Fundamentally,momentumisfundamentalmomentumRobertNovy-Marx - PDF document

Fundamentally,momentumisfundamentalmomentumRobertNovy-MarxŽAbstractMomentuminrmfundamentals,i.e.,earningsmomentum,exp  1.IntroductionPricemomentum,i.e.,thetendencyofstocksthathaveperformedwellovertheprioryeartooutperform,goingforward,stocksthathaveperformedpoorlyovertheprioryear,isoftenregardedasthemostimportantnancialanomaly.Theanomalyisobservedoverlongperiodsandacrossmarkets.Momentumhasgeneratedlarge,thoughhighlyvolatile,returns.Theanomalyhasbeenparticularlychallengingforproponentsofmarketefciency,asitisdifculttoimaginearisk-basedstoryconsistentwithboththelargemagnitudeandtransientnatureofmomentumreturns.Itisalsoproblematicfortheprofession'sdominantempiricalpricingmodel,theFamaandFrench(1993)threefactormodel,whichpredictsthatmomentum,becauseitcovariesnegativelywithvaluestrategies,shouldhavenegativeaverageexcessreturns.Thesefactshavebroughtmomentumenormousattentioninthenanceliterature.Thispaperarguesthatsuchattentionisnotdeserved.Itshowsthatmomentumisnotanindependentanomaly,butdrivenbyfundamentalmomentum.Thatis,pricemomentumismerelyaweakexpressionofearningsmomentum,reectingthetendencyofstocksthathaverecentlyannouncedstrongearningstooutperform,goingforward,stocksthathaverecentlyannouncedweakearnings.Thismayseemsurprising,inlightofChan,Jegadeesh,andLakonishok's(1996,hereafterCJL)wellknownandwidelyacceptedconclusionthat“pastreturn[s]andpastearningssurprise[s]eachpredictlargedriftsinfuturereturnsaftercontrollingfortheother”(p.1681).CJLactuallyconsiderthepossibility“thattheprotabilityofmomentumstrategiesisentirelyduetothecomponentofmedium-horizonreturnsthatisrelatedtotheseearnings-relatednews,”butexplicitlyrejectthishypothesis,concludingthat“eachmomentumvariablehasseparateexplanatorypowerforfuturereturns,soonestrategydoesnotsubsumetheother”(pp.1682–3).Theydrawthisconclusionprimarilyonthebasisofreturnspreadstheyseeinbothdirectionsfromanindependentthreebythreeportfolio1 sortonpastperformanceandearningssurprises.Thisisratherweakevidenceonwhichtobasetheirconclusion.Thesesortsarefartoocoarsetoprovideadequatecontrolsforthetwovariables.Inanythirdofthestockuniversepickedonthebasisofearningssurprises,sortingonpastperformancestillinducessignicantvariationinearningssurprises.Againstthisweaktest,apreponderanceofstrongerevidencesuggeststhatearningsmomentumdrivespricemomentum.Incrosssectionalregressionsofrms'returnsontopastperformanceandearningssurprises,earningssurpriseslargelysubsumethepowerofpastperformancetopredictcrosssectionalvariationinexpectedreturns.Addingearningssurprisesasanexplanatoryvariableincrosssectionalregressionsdramaticallyattenuatesthecoefcientonpastperformance,whichlosesitssignicance,whileaddingpastperformanceasanexplanatoryvariableleavesthecoefcientonearningssurprisesessentiallyunchanged.Time-seriesregressionsemployingthereturnstopriceandearningsmomentumstrategiesareevenmoreconclusive.Thesetestsaremorerobusttomeasurementerrorthancrosssectionalregressions,anddonotrequireparametricassumptionsregardingthefunctionalformoftherelationbetweenexpectedreturnsandthepredictivevariables.Thesetime-seriesregressionssuggestthatpricemomentumisfullycapturedbyearningsmomentum.Pricemomentumstrategiesdonothaveapositivealpharelativetoearningsmomentumstrategies,whileearningsmomentumstrategieshavelarge,highlysignicantalphasrelativetopricemomentumstrategies.Thissuggeststhataninvestorwhowantstotrademomentumwouldlosenothingbycompletelyignoringpricemomentum.TheseresultsareconsistentwithChordiaandShivakumar's(2006)ndingthat“thepricemomentumanomalyisamanifestationoftheearningsmomentumanomaly”(p.629).Theirconclusionisbased,however,ontestsidentiedprimarilyoffofsmallcapstocks.Thispapershowstheseresultsholdamonglargecapstocks.Italsoshows,perhapsmoresurprisingly,thatearningsmomentumsubsumesevenvolatilitymanaged2 momentumstrategies.BarrosoandSanta-Clara(2013)andDanielandMoskowitz(2014)ndthatpricemomentumstrategiesthatinvestmoreaggressivelywhenvolatilityislowhaveSharperatiostwiceaslargeasthealreadyhighSharperatiosobservedontheirconventionalcounterparts.Ishowherethatmanagingvolatilityalsoimprovestheperformanceofearningsmomentumstrategiesand,moreimportantly,thatthesevolatilitymanagedearningsmomentumstrategiessubsumevolatilitymanagedpricemomentum.Thispaperalsogoesevenfurther,showingnotonlythatearningsmomentumsubsumepricemomentum,butthatpricemomentuminearningsmomentumstrategiesisactuallydetrimentaltoperformance.Thatis,whileinvestorstradingearningsmomentumwouldnotbenetfromtradingpricemomentum,theycanbenetfromaccountingforpastperformance,iftheyuseittoavoidpricemomentum.Pricemomentumcontributestothevolatilityofearningsmomentumstrategies,anddrivesthestrategies'largestdrawdowns.Earningsmomentumstrategiesexplicitlyconstructedtoavoidpricemomentumconsequentlyhavelowervolatility,andnoneofthenegativeskew,oftraditionalearningsmomentumstrategies.Becausetheseearningsmomentumstrategiesunpollutedbypricemomentumgenerateaveragereturnscomparabletotheirtraditionalcounterparts,theyhavesignicantlyhigherSharperatios.Theremainderofthepaperproceedsasfollows.Section2establishesthebasicassetpricingfacts,thatearningssurprisessubsumethepowerofpastperformancetopredictreturnsinbothcrosssectionalandtime-seriesregressions.Section3showsthatcontrollingforpastperformancewhenconstructingearningsmomentumstrategiesimprovestheirperformancebydecreasingvolatility,whilecontrollingforearningssurpriseswhenconstructingpricemomentumstrategieshurtstheirperformancebydecreasingreturns.Section4showsthatthesuperiorperformanceofvolatilitymanagedpricemomentumstrategiesisalsoexplainedbyearningsmomentum.Section5concludes.3 2.BasicassetpricingresultsThissectionestablishesthebasicassetpricingfacts,thatearningssurprisessubsumethepowerofpastperformancetopredictcrosssectionalvariationinexpectedreturns,andthatthetime-seriesperformanceofpricemomentumstrategiesisfullyexplainedbytheperformanceofstrategiesbasedonearningssurprises.Italsoshowsthattheseresultsarerobustacrossthespectrumofrmsize.2.1.MeasuringpastperformanceandearningssurprisesComparingthepowerofpastperformanceandearningssurprisestopredictexpectedreturnvariationrequiresmeasuresforeach.ForpastperformanceIusethemeasuremostcommonlyassociatedwithpricemomentumstrategies,performancemeasuredovertheprecedingyear,skippingthemostrecentmonthtoavoiddilutingpricemomentumwithshorttermreversals(r2;12).ForearningssurprisesIusetwomeasurescommonlyemployedintheliterature,standardizedunexpectedearnings(SUE)andcumulativethreedayabnormalreturns(CAR3).SUEisdenedasthemostrecentyear-over-yearchangeinearningspershare,scaledbythestandarddeviationoftheearningsinnovationsoverthelasteightannouncements,subjecttoarequirementofatleastsixobservedannouncementsoverthetwoyearwindow.ForearningspershareIuseCompustatquarterlydataitemEPSPXQ(EarningsPerShare(Basic)/ExcludingExtraordinaryItems).EarningsannouncementdatesareCompustatquarterlydataitemRDQ.CAR3isdenedasthecumulativereturninexcessofthatearnedbythemarketoverthethreedaysstartingthedaybeforethemostrecentearningsannouncementandendingattheendofthedayfollowingtheannouncement.Thetime-seriesaveragerankcorrelationbetweenr2;12andSUEis29.1%,betweenr2;12andCAR3is13.7%,andbetweenSUEandCAR3is19.9%.Thissuggeststhat4 