Open Source Cross-Sectional Asset Pricing

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Open Source Cross-Sectional Asset Pricing Andrew Y. Chen and Tom Zimmermann 2021-037 Please cite this paper as: Chen,AndrewY.,andTomZimmermann(2021). “OpenSourceCross-SectionalAssetPricing,” Finance and Economics Discussion Series 2021-037. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.037. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Open Source Cross-Sectional Asset Pricing AndrewY.Chen TomZimmermann FederalReserveBoard UniversityofCologne andrew.y.chen@frb.gov tom.zimmermann@uni-koeln.de ∗ March2021 Abstract We provide data and code that successfully reproduces nearly all crosssectional stock return predictors. Our 319 characteristics draw from previous meta-studies, but we differ by comparing our t-stats to the original papers’ results. For the 161 characteristics that were clearly significant in theoriginalpapers,98%ofourlong-shortportfoliosfindt-statsabove1.96. Forthe44characteristicsthathadmixedevidence,ourreproductionsfind t-statsof2onaverage. Aregressionofreproducedt-statsonoriginallongshortt-statsfindsaslopeof0.90andanR2of83%.Meanreturnsaremonotonic in predictive signals at the characteristic level. The remaining 114 characteristics were insignificant in the original papers or are modificationsoftheoriginalscreatedbyHou,Xue,andZhang(2020).Theseremainingcharacteristicsarealmostalwayssignificantiftheoriginalcharacteristic wasalsosignificant. ∗ First posted to SSRN: May 18, 2020. We thank Ivo Welch for encouraging us to work on thisproject,andthankShaneCorwin,PaulSchultz,LuisPalacios,RabihMoussawi,andDenys Glushkovformakingtheircodepublicallyavailable.Wealsothankananonymousreferee,Guillaume Coqueret, Sebastian Hillenbrand, Liang Jiang, Yang Liu (from Tsinghua Finance), Yue Zhao,andanonymouscontributorstoourGitHubrepoforhelpfulcomments.Wearegratefulto SebastianWeilbelsandArneRodloffforexcellentresearchassistance. TheprojectreceivedsupportfromtheDeutscheForschungsgemeinschaft(DFG)underGermany’sExcellenceStrategy- EXC2126/1-39083886.TheviewsexpressedhereinarethoseoftheauthorsanddonotnecessarilyreflectthepositionoftheBoardofGovernorsoftheFederalReserveortheFederalReserve System.

1. Introduction Academic finance progresses through a mixture of open collaboration and closed competition. In this paper, we attempt to push the culture toward open collaborationbyprovidingan“opensourcedataset”ofhundredsofpredictorsof thecross-sectionofstockreturns. In our view, an open source dataset is essential because recent studies cast doubt on the credibility of the entire cross-sectional asset pricing literature. A seriesofinfluentialcritiquesarguethatatleast 45%ofthefindingsinthisliteraturearefalse(Harvey,Liu,andZhu2016,LinnainmaaandRoberts2018,Chordia,Goyal,andSaretto2020).1 Hou,Xue,andZhang(2020)gofurtherandclaim thatroughly50%oftheliteraturecannotbereplicated—evenwhenfollowingthe original methodologies.2 This finding implies that much of the literature fails tosurvivereproduction, muchlessreanalysis.3 Thesedoubtsechotheongoing credibilitycrisesinotherfieldsrangingfrommedicinetomanagement(Ioannidis2005;Nosek,Spies,andMotyl2012;Bettis2012). Our open source dataset takes a key step toward restoring the credibility of cross-sectional asset pricing. It shows that nearly 100% of the literature’s predictability results can be reproduced, including the predictability results for 100% of the characteristics studied in Hou, Xue, and Zhang (2020). Readers may be highly skeptical of our findings, given the critiques noted above. However, they do not need to take our word for it. Anyone with access to WRDS and Stata can perform this massive replication themselves using our code at https://github.com/OpenSourceAP/CrossSection. Indeed, our code is written with the user in mind. The code is modular, so users can quickly examine a particular characteristic without worrying about mostofthecode. Thecodeusesexceptionhandlingtogracefullymovepaster- 1Harvey,Liu,andZhu’s(2016)“arguethatmostclaimedresearchingfindingsinfinancialeconomicsarelikelyfalse.”Chordia,Goyal,andSaretto(2020)“estimatetheexpectedproportionof falserejectionsthatresearcherswouldproduceiftheyfailedtoaccountformultiplehypothesis testing to be about 45%.” Linnainmaa and Roberts (2018) “show the majority of accountingbasedreturnanomalies,includinginvestment,aremostlikelyanartifactofdatasnooping.” 2Hou,Xue,andZhang(2020)(HXZ)state“[r]epeatingourtestsontheshortersamplesinthe originalstudies,wefindthat65.4%ofanomaliescannotclearthesingletesthurdleof|t|≥1.96 withNYSEbreakpointsandvalue-weightedreturns. Thefailureratedropsto43.1%ifweallow microcapstorunamokwithNYSE-Amex-NADSQbreakpointsandequal-weightedreturns. 3FollowingWelch’s(2019)terminology,weusetheterm“reproduction”torefertoanattempt toproducethesameresultusingthesamesamplewiththesamecode. Reanalysisreferstoa broaderconceptthatincludesextensionsandre-examinations. 1

rorsandsemanticversioningtomakeupdateseasytounderstand.4 Last,weare committed to updating these data on an annual basis. We hope this demonstrationofopencollaborationwillinspireotherstoopenuptheiranalyses, and furthersupportthecredibilityofacademicfinance.5 Ourcodeproduces319firm-levelcharacteristics,andonlythreefailtoreproducetheoriginalpaper’sevidenceofstatisticalsignificanceforlong-shortportfolio returns. Our t-stats even match the originals quantitatively: A regression ofreproducedt-statsonhand-collectedt-statsfindsaslopeof0.90andanR2 of 83%. Wealsofindthatmeanreturnsarenicelymonotonicinthepredictors. The probability that predictor decile k has a higher mean return than decile k−2 is roughly96%. Thisnear-100%reproductionsuccessratewasmadepossiblebyacarefulexamination of the original papers. For each of our 319 signals, we hand-collect the key table, empirical test, the sign of predictability, t-stat, and other details fromtheoriginalpapers.Thishand-collecteddataisalsopartofouropensource dataset,andavailableforpublicinspection.6 Thehand-collecteddatashowsthatcharacteristicsinpreviousmeta-studies vary wildly in their original predictability evidence. They include everything from dividend seasonality, which was shown to produce a long-short t-stat of 16.2(HartzmarkandSolomon2013),toR&Dtosales,whichutterlyfailedtopredictreturns(Chan, Lakonishok, andSougiannis2001). Manyotherswerenever explicitlytestedforreturnpredictability(e.g. Francisetal.’s(2004)accrualquality). Asaresult,judgingthereproducibilityofthesecharacteristicscannotcome downtoasinglet-stat>1.96rule.7 Instead,weapplythet-stat>1.96ruleonlywhenitisappropriate. Thisrule isappropriateforthe161characteristicswecategorizeas“clearpredictors.” For these characteristics, the original papers showed clear evidence of significant predictabilityforourlong-shortportfolios. Wefindthat158of161clearpredic- 4Thecurrentversionofthecodeisv1.0.0,indicatingamajorrevisiontothepreviousv0.1.2. Themodularstructureandexceptionhandlingwaspartofthisrevision. 5Jensen,Kelly,andPedersen(2021)isanotheropensourceprojectthatprovidescodeformany cross-sectionalpredictors. HarveyandLiu(2019)providescrowd-sourcedhand-collecteddata oncross-sectionalassetpricingt-stats. 6Handcollecteddataishere: https://github.com/OpenSourceAP/CrossSection/raw/master/SignalDocumentation.xlsx 7Throughoutthepaper,wesignpredictorportfoliostohavepositivemeanreturnsbasedon theoriginalstudies.Thus,theruledoesnotinvolvetheabsolutevalue,andt-stat<-1.96typically indicatesareproductionfailure. 2

torsmeett-stat>1.96, andoneofthethreewhichdidnotstillachievedat-stat of1.93. Amoresubtleevaluationisrequiredforour44characteristicsthathadmixed evidenceofpredictabilityintheoriginalpapers.These“likelypredictors”include 52-weekhigh,withitsoriginallong-shortt-statof2.00(GeorgeandHwang2004), andsalesgrowthoverinventorygrowth, withitsoriginalt-statof2.4inamultivariateregression(AbarbanellandBushee1998). Evaluatingthereproducibility of these t-stats is a subtle exercise, as an immaterial change can cause the 52weekhightodipbelowt =1.96,andwedonotemployAbarbanellandBushee’s (1998)controlvariablesinourportfoliosorts. Complicatingissuesfurtheristhe factthatafewofourlikelypredictorsdeviatesignificantlyfromtheoriginalpapers in terms of methodology. In a replication project as large as ours, a few large deviations are unavoidable, and simply dropping these reproductions (or attemptedreproductions)isinconsistentwithourphilosophyofopenness. Toexaminethereproducibilityoflikelypredictors,wefirstexaminethesubsetforwhichtheoriginalpapersprovidelong-shortt-stats. Allbutfourofthese predictorsleadtosimilart-statsinourlong-shortportfolios. Theexceptionsare almostallaccountedforbysignificantdeviationsbetweenourmethodologyand theoriginalpapers,necessitatedbythescaleandopennessofourproject.8 The likely predictors that did not have long-short t-stats largely had borderline regressionresults. Ourreproductionsofthesepredictorsfindsimilarlyborderline significanceinlong-shortportfolios. Onceagain, wecantracedeviationsinresultstodeviationsinmethodology. Forexample,somelikelypredictorsthatperformpoorlyinoursingle-sortlong-shortportfolioswerestudiedinmultivariate regressionswithmanysignificantcontrolsintheoriginalpapers. Overall,onlythreeofour205clearandlikelypredictorsfailedtoachievethe predictability evidence found in the original papers. These three predictors are R&D ability from Cohen, Diether, and Malloy (2013) and the two shareholder activism measures from Cremers and Nair (2005). These failures should not be takenasacriticismofthesepapers,however,asitisquitelikelythatthereareremainingdeviationsorcodingerrorsamongourhundredsofreproducedcharac- 8Forexample,oursimpleregressionversionofslope-basedpricedelayproducesarawreturn t-statof2.01, farsmallerthanHouandMoskowitz’s(2005)characteristicadjustedt-statof7.7 fromtheirtwo-stageshrinkageestimate. However,HouandMoskowitz(2005)alsoshowasimilar difference in t-stats for their baseline R2-based price delay when the move from a simple regressionestimatewithnoadjustment(t-stat=3.4)toatwo-stageestimatewithcharacteristic adjustments(t-stat=8.0). 3

teristics. Indeed,apreviousversionofthispaperfailedtoreproduceHarveyand Siddique’s (2000) coskewness, but we have since fixed an error which restored thepowerofthispredictor. The rest of the dataset consists of 14 “not-predictors” that produced clearly insignificant predictability in the original papers, and 100 “indirect signals” which had only suggestive predictability evidence. Most of the indirect signals are variations on other characteristics created by Hou, Xue, and Zhang (2020). Werefrainfrompreciselyjudgingthereproducibilityofthesecharacteristics, as assessing the success of indirect signals requires multiple stages of judgment. Nevertheless, visual inspection of the reproduced t-stats for not-predictors and indirectsignalssuggeststhatthecross-sectionalliteratureisnotonlyshockingly replicable,butrobust. Almostalloftheindirectsignalsthataremodificationsof clearpredictorsalsoproducedsignificantpredictabilityinourreproductions. Wealsoprovideseveralsupportingdemonstrationsofthequalityofour205 clear and likely predictors. Pairwise correlations demonstrate that the dataset consistsofmanydistinctpredictors. Thedatasetalsodisplaysintuitivepropertieswithrespecttorebalancingfrequenciesandliquidityscreens. Notably,using eithervalue-weightingorscreeningoutstocksbelowthe20thpercentileofNYSE market equity leads to in-sample mean returns that are about 30% (20 bps per month)lower,consistentwithChenandVelikov’s(2019)in-sampleresults. Relation to the Literature Our results contrast with Hou, Xue, and Zhang (2020) (HXZ), who find that “most anomalies fail to replicate.” HXZ emphasize a 65% “failure” rate from value-weighting and NYSE breakpoints, but they also findreplicabilityisquitepoorwhentheyusemethodsthatareclosetothemodal equal-weightedimplementationoftheoriginalpapers(Green,Hand,andZhang 2013; McLean and Pontiff 2016). Specifically, HXZ state that “[t]he failure rate drops to 43.1% if we allow microcaps to run amok with NYSE-Amex-NASDAQ breakpointsandequal-weightedreturns.” We find that HXZ’s findings are driven by their permissive definition of an “anomaly.” HXZ analyze 452 “anomalies,” but these derive from only 240 characteristics, as 212 of these anomalies are just different rebalancing frequencies ofthe240basicstrategies. Andofthe240characteristics,only118showedclear evidence of significance for long-short returns in the original papers. In fact, ourreproductionsfindthat117 outofthese 118clear predictorsachieve t-stats 4

>1.96,andtheremainingpredictorhasat-statof1.93. Inotherwords,muchof HXZ’s “replication failures” are simply due to misclassification: these “anomalies”neverhadlong-shortportfoliosignificancetoreplicateinthefirstplace. OurreproductionratesalsocontrastwithChangandLi(2018),whofindreplicationratesof30-50%for67papersfromgeneralinterestandmacroeconomics journals. Our studies differ in several ways, but a key difference is that Chang and Li define a successful replication as “when the authors or journals provide dataandcodethatallow[them]toqualitativelyreproducekeyresultsofthepaper.” Indeed,lackofauthor-provideddataandcodeisthemostcommonreason ChangandLicitefortheirunsuccessfulreplications. Incontrast,wedidnotuse author-providedcodeatall,andsimplywrotecodebasedonthetextandexhibits intheoriginalpapers.9 Theseresultssuggestthatthewidespreadreplicationfailuresdocumentedinpreviousstudies(e.g.Dewald,Thursby,andAnderson1986, McCullough,McGeary,andHarrison2006)couldberemediedbyapplyingmore effort. OurreproductionratesmayalsolookhighcomparedtoMcLeanandPontiff (2016), who find that 12% of their 97 predictor portfolios produce t-stats < 1.5. Theseresultsarereconciled,however,bythefactthat24ofMP’spredictorshave whatwedescribeasborderlineevidenceofstatisticalsignificanceintheoriginal papers. Amongthe85ofourcharacteristicsthatarealsostudiedbyMP,14%of our reproductions lead to t-stats < 1.96, quite close to MP’s numbers. Most of these low t-stats come from “likely predictors,” however, and we do not judge themasreproductionfailures. WeshouldnotethatMP’sinclusionoflikelypredictorsisentirelyvalidforthegoalsoftheirstudy. Indeed, our open source data is highly consistent with MP’s findings. Like MP, we find that returns decay post-publication but remain positive, and that thisdecayisstrongerforpredictorsthatarestrongerin-sample. Ourresultsare quantitatively similar to those in MP, even for the subset of our predictors that are not studied by MP. These results echo previous papers that replicate MP in largersetsofpredictors(ChenandZimmermann2020;JacobsandMüller2020). Our paper adds to the evidence that the cross-sectional predictability literature is actually quite credible. These studies include out-of-sample tests (McLean and Pontiff 2016; Jacobs and Müller 2020), as well as multiple-testing adjustments(ChenandZimmermann2020; Chen2020; Jensen, Kelly, andPed- 9Foronecharacteristic,wedownloadcharacteristicdatafromtheauthors’website. 5

ersen 2021). Relative to these papers, ours adds novel evidence that the crosssectional literature is extremely replicable by comparing reproduced t-stats to hand-collectedt-stats. Animportantcaveatisthatwedonotaddressthedistinctbutrelatedquestion of whether the literature offers implementable trading profits. In a closely related paper, Chen and Velikov (2019) suggest that the answer is no. Building on Novy-Marx and Velikov (2016), Chen and Velikov find that effective bid-ask spreadswipeoutmostofthepost-publicationreturnsforalargesetofanomalies. Thepaperproceedsasfollows. Section2describesourmethodology,including our characteristics selection and predictor category definitions. Section 3 containsthemainresults: literature-levelreproductionperformance. Section4 takesacloserlook, examiningreproductionsatthecharacteristiclevel. Section 5 provides additional evidence supporting the quality of our dataset. Section 6 concludes. 2. Methods: Characteristic Selection, Variable Construction, and Predictability Categories This section describes our methodology. We describe how we select characteristics, how we construct characteristics and portfolios, and how we classify characteristics based on predictability evidence. Table 1 provides a broad overviewofthedataset. Weexplaintheterminologyandnumbersinthistablein whatfollows. [Table1: “OverviewofOpenSourceAssetPricingData”aroundhere] 2.1. CharacteristicSelection Weselectcharacteristicstobalancethreeobjectives: (1)comprehensivecoverageofpreviousmeta-studies,(2)comprehensivecoverageoffirm-levelcrosssectional predictors, and (3) completion of high quality code and data with a reasonableamountofeconomist-hours. To balance these goals, our list begins with the 240 characteristics used in 6

