLassoinpredictingmarketreturnsacrosscountries,while

MoritzandZimmermann

(2016

)applytree-basedconditionalportfoliosortstoexaminetherelationbetweenpastandfuturestockreturns.

Kelly,Pruitt,andSu

(2019

)applyinstrumentedprincipalcomponentanalysis(IPCA),detailedin

Kelly,Pruitt,andSu

(2020

),tomodelthecrosssectionofreturnsthatallowforlatentfactorsandtime-varyingloadings.

Gu,Kelly,andXiu(2020

)performacomparativeanalysisofmachinelearningmethodstomeasureequityriskpremiabasedonalargesetofstockcharacteristics.Theauthorsuseabroadsetofstockcharacteristics,

10

Nagel

(2021

)providesanoverviewofmachinelearningmethodsandthechallengesinvolvedwhenapplyingthemtoquestionsinempiricalassetpricing.

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OptionReturnPredictabilitywithMachineLearningandBigData

following

Green,Hand,andZhang

(2017

),whereas

Murray,Xiao,andXia

(2021

)focussolelyonhistoricalpricedata.

Neuhierletal.

(2021

)examinethepredictivepowerofoptioncharacteristicsforthecrosssectionofstockreturns.

Kozak,Nagel,andSantosh

(2020

)imposeaneconomicallymotivatedprioronstochasticdiscountfactorcoefficientsthatshrinkscontributionsoflow-varianceprincipalcomponentsforthecrosssectionofstockreturns,and

Chen,Pelger,andZhu

(Forthcoming

)addtotheseinsights,usingdeepneuralnetworkst

oestimateanassetpricingmodelforindividualstockreturns.

Martin

andNagel(2022

)showthatassetreturnsmayappearpredictablein-samplewhenanalyzingtheeconomyex-postandstresstheimportanceofout-of-sampletests.

Feng,Giglio,andXiu

(2020

)proposeanewmodelselectionmethodthataccountsformodelselectionmistakesthatproduceabiasduetoomittedvariables,and

LettauandPelger

(2020

)constructanewestimatorthatgeneralizesprinciplecomponentanalysisbyincludingapenaltyonthepricingerrorinexpectedreturns.Anonparametricmethodtodissectcharacteristicsbased

ontheadaptivegroupLassoisproposedby

Freyberger,Neuhierl,and

Weber(2020

).

Giglio,Liao,andXiu

(2021

)perform“thousandsofalphatests”todevelopanewframeworktorigorouslyperformmultiplehypothesistestinginlinearassetpricingmodels.

Grammigetal.

(2020

)contrasttheory-basedandmachinelearningmethodsformeasuringstockriskpremia.

TheaforementionedstudieshavemainlyfocusedonthecrosssectionofU.S.stocks.

Leippold,Wang,andZhou

(2021

),instead,employmachinelearningalgorithmstoanalyzereturnpredictionfactorsintheChinesestockmarket.Recentresearchalsoexpandstheapplicationofmachinelearningmodelsforthepredictionofotherassetclasses:

Kelly,Palhares,andPruitt

(Forthcoming

)proposeaconditionalfactormodelforcorporatebondsreturnsbasedontheIPCAapproach.

Hull,Li,andQiao

(2023

)buildapredictivemodelofbreakevenimpliedvolatilitiesofS&P500indexoptions.

Balietal.

(2021

)findthatmachinelearningmodelssubstantiallyimprovetheout-of-sampleperformanceofstockandbondcharacteristicswhenpredictingthecrosssectionofcorporatebondretu