theearningsinnovationsscaledtocreatestandardizedunexpectedearningsareactuallylargelyexpected;SUEcorrelatesmorestronglywithpastperformancethanitdoeswiththemarket'scontemporaneousreactiontotheearnings'announcements.Pastperformancereectsinnovationstoinvestors'beliefsaboutarm'sprospects,includingguidancethermhasprovidedregardingitoperations,someofwhichisreecteddirectlyinannouncedearnings.ThefactthatSUEcorrelatesmorestronglywithr2;12thanwithCAR3indicatesthatmoreoftheinformationregardingthechangeinearningspershareisincorporatedintopricesbeforeannouncementsthaninthedaysimmediatelysurroundingannouncements.2.2.Fama-MacBethregressionsTable1reportsresultsofFama-MacBeth(1973)regressionsofindividualmonthlystockreturnsontothepastperformance(r2;12),andthemostrecentearningssurprisesmeasuredbybothstandardizedunexpectedearnings(SUE)andcumulativethreedayabnormalreturns(CAR3).Regressionsincludecontrolsforothervariablesknowntopredictthecrosssectionalofreturns,size,relativevaluations,protability,andshorthorizonpastperformance.Imeasurethesevariablesbythelogofmarketcapitalizations(ln(ME)),thelogofbook-to-marketratio(ln(B/M)),grossprotability(GP/A,whereGPisrevenuesminuscostofgoodssoldandAisassets,asinNovy-Marx(2013)),andpriormonth'sreturn(r0;1).1Independentvariablesaretrimmedattheoneand99%levels.ThefullsamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequirementsformakingtheSUEandCAR3strategies.Thetablealsoreportssubsampleresults.Therstperiod,January1975throughDecember1993,largelycoincideswiththe1Chan,Jegadeesh,andLakonishok(1996)alsorunFama-MacBethregressionsofrms'returnsonpastperformanceandearningssurprises,buttheirtests,inadditiontocoveringamuchshortersample,differfromthosepresentedhereinatleastthreeimportantways.First,forthedependentvariabletheyusestocks'subsequentsixmonthoroneyearreturns,whichweakensthetestsduetothetransientnatureofmomentumeffects.Second,andmostimportantly,theytransformtheirindependentvariablesintopercentilerankings,whichreducesthepoweroftheearningssurprisevariables.Lastly,theydonotincludecontrolsforotherknowncrosssectionalreturnpredictors.5 Table1.Fama-MacBethregressionsThetablereportsresultsofFama-MacBeth(1973)regressionsofindividualmonthlystockreturnsontopastperformance,measuredovertheprecedingyearskippingthemostrecentmonth(r2;12),andrms'mostrecentearningssurprises,measuredusingbothstandardizedunexpectedearnings(SUE)andthecumulativethreedayabnormalreturnsaroundthemostrecentearningsannouncement(CAR3).Regressionsincludecontrolsforothervariablesknowntopredictcrosssectionalvariationinexpectedreturns,thelogofrms'marketcapitalizations(ln(ME)),thelogofrms'book-to-marketratios(ln(B/M)),grossprotability(GP/A,whereGPisrevenuesminuscostofgoodssoldandAisassets),andstocks'priormonthreturns(r2;12).Independentvariablesaretrimmedattheoneand99%levels.ThesamplecoversJanuary1975throughDecember2012,withthedatesdeterminedbythedatarequirementsformakingtheSUEandCAR3strategies.Fullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)r2;120.590.150.800.300.38-0.00[2.84][0.70][3.79][1.28][1.05][-0.00]SUE0.270.260.300.21[17.0][19.2][16.4][11.2]CAR35.845.756.634.87[19.7][20.4][15.2][13.9]ln(ME)-0.06-0.08-0.08-0.11-0.13-0.01-0.04[-1.39][-1.69][-1.93][-1.92][-2.11][-0.11][-0.64]ln(B/M)0.440.300.320.460.380.420.27[5.96][3.82][4.47][4.94][3.93][3.65][2.47]GP/A0.910.760.750.890.740.930.77[6.82][5.58][5.60][5.00][4.17][4.67][3.79]r0;1-4.66-5.83-6.00-6.49-8.07-2.83-3.92[-10.2][-11.9][-12.9][-12.1][-14.0][-3.89][-5.53]January1977throughJanuary1993samplestudiedinCJL.ThesecondcoversJanuary1994throughDecember2012.AppendixBprovidesresultsofsimilarregressionsrestrictedtothelarge,small,andmicrocapuniverses,wherethesearedenedasstockswithabovemedianNYSEmarketcapitalization,stocksinNYSEsizedeciles3-5,andstocksinbottomtwoNYSEsizedeciles,respectively.Resultsoftheseregressionsareconsistentwiththoseusingallstocks.Thersttwospecicationsshowthecoefcientestimatesonpastperformanceandthetwoearningssurprisemeasures,respectively,overtheentiresample.Therstspecication6 showsasignicantpositivecrosssectionalcorrelationbetweenprioryear'sperformanceandexpectedreturns,whilethesecondshowsfarmoresignicantcorrelationsbetweenearningssurprisesandexpectedreturns.Thethirdspecicationshowsthatintheregressionthatincludesbothpastperformanceandearningssurprises,thecoefcientonpastperformanceshrinksbythreequarters,andbecomesstatisticallyinsignicant,whilethecoefcientsontheearningssurprisemeasuresareessentiallyunchanged.Thissuggeststhatthepowerpastperformancehaspredictingcrosssectionalvariationinexpectedreturnsderivesfromitscorrelationwithearningssurprises.Thelastfourspecicationsshowsubsampleresultsconsistentwiththeconclusionthatearningssurpriseshaveindependentpowerpredictingexpectedreturndifferencesacrossstocks,whilethepowerofpastperformancederivesprimarilyfromitscorrelationwithearningssurprises.2.3.SpanningtestsTheresultsoftheFama-MacBethregressionsshowninTable1suggestthatthepowerofpastperformancetopredictthecrosssectionofreturnsislargelysubsumedbyearningssurprise.Thissubsectionshowsthatpricemomentumisfullycapturedbyearningsmomentumintime-seriesregressions.Thesetime-seriesregressions,orspanningtests,essentiallyaskwhichmomentumstrategies,amongthoseconstructedusingpastperformanceandthetwomeasuresofearningssurprises,generatesignicantalpharelativetotheothers.Theydosobyregressingthereturnsofateststrategy,takenfromthesetofmomentumstrategies,ontothereturnsofexplanatorystrategies,whichincludetheFamaandFrenchfactorsandtheothermomentumstrategies.Signicantabnormalreturnssuggestaninvestoralreadytradingtheexplanatorystrategiescouldrealizesignicantgainsbystartingtotradetheteststrategy.7 