Hou,Xue,andZhang(2020)(HXZ).10 WefocusonHXZbecausetheirstudyalso examines the replicability of cross-sectional predictors. We then add an additional 49 characteristics for near-complete coverage of McLean and Pontiff (2016)(MP)andGreen,Hand,andZhang(2017)(GHZ).Finally,weadd30firmlevelstockreturnpredictorsfromHarvey,Liu,andZhu(2016)(HLZ). Thiscollectionleadstoatotalof319characteristicsdrawnfrom153papers. Covering HXZ requires that we sometimes include many characteristics based onasinglestudy. We do notaddall characteristicsfromMP and GHZ due to our thirdgoal of completinghighqualitycodeinareasonableamountoftime.Weomitthemergers and SEOcharacteristics from MP because they use the difficult-to-integrate SDCdataset. FromtheGHZdataset,weomitsevencharacteristicsfromunpublished working papers (Asness, Porter, and Stevens 2000; Gettleman and Marks 2006; Lerman, Livnat, and Mendenhall 2008; Bandyopadhyay, Huang, and Wirjanto2010),andonepredictorfromaretractedpaper(ChenandZhang2010). In adding characteristics from HLZ, we require that the characteristic was clearlyshowntopredictfirm-levelstockreturnsintheoriginalpaper. Thefirmlevel requirement eliminates many papers that target only portfolio returns, whichwasaprevalentfeatureofassetpricingpapersbeforethe1990s(e.g.Chan, Chen, and Hsieh 1985; Chen, Roll, and Ross 1986) and of macroeconomicsmotivatedpapersmoregenerally(e.g. Vassalou2003; BalversandHuang2007). This requirement is motivated by our second goal of a covering firm-level predictors. However, our first goal of meta-study coverage motivates us to not require clearfirm-levelpredictabilityoncharacteristicsfromHXZ,MP,orGHZ.Asaresult,ourcharacteristicsvarygreatlyintheirpredictivepowerbasedpurelyonthe resultsintheoriginalstudies. 2.2. CharacteristicConstruction We try to follow the original papers as closely as possible. We aim for “reproductions” in the sense of Welch (2019), and avoid reassessing the validity of the original papers. In our view, extensions and reexaminations require focused studies (e.g. Pontiff and Singla 2019, Novy-Marx and Velikov Forthcom- 10HXZ use these 240 characteristics to generate 452 “anomalies” by varying rebalancing frequencies. 7

ing), and are inappropriate for a large-scale meta-study like ours. Indeed, our large-scalestudynecessitatesdeviationsfromtheoriginalpapers,asweexplain shortly.11 As a result, our reproductions may be better described as “attempted reproductions,”butforeaseofreadingwetypicallydropthe“attempted”modifierthroughoutthetext. Westandardizeseveralofourreproductionprocedurestomaintainthetransparencyofourliterature-levelresults,aswellastheusabilityofourdata.Allcharacteristicsarecomputedatamonthlyfrequency. Forvariablesthatareupdated atalowerfrequency,themonthlyvalueisthemostrecentlyobservedvalue. This allows for portfolios that update at a lower frequency, while maintaining flexibility for alternative implementations.12 However, our monthly characteristics implythatwedeviatefromthehandfulofstudiesthatuseweeklyrebalancing. For almost all characteristics, we use the standard six-month lag for annual accountingdataavailabilityandaone-quarterlagforquarterlyaccountingdata availability. In a couple cases, we use the earnings reporting date (RDQ) to indicate availablility of quarterly data in order to more closely match the original papers. For IBES, we assume earnings estimates are available by the statistical periodenddate. Otherdataisassumedtobeavailablefollowingtheoriginalpapers.Asaconsequenceofthisstandardization,wedeviatefromafewaccounting studies,whichuseashorterdatalag.13 Many characteristics were only shown to be predictive in particular subsets of the data. We try to put off this subsetting until the portfolio generation step. Thus, the characteristics code and data omit price and exchange filters, which areinsteadimposedinportfoliogeneration. Otherfilters,however,arequitediverseanddifficulttoimplementattheportfoliostage.SeveralpapersexcludestocksbasedonSICcodesormissingaccountingdata.Stillothersfindpredictabilityonlyinsubsetsofstocksbasedonspecific characteristics (Piotroski 2000; Elgers, Lo, and Pfeiffer 2001). To accommodate thesefiltersinamanageablefashion,wesettomissingstock-monthsthatdon’t satisfythesefiltersinthecharacteristicscode. 11Evenforasmall-scalestudy,aperfectreproductionislikelyimpossible.WRDS’reproduction ofHMLobtainsacorrelationof98.9%withKenFrench’sdata,butthemonthlyreturnsstillhave deviationsofupto1%inparticularmonths(VoraandPalacios2010) 12Forahandfulofstudies,weenforcethetimingoftheupdatinginthecharacteristicscode. This was done help us find the code that closely matches the original results in a handful of difficultcases. 13Forusersofthecode: theaccountingdatalagisimposedinthedatadownloadstep,andis notvisibleinthefilesthatgeneratecharacteristics. 8

Inafewcases,wedeviatefromtheoriginalpaperstotradeoffcostsandbenefits. For most of these cases, we deviate by not acquiring the data used in the originalpapers. Forexample,Barberetal.(2001)andJegadeeshetal.(2004)use Zack’s analyst recommendations data, which goes back much further than the easily accessible IBES recommendations on WRDS. Similarly, we do not obtain theNYSEarchivedatarequiredforBarryandBrown(1984)ortheFitch’sQuotationdatausedbyAmihudandMendelson(1986). But other deviations are more idiosyncratic. We include a “number of consecutive earnings increases” predictor that is somewhat distant from the earningsstreakpredictorinLohandWarachka(2012)inordertocoverapredictorin Green, Hand, and Zhang (2017). We do, however, also include a characteristic that is closely-based on Loh and Warachka’s (2012) earnings streaks. All of our pricedelaypredictors(HouandMoskowitz2005)userollingregressionsofdaily individual stock returns, while the original paper typically uses a 2-stage procedure that first estimates a noisy measure of price delay on individual stocks andthenreducesthenoisebyrunningasecondsetofregressionsonportfolios formedfromthefirststage. Weusethesimplerestimatesofpricedelaylargelyto duetooureconomist-hoursbudget. These deviations imply that, in a handful of cases, our reproduced portfolios are very far from the originals. We include these attempted reproductions to maintain openness, which we believe is important for the credibility of the literature. 2.3. PortfolioConstruction The core of our portfolio data consists of predictive long-short portfolios formed following the original papers. Like other predictability studies, we implicitlyassumedataattheendofmontht canbeusedtomaketradesinclosing auctions on the last day of month t.14 These are the portfolios we use in our evaluationsofreproductionsuccess. Usingtheoriginalpaper’sresults,weselectthestock-weighting,rebalancing frequency, and quantile sort (if applicable). Each portfolio implementation is listed in our hand-collected data. Once again, we deviate from the original pa- 14As pointed out in Chen and Velikov (2019), the hypothetical traders in our portfolio tests wouldadddemandtotheclosingauctionsforthelonglegs,therebyincreasingthebuyingprices andreducingtradingprofits. 9

persforahandfulofportfoliosinthespiritofstandardizingourcodeandresults. The most notable deviation is that we use a simple equal-weighted decile sort portfolioforreproductionofFrazziniandPedersen’s(2014)betting-against-beta insteadoftheoriginalconstructionwhereeachstockisweighteddependingon itsbetaranking. We also offer portfolios implementations with alternative rebalancing frequencies and liquidity screens, as well as decile sorts and value-weighted only portfolios. We caution the user, however, in that these alternative implementationsarenotascloselyexaminedastheportfoliosthatfollowtheoriginalpapers. Inourbaselinedata,wedonotsignourcharacteristics,butdosignourportfolios. That is, a higher idiosyncratic volatility characteristic implies a lower meanreturn,butthecorrespondinglong-shortportfoliohasapositivemeanreturn. Thehand-collecteddatahasthissigninformation, whichuserscanapply totransformcharacteristicsifthisfitstheirapplications.15 Forsimplicity,wedo not sign portfolios if the original papers do not provide direct evidence on the correctsign. 2.4. PredictabilityCategories Todeterminepredictabilitycategories,wecompareresultsfromtheoriginal paperstoourcharacteristicreproductioncode. The original results are hand-collected. We hand-collect the key table demonstratingpredictivepower,theempiricaltestused,thesignofpredictability,meanreturn,t-stat,individualstockweighting,portfoliosortquantile,rebalancingfrequency, amongothernotes. Figure1showsanexcerptofourspreadsheetforillustration.16 Comparingthehand-collecteddatatoourcode,weassignourcharacteristics tofourcategories: • “ClearPredictor”:Ourcharacteristicisexpectedtoachievestatisticallysignificant mean raw returns in long-short portfolios (e.g. t-stat > 2.5 in a long-short portfolio, monotonic portfolio sort with 80 bps spread, t-stat >4inaregression,t-stat>3in6-montheventstudy). 15Wealsoprovideadatasetofsignedpredictorsfordirectdownload. 16Thefullspreadsheetisfoundat https://github.com/OpenSourceAP/CrossSection/raw/master/SignalDocumentation.xlsx. 10

• “LikelyPredictor”:Ourcharacteristicisexpectedtoachieveborderlineevidenceforthesignificanceofmeanrawreturnsinlong-shortportfolios(e.g. t-stat=2.0inlong-shortwithfactoradjustments,t-statbetween2and3in aregression,larget-statin3-dayeventstudy). • “Not-Predictor”: Expected to be statistically insignificant in long-short portfolios. (e.g. t-stat=1.5inlong-short,t-stat=1inaregression). • “Indirect Signal”: Only suggestive evidence of predictive power (e.g. correlatedwithearnings/price, modifiedversionofadifferentcharacteristic, in-sampleevidenceonly). These categorizations are necessary in order to measure reproduction success. Forclearpredictors,themeasurementisstraightforward,asat-stat>1.96 easilyidentifiesasuccess. Notethatwesignourlong-shortportfoliosbasedon the original results, so this rule does not involve the absolute value. For notpredictors,thesignflips,andat-stat<1.96isindicativeofasuccess. Measuringreproductionsuccessismoresubtlefortheothercategories,however.Somelikelypredictorshadt-statsverycloseto1.96inarawlong-shortportfoliointheoriginalpaper. Giventhatdataupdateswillsurelymovethet-statup or down, one should then place 50/50 odds that the reproduced t-stat will be aboveorbelow1.96. Similarly,iftheoriginalpaperfoundat-statof2.6inaunivariate regression, it’s hard to say if the reproduced long-short portfolio should alsoproduceat-stat>1.96. Deviationsbetweenourcharacteristicscodeandthe original recipes also lead to likely predictors, and necessitate subtle judgment calls. Indirectsignalsarealsotricky. Mostofourindirectsignalsaremodifications of other characteristics, and whether the modification should increase or decreasethet-statrequiresjudgment. Complicatingtheissueisthefactthatsome indirectsignalsaremodificationsoflikelyornot-predictors,implyingthatmultiplestepsofjudgmentarerequiredtodeterminewhichsideoft-stat=1.96our long-shortportfolioshouldlandon. Each characteristic’s predictability category can be found in Tables 2-4, and theassignmentsarediscussedinsomemoredetailinSection4.1. Table 1 briefly summarizes our predictability category assignments. Of our 319characteristics,161areclearpredictorsand44arelikelypredictors.Throughoutthetext,wedescribethesetwocategoriesassimply“predictors.”Wealsosep- 11

arate these predictorsfromthe other characteristics inour data and code. This separationishelpfulbecauseofclearandlikelypredictorsarequitedistinctfrom theothercharacteristicsinhowoneshouldanalyzethem. 14 of our characteristics are not-predictors, and 100 are indirect signals. As seen in the top panel, not-predictors and indirect signals play a minor role in mostothermeta-studies,withtheexceptionbeingHou,Xue,andZhang(2020). Indeed, the vast majority of our not-predictors and indirect signals are drawn fromHou,Xue,andZhang(2020). ThebottompanelofTable1showsthatourdataprovidesmore-or-lesscomprehensive coverage of other meta-studies. We cover all 452 of Hou, Xue, and Zhang’s(2020)“anomalies”,97%oftheclearpredictorsfromMcLeanandPontiff (2016),88%oftheclearpredictorsfromGreen,Hand,andZhang(2017),and90% oftheclearfirm-levelpredictorsthatusewidely-availabledatafromHarvey,Liu, andZhu(2016). WealsocoverallofthelikelypredictorsinMcLeanandPontiff (2016),Green,Hand,andZhang(2017),andHou,Xue,andZhang(2020).Indeed, mostoftheclear, widely-availablepredictorsthatwearemissingarecloselyrelatedtopredictorsthatweoffer(e.g.theindustry-adjustedvalueandmomentum predictorsofAsness,Porter,andStevens2000). Throughoutthepaperandcode,weseparateouttheclearandlikelypredictors. Wesometimesrefertothesecharacteristicsasjust“predictors,”forshort. For many purposes, predictors are the only characteristics that should be examined. Moreover, predictors are substantially less redundant than the full dataset. While the full dataset consists of 319 characteristics from 153 studies, the predictors consist of 205 predictors from 137 studies. For 101 studies, we drawonlyasinglepredictorfromthestudy.17 3. Literature-Level Reproduction Performance Thissectioncontainsourmainresults.Webeginbyexaminingliteraturelevel reproductionperformanceforclearandlikelypredictors(Section3.1). Wethen broaden the scope to not-predictors and indirect signals when we compare to 17Thedistributionofpredictorsperstudyisrightskewed.Moststudieshavejustonepredictor, but 20 have 2, and a few have many more. Heston and Sadka (2008) provide 10 strategies relatedtoreturnseasonality,andweincludeall10asclearpredictorstoavoidimposingjudgment onwhichisthe“right”strategy. Asimilarphilosophyleadsustoincludemanypredictorsfrom Richardsonetal.(2005)andDanielandTitman(2006). 12

othermeta-studies(Section3.2). 3.1. SuccessofPredictorReproductions Our first measure of reproduction success is a simple indicator: does the long-short raw return t-stat exceed 1.96? This measure is the primary focus of Hou, Xue, and Zhang (2020) (HXZ), and provides an easy-to-understand measureofreproductionsuccess. Figure 2 shows the share of clear predictors that exceed the simple t-stat > 1.96cutoff,brokendownbydatafocus: accounting,analystforecasts,corporate events, stock prices, trading data, and a broad “other” category. It shows only clear predictors, as likely predictors had borderline significance in the original papers (Section 2.4). As in all of our reproduction success evaluations, we use thesamesampleperiodintheoriginalpapers. The figure shows that reproductions are extremely successful. Our success rates are nearly 100% in every category. 73 out of our 74 accounting focused clear predictor reproductions succeeded. 40 out of 41 price-focused reproductionssucceeded. And43outof44reproductionssucceededamongtheremainingcategories. [Figure2“ReproductionSuccessRatesforClearPredictors”abouthere.] Onemightbeconcernedthatourextremelyhighsuccessrateissensitiveto ourdefinitionofaclearpredictor. Similarly,onemaybeconcernedthat,evenif ourt-statsexceed2.0,theymaybemuchsmallerthantheoriginalt-stats. Figure 3 should assuage both of those concerns. The figure examines both clear and likely predictors, and evaluates reproduction success more qualitatively,bysimplyplottingourreproducedt-statsagainstthet-statsoftheoriginal papers. Toensurethatt-statsarecomparable,thefigureexcludespredictorsthat were only examined in regressions or event studies in the original papers. We alsodropt-statsfromBarberetal.(2001),FrazziniandPedersen(2014),andHou andMoskowitz(2005)becauseourportfolioconstructionsareveryfarfromthe originalsforidiosyncraticreasons(seeSections2.2and2.3). [Figure3“ComparisonofReproducedandOriginalt-stats”abouthere.] 13