Insignicantabnormalreturnssuggestthattheinvestorhaslittletogainbystartingtotradetheteststrategy.ForthepricemomentumstrategyIusetheup-minus-downfactor,UMD,availablefromKenFrench'sdatalibrary.2FortheearningsmomentumfactorsIconstructanaloguestoUMDbasedonthetwomeasuresofearningssurprises.Specically,thesefactorsareconstructedfromunderlyingportfoliosthatareformedmonthly,astheintersectionoftwosizeandthreeearningsmomentumportfolios.Thesizeportfoliosdividestocksintolargeorsmallcapuniverses,basedonNYSEmedianmarketcapitalization.Theearningsmomentumportfoliosdividetheworldintothreeportfoliosdividedatthe30thand70thpercentiles,usingNYSEbreaks,ofearningssurprises,measuredusingeitherSUEorCAR3.Theearningsmomentumfactorsareeachformedasanequalweightedaverageofvalueweightedlargecapandsmallcapearningsmomentumstrategies,whichbuytheuppertertileandshortthebottomtertileoftheearningssurprisesportfoliosbasedonthecorrespondingmeasureofearningssurprises.Inaconvenientabuseofnotation,theseearningsmomentumfactorsaredenotedSUEandCAR3,thesameastheearningssurprisemeasuresonwhichtheyarebased.TheperformanceoftheportfoliosunderlyingthesefactorsisprovidedintheAppendix,inTableA4.Figure1showstheperformanceofthethreemomentumfactors,UMD,SUE,andCAR3.Thegureshowsthegrowthofadollar,netofnancingcosts,investedinthebeginningof1975intoeachofthestrategies.Tofacilitatecomparison,thestrategiesareallleveredtorunatasamplevolatilityof10%.Thegureshowsthatbothoftheearningsmomentumstrategiesdramaticallyoutperformedthepricemomentumstrategy,suggestingthatthesestrategieshadsignicantlyhigherSharperationsthanUMD.Table2analyzestheperformanceofthethreemomentumfactorsformally.PanelAshowstheperformanceofUMD.Specicationoneshowsthatoverthe38yearsample2Thelibraryresidesathttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/datalibrary.html.8 CAR3SUEUMDPerformanceof$1(logscale)Fig.1.Comparisonofmomentumfactorperformance.Thegureshowsthevalueofadollarinvestedatthebeginningof1975inthepricemomentumfactor,UMD(dashedline),andtheearningsmomentumfactors,SUE(solidline)andCAR3(dottedline).Returnsarecalculatednetofnancingcosts(i.e.,areexcessreturns).Tofacilitatecomparison,factorsarescaledtohaveasamplevolatilitiesof10%.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.thestandardpricemomentumfactorearnedahighlysignicant64basispointspermonth,withat-statisticof3.03.Specicationtwoprovidesthestandardresultthatmomentum'sFamaandFrenchthree-factoralphaisevenlarger.SpecicationthreeshowsthatUMDloadsheavilyonbothSUEandCAR3,andasaresulthasasignicantnegativealpharelativetoearningsmomentum,evenaftercontrollingforthethreeFamaandFrenchfactors.Thisfact,thatearningsmomentumsubsumespricemomentumintime-seriesregressions,drivesthesuccessofHou,Xue,andZhang's(2014)alternativefactormodel9 pricingmomentumstrategies.Novy-Marx(2015)showsthattheirmodel'ssuccesspricingportfoliossortedonpastperformanceisdrivenentirelybypostearningsannouncementdriftinitsprotabilityfactor,ROE.Italsoshowsthatitsucceedsinpricingportfoliossortedongrossprotabilityonlybyconatingthelevelofearningswithearningssurprises.EarningsprotabilitydrivestheROEfactor'scovariancewithgrossprotabilitywithoutsignicantlycontributingtofactorperformance,whileearningssurprisesdrivethefactor'shighaveragereturnsbutareunrelatedtogrossprotability.Specicationsfourthroughsevenshowconsistentsubsampleresults.UMDgeneratespositivereturnsoverboththeearlyandlatehalvesofthesample,thoughthesewereonlystatisticallysignicantovertheearlysample.Yetevenintheearlysample,whenUMDearns85bps/month,itfailstogenerateabnormalreturnsrelativetothepricemomentumfactors.PanelsBandCshowthattheperformanceofeachoftheearningsmomentumfactors,SUEandCAR3,isnotexplainedbytheotherfactors.Theearningsmomentumstrategiesbothgeneratehighlysignicantreturnsoverthewholesample,witht-statisticsexceedingsevenforSUEandeightforCAR3.Forbothfactorsthereturnsarehighlysignicantoverbothsubsamples,thoughroughly50%largerandmoresignicantovertheearlysample.Bothearningsmomentumfactors'abnormalperformanceremainshighlysignicantaftercontrollingforthethreeFamaandFrenchfactorsandtheothertwomomentumfactors,eveninthelatesamplewhentheirperformanceislessimpressive.AppendixAreplicatestheresultsofthissubsectionaccountingfortransactioncosts.Thesecostssignicantlyreducestherealizedperformanceofallthreestrategies,butdoesnotalterthebasicconclusionthatearningsmomentumsubsumespricemomentum.10 Table2MomentumfactorspanningtestsThistablepresentsresultsoftime-seriesregressionsoftheform:ytDC000XtC"twheretheytarethemonthlyexcessreturnstothepricemomentumfactor,UMD,ortheearningsmomentumfactors,SUEandCAR3,andtheexplanatoryfactorsarethereturnstotheFamaandFrenchfactors(MKT,SMB,andHML),orthesefactorsandtheothertwomomentumfactors.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Fullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelA:yDUMD0.640.85-0.480.82-0.030.46-0.60[3.03][4.05][-2.55][3.67][-0.13][1.29][-2.16]MKT-0.18-0.040.08-0.08[-3.83][-1.12][1.60][-1.32]SMB0.070.220.020.33[1.07][3.87][0.24][4.05]HML-0.34-0.17-0.16-0.14[-4.65][-2.96][-1.92][-1.66]SUE1.180.901.35[10.9][6.17][8.59]CAR30.840.341.03[6.09][1.82][5.18]adj.-R2(%)5.840.625.450.1PanelB:yDSUE0.590.700.380.710.410.460.34[7.14][8.68][5.31][7.20][4.18][3.53][3.36]MKT-0.08-0.03-0.04-0.05[-4.25][-1.94][-1.74][-2.11]SMB-0.11-0.11-0.03-0.15[-3.94][-5.21][-0.80][-5.10]HML-0.10-0.02-0.090.00[-3.44][-0.80][-2.51][0.04]UMD0.180.160.18[10.9][6.17][8.59]CAR30.300.390.22[5.52][5.03][2.91]adj.-R2(%)8.341.431.349.311 Table2continuedFullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelC:yDCAR30.530.590.370.630.390.430.34[8.42][9.35][6.18][8.43][4.81][4.26][3.96]MKT-0.06-0.020.02-0.05[-3.87][-1.77][1.22][-2.62]SMB-0.02-0.01-0.04-0.01[-1.08][-0.36][-1.43][-0.26]HML-0.06-0.010.03-0.03[-2.78][-0.50][1.19][-1.23]UMD0.090.040.10[6.09][1.82][5.18]SUE0.210.260.16[5.52][5.03][2.91]adj.-R2(%)3.828.217.035.92.4.ResultsbysizeBecausetheyaresonumerous,smallcapstocksdominatetheFama-MacBethregressioninTable1.TheperformanceofallthreemomentumstrategiesinTable2isalsodrivendisproportionatelybysmallcapstocks,thereturnstowhichareover-weightedwhencalculatingfactorreturns.Thesefactsraiseconcernsthattheresultsoftheprevioussubsectionsareabsentfromthelargecapuniverse,whichaccountsforalargemajorityofmarketcapitalization.Thissubsectionshowsthatthisisnotthecase.Theresultsalsoholdamonglargecapstocks.Table3providesresultsofspanningtests,similartothosepresentedinTable2,performedwithinNYSEsizequintiles.WithineachsizequintileIconstructpriceandearningsmomentumstrategies.Thesebuyandsellthetopandbottom30%ofstockswithinthatsizequintileonthebasisofthecorrespondingsortingcharacteristic,r2;12,SUEorCAR3.Portfoliosarerebalancedmonthly,andreturnsarevalueweighted.12 Table3.Spanningtestsofvalue,protability,andvolatility-baseddefensivestrategies,constructedwithinsizedecilesThetablereportstheperformanceofpricemomentum(winner-minus-loser;WML)andearningsmomentum(SUEandCAR3)strategies,constructedwithineachNYSEsizequintile.Thesestrategiesbuyandsellthe30%ofstockswiththehighestandlowestvaluesofthecorrespondingsortingcharacteristicamongstocksinthesamesizequintile.Portfoliosarerebalancedmonthly,andreturnsarevalue-weightedandignoretransactioncosts.Thetablereportstheaveragemonthlyexcessreturnstoeachsetofstrategies,aswellasresultsoftime-seriesregressionsofeachsetofstrategies'excessreturnsontothereturnsofthreeFamaandFrenchfactorsandtheothertwomomentumfactorsconstructedwithinthesamesizequintile.