The figure shows that our extremely high reproduction success rate is not sensitivetoourpredictorcategorizations.Includedinthischartare11likelypredictors(triangles),allofwhichhadt-statscloseto2intheoriginalpapers(horizontalaxis).Consistentwiththeoriginalpapers,ourreproductionsalsotypically producet-statscloseto2.0,thoughroughlyhalfofthemfallbelowthearbitrary 1.96threshold.Morebroadly,ourextremelyhighsuccessrateforclearpredictors isnotduetot-statsjustabove2.0.Manyreproducedt-statsexceed5.0,andafew evenexceed10.0. Perhaps most important, Figure 3 shows that our reproductions match the original results not just qualitatively but quantitatively. A regression of our reproducedt-statsontheoriginalt-statsproducesacoefficientof0.90,notfarfrom theidealslopeof1.0.TheR2is83%,implyingthatthereproductionsdonotstray farfromtheoriginals. Indeed,muchoftheremainingdeviationsmaybedueto the fact that our t-stats use simple raw mean long-short returns, while many of theoriginalt-statsadjustforcharacteristicsorfactorexposures. As a final demonstration of the reproducibility of the cross-sectional literature, weexaminewhethermeanreturnsaremonotonicinthepredictors. From our experience, the vast majority of papers that showed portfolio sorts also showedmonotonicity—thoughwedidnothand-collectthisinformation. Figure4examinesthemonotonicityofdecilesortsforclearandlikelypredictors. Thefigurelimitsthedatato170continuouspredictors,asdiscretepredictorsarepoorlybehavedindecilesorts. Itplotsthemeanreturnasafunctionof thedecile,witheachmarkerrepresentingonepredictor-decile,andboxessummarizingthe25th,50th,and75thpercentilemeanreturnwithineachdecile.The figureshowsthatmeanreturnsareindeedmonotonicallyincreasinginthepredictors. Themedianacrosspredictorsincreasesmonotonicallyfromonedecile tothenext,asdoesthe25thpercentileandthe75thpercentile. [Figure4“Monotonicity”abouthere.] The box plots do not show predictor-level monotonicity, however, so we color-codethemarkersforacloserlook. Filledmarkersindicatepredictor-level monotonicityforagivenpredictor-decile.Thatis,themarkerisfilledifthemean return in decile k for predictor i exceeds the mean return for decile k−1 for thesamepredictori. Thefigureshowsthatroughly80%ofthepredictor-deciles show anincrease, astrongindicationofmonotonicity atthe predictor level. To 14

getasenseofthisratio,notethatitsuggeststheprobabilitythatdecilek exceeds the return of decile k−2 is 1−0.22 =96% in a simple binomial framework, and thatthisprobabilityisevenhigherwhencomparingdecilesfurtherapart. Beyond supporting reproducibility, this monotonicity result demonstrates robustness of the cross-sectional predictability literature. That is, monotonicity shows that the predictability evidence we find is not sensitive to the details of the empirical test. Deciles sorts, cross-sectional regressions, event studies should all produce consistent results. This finding is consistent with early versions of McLean and Pontiff (2016), which found that their results were similar usingFama-Macbethregressionsinsteadoflong-shortportfolios. Interestingly,Figure4alsoprovidesevidenceagainstthep-hackingexplanation for predictability. For p-hacking to explain predictability, it would have to operate across the entire predictor distribution, incrementally increasing mean returns from one level of the predictor to the next. This fine-tuning is an issue thatisnotexaminedinpreviousstudiesthatmodelp-hacking(Harvey,Liu,and Zhu(2016);ChenandZimmermann2020;Chen2020),norisitexaminedinHou, Xue,andZhang(2020). This concludes our main results. Nearly 100% of the literature on cross-sectional stock return predictability can be replicated. This finding implies not only the veracity of the literature, but defends the credibility of the asset pricing community more generally. Finally, these results support the quality of our open source dataset, publically available at https://github.com/OpenSourceAP/CrossSection. 3.2. Not-Predictors, Indirect Signals, and Comparison with OtherMeta-Studies The overwhelming success of our reproductions may appear to be at odds with the literature. McLean and Pontiff (2016) (MP) find that 12% of their 97 predictors produce t-stats < 1.5, suggesting a far higher “failure rate” than to our main results. More strikingly, Hou, Xue, and Zhang (2020) (HXZ) find that roughly50%oftheir452long-shortportfoliosproducet-stats<1.96inabsolute value,evenwithequal-weightingandwhenlimitingtotheoriginalpapers’sampleperiods. OurresultsdifferfromMPandHXZprimarilybecausewecarefullyexamine 15

theoriginalpaperstocheckifreproducedlong-shortt-statsshouldexceed1.96 beforetestingthisthresholdinourreproductions. Incontrast,MPhaveasomewhatmorelenientcriterion,limitingthemselvestopapers“inwhichthenullof noreturnpredictabilityisrejectedatthe5%level.” HXZaremuchmorelenient. HXZstatetheir“listencompassesthebulkofthepublishedanomaliesliterature infinanceandaccounting,”butdonotspecifyanymorerequirementsforinclusionthatwecouldidentify. OurcarefulexaminationisillustratedinFigure5,whichshowsajitterplotof reproducedt-statisticsforallofourcharacteristics,includingthoseinthe“notpredictor” and “indirect signal” categories. The first two rows echo Figures 2 and 3: Clear predictors almost uniformly have t-stats > 1.96 and many t-stats are much larger. Likely predictors are roughly evenly distributed around 1.96. Notably, these rows include predictors with evidence based on regressions and eventstudies,andthuscoverfarmorelikelypredictorsthanFigure3. [Figure5“PredictiveSignificanceintheExtendedDataset”abouthere.] Unliketheclearandlikelypredictors,not-predictorsandindirectsignalsgenerallyfailedtoachievestatisticalsignificanceinourreproductions. Alargemass ofindirectsignalsliestotheleftoft-stat=1.6,andalmostallofthenot-predictors fallinthesameregion. Figure 6 shows the analogous plot, restricted to the predictors that also appearinMP(toppanel)orHXZ(bottompanel). [Figure6“PerformancevsOtherMeta-Studies”abouthere.] ThetoppanelechosMP’sfindingthatabout12%theirpredictorshavesmall t-stats. 14ofour85characteristicsthatoverlapwithMPhavet-stats<1.96(dotted line). Most of these we judged as likely predictors, though a handful were judged as indirect signals and one was judged as a not-predictor. In particular, wejudgedDichev’s(1998)Z-Scoreasanot-predictor,asitfindsat-statof1.59ina univariateregression(seeDichev’sTable3A).It’slikelythatMPincludedZ-Score due to its t-stat of 3.37 in a multivariate regression with size and B/M controls, and reasonable people can disagree on the proper classification of this predictor. Nevertheless,wearguethatourreproducedt-statof1.20forZ-Score(Table 4) should not be judged as a reproduction failure, as it is quite consistent with Dichev’sunivariateresults. 16

The bottom panel of Figure 6 shows the breakdown for characteristics that overlap with HXZ’s. The data looks quite similar to our full dataset (Figure 5): Clear predictors are almost entirely above 1.96, likely predictors center around 1.96, not-predictors are below, and indirect signals are dispersed but many fall below the 1.96 cutoff. Thus, HXZ’s failure rate of around 50% seems to be due tothemisclassificationofthe“anomalies.” Inourreproductions, almostallapparentfailuresarelinkedtostudiesthatneverdemonstratedpredictabilityinthe firstplace. Importantly, MP’s choice to be more lenient in determining original-studypredictability is entirely valid for the goals of their study. MP seek to measure the decline in the magnitude of predictability out-of-sample, and one may be interestedinthisdeclineforpredictorsthatdon’tquitemeetthe1.96cutoff. Indeed,wefindthatwecancloselyreplicateMP’sresults,evenifwelimitour sampletoclearpredictors. ThisrobustnessisseeninFigure7, whichreplicates (MP’s) Figure 1 using only clear predictors. The top panel plots the in-sample returnvsthepost-publicationreturndecay,andthebottompanelswapsoutthe in-samplereturnforthe in-samplet-stat. Inbothpanels, we subsetthedata to clearpredictorsinMP(darkcircle)andclearpredictorsthatarenotinMP(light triangles). [Figure7“McLeanandPontiff(2016)Replication”abouthere.] The figure replicates and extends three important facts documented by MP about post-publication decay: (1) decay increases in the in-sample return, (2) decayincreasesinthein-samplet-stat,and(3)thedecayisnotlargeenoughto wipeoutthein-samplereturn. The first two facts can be seen in the upward slope of the regression lines in Figure 7. Strikingly, the upward slope does not depend on whether we fit the regression to predictors that are studied by MP (solid) or missing from MP (dashed). Indeed,thetwostandarderrorconfidencebandslargelyoverlap,indicatingthatMP’sfindingsholdquantitativelyinanout-of-sampletest(orperhaps out-of-out-of-sample test). Visual inspection of MP’s Figure 1 suggests our resultsarealsoquantitativelyconsistentwithMP’s,eventhoughwelimitoursample to clear predictors. We also find that using of all of MP’s predictors leads to similarresults. Thethirdfactcanbeseenbycomparingthepredictormarkerstothe45de- 17

gree dotted line in the top panel. If post-publication decay is strong enough to wipe out in-sample returns, then the predictors would be evenly distributed aroundthis45degreeline. However, themajorityofpredictorslieabovethe45 degreeline,showingthatpredictabilitysurvivespost-publication. It’simportant to note, however, that these results do not account for trading costs. Indeed, Chen and Velikov (2019) find that the remaining predictability is eliminated by effectivebid-askspreads. Overall,ourresultsappeartodifferfromothermeta-studiesbecausewecarefully categorize predictors based on the original results. Only with this carefulcategorizationcanameta-studyaccuratelyevaluatewhetherreplicationsare successfulonsuchalargescale. ThesecategorizationsdonotaffectMcLeanand Pontiff’s (2016) analysis and indeed we replicate their results among predictors withahigherstandardfor“originalsignificance.” In contrast, Hou, Xue, and Zhang’s (2020) finding of widespread replication failure for equal-weighted portfolios does not survive a more careful inspection.OurresultscallintoquestionHXZ’smainfindingsregardingvalue-weighted portfolios, though it is certainly true that anomalies are weaker when valueweighted(SeeSection5.2). 4. Characteristic-Level Reproduction Performance Behind the literature-level results are 319 firm-level characteristics, each of which has its own story, original statistics, and reproduction quality. Tables 2- 4 explore this rich data, listing each individual characteristic, the reproduced mean return and t-stat, and the evidence for predictability in the original papers. Table2listsclearpredictors,Table3listslikelypredictors,andTable4lists not-predictorsandindirectsignals. At the surface level, these tables provide a quick reference guide to our dataset. Wesortcharacteristicsbyauthornamesandprovidetheacronymused inourcode,soreaderscaneasilylookupcharacteristicsofinterest. At a deeper level, the tables provide a detailed characterization of our judgmentsofpredictorcategories(Section4.1),ourreproductionfailuresandstruggles(Section4.2),andthereproductionsthatledtoextremelylarget-stats(Section4.3). 18

[Table2“IndividualClearPredictors”abouthere.] [Table3“IndividualLikelyPredictors”abouthere.] [Table4“AdditionalCharacteristics”abouthere.] 4.1. WhichPredictorsAre“Clear,”“Likely,”or“Not?” Whichare “IndirectSignals?” We explained our predictor categorizations in Section 2.4 and showed that thecategorizationsdonotaffectourassessmentoftheliterature’sreproducibilityforlong-shortportfoliost-statsinSection3. However,readersmaystillhave questionsaboutwhycertainpredictorsarerelegatedtothe“likely,”“not,”or“indirectsignal”categories. Tables2-4shouldanswerthisquestion. 4.1.1. CategorizationDetailsforClearandLikelyPredictors Table 2 shows that most clear predictors produced t-stats that exceed 2.5 in long-short portfolios in the original papers (e.g. Ang et al.’s (2006) idiovol, Belo andLin’s(2012)inventorygrowth,Dichev’s(1998)long-shortO-Scorestrategy). Most of the remaining ones were shown to generate t-stats of 4 or more in regressions(e.g.FamaandFrench’s(1992)book-to-market,PontiffandWoodgate’s (2008)shareissuance).Aswithportfoliosorts,weonlyconsiderregressionstobe predictiveiftheyforecastreturnsinperiodt+1usingdataavailableattimet. Incontrast,mostofthelikelypredictors(Table3)hadmarginalt-statsinthe original papers. Several predictors had t-stats very close to 1.96 in long-short portfolios(Balletal.’s(2016)operatingprofitability, GeorgeandHwang’s(2004) 52-week high). Others have t-stats between 2 and 3 in regressions (Abarbanell and Bushee’s (1998) sales growth over inventory growth, Fama and MacBeth’s (1973) CAPM beta). It’s worth noting that the t-statistic cutoff of 1.96 is fairly arbitrary,andforsomequestionsregressionsaremorerelevantthanlong-short portfolios. Other likely predictors were more ambiguous. Amihud and Mendelson’s (1986) bid-ask spread predictor showed strong portfolio sorts, but the original paperdidnotprovidealong-shortt-stat. Moreover, theyuseFitch’sStockQuotations on the NYSE, while we use Corwin and Schultz’s (2012) effective spread 19

basedondailyCRSPdata(alsousedinMcLeanandPontiff(2016)).Chan,Lakonishok,andSougiannis’s(2001)advertisingexpensetomarketproduceda50bps spread in portfolio sorts, but they did not provide a t-stat. Haugen and Baker (1996) suggest several predictors based on the average t-stat across 180 differentmultipleregressions,butit’shardtotellsayifthisprocedureshouldresultin t-stats>2.0insimplelong-shortportfolios. Overall, the individual reproduced t-stats in Table 3 are almost uniformly consistent with the original study’s predictability evidence. t-stats much less than 2.0 are in almost every case associated with either middling t-stats in multi-variate regressions (Abarbanell and Bushee’s (1998) sales gross to overheadgrowth),specializeddatathatwedidnotemploy(AmihudandMendelson (1986)), or nonstandard methodologies that we did not use (Haugen and Baker (1996)). 4.1.2. CategorizationofNot-PredictorsandIndirectSignals Table4showsthatthenot-predictorshaveastraightforwarddefinition. Most not-predictors had t-stats < 1.96 in long-short portfolios in the original studies (Ang,Chen,andXing’s(2006)pastdownsidebeta;Anderson,Ghysels,andJuergens’s (2005) long-term forecast dispersion; Whited and Wu’s (2006) financial constraintsindex). It’simportanttomentionthatthislackofsignificanceshould notbeconsideredacriticismoftheoriginalpapers. The5%significancecutoffis arbitrary,andsomeofthesepredictorsfalljustbelowthecutoff. Manyindirectsignalssimplydidnotcomewithpredictabilityevidenceinthe originalpapers. Accrualquality, earningsconservatism, andearningsvaluerelevanceallcomefromFrancisetal.(2004),whichstudiescharacteristicsthatare relatedtoanimpliedcostofcapitalestimatebasedonValueLine’spricetargets. This paper does not, however, examine return prediction. Belo, Lin, and Bazdresch’s(2014)modelfeaturesavariablecalledbrandcapital,butthepaperdoes notexaminethepredictivepowerofthisvariable. Other indirect signals came with predictability-related information in the original papers, but we judged this evidence as too weak allow us to judge statistically significant predictability in portfolio sorts. Several of these weak evidence predictors come from Acharya and Pedersen’s (2005) study of liquidity betas. Acharya and Pedersen estimated market prices of risk for these betas in aGMMframework,whichwouldimplypredictabilityiftheparametersarevery 20

stable. But since betas tend to be unstable (Ang, Chen, and Xing 2006, for example)wejudgethisGMMresultasclosetonoevidenceregardingtheresultsof portfolio sorts. Similarly, we judged the multi-variate regressions of Abarbanell and Bushee (1998) and Soliman (2008) provide insufficient information for our purposeswhenthecoefficientonaregressorisinsignificant. But the bulk of the indirect signals are Hou, Xue, and Zhang’s (2020) variationsoncharacteristicsinotherstudies. Thesecharacteristicsarenotedas“HXZ variant” in the rightmost column of Table 4. Most of these modifications use quarterlyversionsofannualaccountingvariables. Afewinvolvearbitrarylagsof thedenominatororusingalternativefactormodeladjustmentswhengenerating returnresiduals(asinidiosyncraticvolatility). We refrain from assessing the predictor category of HXZ’s variants, because someofthemrequiresubtlejudgments. Forexample,HXZ’sproduceaquarterly versionofWhitedandWu’s(2006),whichproducedat-statof1.2intheoriginal paper. It’sveryhardtosaywhetheramoretimelyversionofthisvariablewould leadtostatisticalsignificance.Similarly,it’shardtosayifaquarterlyversionofan annual accounting-based variable will have too much seasonality to be predictive.Theseasonalitywoulddependontheprecisedetails,andwedidnotwantto exercisethismuchjudgment. Wedecided,therefore,tosimplylabelallofHXZ’s variantsasindirectsignals. Nevertheless, inspection of Table 4 shows that almost all of HXZ’s variants demonstrate the robustness of the original results. Chan, Lakonishok, and Sougiannis’s(2001)findthatR&Dtosalesfailstopredictreturns,andourreproduction of HXZ’s quarterly version also fails to achieve statistical significance. Meanwhile, our reproductions of HXZ’s variations on Anderson and Garcia- Feijoo’s(2006)capxgrowth,Balletal.’s(2016)cash-basedoperatingprofitability, andLakonishok,Shleifer,andVishny’s(1994)cashflowtomarketareallstatisticallysignificant,consistentwiththeoriginalconstructions. 4.2. ReproductionFailuresandStruggles Despitetheoverwhelmingsuccessinaggregate,Tables2and3illustratehow our reproductions struggle or even fail in a few instances. As emphasized in the introduction, these failures should not be takenas criticisms ofthe original papers, as it is quite likely that there are coding errors or remaining deviations amongourhundredsofreproducedcharacteristics. 21

The smallest reproduced t-stat among our clear predictors (Table 2) is Cremers and Nair’s (2005) (CN) takeover vulnerability. Our t-stat is just 1.00 with a meanreturnof25bpspermonth,despitethefactthattheoriginalpaperfounda t-statof3.1andanalphaof90bpspermonth. Ourreproductionusesrawmean returns, while CN use the Carhart (1997) four-factor alpha, so perhaps this deviationisdrivingthedifferenceinresults. However,wetypicallyfindthatfactor adjustmentshaverelativelyminoreffects(Figure3),andwealsohadtroublereproducingCN’sactiveshareholderspredictor, whichwecategorizedasa“likely predictor.” AsseeninTable3, ourreproductionproducedat-statof1.02, comparedtotheoriginalt-statof2.04. The second smallest t-stat comes from our reproduction of Cohen, Diether, and Malloy’s (2013) R&D ability. Our reproduction achieves a positive but insignificant t-stat of 1.50, compared to the original paper’s t-stat of 2.6. Cohen, Diether, andMalloymeasureR&DabilitybyarollingestimationofasalesforecastingmodelthatinvolvesseverallagsofR&D.AsR&Dispronetomissingand zerovalues,itisquitepossiblethatwefailedtofollowtheexactsameprocedures astheoriginalauthors. Among our clear predictors, the only other t-stat < 1.96 is Pástor and Stambaugh’s (2003) liquidity beta. However, our reproduced t-stat is 1.93, just a hair belowthearbitrarycutoffof1.96,andnotfarfromtheoriginalCAPM-adjustedtstatof2.5.WeshouldnotethatweonlyaimtoreproducePastorandStambaugh, andotherreplicationpapersfindthatthispredictorissensitivetoconstruction details(Li,Novy-Marx,andVelikov2019;PontiffandSingla2019). A few clear predictors have reproduced t-stats that are notably smaller than the originals, despite being larger than the 1.96 cutoff. The acronyms for these predictorsareclearlyseeninFigure3,andthedetailsofthesepredictorscanbe foundinTable2. Severalofthesepredictorscomefromaccountingpapersthatlagannualaccounting data by only 3 or 4 months rather than the 6 months used in the finance literature (Piotroski 2000; Xie (2001); Mohanram 2005). Similarly, we deviate from Johnson and So (2012) in rebalancing our portfolios monthly rather thanweekly.Intuitively,thesemoretimelysignalswouldproducenotablyhigher returns,andwedonotjudgethesedeviationsasreproductionfailures. Another underperforming reproduction is Elgers, Lo, and Pfeiffer’s (2001) earnings forecast to price, which in our data has a t-stat of 2.6, far lower than 22

theoriginalt-statof5. Theoriginalt-statwassize-adjusted,however,andother tablesinthispaperalsoshowsubstantialsizeeffectsintheirdata. The last clear predictor struggle worth mentioning comes from our reproduction of Boudoukh et al.’s (2007) payout yield portfolio. For this predictor, we chose to deviate from the original paper in a subtle way. At the very end of the original paper, the authors offer a long-short strategy that produces a t-stat of 3.92 from a tercile sort with NYSE breakpoints. We found our reproduction of this strategy was sensitive to how we lagged the signal before merging with return data, and that the more robust lagging method generated a very small tstat. However, NYSE terciles seemed unnecessarily conservative and moreover, Boudoukhetal.(2007)showadecilesortastheirfirstpredictabilitytable,which wecanreproducequitewell. Thus,ourimplementationfollowsthisdecilesort, though they do not provide a long-short t-stat for this procedure. All told, we judgethispredictortohavereplicatedreasonablywell. Amonglikelypredictors(Table3),mostoftheapparentreproductionfailures aresimplyduetodeviationsbetweenourreproductionattemptsandtheoriginal papers.AmihudandMendelson(1986),Barberetal.(2001),andBarryandBrown (1984)allusespecializeddatasetsthatwedonothaveaccessto(seeSection2). We also did not employ the multivariate regressions of Abarbanell and Bushee (1998), the aggregation of 180 multiple regressions used by Haugen and Baker (1996),orthespecializedportfoliosortusedbyFrazziniandPedersen(2014). The most notable likely predictors in terms of reproduction difficulty come from Frankel and Lee (1998). This paper uses analyst forecasts and a present value model to generate three trading strategies that we reproduce. Our reproductions lead to t-stats between 0.96 and 2.01, despite the fact that the original paper finds 1% statistical significance across the board. However, this high statistical significance was “derived using Monte Carlo simulation,” and is hard to squarewiththeirsmallreturnspreadsandshort15-yearsample.Indeed,wefind thatB/Mismuchlesssignificantintheirsamplethanthehighsignificancethey showusingtheirMonteCarlotest.Inshort,weattributeoursmallert-statstodeviationsinmethodologyratherthanfailedreproductions,butreasonablepeople candisagreeonhowtoevaluatethesereproductions. 23

4.3. ExtremelyStrongPredictors Figure3showedthatmanyreproductionsachievehuget-statsof6.0ormore. The corresponding p-value is 0.000000002, implying that it is absurdly unlikely thatthesepredictorsaredrawnfromthenullofnopredictability. Indeed,Chen (Forthcoming)arguesthatitwouldtakeinexpectationatleast400yearstogenerate these predictors from p-hacking alone. Consistent with this argument, Harvey, Liu, and Zhu’s (2016) SMM estimates and Chordia, Goyal, and Saretto’s (2020)calibrationsimplythatt-statsinexcessof4.0arealmostguaranteedtobe truediscoveries. Table2takesacloserlookatthesepredictors. Almostalloftheseoutstanding predictors focus on accounting data, analyst forecasts, or stock prices. Stated differently,almostnoneofthemcomefromthemoreexoticdatacategories. These outstanding performers are quite diverse. They include earnings surprise streaks (Loh and Warachka 2012); net external financing (Bradshaw, Richardson,andSloan2006),changeinrecommendation(Jegadeeshetal.2004), return seasonality (Heston and Sadka 2008), conglomerate return (Cohen and Lou 2012), dividend seasonality (Hartzmark and Solomon 2013), employment growth (Belo, Lin, and Bazdresch 2014), asset growth (Cooper, Gulen, and Schill 2008), change in taxes (Thomas and Zhang 2002), and enterprise multiple(LoughranandWellman2011). Thesepredictorslackanyobviouseconomic connection, consistent with the near zero median correlation we find among clear predictors (Section 5.1). However, these predictors do have in common extremelylarget-statsintheoriginalpapers,asseeninTable2andFigure3. 5. Additional Evidence of Dataset Quality Thissectionprovidesadditionalresultsonourdataset’squality. Welimitthis analysistothe205clearandlikelypredictors. Werefertoclearandlikelypredictors as just “predictors,” for short. We focus on predictors here because evaluating the quality of not-predictors and indirect signals is a much more complicated. The section shows that the dataset contains many distinct predictors (Section 5.1) and that the portfolio returns decline if we impose different liquidity adjustments (Section 5.2) or decrease the rebalancing frequency (Section 5.3). 24

Theseresultsalsoprovideusefulbenchmarknumbersregardingliquidityeffects. Namely, imposing value-weighting or market equity screens reduces mean returns by roughly a factor of 1/3. The results also illustrate the flexibility of our portfoliogenerationcode. 5.1. DistinctPredictors Inselectingcharacteristics,weaimprimarilyforcompletecoverageofpreviousmeta-studies(Section2.1). Wemakenoattempttoeliminatepredictorsdue tosubjectivesimilarities. Thus,weincludeseveralprofitability-relatedpredictorsincludingthosefrom Fama and French (2006); Balakrishnan, Bartov, and Faurel (2010); and Novy- Marx (2013). Being liberal about distinct predictors is necessary as there is, as of yet, no established methodology for determining distinct predictors. By including all predictors, we allow future users of our code and data to make their owndeterminationonwhichversionofprofitabilityisthe“right”one. Despitethispotentialredundancy,asimpleanalysissuggeststhatthisdataset isveryhigh-dimensional. Figure8examinesthisquestionbyshowingdistributionsofcorrelations. [Figure8“CorrelationsBetweenPairsofPredictorsorPortfolioReturns”about here.] Panel (a) shows correlations at the characteristic level. It shows the distributionofpairwiserankcorrelationsbetweenstock-levelpredictors(characteristics). Beforecomputingcorrelations,wesignallpredictorssothatahigherpredictorvalueimplieshighermeanreturnsbasedontheoriginalpapers.Thepanel showsthatpredictor-levelpairwisecorrelationsaregenerallyclosetozero,suggesting that the predictors contain distinct information. These results are consistent with Green, Hand, and Zhang (2013) who also find correlations close to zeroamongtheirsetof39readilyprogrammedpredictors. Panel (b) shows this high dimensionality extends to the portfolio level. It alsoshowsthedistributionofpairwisecorrelations,thistimeusingpairsoflongshortportfolioreturns. Aswithallofourlong-shortpredictorportfolios,portfoliosaresignedtohavepositivemeanreturnsfollowingtheoriginalpapers. Similartothepredictorcorrelations,portfolioreturncorrelationsareclosetozerofor 25

thebulkofthedistribution. Indeedthevastmajorityofcorrelationsliebetween -0.5and+0.5. Panels (c) and (d) examine whether the HML and momentum factors subsume our long-short portfolios. HML and momentum factors are both downloadedfromKenFrench’swebsiteandconstructedfrom2x3sortsfollowingFama and French (1993). That is, (1) stocks are independently assigned to “S” or “B” basedontheNYSEmediansizeand“H”or“L”basedonthe30thand70thpercentiles of either B/M or the past year’s return within NYSE stocks, (2) valueweightedportfoliosareformedforS/L,B/L,S/H,andB/Hintersections,and(3) factor returns computed as 0.5(S/H+B/H) - 0.5(S/L+B/L). In contrast, our B/M andmomentumportfoliosarejustsinglesorts. WefollowRosenberg,Reid,and Lanstein (1985), Fama and French (1992), and Jegadeesh and Titman (1993) in constructing these portfolios, and like most of our predictors these original papersdonotemploytheFamaandFrench(1993)2x3factorconstructionfortheir anomalystrategies.18 Panel (c) shows that a handful of our portfolios have correlations of 0.6 of more with HML, but the bulk of the correlation distribution remains close to zero. Panel (d) shows a similar result for the momentum factor. Overall, our long-short portfolios contain many distinct strategies, consistent with McLean andPontiff’s(2016)findingofanearzeroaveragecorrelationamongtheirreproductedreturns. 5.2. PerformancebyLiquidityAdjustment Following our philosophy of “reproduction,” our baseline portfolios follow theoriginalpapersasmuchaspossible(Sections2.2-2.3). Theseportfolioslikely overstate the profits traders could have earned from these predictors, however, as most of them are equal-weighted (Green, Hand, and Zhang 2013). Equalweighted portfolios require the trading of illiquid stocks and huge transaction costs(Novy-MarxandVelikov2016,forexample). Figure9examineshowsimpleliquidityadjustmentsaffectpredictorperformance. Thefigureshowsjitterplotsofin-samplemeanreturns, comparingthe 18Rosenberg,Reid,andLanstein(1985)useacomplicatedproceduretoremoveexposuretoa varietyof“riskindexes,”whichissimilarinspirittotheFamaandFrench(1993)2x3approachin thattheybothremoveexposuretosize. However,Rosenbergetal’sprocedureisnotverytransparentanddifficulttoimplement,sowejustuseourdefaultquintilesortforsimplicityandtransparency. 26