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Sizequintile(1)(2)(3)(4)(5)MeanPanelA:Sizeportfoliotime-seriesaveragecharacteristics#ofnames3,382774503390333%ofnames62.414.49.47.46.4Firmsize,$1066.737872131,553%ofmktcap.3.54.46.913.272.0PanelB:Momentumstrategyaveragemonthlyexcessreturns,bysizequintile,andresultsofWMLiMKTMKTSMBSMBHMLHMLSUEiSUEiCAR3iCAR3iMean(WMLi)1.430.880.690.470.350.77[5.48][3.95][3.06][1.97][1.48][3.55]-1.47-0.13-0.040.080.18-0.28[-5.79][-0.61][-0.20][0.41][0.83]MKT-0.24-0.14-0.07-0.11-0.03-0.12[-5.24][-3.32][-1.56][-2.43][-0.63]SMB0.010.290.310.420.300.27[0.15][4.59][4.71][6.46][4.10]HML-0.09-0.17-0.14-0.36-0.36-0.23[-1.33][-2.72][-2.08][-5.37][-4.79]SUEi1.131.070.711.140.430.90[10.8][12.2][7.72][11.4][4.48]CAR3i1.080.340.780.520.550.65[8.99][3.00][7.26][4.72][5.11]Adj.-R2(%)49.034.531.437.620.034.513 Table3continuedSizequintile(1)(2)(3)(4)(5)MeanPanelC:SUEstrategyaveragemonthlyexcessreturns,bysizequintile,andresultsofSUEiMKTMKTSMBSMBHMLHMLWMLiWMLiCAR3iCAR3iMean(SUEi)1.500.760.530.260.260.66[15.6][7.17][5.21][2.75][2.46][8.59]0.940.410.440.180.290.45[9.84][4.23][4.61][2.23][2.83]MKT0.080.02-0.02-0.03-0.11-0.01[4.14][1.21][-0.98][-1.46][-4.51]SMB-0.05-0.16-0.17-0.17-0.11-0.13[-1.80][-5.47][-5.42][-6.16][-3.04]HML-0.10-0.03-0.080.050.01-0.03[-3.65][-1.11][-2.32][1.60][0.33]UMDi0.180.230.160.200.100.17[10.8][12.2][7.72][11.4][4.48]CAR3i0.230.250.140.110.160.18[4.50][4.83][2.62][2.31][3.03]Adj.-R2(%)39.437.022.431.414.228.9PanelD:CAR3strategyaveragemonthlyexcessreturns,bysizequintile,andresultsofCAR3iMKTMKTSMBSMBHMLHMLWMLiWMLiSUEiSUEiMean(CAR3i)1.290.760.460.320.200.61[14.8][9.41][5.22][3.77][2.12][10.8]0.790.600.350.280.150.43[9.03][7.29][4.17][3.36][1.66]MKT-0.03-0.03-0.03-0.04-0.02-0.03[-2.01][-1.63][-1.78][-1.90][-1.14]SMB-0.02-0.060.04-0.000.03-0.00[-1.02][-2.30][1.30][-0.14][0.95]HML0.110.01-0.08-0.02-0.04-0.00[4.57][0.40][-2.88][-0.69][-1.34]UMDi0.140.060.130.090.100.10[8.99][3.00][7.26][4.72][5.11]SUEi0.190.200.110.110.130.14[4.50][4.83][2.62][2.31][3.03]Adj.-R2(%)39.416.321.812.211.020.114 PanelAofTable3reportscharacteristicsofthesizeportfolios.Itgivestime-seriesaveragesofthenumberofstocksandaveragesizeofstocksineachportfolio,aswellasthefractionofthenamesandmarketcapineachportfolio.PanelBshowstheperformanceofthepricemomentumportfoliosconstructedwithinNYSEsizequintiles.Itshowsthatsortingonpastperformancegeneratespositivereturnspreadsacrossthesizeportfolios,thoughthesespreadsaredecreasingmonotonicallywithsize.Thatis,momentumisstrongeramongsmallerstocks.Italsoshowsthatexceptamongthesmalleststocks,whichmakeuponaverageonly3.5%ofmarketcapitalization,thereturnstothemomentumstrategiesarecompletelyinsignicantrelativetotheearningsmomentumstrategiesconstructedwithinthesamesizequintiles,evenaftercontrollingfortheFamaandFrenchfactors.Amongthesmalleststocks,wherepastperformancegeneratesbyfarthelargestspreadreturn,thepricemomentumstrategyhasalarge,highlysignicant,negativealphawithrespecttotheearningsmomentumstrategies.PanelsCandDshowthatbothearningssurprisemeasuresgeneratereturnsspreadsineachsizequintilethataremoresignicantthanthosegeneratedbysortingonpastperformance.TheyalsoshowthatalltenoftheearningsmomentumstrategiesgeneratedpositivealphasrelativetotheFamaandFrenchfactorsandtheothermomentumstrategiesconstructedwithinthesamesizequintiles.Thesealphasareallsignicantatthe5%level,exceptfortheCAR3strategyconstructedusingstockswiththelargestcapitalizations,forwhichthealphaissignicantonlyatthe10%level.3ConditionalstrategiesPastperformanceandearningssurprises,especiallysurprisesmeasuredbySUE,arepositivelycorrelated.SortingonpastperformanceconsequentlyyieldssystematicvariationinSUEacrossportfolios,whilesortingonSUEyieldssystematicvariationinpast15 performanceacrossportfolios.Thisconationmakesitdifculttoevaluatetheimpactofthetwoeffectsindependently.ThissectionaddressesthisissuebyconstructingmomentumstrategiesthatareneutralwithrespecttoSUE,andSUEstrategiesthatareneutralwithrespecttopastperformance.Thesestrategiesareconstructedbycontrollingforonevariablewhilesortingontheother.Specically,stocksarerstmatchedonthecontrolvariable,andthenassignedtoportfoliosonthebasisoftheprimarysortingvariable.Forexample,astrategythatidentiespairsofstocksmostcloselymatchedonSUE,andthenbuysthememberofeachpairwithstrongerpastperformanceandshortstheonewithweakerpastperformance,wouldhavesubstantialvariationinpastperformance,butessentiallynoneinrecentearningssurprises.Tomaketheconditionalstrategies,UMDjSUE(“UMDconditionalonSUE”)andSUEjr2;12(“SUEconditionalonprioryear'sperformance”),asdirectlycomparableaspossibletoUMDandSUE,Iwouldlikethemtohavethesamevariationintheprimarysortingcharacteristicastheirtraditionalcounterparts.Thatis,IwouldlikeapastperformancespreadinUMDjSUEsimilartothatinUMD,andanearningssurprisespreadinSUEjr2;12similartothatinSUE.UMDandSUEholdthe30%ofstockswiththehighestpastperformanceorearningssurpriserankings,andshortthe30%withthelowestrankings,sotheaveragerankingoftheprimarysortingvariableonthelongandshortsidesofUMDandSUEare85%and15%,respectively.Ifpastperformanceandearningssurpriseswereuncorrelated,thenselectinggroupsofstocksmatchedonthecontrolvariablewouldnotaffectthedistributionoftherankingsontheprimarysortingcharacteristic.Thestocks'rankingsontheprimarysortingcharacteristicwouldthenbelikenindependentdrawsofastandarduniformvariable.Themaximalorderstatisticofnindependentstandarduniformvariablesisdistributednxn1,sohasanexpectedvalueofR10x.nxn1dx/Dn=.nC1/.Theexpectedvalueoftheminimalorderstatisticis,bysymmetry,1=.nC1/.Soifpastperformanceandearningssurprises16 