originalpaper’sadjustments(ifany)tovariousliquidityscreensaswellastheenforcement of value-weighting. The original liquidity adjustments can be found inourhand-collecteddataathttps://github.com/OpenSourceAP/CrossSection. [Figure9“PerformancebyLiquidityScreen”abouthere.] Intuitively, all liquidity adjustments lead to lower mean returns. The price screen (limiting to stocks with share price > $5) appears to be the softest adjustment, producing the smallest decline in performance. The other liquidity adjustmentshaverelativelysimilareffects. Overall, simple liquidity adjustments reduce mean returns by a factor of about 1/3, on average. The typical mean return drops from around 60 bps per month to about 40 bps per month regardless of whether the adjustment is an NYSE only screen, a market equity screen, or the enforcement of valueweighting. These results are quantitatively similar to Chen and Velikov (2019), whofindthateffectivebid-askspreadseliminateabout1/3ofmeanreturnsinsample,evenaftercost-mitigation. Figure9alsoillustratestheflexibilityofourcode. Thesevariousscreensare madepossiblebythefactthatwetrytodelayimposingscreensuntiltheportfolio generationstep.Asaresult,theusercanchoosewhetherheorshewishestotake signalfromallstocks,orjustthemoreliquidones. 5.3. PerformancebyRebalancingFrequency Ourcodealsoallowsforaflexiblechoiceoftherebalancingfrequency. More precisely, the code allows the user to choose how often stocks are re-assigned to portfolios. We refer to this as “rebalancing,” following the cross-sectional literature.19 This flexibility may be important, for example, when accounting for tradingcosts. Figure10showsthatourcodeleadstointuitiveresultswhenwealtertherebalancing frequency. This figure plots the distribution of mean returns across 19 Following the cross-sectional literature, our portfolios are always rebalanced monthly in the sense that stock weights are adjusted every month to provide equal- or valueweighting. Most papers do not provide precise explanations of these details, but in our experience this procedure is required for replicating papers. For an explicit example, see https://wrds-www.wharton.upenn.edu/pages/support/applications/risk-factors-andindustry-benchmarks/fama-french-factors/. 27

predictors for 1-, 3-, 6-, and 12-month rebalancing. For comparison, we also showresultsusingtherebalancingfrequencyintheoriginalpapers. [Figure10“PerformancebyRebalancingFrequency”abouthere.] Rebalancing at a monthly frequency leads to slightly higher mean returns comparedtotheoriginalspecifications. Thisisduetothefactthatmanyofthe original papers follow Fama and French (1992) and rebalance annually (every June). Performancedeclinesmonotonicallyastherebalancingfrequencydecreases from 1- to 12-months. This pattern is intuitive as less frequent rebalancing implieslessexposuretothepredictivesignal. 6. Conclusion Thecredibilityofcross-sectionalassetpricingisindoubt. Severalpapersarguethatmuchoftheliteratureisfalsedotoarelianceonstatisticalmethodsthat are no longer valid (Harvey, Liu, and Zhu 2016; Linnainmaa and Roberts 2018; Chordia,Goyal,andSaretto2020). Oneheavily-citedstudyclaimsthat,notonly are the statistical methods invalid, but the numbers cannot be replicated, even whenfollowingtheoriginalmethodologies(Hou,Xue,andZhang2020). We provide data and code that takes a key step toward restoring the credibility of the literature. The data shows that nearly 100% of the literature’s predictability results can be reproduced, and our code shows how this surprising result is achieved. This reliability adds to the evidence that the cross-sectional predictability literature is quite credible (McLean and Pontiff 2016; Jacobs and Müller2020;ChenandZimmermann2020;Jensen,Kelly,andPedersen2021). Ourcodeiswrittenexplicitlywiththeuserinmind. Thestructureismodular andparallel,sothatpiecesofthecodecanbeeasilyfixedorimproveddespitethe massive size of the entire package. We welcome users to examine and build on ourcodebyvisitinghttps://github.com/OpenSourceAP/CrossSection. Wehope thisdemonstrationofopencollaborationinspiresotherstoopenuptheiranalyses.Inourview,ashifttowardopennessisnotonlyimportantfortheprofession’s understandingofriskandreturn,itisalsoimportantforprotectingthecredibility ofacademicfinanceintheeyesofthebroaderpublic. 28

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Figure 1: Illustration of Hand-Collection from Original Papers. Description: The figure shows an excerpt from the spreadsheet we used to hand-collect predictabilityevidencefromtheoriginalpapers. Thefullspreadsheetcanbefound at https://github.com/OpenSourceAP/CrossSection. Interpretation: Evidence required for evaluating reproductions is documented at the characteristic level andreaderscaneasilytraceourpredictorcategorizationstotheoriginalpapers’ exhibits. 43

Figure 2: Reproduction Success Rates for Clear Predictors. Description: We constructonelong-shortportfoliofromeachclearpredictorfollowingtheoriginalpapers’resultsandexaminethet-statforthehypothesisthatthemeanreturn is zero in the original papers’ sample periods. Clear predictors are those where theoriginalpapersclearlydemonstratethatourportfoliosshouldbestatistically significant(see Section2.4). Interpretation: Almost100% ofthecross-sectional predictabilityliteraturecanreproducedandourcodeanddatashowhow. 44

Figure 3: Comparison of Reproduced Long-Short t-stats with Original Long-Short t-stats for All Predictors. Description: We compare reproducedlong-shortt-statstohand-collectedt-statsfromtheoriginalstudies. Weincludebothclearandlikelypredictors(definedinSection2.4). We exclude t-stats from regressions and event studies, and also drop t-stats from three studies because our portfolios deviate significantly from the originals for idiosyncratic reasons (Barber et al. 2001, Frazzini and Pedersen 2014, Hou and Moskowitz 2005, see Section 2). Reproduced t-stats userawreturnsbutoriginalt-statsmayincludefactororcharacteristicadjustments. Axesarelog-scaletomakethepredictoracronymseasierto read. FullreferencesarefoundinTables2and3. RegressionfitusesOLSinlevels, thoughlogsleadstosimilarresults. Interpretation: TheoverwhelmingreproductionsuccessinFigure2isnotduetopredictorcategorizationsormarginallysignificantreproductions. Ourreproducedt-stats quantitativelymatchtheoriginalpapers’forbothclearandlikelypredictors. 45

Figure4:MonotonicityofMeanReturns.Description:Weformdecileportfolios andexaminethemeanmonthlyreturnineachdecile. Dataislimitedtothe170 continuous predictors. Each marker is one predictor-decile. Filled circles indicatethatthemeanreturnindecilek exceedsthemeanreturnfordecilek−1for thesamepredictor. Interpretation: Meanreturnsincreasemonotonicallyinthe signal, reproducing the fact that most original portfolio sorts show monotonicity,andshowingpredictabilityisrobusttoimplementationdetails.Monotonicity supportstheideathatp-hackingdoesnotexplainanomalies,asp-hackingwould havetooperateacrosstheentirepredictordistribution. 46

Figure5: Reproduction Performancefor All Characteristics. Description: We construct one long-short portfolio from each characteristic following the original papers and examine the t-stat for the hypothesis that the mean return is zero in the original papers’ sample periods. Predictor categories use results fromtheoriginalpaperstojudgmentallydeterminewhetherweshouldexpectto find statistical significance inour portfolio tests(see Section2.4). Clear predictorsprovideclearevidence,likelypredictorshaveborderlineevidence,andnotpredictorsimplyinsignificance. Indirectsignalshadonlysuggestiveevidenceof predictive power. Almost all indirect signals come from Hou, Xue, and Zhang (2020). Interpretation: Likely predictors have reproduced t-stats that average around 2.0, consistent with the original evidence. Not predictors are also reliablyreproduced. Indirectsignalsvarywildlyintermsoftheirperformance. 47

Figure6: ReplicationofOtherMeta-StudyReplicationRates. Description: We examinesubsetsofourcharacteristicsthatareinMcLeanandPontiff(2016)(top panel)orHou,Xue,andZhang(2020)(bottompanel). Eachmarkerisonecharacteristic’slong-shortt-stat. Predictabilitycategoriesarebasedonresultsinthe original papers (see Sections 2.4 and 4.1). Vertical line is 1.96. Interpretation: WereplicateMP’sfindingthatroughly12%oftheirpredictorshavesmallt-stats. HXZ’s high “failure rate” seems to be driven by indirect signals, which were not testedforpredictabilityintheoriginalpapers. (a)McLeanandPontiff(2016) (b)Hou,Xue,Zhang(2020) 48

Figure 7: Out-of-Sample Replication of McLean and Pontiff’s (2016) Out-of- Sample Tests (MP). Description: we compare the in-sample return (top panel) orin-samplet-stat(bottompanel)withthedifferencebetweenin-samplemean returns and post-publication mean returns (ppt per month). OLS fit is shown using either predictors in MP (solid line) or predictors not in MP (dashed line). Fits in bottom panel are difficult to see because both fits are nearly identical. Shadedareais2S.E.AxislimitsareidenticaltoMP’sFigure1.Dottedlineisthe45 degreeline. Interpretation: MP’sfindingsreplicate,evenout-of-sample. Returns decay post-publication (markers are right of 0) but remain positive (above 45 deg line in top panel), and the decay is higher for predictors that are stronger in-sample(upwardslopes),consistentwithinvestorslearningaboutmispricing fromacademicstudies. 49

Figure 8: Correlations Between Pairs of Predictive Characteristics or Pairs of Portfolio Returns. Description: We show the distribution of correlations for (a) pairs of characteristics, (b) pairs of long-short portfolio returns, (c) longshort returns paired with HML, and (d) long-short returns paired with a Fama andFrench(1993)-stylemomentumfactor. HMLandFF3-stylemomentumare downloaded from Ken French’s website. Data is limited to clear and likely predictors. Characteristics are signed so that a higher value implies higher mean returns and portfolios are signed to have positive mean returns, both following the original papers. Characteristic are pooled across all firm-months available and returns are pooled across the longest overlapping sample. Interpretation: Ourdatasetcontainsmanydistinctpredictors. (a)SignedPredictiveCharacteristics (b)SignedPredictorPortfolioReturns (c)SignedPortfoliosandHML (d)SignedPortfoliosandFF3Momentum 50

Figure 9: Performance by Liquidity Adjustment. Description: We use predictivecharacteristicstoconstructlong-shortportfoliosusingvariousliquidityadjustments. “Originalpapers”usesadjustmentsfromtheoriginalpapers(ifany); “price > 5,” “NYSE only,” and “ME > NYSE 20 pct” only take positions in stocks ifthesharepriceexceeds$5, stockislistedontheNYSE,orifmarketequityexceeds to 20th percentile among NYSE stocks in the month. “VW force” forces value-weighting. Each dot is one portfolio. Middle line is median, boxes are 25 and75percentiles,andthewhiskersextendtothesmallest(largest)valuewithin the 25th (75th) percentile minus (plus) 1.5 times the interquartile range. Interpretation: Ourcodecanimposeavarietyofliquidityadjustmentsandproduces the intuitive result that liquid stocks are less predictable. Most simple liquidity adjustmentsreducemeanreturnsbyafactorofabout1/3. 51

Figure 10: Performance by Rebalancing Frequency. Description: We use predictivecharacteristicstoconstructlong-shortportfoliosthattakeonnewsignal dataevery1-,3-,6-,or12-monthsandmeasuremeanreturnsintheoriginalsampleperiods. “Originalpapers”usestherebalancingfrequencyintheoriginalpapers.Middlelineismedian,boxesare25and75percentiles,andthewhiskersextendtothesmallest(largest)valuewithinthe25th(75th)percentileminus(plus) 1.5timestheinterquartilerange. Interpretation:Ourcodeisflexibleinrebalancing frequencies and produces the intuitive result that less frequent rebalancing leadstolowermeanreturns. Enforcing12-monthholdingperiodsreducesmean returnsbyroughly20%comparedtotheoriginalspecifications. 52

Table1:AnOpenSourceDatasetforAssetPricing Description:ThistablecomparesourdatasettoMcLeanandPontiff(2016)(MP);Green, Hand,andZhang(2017)(GHZ);Harvey,Liu,andZhu(2016)(HLZ);andHou,Xue,and Zhang(2020)(HXZ).Predictorcategoriesuseresultsfromtheoriginalpaperstodetermine whether we should expect to find statistical significance in our long-short portfolio tests. Clear predictors provide clear evidence (e.g. long-short t-stat > 4), likely predictors have borderline evidence (e.g. multi-variate regression t-stat ≈ 2.5), and not-predictors have t-stats < 1.96. Indirect signals had suggestive evidence of predictivepower(e.g. usedasaningredientinalargermodel, correlatedwithB/M).WidelyavailabledataincludesCRSP-Compustat,IBES,OptionMetrics,13F,amongothers.AdetailedlistofcharacteristicdefinitionsisintheOnlineAppendix.Codeanddataareavailable at https://github.com/OpenSourceAP/CrossSection. Interpretation: Our dataset offerscomprehensivecoverageoffirm-levelpredictors. PanelA:VariableCounts OurData OtherMetastudies Predictor Extended MP GHZ HLZ HXZ Firm-LevelCharacteristicsfromWidely-AvailableData ClearPredictor 161 161 68 66 229 118 LikelyPredictor 44 44 24 13 7 27 Not-Predictor 14 1 3 1 10 IndirectSignals 100 4 20 46 85 Total 205 319 97 102 283 240 AdditionalPortfoliosMadefromAlternativeRebalancingFrequencies 957 212 OtherVariables Theory 22 NotFirm-Level 91 Non-WidelyAvailableData 38 Total 205 1276 97 102 283 452 PanelB:OurCoverageofOtherMetastudies(%) MP GHZ HLZ HXZ Firm-LevelCharacteristicsfromWidely-AvailableData ClearPredictor 97 88 90 100 LikelyPredictor 100 100 43 100 not-predictor 100 100 100 100 IndirectSignals 100 100 91 100 53

Table2: PerformanceofIndividualClearPredictors. Description: This table lists clear predictors (defined in Section 2.4) in the baseline data along with their original in-sample periods; the in-sample mean return (% monthly) and t-stat in our reproduced portfolio; and the predictability evidence in the original paper. “port sort” is portfolio sort, “LS” is long-short portfolio, “mv reg” is multivariate regression. Interpretation: Reproduced t-stats are close to the original results and support the credibility of the literatureaswellasthequalityofourcodeanddata. Thetablealsoprovidesaquick-referenceguidetoourcodeanddata. Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat AbarbanellandBushee(1998) Changeincapitalinv(indadj) ChInvIA 1974-1988 0.50 5.50 t=2.9inmvreg Ali,Hwang,andTrombley(2003) Idiosyncraticrisk(AHT) IdioVolAHT 1976-1997 0.89 2.53 t=2.7inmvreg Alwathainani(2009) Earningsconsistency EarningsConsistency 1971-2002 0.21 2.51 t=2.7incomplicatedLSport Amihud(2002) Amihud’silliquidity Illiquidity 1964-1997 0.57 3.51 t=6.6inunivariatereg AndersonandGarcia-Feijoo(2006) Changeincapex(twoyears) grcapx 1976-1999 0.50 4.96 t=5inportsort AndersonandGarcia-Feijoo(2006) Changeincapex(threeyears) grcapx3y 1976-1999 0.59 4.77 t=4.7inportsort Angetal.(2006) Systematicvolatility betaVIX 1986-2000 1.07 3.54 t=3.9inportsort Angetal.(2006) Idiosyncraticrisk IdioRisk 1963-2000 0.99 3.25 t=2.9inportsort Angetal.(2006) Idiosyncraticrisk(3factor) IdioVol3F 1963-2000 0.96 3.12 t=3.1inportsort Ang,ChenandXing(2006) Coskewnessusingdailyreturns CoskewACX 1963-2001 0.29 2.62 t=2.8inportsort Avramovetal(2007) JunkStockMomentum Mom6mJunk 1985-2003 1.58 3.30 t=4.3inportsort BaikandAhn(2007) Changeinorderbacklog OrderBacklogChg 1971-1999 0.38 2.49 p<0.01inportsort Balakrishnan,BartovandFaurel(2010) Returnonassets(qtrly) roaq 1976-2005 1.69 5.90 t=6.5inportsort,nontraditional Bali,Cakici,andWhitelaw(2010) Maximumreturnovermonth MaxRet 1962-2005 0.89 2.74 t=2.8inportsort Bali,EngleandMurray(2015) Returnskewness ReturnSkew 1963-2012 0.41 5.27 t=4inportsort Bali,EngleandMurray(2015) Idiosyncraticskewness(3Fmodel) ReturnSkew3F 1963-2012 0.29 4.76 t=4.4inportsort Balletal.(2016) Cash-basedoperatingprofitability CBOperProf 1963-2014 0.46 3.20 t=3.2inportsort Banz(1981) Size Size 1926-1975 0.50 2.61 t=3.1inlong-short BarthandHutton(2004) ChangeinForecastandAccrual ChForecastAccrual 1981-1996 1.22 12.30 p-val<0.001inportsort BartovandKim(2004) Book-to-marketandaccruals AccrualsBM 1980-1998 1.44 4.85 t=5.5inlong-short Basu(1977) Earnings-to-PriceRatio EP 1957-1971 0.39 2.21 monotonicportsortbutnoLS Bazdresch,BeloandLin(2014) Employmentgrowth hire 1965-2010 0.51 5.67 t=5.8inportsort BeloandLin(2012) InventoryGrowth InvGrowth 1965-2009 0.87 7.19 t=6.6inportsort Bhandari(1988) Marketleverage Leverage 1952-1981 0.36 2.64 t=3.9inregression Blitz,HuijandMartens(2011) MomentumbasedonFF3residuals ResidualMomentum 1930-2009 0.95 8.27 t=8inlong-shortff3+alpha BlumeandHusic(1972) Price Price 1932-1971 1.43 3.06 t=3inregressions Boudoukhetal.(2007) NetPayoutYield NetPayoutYield 1984-2003 0.87 2.57 t=2.8inconservativeLS,strongportsort Boudoukhetal.(2007) PayoutYield PayoutYield 1984-2003 0.43 2.27 t=3.9inconservativeLS,strongportsort Bradshaw,Richardson,Sloan(2006) Netdebtfinancing NetDebtFinance 1971-2000 0.75 7.70 t=6.9inportsort continuedonnextpage 54

Table2:(continued) Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat Bradshaw,Richardson,Sloan(2006) Netequityfinancing NetEquityFinance 1971-2000 1.06 5.40 t=3.8inportsort Bradshaw,Richardson,Sloan(2006) Netexternalfinancing XFIN 1971-2000 1.14 4.84 t=5.7inportsort Brennan,Chordia,Subra(1998) Pasttradingvolume DolVol 1966-1995 0.75 2.72 t=2.9inregression Cen,Wei,andZhang(2006) Analystearningspershare FEPS 1983-2002 1.46 3.04 t=2.7inportsort ChanandKo(2006) MomentumandLTReversal MomRev 1965-2001 1.19 4.38 t=4.3inlong-short Chan,JegadeeshandLakonishok(1996) Earningsannouncementreturn AnnouncementReturn 1977-1992 1.20 13.34 t=9.3inregression Chan,JegadeeshandLakonishok(1996) Earningsforecastrevisions REV6 1977-1992 1.29 5.44 t=4.1inregression Chan,LakonishokandSougiannis(2001) R&Dovermarketcap RD 1975-1995 1.23 6.91 strongportsort ChandrashekarandRao(2009) CashProductivity CashProd 1963-2003 0.56 3.40 t=3.6inregression Chen,HongandStein(2002) Breadthofownership DelBreadth 1979-1998 0.69 3.69 t=4.0inportsort Chordia,Subra,Anshuman(2001) Shareturnovervolatility std_turn 1966-1995 0.80 3.42 t=3.7inregression Chordia,Subra,Anshuman(2001) VolumeVariance VolSD 1966-1995 0.38 2.82 t=3.6inregression CohenandFrazzini(2008) Customermomentum CustomerMomentum 1980-2004 1.16 3.27 t=3.8inportsort CohenandLou(2012) Conglomeratereturn retConglomerate 1977-2009 1.32 6.50 t=5.5inportsort Cohen,DietherandMalloy(2013) R&Dability RDAbility 1980-2009 0.27 1.50 t=2.6indoublesort Cooper,GulenandSchill(2008) Assetgrowth AssetGrowth 1968-2003 1.50 7.64 t=8.5inportsort CremersandNair(2005) Takeovervulnerability Activism1 1990-2001 0.24 1.00 t=3.1inportsort DaandWarachka(2011) Long-vs-shortEPSforecasts EarningsForecastDisparity 1983-2006 0.66 4.38 t=5.1inLSport DanielandTitman(2006) Compositeequityissuance CompEquIss 1968-2003 0.27 2.41 t=4.4inmvreg DanielandTitman(2006) IntangiblereturnusingBM IntanBM 1968-2003 0.40 2.29 t=4.0inmvreg DanielandTitman(2006) IntangiblereturnusingCFtoP IntanCFP 1968-2003 0.40 2.32 t=4.9inmvreg DanielandTitman(2006) IntangiblereturnusingEP IntanEP 1968-2003 0.34 2.46 t=4.6inmvreg DanielandTitman(2006) IntangiblereturnusingSale2P IntanSP 1968-2003 0.53 2.42 t=4.3inmvreg DanielandTitman(2006) Shareissuance(5year) ShareIss5Y 1968-2003 0.52 4.32 t=4.4inunivarreg Datar,NaikandRadcliffe(1998) ShareVolume ShareVol 1962-1991 0.91 3.87 t=8.9inunivariatereg DeBondtandThaler(1985) Long-runreversal LRreversal 1929-1982 0.79 3.04 t=3.3inlong-short Dechow,SloanandSoliman(2004) EquityDuration EquityDuration 1962-1998 0.60 3.28 t=4.4inconservativelong-short Desai,Rajgopal,Venkatachalam(2004) OperatingCashflowstoprice cfp 1973-1997 0.36 2.18 t=2.77inportsort DharanandIkenberry(1995) ExchangeSwitch ExchSwitch 1962-1990 0.45 2.89 t=3.6ineventstudy Dichev(1998) OScore OScore 1981-1995 1.01 3.39 t=3.36inLSport DichevandPiotroski(2001) CreditRatingDowngrade CredRatDG 1986-1998 0.73 2.92 t=11ineventstudyw/specialdata Diether,MalloyandScherbina(2002) EPSForecastDispersion ForecastDispersion 1976-2000 0.65 3.05 t=2.9inportsort Doyle,LundholmandSoliman(2003) ExcludedExpenses ExclExp 1988-1999 0.27 3.02 t=5.7inmvreg Eberhart,MaxwellandSiddique(2004) UnexpectedR&Dincrease SurpriseRD 1974-2001 0.29 3.00 t=3.5inlong-short EisfeldtandPapanikolaou(2013) Organizationalcapital OrgCap 1970-2008 0.36 2.61 t=2.9inportsort continuedonnextpage 55

Table2:(continued) Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat Elgers,LoandPfeiffer(2001) EarningsForecasttoprice sfe 1982-1998 0.81 2.61 t=5inlong-shortsizeadjusted FamaandFrench(1992) Totalassetstomarket AM 1963-1990 0.69 3.42 t=5.7inunivarreg FamaandFrench(1992) BooktomarketusingDecemberME BMdec 1963-1990 0.98 5.37 t=5.71inunivariatereg FamaandFrench(1992) Bookleverage(annual) BookLeverage 1963-1990 0.29 3.37 t=5.3inmvreg Foster,OlsenandShevlin(1984) EarningsSurprise EarningsSurprise 1974-1981 1.16 4.94 hugespreadineventstudy Gompers,IshiiandMetrick(2003) GovernanceIndex Governance 1990-1999 0.52 2.11 t=2.7inlongshortFF3alpha Gou,LevandShi(2006) IPOandnoR&Dspending RDIPO 1980-1995 0.97 2.97 t=2.68inportsortFF3+Momalpha GrinblattandMoskowitz(1999) IndustryMomentum IndMom 1963-1995 0.27 2.55 t=4.6inlong-short Hafzalla,Lundholm,VanWinkle(2011) PercentOperatingAccruals PctAcc 1989-2008 0.46 3.51 t>2.6insize-adjustedlong-short Hafzalla,Lundholm,VanWinkle(2011) PercentTotalAccruals PctTotAcc 1989-2008 0.50 4.70 t>2.6insize-adjustedlong-short HahnandLee(2009) Tangibility tang 1973-2001 0.71 3.67 t=3.37inunivariateFMB HartzmarkandSalomon(2013) Dividendseasonality DivSeason 1927-2011 0.33 14.54 t=16inlong-short Hawkins,Chamberlin,Daniel(1984) EPSforecastrevision AnalystRevision 1975-1980 0.91 5.12 t=3.2inlongonlyCAPMalpha HestonandSadka(2008) Momentumwithouttheseasonalpart Mom12mOffSeason 1965-2002 1.23 3.85 t=4inportsort HestonandSadka(2008) Offseasonlong-termreversal MomOffSeason 1965-2002 1.31 4.93 t=5.6inportsort HestonandSadka(2008) Offseasonreversalyears6to10 MomOffSeason06YrPlus 1965-2002 0.59 4.36 t=4.6inportsort HestonandSadka(2008) Offseasonreversalyears16to20 MomOffSeason16YrPlus 1965-2002 0.35 2.54 t=3.4inportsort HestonandSadka(2008) Returnseasonalityyears2to5 MomSeason 1965-2002 0.82 5.86 t=5inportsort HestonandSadka(2008) Returnseasonalityyears6to10 MomSeason06YrPlus 1965-2002 0.74 6.17 t=6.1inportsort HestonandSadka(2008) Returnseasonalityyears11to15 MomSeason11YrPlus 1965-2002 0.75 6.94 t=6.4inportsort HestonandSadka(2008) Returnseasonalityyears16to20 MomSeason16YrPlus 1965-2002 0.59 5.05 t=4.5inportsort HestonandSadka(2008) Returnseasonalitylastyear MomSeasonShort 1965-2002 1.36 8.62 t=7.6inportsort Hirschleifer,HsuandLi(2013) CitationstoRDexpenses CitationsRD 1982-2008 0.21 2.21 t=2.6inFF3stylelong-short Hirschleifer,HsuandLi(2013) PatentstoRDexpenses PatentsRD 1982-2008 0.30 3.18 t=4.1inFF3stylelong-short Hirshleiferetal.(2004) NetOperatingAssets NOA 1964-2002 1.07 7.51 t=8.5inlong-short Hirshleifer,Hou,Teoh,Zhang(2004) changeinnetoperatingassets dNoa 1964-2002 1.05 9.25 t=8.9inmvreg Hou(2007) Earningssurpriseofbigfirms EarnSupBig 1972-2001 0.37 2.38 t=9inmvregweekly Hou(2007) Industryreturnofbigfirms IndRetBig 1972-2001 2.22 9.26 t=11inmvreg HouandMoskowitz(2005) Pricedelayrsquare PriceDelayRsq 1964-2001 0.48 2.69 t=3.4inportsortcharadj HouandRobinson(2006) Industryconcentration(sales) Herf 1963-2001 0.21 2.30 t=2.14inportsort HouandRobinson(2006) Industryconcentration(equity) HerfBE 1963-2001 0.22 2.04 t=2.52incharacteristics-adjustedportsort Jegadeesh(1989) Shorttermreversal STreversal 1934-1987 2.97 14.21 t=12inportsort JegadeeshandLivnat(2006) RevenueSurprise RevenueSurprise 1987-2003 0.75 5.99 t>2.6inmanyeventstudies JegadeeshandTitman(1993) Momentum(12month) Mom12m 1964-1989 1.37 4.58 t=3.7long-short JegadeeshandTitman(1993) Momentum(6month) Mom6m 1964-1989 1.04 3.68 t=2.4long-short continuedonnextpage 56