wereuncorrelated,thenassigningstocksonthebasisoftheprimarysortingvariableamonggroupsofnD6stocksmatchedonthecontrolvariablewouldyieldexpectedaveragerankingsoftheprimarysortingvariableinthehighandlowportfoliosof6=7D85:3%1=7D15:3%,respectively,similartothoseobtainedfromaunivariatetertilesort.Pastperformanceandearningssurprisesaresignicantlycorrelated,however,whichiswhatconatespriceandearningsmomentumstrategiesintherstplace.Thiscorrelationreducesthespreadintheprimarysortingcharacteristicbetweenthehighandlowportfoliosoftheconditionalstrategies.Groupsofnstocksmatchedononeofthecharacteristicsexhibitlessvariationintheothercharacteristics,becauseofthecorrelation,thanwouldnrandomlyselectedstocks.Variationintheprimarysortingcharacteristicamongstocksmatchedonthecontrolvariablecomesonlyfromthevariationintheformerunexplainedbythelatter.Toachieveaspreadintheprimarysortingcharacteristicfortheconditionalstrategiescomparabletothatobservedinthetraditionalpriceandearningsmomentumstrategiesconsequentlyrequiresinitiallyselectinglargergroupsofmatchedstocks.Selectinggroupsofsevenstocksmatchedonthecontrolvariableyieldsconditionalstrategieswithvariationintheprimarysortingcharacteristicthatmostcloselymatchesthevariationresultingfromtheunivariatetertilesorts.Finally,tomaketheseconditionalstrategiesascomparabletoUMDandSUEaspossible,thereturnstotheconditionalstrategiesarealsoaveragedacrosslargeandsmallcapstrategies.Specically,largeandsmallcapstocks,denedasthosewithaboveandbelowNYSEmedianmarketcapitalizations,arematchedintogroupsofsevenonthebasisofeitherpastperformance(r2;12)orrecentearningssurprises(SUE).Stocksarethenassignedtoportfoliosonthebasisoftheirrankingsontheothervariable,earningssurprisesorpastperformance.Theconditionalearningssurprisefactor,SUEjr2;12,andtheconditionalmomentumfactor,UMDjSUE,areanequal-weightedaverageofthevalue-weightedlargeandsmallcapstrategiesthatholdthecorrespondinghighportfolios17 UMDUMD | SUESUESUE | r12,2LowMidHigh102030405060708090 SUESUE | r12,2UMDUMD | SUEPanelA:Averagepastperformancerank(%),byportfolioPanelB:AverageSUErank(%),byportfolioFig.2.Portfolioaveragepastperformanceandearningssurpriseranks.Thegureshowsthetime-seriesaverageoftheaverager2;12(PanelA)andSUE(PanelB)oftheportfoliosunderlyingtheunconditionalpriceandearningsmomentumstrategies(UMDandSUE)andtheconditionalpriceandearningsmomentumstrategies(UMDSUEandSUEr2;12).Thesearetertilesortedonr2;12andSUE(unconditionalstrategies),orsortedintosevenportfoliosononeofthesevariablesfromamonggroupsmostcloselymatchedontheother(conditionalstrategies).ThesamplecoversJanuary1975throughDecember2012.18 andshortthecorrespondinglowportfolios.3Figure2showsthetime-seriesaverageoftheaveragepastperformanceandearningssurpriseranksoftheportfoliosunderlyingtheconditionalmomentumandearningssurprisefactors,aswellastheunconditionalfactorsUMDandSUE.PanelAshowspastperformanceranks.TheUMDportfoliosandUMDjSUEexhibitnearlyidenticalvariationinpastperformanceranks.TheunconditionalSUEfactorexhibitsaboutathirdofthisvariation,despitebeingconstructedwithoutconsiderationforpastperformance.Theconditionalearningssurprisefactorsexhibitessentiallynovariationinpastperformancerankings,asintended.PanelBshowssimilarresultsforearningssurpriseranks.TheunconditionalSUEfactorandSUEjr2;12exhibitalmostindistinguishablelevelsofearningssurpriserankvariation,UMDshowssomewhatlessthanonethirdthisvariation,andtheconditionalmomentumfactoressentiallynovariation,inearningssurpriseranks.Figure3showstheperformanceovertimeofthefourstrategies,UMD,UMDjSUE,SUE,andSUEjr2;12.Thegureshowsthegrowthofadollar,netofnancingcosts,investedinthebeginningof1975intoeachofthestrategies,wherethestrategiesareallleveredtorunatanexpostvolatilityof10%.Thegureshowsthatpurgingpricemomentumfromtheearningsmomentumstrategyimprovesitsperformance.ItalsoeliminatesthelargedrawdownthattheunconditionalSUEstrategyexperiencedduringthemomentumcrashinthespringof2009.ThegureshowsthatpurgingearningsmomentumfromUMD,however,yieldsasignicantworseningintheperformanceofthepricemomentumstrategy.Table4analyzestheperformanceofthefourstrategiesformally.Therstspecication3Theappendixalsoreportsresultsforconditionalstrategiesconstructedbyselectingonlymatchedtriplesontheconditioningvariable.ThisyieldssimilarnamediversicationtoUMDandSUEonthelongandshortsides,butsignicantlylessvariationintheprimarysortingcharacteristicbetweenthehighandlowportfolios.Resultsusingthisalternativemethodologyforconditionalfactorconstructionareconsistentwiththosepresentedhere.19 SUE | r12,2SUEUMDUMD | SUEPerformanceof$1(logscale)Fig.3.Comparisonofconditionalandunconditionalpriceandearningsmomentumstrategies.Thegureshowsthevalueofadollarinvestedatthebeginningof1975inUMD(lightdashedline),theSUEfactor(darkdashedline),thepricemomentumfactorconstructedtobeneutralwithrespecttoearningsmomentum(UMDSUE;solidlightline),andtheearningsmomentumfactorconstructedtobeneutralwithrespecttopricemomentum(SUEr2;12;soliddarkline).Returnsarecalculatednetofnancingcosts(i.e.,areexcessreturns).Tofacilitatecomparison,factorsarescaledtohaveasamplevolatilitiesof10%.ThesamplecoversJanuary1975throughDecember2012.showsthatUMDgeneratsahighlysignicantgrossspreadsoverthe38yearsample.ThesecondshowsthatUMDhasasignicantinformationratiorelativetothemomentumfactorconstructedtobeneutralwithrespecttoearningssurprises,UMDjSUE,suggestingearningsmomentumsignicantlycontributestotheperformanceofthestandardpricemomentumfactor.ThethirdspecicationshowsthatUMDloadsheavilyonboththeconditionalfactorsUMDjSUEandSUEjr2;12,andthattheseloadingsexplainUMD'sperformance.UMD'sloadingontheconditionalearningsmomentumfactorisroughly20 athirdofitsloadingsontheconditionalpricemomentumfactor,consistentwiththeUMDportfolios'earningssurpriserankspreadonethirdaslargeastheirpastperformancerankspread,observedinFigure2.SpecicationsfourthroughsixshowthattheunconditionalearningsmomentumfactorSUEgeneratesaspreadsimilarto,butmuchmoresignicantthan,thatonUMD.TheyalsoshowthatSUE,likeUMD,loadsheavilyonboththeconditionalfactors,andthattheseloadingsalsoexplainSUE'sperformance.SUE'sloadingontheconditionalpricemomentumfactorisroughlyaquarterofitsloadingsontheconditionalearningsmomentumfactor,againconsistentwiththerelativeearningssurpriseandpastperformancerankspreadsobservedonthefactors'underlyingportfoliosinFigure2.SpecicationsevenshowsthatUMDjSUE,thepricemomentumfactorpurgedofearningsmomentum,generatedonlytwo-thirdsthespreadofthestandardUMDfactor,andthatthisspreadissignicantatthe10%level,butnotatthe5%level.SpecicationeightshowsthatUMDjSUEhasasignicantnegativealpharelativetoUMD,whilespecicationnineshowsthatthisnegativealphaisinsignicantaftercontrollingfortheshortpositionUMDjSUEtakesinSUEaftercontrollingforUMD.SpecicationstenthroughtwelveshowthatSUEjr2;12,theearningsmomentumconstructedtobeneutralwithrespecttopastperformance,generatedasimilar,evenmoresignicant,spreadtothatobservedontheunconditionalfactorSUE,andthatithasanextremelylargeinformationratiorelativebothtoSUEandtoSUEandUMD.NoneoftheinferencesdiscussedherechangeifoneincludescontrolsforthethreeFamaandFrenchfactorsinthetime-seriesregressions.TheresultsarealsoevenstrongeriftheconditionalstrategiesareconstructedsuchthattheunderlyingportfolioshavesimilarnamediversicationtotheportfoliosunderlyingUMDandSUE—i.e.,iftheyareconstructednottomatchthevariationintheprimarysortingcharacteristic,buttohaveroughlythesamenumberofrmsonthelongandshortsides(resultsprovidedinTableA5,intheappendix).21 Table4ConditionalpriceandearningsmomentumstrategyperformanceThistablepresentsresultsoftime-seriesregressionsoftheform:ytDC000XtC"twheretheytarethemonthlyexcessreturnstoeitherUMD(specicationsonetothree),theearningsmomentumfactorSUE(specicationsfourtosix),thepricemomentumfactorconstructedtobeneutralwithrespecttoearningsmomentumUMDjSUE(specicationsseventonine),andtheearningsmomentumfactorconstructedtobeneutralwithrespecttopricemomentumSUEjr2;12(specicationstentotwelve).TheconditionalfactorsareconstructedsimilartoUMD,butsortstocksontheprimarysortingcharacteristic(r2;12orSUE)fromamongstocksmatchedontheothercharacteristic.Theinitialmatchselectsgroupsofsevenstocks,whichyieldsvariationintheprimarysortingcharacteristicnearlyidenticaltothatobtainedfromaunivariatetertilesort.Explanatoryfactorsaretakenfromthesamesetofstrategies.ThesamplecoversJanuary1975throughDecember2012.dependentvariableyDUMDyDSUEyDUMDjSUEyDSUEjr2;12(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)0.640.250.090.590.130.040.45-0.23-0.070.580.250.22[3.03][3.95][1.38][7.14][1.97][0.86][1.93][-3.18][-0.99][8.42][4.68][4.74]UMDjSUE0.860.860.17[68.1][71.4][17.4]SUEjr2;120.280.790.81[6.68][18.6][24.6]UMD1.061.14-0.15[68.1][64.0][-12.4]SUE-0.350.550.76[-7.64][18.6][24.8]adj.-R2(%)91.191.843.265.991.192.143.257.622 Table5HighermomentsofmomentumstrategyperformanceThistablegivesthehighermomentsanddrawdownperformanceoftheunconditionalpriceandearningsmomentumstrategies,UMDandSUE,thepricemomentumstrategyconstructedtobeneutralwithrespecttoearningsmomentum,UMDjSUE,andSUEjr2;12andtheearningsmomentumstrategyconstructedtobeneutralwithrespecttopricemomentum.Resultsforthemarketareprovidedforcomparison.ThesamplecoversJanuary1975throughDecember2012.MKTUMDSUEUMDjSUESUEjr2;12Volatility(%)15.815.66.117.35.1Skewness-0.64-1.50-1.74-1.050.46Excesskurtosis2.1011.415.08.370.96Maxloss%(nat.vol.)54.357.621.467.38.7Maxloss%(10%vol.)37.240.733.742.316.6Sharperatio0.480.491.160.321.35Pricemomentumstrategiesarealsoknowntoexhibitlargenegativeskewandsignicantexcesskurtosis,i.e.,theygenerateextrememovesmorefrequentlythanifthereturnswerelog-normallydistributed,andtheseextrememovesaremorelikelytobecrashes.Table5demonstratesthatthesefeaturesofmomentumstrategyperformancearedrivenbyprice,notearnings,momentum.Whilethetableshowsthatearningsmomentumstrategyalsoexhibitslargenegativeskewandsignicantexcesskurtosis,theearningsmomentumstrategyconstructedcontrollingforpricemomentumhaspositiveskewandonlymildexcesskurtosis.4.ConstantvolatilitystrategiesThenegativeskewandexcesskurtosisinpricemomentumstrategiesarealsoanalyzedindetailbybothBarrosoandSanta-Clara(2013)andDanielandMoskowitz(2014).Thesepapersarguethatmomentum'scrashriskistime-varyingandpredictable,andthatmanagingcrashrisksignicantlyimprovesmomentumstrategyperformance,makingmomentumevenmoredifculttoexplain.Thissectionshowsthatfundamentalmomentum23 explainseventhesehighSharperatio,risk-managed,pricemomentumstrategies.Toconstructtherisk-managedmomentumstrategiesIfollowBarrosoandSanta-Clara(2013),wholeverawinners-minus-losersstrategyeachmonthattemptingtohitatargetvolatility,i.e.,theyscaleastandardmomentumstrategybyitstrailingvolatility.4IconstructtheconstantvolatilitystrategiesUMD,SUE,andCAR3similarly,leveringeachcorrespondingdollarlong/dollarshortstrategybyanamountthatisinverselyproportionaltothatstrategy'srealizeddailyvolatilityovertheprecedingmonth.Tofacilitatecomparisonbetweentheconstantvolatilitystrategiesandthedollarlong/dollarshortstrategies,thetargetvolatilityispickedsuchthattheaverageleverageemployedineachoftheconstantvolatilitystrategiesisclosetoone.Figure4showsthetrailing12-monthaverageleverageforeachstrategy.Thegurealsoincludes,forcomparison,theleverageforasimilarlyconstructedconstantvolatilitymarketfactor,MKT.Thestrategiesexhibitsimilarleverageateachpointintime.Forexample,allthestrategiesshowdramaticreductionsinleverageduringtheNASDAQdeation,roughlycoincidentwiththeterroristattacksof9/11/2001,andfollowingthestartofthegreatrecessionafter2008,bothtimesofmarketstressandhighuncertainty.WhileBarrosoandSanta-Clara(2013)claimintheirabstractthat“themajorsourceofpredictabilityisnottime-varyingmarketriskbutrathermomentum-specicrisk,”theguresuggeststhatthevolatilityofmomentumstrategiesisactuallyrelatedtothelevelofgeneralmarketuncertainty.Figure5showstheperformanceovertimeofthethreeconstantvolatilitymomentumstrategies,UMD,SUE,andCAR3,andincludestheconventionalmomentumfactorUMDforcomparison.Thegureshowsthegrowthofadollar,netofnancingcosts,4DanielandMoskowitz(2014)employasimilarprocedure,butalsoincorporateinformationregardingtheirestimationofmomentum'sconditionalexpectedreturns,basedontheirobservationthatmomentumhasperformedpoorlywhenitsvolatilityhasbeenhighinperiodsafterthemarkethasperformedpoorly.Whilegeneratingstrongerresults,theirprocedureismorecomplicated.Italsoemploysttedreturnsbasedonparametersestimatedoverthewholesample,raisingconcernsaboutalook-aheadbias.24 UMD*SUE*CAR3*MKT*ConstantvolatilitystrategyleverageFig.4.Constantvolatilitystrategyleverage.ThegureshowstheleverageemployedeachmonthtoconstructtheconstantvolatilitystrategiesUMD,SUE,andCAR3.Thisleverageisinverselyproportionaltothedollarlong/dollarshortstrategies'realizeddailyvolatilityovertheprecedingmonth.Thetargetvolatilityispickedsuchthattheaverageleverageforeachoftheconstantvolatilitystrategiesisclosetoone.Leverageforasimilarlyconstructedconstantvolatilitymarketstrategy,MKT,isprovidedforcomparison.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.investedinthebeginningof1975intoeachofthestrategies,wheretofacilitatecomparisonthestrategiesareallleveredtorunatanaveragesamplevolatilityof10%.ConsistentwithBarrosoandSanta-Clara(2013)andDanielandMoskowitz(2014),thegureshowsthattheconstantvolatilitypricemomentumstrategy,UMD,generatessuperiorperformancetoitsconventionalcounterpart,andmostlyavoidsthemomentumcrashinthespringof2009.Thegurealsoshows,however,thattheconstantvolatilityearningsmomentumstrategies25 CAR3*SUE*UMD*UMDPerformanceof$1(logscale)Fig.5.Constantvolatilitystrategyperformance.Thegureshowsthevalueofadollarinvestedatthebeginningof1975intheconstantvolatilitypricemomentumfactor,UMD(dottedline),andtheconstantvolatilityearningsmomentumfactors,SUE(solidline)andCAR3(dashedline).Theperformanceoftheconventionalmomentumfactor,UMD(dot-dashedline),isprovidedasabenchmark.Returnsarecalculatednetofnancingcosts(i.e.,areexcessreturns).Tofacilitatecomparison,factorsarescaledtohaveasamplevolatilitiesof10%.