Table2:(continued) Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat Jegadeeshetal.(2004) Changeinrecommendation ChangeInRecommendation 1985-1998 1.04 6.65 p<0.01inLSport,butwelackthedata JohnsonandSo(2012) Optiontostockvolume OptionVolume1 1996-2010 0.68 2.04 t=3.45inportsortCAPMalphaweekly KellyandJiang(2014) Tailriskbeta BetaTailRisk 1963-2010 0.46 3.30 Tab4At-stat2.48 LaPorta(1996) Long-termEPSforecast fgr5yrLag 1983-1990 0.83 2.06 t=4.9inregression Lakonishok,Shleifer,Vishny(1994) Cashflowtomarket CF 1968-1990 0.83 4.04 t=3.4inportsort Lakonishok,Shleifer,Vishny(1994) RevenueGrowthRank MeanRankRevGrowth 1968-1990 0.53 3.89 t=4.5indoublesort Landsmanetal.(2011) Realdirtysurplus RDS 1976-2003 0.49 3.83 t=5.8inportsort LeeandSwaminathan(2000) Momentuminhighvolumestocks MomVol 1965-1995 1.59 5.05 t=6inlong-short,lotsofrobustness LevandNissim(2004) Taxableincometoincome Tax 1973-2000 0.45 3.52 t=3.9inregression Li(2011) R&Dcapital-to-assets RDcap 1980-2007 0.46 2.32 t=2.6inlong-short LitzenbergerandRamaswamy(1979) Predicteddivyieldnextmonth DivYieldST 1936-1977 0.41 4.23 t=6inmvreg Liu(2006) Dayswithzerotrades zerotrade 1960-2003 0.49 2.63 t=4.1inportsort Liu(2006) Dayswithzerotrades zerotradeAlt1 1960-2003 0.64 3.80 t=3.46inportsort(12mholding) Liu(2006) Dayswithzerotrades zerotradeAlt12 1960-2003 0.40 2.79 t>4inportsort(diffholdingperiods) LockwoodandPrombutr(2010) Growthinbookequity ChEQ 1964-2007 0.61 4.41 t=5.38inEWportsort LohandWarachka(2012) Earningssurprisestreak EarningsStreak 1987-2009 1.09 10.60 t=9.5inportsortff3alpha Lou(2014) Growthinadvertisingexpenses GrAdExp 1974-2010 0.44 3.89 t=3.5inlong-short LoughranandWellman(2011) EnterpriseMultiple EntMult 1963-2009 1.08 6.57 t=6.54indecilesortCAPMalpha Lyandres,SunandZhang(2008) Compositedebtissuance CompositeDebtIssuance 1970-2005 0.41 6.82 t=8.59inportsortCAPMalpha Lyandres,SunandZhang(2008) changeinppeandinv/assets InvestPPEInv 1970-2005 0.80 7.86 t=7inlong-shortport MenzlyandOzbas(2010) Customersmomentum iomom_cust 1986-2005 0.71 2.53 t=2.6inindustryportsort MenzlyandOzbas(2010) Suppliersmomentum iomom_supp 1986-2005 0.60 2.31 t=3.4inindustryportsort Michaely,ThalerandWomack(1995) DividendInitiation DivInit 1964-1988 0.58 5.65 t=3.4ineventstudy Michaely,ThalerandWomack(1995) DividendOmission DivOmit 1964-1988 0.51 3.06 t=6ineventstudy Mohanram(2005) MohanramG-score MS 1978-2001 1.34 5.44 t=9inportsortnonstandarddatalag Nagel(2005) InstOwnandForecastDispersion RIO_Disp 1980-2003 0.62 2.60 t=2.47inconditionalsort Nagel(2005) InstOwnandMarkettoBook RIO_MB 1980-2003 0.90 3.74 t=4.91inconditionalsort Nagel(2005) InstOwnandTurnover RIO_Turnover 1980-2003 0.65 2.78 t=2.71inconditionalsort Nagel(2005) InstOwnandIdioVol RIO_Volatility 1980-2003 1.01 4.19 t=4.38inconditionalsort NguyenandSwanson(2009) Efficientfrontierindex Frontier 1980-2003 2.09 6.24 t=5inportsort Novy-Marx(2010) Operatingleverage OPLeverage 1963-2008 0.38 2.73 t=3.38inportsort Novy-Marx(2012) IntermediateMomentum IntMom 1927-2010 1.24 5.90 Tab2t-stat5.79 Novy-Marx(2013) grossprofits/totalassets GP 1963-2010 0.30 2.38 t=2.5inVWLSquint Palazzo(2012) Cashtoassets Cash 1972-2009 0.70 2.97 t=2.14inportsortbutstrongwithadjustments PastorandStambaugh(2003) Pastor-Stambaughliquiditybeta BetaLiquidityPS 1968-1999 0.35 1.93 t=2.54inVWportsortCAPMalpha continuedonnextpage 57

Table2:(continued) Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat Penman,RichardsonandTuna(2007) LeveragecomponentofBM BPEBM 1963-2001 0.22 2.83 t=4.1inunivariatereg Penman,RichardsonandTuna(2007) EnterprisecomponentofBM EBM 1963-2001 0.31 4.14 t=3.0indoublesort Penman,RichardsonandTuna(2007) Netdebttoprice NetDebtPrice 1963-2001 0.55 3.88 t=2.3indoublesort Piotroski(2000) PiotroskiF-score PS 1976-1996 0.92 3.29 t=5.59inportsortnonstandarddatalag PontiffandWoodgate(2008) Shareissuance(1year) ShareIss1Y 1970-2003 0.62 4.97 t=7.08inunivariatereg Rajgopal,Shevlin,Venkatachalam(2003) Orderbacklog OrderBacklog 1981-1999 0.40 2.80 t=2.38inunivariatesize-adjustedFMB Richardsonetal.(2005) Changeincurrentoperatingassets DelCOA 1962-2001 0.54 6.01 t=9inmvreg Richardsonetal.(2005) Changeincurrentoperatingliabilities DelCOL 1962-2001 0.35 4.35 t=4.5inmvreg Richardsonetal.(2005) Changeinequitytoassets DelEqu 1963-2001 0.47 3.18 t=6.3inmvreg Richardsonetal.(2005) Changeinfinancialliabilities DelFINL 1962-2001 0.73 12.23 t=8inunivariatereg Richardsonetal.(2005) Changeinlong-terminvestment DelLTI 1962-2001 0.17 2.55 t=3.4inmvreg Richardsonetal.(2005) Changeinnetfinancialassets DelNetFin 1962-2001 0.55 9.00 t=6inunvivariatereg Richardsonetal.(2005) Totalaccruals TotalAccruals 1962-2001 0.28 2.63 t=6inmvreg Ritter(1991) InitialPublicOfferings IndIPO 1975-1987 0.66 2.36 t=4ineventstudy Rosenberg,Reid,andLanstein(1985) BooktomarketusingmostrecentME BM 1973-1984 1.60 3.79 t=6innonstandardlong-short Scherbina(2008) DeclineinAnalystCoverage ChNAnalyst 1982-2005 1.09 3.65 t>3inportsortFF3alphaforsmallstocks Sloan(1996) Accruals Accruals 1962-1991 0.56 5.07 t>4inportsortCAPMalpha12monthholding Soliman(2008) ChangeinAssetTurnover ChAssetTurnover 1984-2002 0.29 3.77 t=5inmvreg Soliman(2008) ChangeinNetNoncurrentOpAssets ChNNCOA 1984-2002 0.35 4.43 t=4.3inmvreg Soliman(2008) ChangeinNetWorkingCapital ChNWC 1984-2002 0.16 2.83 t=4.6inmvreg ThomasandZhang(2002) InventoryGrowth ChInv 1970-1997 0.77 6.24 t>2.6inportsort ThomasandZhang(2011) ChangeinTaxes ChTax 1977-2006 1.09 9.50 t=11.26indecilesort Titman,WeiandXie(2004) Investmenttorevenue Investment 1973-1996 0.25 2.28 t=2.86inVWportsort Valta(2016) Convertibledebtindicator ConvDebt 1985-2012 0.38 4.34 t>2.6inmvreg Xie(2001) AbnormalAccruals AbnormalAccruals 1971-1992 0.54 5.10 t=8portsortw/nonstandarddatalag Yan(2011) Putvolatilityminuscallvolatility SmileSlope 1996-2005 1.78 7.62 t=8inportsort Zhang(2004) FirmAge-Momentum FirmAgeMom 1983-2001 2.29 5.40 t=7.21inlongportfolio 58

Table3: PerformanceofIndividualLikelyPredictors. Description: Thistablelistslikelypredictors(definedinSection2.4)inthe baseline data along with their original in-sample periods; the in-sample mean return (% monthly) and t-stat in our reproduced portfolio; and the predictability evidence in the original paper. “port sort” is portfolio sort, “LS” is long-short portfolio, “mv reg” ismultivariateregression. Interpretation: Ourcategorizationofpredictorsas“likely”canbejustifiedbytheoriginalstudies. Asin Table 2, reproduced t-stats are close to the original results and support the credibility of the literature as well as the quality of our codeanddata. Thetablealsoprovidesaquick-referenceguidetoourcodeanddata. Reproduction RelatedOriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat AbarbanellandBushee(1998) Salesgrowthoverinventorygrowth GrSaleToGrInv 1974-1988 0.31 3.30 t=2.4inmvreg AbarbanellandBushee(1998) Salesgrowthoveroverheadgrowth GrSaleToGrOverhead 1974-1988 -0.06 -0.44 t=2.1inmvreg AmihudandMendelsohn(1986) Bid-askspread BidAskSpread 1961-1980 0.71 1.59 strongportsortsbutnoLSspecialdata AsquithPathakandRitter(2005) Instownamonghighshortinterest IO_ShortInterest 1980-2002 2.22 3.04 strongportsortbutnolong-short Balletal.(2016) OperatingprofitabilityR&Dadjusted OperProfRD 1963-2014 0.33 1.91 t=1.8inportsort Barbee,MukherjiandRaines(1996) Sales-to-price SP 1979-1991 0.71 2.86 t=2.5inmvreg Barberetal.(2002) ConsensusRecommendation ConsRecomm 1985-1997 0.53 1.35 t=3.2inportsortnonstandarddata Barberetal.(2002) DownforecastEPS DownRecomm 1985-1997 0.63 5.54 t>8in3-dayeventstudy Barberetal.(2002) UpForecast UpRecomm 1985-1997 0.61 4.62 t>8in3-dayeventstudy BarryandBrown(1984) FirmagebasedonCRSP FirmAge 1931-1980 -0.01 -0.06 t=2.5inregnonstandarddata Belo,LinandVitorino(2014) Brandcapitalinvestment BrandInvest 1975-2010 0.56 1.97 t=2.0inportsort Chan,LakonishokandSougiannis(2001) AdvertisingExpense AdExp 1975-1996 0.97 4.28 53bpsspreadbutnot-stat CremersandNair(2005) Activeshareholders Activism2 1990-2001 0.43 1.02 t=2.0inportsort Cusatis,MilesandWoolridge(1993) Spinoffs Spinoff 1965-1988 0.40 2.22 t=2.3ineventstudy DeBondtandThaler(1985) Medium-runreversal MRreversal 1933-1980 0.39 2.08 largeretinsimilarlong-short Dechowetal.(2001) ShortInterest ShortInterest 1976-1993 0.83 5.30 35bpsspreadinportsort Easley,HvidkjaerandO’Hara(2002) ProbabilityofInformedTrading ProbInformedTrading 1984-1998 1.30 4.34 t=2.5inmvreg Fairfield,WhisenantandYohn(2003) Growthinlongtermoperatingassets GrLTNOA 1964-1993 0.41 3.97 61bpsspreadinlong-short FamaandFrench(2006) operatingprofits/bookequity OperProf 1977-2003 0.72 3.00 t=2.6inmvreg FamaandMacBeth(1973) CAPMbeta Beta 1929-1968 0.66 1.72 t=2.6univarreg FrankelandLee(1998) AnalystValue AnalystValue 1975-1993 0.26 1.73 p<0.01inportsortbutnonstandardstats FrankelandLee(1998) AnalystOptimism AOP 1975-1993 0.36 2.01 p<0.01inportsortbutnonstandardstats FrankelandLee(1998) PredictedAnalystforecasterror PredictedFE 1979-1993 0.30 0.96 p<0.01inregbutnonstandardstats FranzoniandMarin(2006) PensionFundingStatus FR 1980-2002 0.31 1.74 49bpslong-short FrazziniandPedersen(2014) Frazzini-PedersenBeta BetaFP 1929-2012 0.03 0.08 t=7innonstandardportsort GeorgeandHwang(2004) 52weekhigh High52 1963-2001 0.51 1.94 t=2.0inlong-short HarveyandSiddique(2000) Coskewness Coskewness 1964-1993 0.27 2.18 p-val<0.05inlong-short continuedonnextpage 59

Table3:(continued) Reproduction OriginalStudy Predictor Acronym Sample OriginalStudy’sPredictabilityEvidence MeanRet t-Stat HaugenandBaker(1996) netincome/bookequity RoE 1979-1993 0.32 2.82 t=4.5inmvregnonstandard HaugenandBaker(1996) Cash-flowtopricevariance VarCF 1979-1993 -0.56 -1.91 t=2.5inmvregnonstandard HaugenandBaker(1996) Volumetomarketequity VolMkt 1979-1993 0.45 1.59 t=4inmvregnonstandard HaugenandBaker(1996) VolumeTrend VolumeTrend 1979-1993 0.54 2.93 t=3inmvregnonstandard HestonandSadka(2008) Offseasonreversalyears11to15 MomOffSeason11YrPlus 1965-2002 0.24 2.03 t=1.8inportsort,butsimilarstratsdobetter HongandKacperczyk(2009) SinStock(selectioncriteria) sinAlgo 1926-2006 0.21 1.92 t-stat=1.8inLSnontraditional HouandMoskowitz(2005) Pricedelaycoeff PriceDelaySlope 1964-2001 0.17 2.01 t=7.7inportsortw/complicatedsignal HouandMoskowitz(2005) PricedelaySEadjusted PriceDelayTstat 1964-2001 0.15 1.53 t=7.39inportsortw/complicatedsignal HouandRobinson(2006) Industryconcentration(assets) HerfAsset 1963-2001 0.18 1.66 t=2.12incharacteristics-adjustedportsort Ikenberry,Lakonishok,Vermaelen(1995) Sharerepurchases ShareRepurchase 1980-1990 0.32 4.01 t=1.85inlong-benchmarkport JohnsonandSo(2012) Optionvolumetoaverage OptionVolume2 1996-2010 0.53 1.79 t=2.5inportsortCAPMalphaweeklydata LohandWarachka(2012) Earningsstreaklength NumEarnIncrease 1987-2009 0.52 6.75 similarresultsinportsortsbutnotexact PrakashandSinha(2012) DeferredRevenue DelDRC 2002-2007 0.71 1.66 t=3.6innonstandardreg5yearsample Ritter(1991) IPOandage AgeIPO 1981-1984 1.41 2.68 Eventstudy,not-stat SpiessandAffleck-Graves(1999) DebtIssuance DebtIssuance 1975-1989 0.17 2.98 t=2.19FF3alphaonlongport Tuzel(2010) Realestateholdings realestate 1971-2005 0.32 2.05 t=1.8(VW)andt=1.28(EW)inportsort Xing,ZhangandZhao(2010) Volatilitysmirknearthemoney skew1 1996-2005 0.55 2.45 t=2.19inportsort 60