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.dramaticallyoutperformtheconstantvolatilitypricemomentumstrategy.Table6formallyanalyzestheperformanceoftheconstantvolatilitystrategies.PanelAinvestigatestheperformanceofUMD.Specicationoneshowsthatoverthe38yearsampletheconstantvolatilitypricemomentumstrategyearned85basispointspermonth.Thispremiumisaboutathirdlargerthanthatontheconventionalfactor(65bps/month)and,becausetheconstantvolatilityfactorislessthantwo-thirdsasvolatile26 Table6ConstantvolatilitystrategyperformanceThistablepresentsresultsoftime-seriesregressionsoftheform:ytDC000XtC"twheretheytarethemonthlyexcessreturnstotheconstantvolatilitypricemomentumfactor,UMD,ortheconstantvolatilityearningsmomentumfactors,SUEandCAR3,andtheexplanatoryfactorsarethereturnstotheFamaandFrenchfactors(MKT,SMB,andHML),orthesefactorsandtheothertwoconstantvolatilitymomentumfactors.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Fullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelA:yUMD0.850.470.021.150.140.56-0.07[6.34][5.65][0.18][5.49][0.58][3.33][-0.43]MKT0.090.010.06-0.02[4.69][0.35][1.26][-0.68]SMB-0.050.050.010.07[-1.75][1.36][0.14][1.61]HML0.03-0.09-0.05-0.11[0.95][-2.24][-0.66][-2.46]UMD0.53[28.9]SUE0.860.820.96[9.23][5.96][7.24]CAR30.570.490.61[5.33][2.89][4.48]adj.-R2(%)65.528.023.532.8PanelB:ySUE0.620.560.360.800.470.430.28[9.96][9.40][5.84][8.20][4.56][5.82][4.02]MKT0.01-0.01-0.02-0.01[0.82][-0.41][-1.03][-0.56]SMB-0.06-0.05-0.01-0.05[-3.21][-2.53][-0.42][-2.51]HML-0.01-0.01-0.090.03[-0.46][-0.73][-2.64][1.21]UMD0.12[8.86]UMD0.180.170.20[9.23][5.96][7.24]CAR30.230.290.13[4.58][3.86][2.00]adj.-R2(%)16.026.926.828.127 Table6continuedFullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelC:yCAR30.540.500.350.690.430.390.28[10.1][9.42][6.22][8.86][4.91][5.42][3.88]MKT0.00-0.010.02-0.03[0.02][-1.09][1.03][-2.29]SMB-0.03-0.02-0.05-0.01[-1.94][-0.95][-1.63][-0.37]HML-0.00-0.000.02-0.01[-0.08][-0.28][0.61][-0.51]UMD0.08[7.24]UMD0.100.070.14[5.33][2.89][4.48]SUE0.190.220.14[4.58][3.86][2.00]adj.-R2(%)10.717.315.718.6astheconventionalfactor(9.8%versus15.6),thet-statisticismorethantwiceaslarge(6.34versus3.03).SpecicationtwoshowsthatUMDalsohasalarge,highlysignicantinformationratiorelativetoconventionalmomentum.UMDhadanalphaof47bps/monthrelativetoUMDandthethreeFamaandFrenchfactors.Thet-statisticonthisalphais5.65,implyinganextremelyhighinformationratio.SpecicationthreeshowsthatUMDhadacompletelyinsignicantalphaof2bps/monthrelativetoSUE,CAR3,andthethreeFamaandFrenchfactors.Thatis,UMDisspannedbytheconstantvolatilityearningsmomentumfactors.Specicationsfourthroughsevenshowconsistentsubsampleresults.UMDgenerateshighlysignicantreturns,evenoverthelatehalfofthesamplewhenUMDfailedtodoso,thoughthestrategydid,similartoUMD,deliveraveragereturnsroughlytwiceashighovertheearlysample.Inbothsubsamples,however,thisperformanceisentirelyexplainedbythestrategy'sloadingsontheconstantvolatilityearningsmomentumfactors.28 PanelsBandCshowthattheconstantvolatilityearningsfactorsSUEandCAR3arebothoutsidethespanofUMDandeachother.Theearningsmomentumstrategiesbothgeneratehighlysignicantreturnsoverthewholesample,witht-statisticsclosetoten.Thesereturnsarehighlysignicantinbothsubsamples,thoughagainmoreimpressiveduringtheearlysample.ThesereturnsareessentiallyunaffectedaftercontrollingforthethreeFamaandFrenchfactorsandUMD,andremainhighlysignicantaftercontrollingforthethreeFamaandFrenchfactorsandtheothertwoconstantvolatilitymomentumfactors.5.ConclusionPastperformancepredictscrosssectionalvariationinaveragestockreturnsbecausestrongpastperformanceisasignalofpositivemovesinfundamentals.Aftercontrollingforfundamentals,pastperformancedoesnotprovidesignicantadditionalinformationregardingexpectedreturns.Fundamentally,momentumisfundamentalmomentum.Pastperformanceshouldnotbeignored,however,whentradingmomentum.Earningsmomentumstrategiesconstructedwithoutregardforpastpriceperformancetakeunintended,performanceimpairing,positionsinpricemomentum.Designingearningsmomentumstrategiesexplicitlytoavoidpricemomentumreducesthestrategies'volatilities,andeliminatestheirtendencytooccasionallycrash,withoutsignicantlyreducingexpectedreturns.ThisresultsinhigherSharperatiosandsmallerdrawdowns.Recentpastperformancemayalsoprovideaninformativesignalinothermarkets.AsimilarphenomenonisobservedwithDeBondtandThaler's(1985)longrunreversals.Valueandsizeexplaintheperformanceofstockmarketstrategiesbasedonlongrunreversal,becausestocksthathaveexperiencedlongperiodsofunderperformancetendtohavelowvaluations.Becauseofthiscorrelation,poorlongrunpastperformancemayalsosignalvalueinmarketsinwhichdirectmeasuresofvalueareunavailable,e.g.,markets29 forassetsthathavenoaccountingvariablesthatcouldbeusedtoscaleprices.Similarly,inmarketswherefundamentalsarenotdirectlyobservable,oraredifculttoquantify,recentpastperformancehelpssignalfundamentalinnovations,oratleastthemarkets'interpretationoftheseinnovations.Pastperformanceisalsoimportantforunderstandingthecrosssectionofrealizedreturns.Recentwinnerstendtoperformstronglytogether,andpoorlypreciselywhenrecentlosersperformstrongly.Thesestrongcomovementsintroducesignicantrisktostrategiesthattilttowardpricemomentum,contributingvolatilityevenwhenthestrategiesarewelldiversiedinnames,andnegativeskewthatexposesthestrategiestolargedrawdowns.Accountingforthesetilts,whentheyarepresent,dramaticallyimprovestheexplanatorypowerthatassetpricingmodelshaveexplainingvariationinrealizedreturns.AppendixAResultsaccountingfortransactioncostsBeforegettingoverlyexcitedabouttheremarkableperformanceofthemomentumstrategiesconsideredinthispaper,itmustberememberedthattradingmomentumentailssignicanttradingcosts,whichthetestshavesofarignored.BoththelongandshortsidesoftheconventionalSUEfactorturnover,onaverage,morethantwiceayear.Thiscostsonaverage35bps/monthtotrade.5TheUMDandCAR3factorsareevenmoreexpensivetotrade,turningoveronaveragethreetimesperyearatanaveragecostof50bps/month.5TransactioncostestimatesareallmadeusingthemethodologyofNovy-MarxandVelikov(2014).ThismethodologyemploysHasbrouck's(2009)Bayesian-GibbssamplingproceduretoestimateeffectivespreadsusingageneralizedversionoftheRoll(1984)model,wheresufcientdataisavailable,andanearestmatchingalgorithmonsizeandvolatilitywhereitisnot.Theprocedureyieldsestimatesoftheeffectivespreadsfacedbyasmallliquiditydemander,andthusrepresentaconservativeestimateforsmalltraderswithoutsignicantmarketimpact.Theestimatesignoretheconvexityinpriceimpactfromlargetrades,andmaythusunderstatethecostsfacedbytraderswithsignicantmarketfootprints.30 