Table4: PerformanceofNot-PredictorsandIndirectSignals.Thistablelistsnot-predictorsandindirectsignals(definedinSection 2.4). ThevastmajorityofthesecharacteristicsareincludedonlytonestHou,Xue,andZhang(2020)(HXZ)(seeTable1). Welistthe original or related study’s in-sample periods; the in-sample mean return (% monthly) and t-stat in our reproduced portfolio; and the predictability evidence in the original paper, if available. Unlike clear and likely predictors, we do not sign these portfolios or select portfolio implementations based on the original papers’ results. All portfolios are equal-weighted and long-short quintiles, unlessthecharacteristicisdiscrete. “HXZvariant”indicatesourcharacteristicisbasedonHXZ’smodificationofa(notnecessarily predictive)characteristicinapreviousstudy. Interpretation: Ourcategorizationofpredictorsas“not”or“indirectevidence”canbe justifiedbyevidenceintheoriginalorrelatedstudies.ManyofHXZ’s“replicationfailures”comefromstudiesthatwerenevershown toproducestatisticallysignificantpredictability. Predictor Reproduction OriginalStudy’sPredictabilityEvidence Original/RelatedStudy Predictor Acronym Category MeanRet t-Stat (ifAvailable) AbarbanellandBushee(1998) EffectiveTaxRate ETR IndirectEvidence 0.01 0.18 t=1.5inmvreg AbarbanellandBushee(1998) Grossmargingrowthtosalesgrowth GrGMToGrSales IndirectEvidence 0.37 3.30 t=1.9inmvreg AbarbanellandBushee(1998) Changeinsalesvschangeinreceiv GrSaleToGrReceivables IndirectEvidence 0.06 0.66 t=1.6inmvreg AbarbanellandBushee(1998) Laborforceefficiency LaborforceEfficiency IndirectEvidence -0.07 -0.74 t=0.6inmvreg AbarbanellandBushee(1998) Changeingrossmarginvssales pchgm_pchsale IndirectEvidence 0.42 3.76 GHZvariantofGrGMToGrSale AcharyaandPedersen(2005) Illiquidity-illiquiditybeta(beta2i) betaCC IndirectEvidence 0.33 1.87 in-sampleonly AcharyaandPedersen(2005) Illiquidity-marketreturnbeta(beta4i) betaCR IndirectEvidence -0.09 -0.98 in-sampleonly AcharyaandPedersen(2005) Netliquiditybeta(betanet,p) betaNet IndirectEvidence 0.35 1.97 in-sampleonly AcharyaandPedersen(2005) Return-marketilliquiditybeta betaRC IndirectEvidence 0.06 0.30 in-sampleonly AcharyaandPedersen(2005) Return-marketreturnilliquiditybeta betaRR IndirectEvidence -0.03 -0.14 in-sampleonly Adrian,EtulaandMuir(2014) Broker-DealerLeverageBeta BetaBDLeverage NotPredictor 0.41 2.22 t=1inconservativeportsort AndersonandGarcia-Feijoo(2006) Investmentgrowth(1year) grcapx1y IndirectEvidence -0.28 -3.74 HXZvariant Anderson,Ghysels,andJuergens(2005) Long-termforecastdispersion ForecastDispersionLT NotPredictor -0.00 -0.00 t=1.0inconservativelong-short Angetal.(2006) Idiosyncraticrisk(CAPM) IdioVolCAPM IndirectEvidence -0.31 -1.01 HXZvariant Angetal.(2006) Idiosyncraticrisk(qfactor) IdioVolQF IndirectEvidence -0.39 -1.16 HXZvariant Ang,ChenandXing(2006) Downsidebeta DownsideBeta NotPredictor 0.07 0.31 t=0.6inportsort Balakrishnan,BartovandFaurel(2010) ChangeinReturnonassets ChangeRoA IndirectEvidence 1.32 12.59 HXZvariant Balakrishnan,BartovandFaurel(2010) ChangeinReturnonequity ChangeRoE IndirectEvidence 1.08 10.53 HXZvariant Bali,EngleandMurray(2015) Idiosyncraticskewness(CAPM) ReturnSkewCAPM IndirectEvidence -0.36 -5.39 HXZvariant Bali,EngleandMurray(2015) Idiosyncraticskewness(Qmodel) ReturnSkewQF IndirectEvidence -0.26 -4.29 HXZvariant Balletal.(2016) Cash-basedoperproflaggedassets CBOperProfLagAT IndirectEvidence 0.46 3.33 HXZvariant Balletal.(2016) Cash-basedoperproflaggedassetsqtrly CBOperProfLagAT_q IndirectEvidence 0.86 6.19 HXZvariant Balletal.(2016) OperprofR&Dadjlaggedassets OperProfRDLagAT IndirectEvidence 0.05 0.33 HXZvariant continuedonnextpage 61

Table4:(continued) Predictor Reproduction OriginalStudy’sPredictabilityEvidence Original/RelatedStudy Predictor Acronym Category MeanRet t-Stat (ifAvailable) Balletal.(2016) OperprofR&Dadjlaggedassets(qtrly) OperProfRDLagAT_q IndirectEvidence 1.17 5.56 HXZvariant Barbee,MukherjiandRaines(1996) Sales-to-pricequarterly SP_q IndirectEvidence 1.18 4.93 HXZvariant Basu(1977) Earnings-to-PriceRatio EPq IndirectEvidence 1.31 6.79 HXZvariant Belo,LinandVitorino(2014) Brandcapitaltoassets BrandCapital IndirectEvidence 0.24 1.25 notstudiedforpredictability Bhandari(1988) Marketleveragequarterly Leverage_q IndirectEvidence 0.26 0.79 HXZvariant Blitz,HuijandMartens(2011) 6monthresidualmomentum ResidualMomentum6m IndirectEvidence 0.39 4.08 HXZvariant Boudoukhetal.(2007) NetPayoutYieldquarterly NetPayoutYield_q IndirectEvidence 0.76 2.04 HXZvariant Boudoukhetal.(2007) PayoutYieldquarterly PayoutYield_q IndirectEvidence 0.72 6.16 HXZvariant BrownandRowe(2007) Returnoninvestedcapital roic NotPredictor 0.08 0.33 t=0.9inportsort Callen,KhanandLu(2013) Accountingcomponentofpricedelay DelayAcct NotPredictor -0.16 -0.83 t=1inlong-short Callen,KhanandLu(2013) Non-accountingcomponentofpricedelay DelayNonAcct NotPredictor 0.27 1.70 t=1inlong-short Campbell,HilscherandSzilagyi(2008) Failureprobability FailureProbability NotPredictor 0.40 0.91 t=1.5inconservativeportsort Campbell,HilscherandSzilagyi(2008) Failureprobability FailureProbabilityJune IndirectEvidence 0.03 0.07 HXZvariant Chan,LakonishokandSougiannis(2001) R&Dovermarketcapquarterly RD_q IndirectEvidence 1.89 5.23 HXZvariant Chan,LakonishokandSougiannis(2001) R&Dtosales rd_sale NotPredictor 0.17 0.71 8bpsspreadinportsort Chan,LakonishokandSougiannis(2001) R&Dtosales rd_sale_q IndirectEvidence 0.71 1.48 HXZvariant Cooper,GulenandSchill(2008) Assetgrowthquarterly AssetGrowth_q IndirectEvidence -0.94 -4.84 HXZvariant Desai,Rajgopal,Venkatachalam(2004) OperatingCashflowstopricequarterly cfpq IndirectEvidence 1.07 8.12 HXZvariant Dichev(1998) OScorequarterly OScore_q IndirectEvidence -1.10 -3.02 HXZvariant Dichev(1998) AltmanZ-Score ZScore NotPredictor -0.35 -1.20 t=1.59inunivarreg Dichev(1998) AltmanZ-Scorequarterly ZScore_q IndirectEvidence -0.13 -0.47 HXZvariant Dimson(1979) DimsonBeta BetaDimson IndirectEvidence -0.23 -1.53 onlyshowntoforecastbeta EisfeldtandPapanikolaou(2013) Orgcapw/oindustryadjustment OrgCapNoAdj IndirectEvidence 0.64 3.31 HXZvariant Elgers,LoandPfeiffer(2001) Numberofanalysts nanalyst IndirectEvidence 0.19 1.02 spreadinmedianreteachlegsizeadj FamaandFrench(1992) Totalassetstomarket(quarterly) AMq IndirectEvidence 0.78 3.31 HXZvariant FamaandFrench(1992) Bookleverage(quarterly) BookLeverageQuarterly IndirectEvidence -0.23 -1.59 HXZvariant FamaandFrench(2006) operatingprofits/bookequity OperProfLag IndirectEvidence 0.40 1.81 HXZvariant FamaandFrench(2006) operatingprofits/bookequity OperProfLag_q IndirectEvidence 1.02 3.40 HXZvariant FamaandMacBeth(1973) CAPMbetasqured BetaSquared NotPredictor -0.66 -1.71 t=0.3inmvreg Francis,LaFond,Olsson,Schipper(2004) Earningsconservatism EarningsConservatism IndirectEvidence -0.00 -0.01 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2004) Earningspersistence EarningsPersistence IndirectEvidence -0.21 -1.59 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2004) EarningsPredictability EarningsPredictability IndirectEvidence -0.60 -3.49 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2004) EarningsSmoothness EarningsSmoothness IndirectEvidence 0.02 0.11 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2004) Earningstimeliness EarningsTimeliness IndirectEvidence -0.02 -0.21 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2004) Valuerelevanceofearnings EarningsValueRelevance IndirectEvidence -0.02 -0.32 correlatedwithBMandotherpredictors continuedonnextpage 62

Table4:(continued) Predictor Reproduction OriginalStudy’sPredictabilityEvidence Original/RelatedStudy Predictor Acronym Category MeanRet t-Stat (ifAvailable) Francis,LaFond,Olsson,Schipper(2004) RoAvolatility roavol IndirectEvidence -0.07 -0.19 correlatedwithBMandotherpredictors Francis,LaFond,Olsson,Schipper(2005) AccrualQuality AccrualQuality IndirectEvidence 0.16 0.62 correlatedwithE/Pandfactorstructure Francis,LaFond,Olsson,Schipper(2005) AccrualQualityinJune AccrualQualityJune IndirectEvidence 0.19 0.73 HXZvariant FrankelandLee(1998) Intrinsicorhistoricalvalue IntrinsicValue IndirectEvidence 0.48 2.45 notstudied.Ingredientvariable. FranzoniandMarin(2006) PensionFundingStatus FRbook IndirectEvidence 0.32 2.58 HXZvariant Hafzalla,Lundholm,VanWinkle(2011) PercentAbnormalAccruals AbnormalAccrualsPercent IndirectEvidence -0.29 -4.09 HXZvariant HahnandLee(2009) Tangibilityquarterly tang_q IndirectEvidence 0.85 5.84 HXZvariant HaugenandBaker(1996) Capitalturnover CapTurnover IndirectEvidence 0.25 1.23 t<2inmvregnonstandard HaugenandBaker(1996) Capitalturnover(quarterly) CapTurnover_q IndirectEvidence 0.85 4.68 HXZvariant HolthausenandLarcker(1992) DepreciationtoPPE depr IndirectEvidence 0.28 1.02 ingredientincomplicatedmodel HolthausenandLarcker(1992) ChangeindepreciationtoPPE pchdepr IndirectEvidence 0.18 1.66 ingredientincomplicatedmodel HouandLoh(2016) Bid-askspread(TAQ) BidAskTAQ NotPredictor 0.12 0.41 t=1.3inmvreg LaPorta(1996) Long-termEPSforecast(Monthly) fgr5yrNoLag IndirectEvidence -0.66 -1.60 HXZvariant Lakonishok,Shleifer,Vishny(1994) Cashflowtomarketquarterly CFq IndirectEvidence 1.69 10.62 HXZvariant Lakonishok,Shleifer,Vishny(1994) Annualsalesgrowth sgr IndirectEvidence -0.60 -4.25 HXZvariant Lakonishok,Shleifer,Vishny(1994) Annualsalesgrowthquarterly sgr_q IndirectEvidence 0.60 3.51 HXZvariant Lamont,PolkandSaa-Requejo(2001) KaplanZingalesindex KZ NotPredictor 0.08 0.53 t=1.1inconservativeportsort Lamont,PolkandSaa-Requejo(2001) KaplanZingalesindexquarterly KZ_q IndirectEvidence -1.49 -9.23 HXZvariant LevandNissim(2004) Taxableincometoincome(qtrly) Tax_q IndirectEvidence 0.03 0.23 HXZvariant LoughranandWellman(2011) EnterpriseMultiplequarterly EntMult_q IndirectEvidence -1.59 -11.96 HXZvariant Naranjo,Nimalendran,Ryngaert(1998) Dividendyieldforsmallstocks DivYield IndirectEvidence 0.34 1.11 mixedresults,smallspread Naranjo,Nimalendran,Ryngaert(1998) Lastyear’sdividendsoverprice DivYieldAnn IndirectEvidence 0.01 0.11 HXZvariant Novy-Marx(2010) Operatingleverage(qtrly) OPLeverage_q IndirectEvidence 0.39 2.37 HXZvariant Novy-Marx(2013) grossprofits/totalassets GPlag IndirectEvidence 0.20 1.85 HXZvariant Novy-Marx(2013) grossprofits/totalassets GPlag_q IndirectEvidence 0.88 6.17 HXZvariant Ortiz-MolinaandPhillips(2014) Assetliquidityoverbookassets AssetLiquidityBook IndirectEvidence 0.35 1.37 nopredictability.CorrelatedwithICC Ortiz-MolinaandPhillips(2014) Assetliquidityoverbook(qtrly) AssetLiquidityBookQuart IndirectEvidence 0.31 0.96 HXZvariant Ortiz-MolinaandPhillips(2014) Assetliquidityovermarket AssetLiquidityMarket IndirectEvidence 1.41 7.46 nopredictability.CorrelatedwithICC Ortiz-MolinaandPhillips(2014) Assetliquidityovermarket(qtrly) AssetLiquidityMarketQuart IndirectEvidence 1.31 6.35 HXZvariant OuandPenman(1989) CFtodebt cashdebt IndirectEvidence -0.06 -0.21 ingredientincomplicatedmodel OuandPenman(1989) CurrentRatio currat IndirectEvidence 0.29 1.93 ingredientincomplicatedmodel OuandPenman(1989) ChangeinCurrentRatio pchcurrat IndirectEvidence 0.21 2.54 ingredientincomplicatedmodel OuandPenman(1989) Changeinquickratio pchquick IndirectEvidence 0.32 3.27 ingredientincomplicatedmodel OuandPenman(1989) Changeinsalestoinventory pchsaleinv IndirectEvidence 0.49 5.24 ingredientincomplicatedmodel OuandPenman(1989) Quickratio quick IndirectEvidence 0.30 1.77 ingredientincomplicatedmodel continuedonnextpage 63

Table4:(continued) Predictor Reproduction OriginalStudy’sPredictabilityEvidence Original/RelatedStudy Predictor Acronym Category MeanRet t-Stat (ifAvailable) OuandPenman(1989) Salestocashratio salecash IndirectEvidence 0.22 1.31 ingredientincomplicatedmodel OuandPenman(1989) Salestoinventory saleinv IndirectEvidence 0.03 0.18 ingredientincomplicatedmodel OuandPenman(1989) Salestoreceivables salerec IndirectEvidence 0.29 1.53 ingredientincomplicatedmodel Penman,RichardsonandTuna(2007) EnterprisecomponentofBM EBM_q IndirectEvidence 0.81 7.09 HXZvariant Penman,RichardsonandTuna(2007) Netdebttoprice NetDebtPrice_q IndirectEvidence -0.73 -3.78 HXZvariant Piotroski(2000) PiotroskiF-score PS_q IndirectEvidence 1.39 6.35 HXZvariant Richardsonetal.(2005) Changeinshort-terminvestment DelSTI NotPredictor -0.04 -0.53 t=0.4inmvreg Rosenberg,Reid,andLanstein(1985) Booktomarket(quarterly) BMq IndirectEvidence 1.65 3.67 HXZvariant Soliman(2008) AssetTurnover AssetTurnover IndirectEvidence 0.40 2.23 t=0.3inmvreg Soliman(2008) AssetTurnover AssetTurnover_q IndirectEvidence 0.59 3.10 HXZvariant Soliman(2008) ChangeinNoncurrentOperatingAssets ChNCOA IndirectEvidence -1.02 -5.68 Nopredictability.Ingredientforpredictor. Soliman(2008) ChangeinNoncurrentOperatingLiab ChNCOL IndirectEvidence -0.54 -3.60 Nopredictability.Ingredientforpredictor. Soliman(2008) ChangeinProfitMargin ChPM IndirectEvidence 0.11 1.35 t=0.3inmvreg Soliman(2008) ProfitMargin PM IndirectEvidence 0.52 1.94 t=1inmvreg Soliman(2008) ProfitMargin PM_q IndirectEvidence 1.29 2.88 HXZvariant Soliman(2008) ReturnonNetOperatingAssets RetNOA IndirectEvidence 0.01 0.05 t=1.4inmvreg Soliman(2008) ReturnonNetOperatingAssets RetNOA_q IndirectEvidence 1.26 3.25 HXZvariant Valta(2016) Secureddebt secured IndirectEvidence -0.00 -0.04 t>1.96inmvreg Valta(2016) Secureddebtindicator securedind IndirectEvidence -0.06 -0.69 GHZvariant WhitedandWu(2006) Whited-Wuindex WW NotPredictor 0.33 1.18 t=1.3inportsort WhitedandWu(2006) Whited-Wuindex WW_Q IndirectEvidence 0.50 1.31 HXZvariant 64