Thesecostsaresufcienttowipeoutmostofthestrategies'excessreturns.Theconstantvolatilityfactorsgeneratesuperiorperformance,butareevenmorecostlytotrade.Changingthestrategies'leverageeachmonthinducessignicantadditionalturnover.Theconstantvolatilityearningsmomentumstrategies'leverageonthedollarlong/dollarshortstrategieschangesonaveragebyalmost25percentagepointspermonth.Theaverageleverageadjustmentfortheconstantvolatilitypricemomentumstrategyisslightlyhigher.Theseleverageadjustmentsresultinanadditional25%averageone-waytransactionseachmonthoneachsideofthestrategies,increasingthecostoftradingbyroughlyanother25bps/month.Thesehighercostsareagainsufcienttoeatupmostoftheconstantvolatilitystrategies'superiorgrossreturns.Thestrategiesconsideredsofar,however,haveallbeenconstructedwithoutregardfortransactioncosts.Consciouslydesigningmomentumstrategiestominimizetransactioncostsyieldsstrategieswithsignicantlybetternetperformance,thoughthisperformanceisstillobviouslysignicantlyworsethanwhatcouldhavebeenachievediftradingwerefree.Novy-MarxandVelikov(2014)ndthatthesinglemosteffectivetradingcostmitigationtechniqueistotradeusingabuy/hold/sellapproach,i.e.,tohaveamorestringentrequirementforactivelytradingintoapositionthanformaintaininganopenposition.Thebuy/holdspreadeliminatesmuchofthetradingthatresultsfromstocksenteringaportfolioonemonthonlytofalloutthenext,atypeoftransactionthatrepresentsasignicantfractionofturnoverwithstandardacademicportfolioconstruction.WhenconstructingstrategiesthataccountfortransactioncostsIconsequentlyfollowNovy-MarxandVelikov(2014),whondthatabuy/holdspreadof20%yieldssignicanttradingcostsreductionswhilemaintainingasimilarexposuretothesortingcharacteristic.Specically,stocksenterthelongportfoliowhentheyenterthetopquintileofthesortingcharacteristicusingNYSEbreaks,andremaininthisportfolioaslongastheyremaininthetoptwoquintiles.Similarlystocksaresoldshortwhentheyenterthebottomquintileof31 thesortingcharacteristicusingNYSEbreaks,andthesepositionsarecoveredonlywhenstocksfalloutofthebottomtwoquintiles.Thestrategies,likeUMD,areconstructedasanequalweightedaverageofthevalueweightedlargeandsmallcapstrategies,wherelargeandsmallstocksaredenedasthosewithaboveandbelowNYSEmedianmarketcapitalization.Tofurtherreduceturnoverandtransactioncosts,reclassicationfromlargetosmall,orsmalltolarge,doesnotforcetheclosingofopenpositions.Usingthisbuy/holdspreadyieldsanearly50%reductioninturnoverandtransactioncostsforthepricemomentumstrategy,andsignicantbutmoremodestreductionsfortheSUEandCAR3strategiesofroughlyonethirdandonequarter,respectively.Figure6showstheperformance,netoftransactioncosts,ofthethreemomentumfactorsconstructedusingthebuy/holdspread,UMDnet,SUEnet,andCAR3net.Thegureshowsthegrowthofadollar,netofnancingcosts,investedinthebeginningof1975intoeachofthestrategies,wheretofacilitatecomparisonthestrategiesareallleveredtorunatanaveragesamplevolatilityof10%.Thegureshowsthatthestrategiesallgeneratepositiveabnormalreturns,evenafteraccountingfortransactioncosts,thoughthisperformanceisseverelyattenuatedrelativetothatcalculatedignoringtransactioncosts.Consistentwithearlierresults,theearningsmomentumstrategiesgeneratesuperiorperformancetothepricemomentumstrategy.TableA1replicatesthespanningtestsofTable2,usingthetransactioncostmitigatedstrategies'netreturns.PanelAshowsthatpricemomentumdeliveredsignicantreturnsevenafteraccountingfortransactioncosts,thoughaccountingfortransactioncostsreducedthemomentumstrategy'sSharperatiobyathirdandmakesitsreturnsonlymarginallysignicant.Italsoshowsthattheearningsmomentumfactorsdoanexceptionaljobpricingthepricemomentumfactor.Thepricemomentumfactors'netalpharelativetotheFamaandFrenchfactorsandthenetearningsmomentumfactorsisonlyonebasispointpermonth,andcompletelyinsignicant.ThisresultisconsistentwiththatobservedinTable32 SUEnet CAR3net UMDnet Performanceof$1(logscale),netoftransactioncostsFig.6.Comparisonofmomentumfactorsnetoftransactioncosts.Thegureshowsthevalueofadollar,netofnancingcosts,investedattheendoftherstquarterof1974intheROEfactor,rebalancedmonthlyonthebasisofthemostrecentlyannouncedquarterlyearnings-to-book,andsimilarlyconstructedfactorsbasedonstandardizedunexpectedearnings(PEAD),earningsinnovations-to-book(ROE),laggedearnings-to-book(lag-ROE),andalowerfrequencyearnings-to-bookstrategybasedonannualreturn-on-equity,whichisonlyrebalancedonceayear,attheendofJune(E/B).Returnsarecalculatednetofnancingcosts(i.e.,areexcessreturns).Tofacilitatecomparison,factorsarescaledtohaveasamplevolatilitiesof10%.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.2.Thattableshowedasignicantnegativealphaonpricemomentumrelativetothetwoearningsmomentumfactor,butthepricemomentumtrackingportfoliotooklargepositionsinbothearningsmomentumfactors,andincurringtransactioncostsonboththesepositionswasmoreexpensivetotrade.Afteraccountingfortradingcoststhepricemomentumfactoranditstrackingportfoliogeneratesimilarreturns.33 TableA1MomentumstrategyperformanceaccountingfortransactioncostsThistablepresentsresultsoftime-seriesregressionsoftheform:ytDC000XtC"twheretheytarethemonthlyexcessreturns,netoftransactioncosts,tothepricemomentumfactor,UMDnet,ortheearningsmomentumfactors,SUEnetandCAR3net,wherethesestrategiesareconstructedusingabuy/holdspreadtoreduceturnoverandtransactioncosts,andtheexplanatoryfactorsarethereturnstotheFamaandFrenchfactors(MKT,SMB,andHML),orthesefactorsandtheothertwonetreturnmomentumfactors.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Fullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelA:yDUMDnet0.450.710.010.590.080.30-0.00[2.03][3.25][0.03][2.55][0.40][0.80][-0.02]MKT-0.18-0.030.06-0.06[-3.66][-0.66][1.34][-0.92]SMB0.020.17-0.010.26[0.23][2.92][-0.15][3.01]HML-0.42-0.21-0.15-0.24[-5.67][-3.57][-1.82][-2.60]SUEnet0.960.781.09[9.77][5.93][7.24]CAR3net0.910.760.90[7.79][4.74][5.24]adj.-R2(%)7.243.334.547.6PanelB:yDSUEnet0.320.460.240.420.330.220.19[3.40][4.96][3.22][3.78][3.39][1.47][1.75]MKT-0.09-0.04-0.03-0.07[-4.32][-2.05][-1.23][-2.79]SMB-0.13-0.12-0.03-0.15[-4.22][-4.99][-0.94][-4.33]HML-0.12-0.01-0.140.06[-3.65][-0.23][-3.61][1.52]UMDnet0.180.180.18[9.77][5.93][7.24]CAR3net0.290.290.29[5.54][3.72][4.19]adj.-R2(%)9.141.034.149.534 TableA1continuedFullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelC:yDCAR3net0.190.290.100.280.120.110.06[2.50][3.74][1.46][3.25][1.38][0.84][0.58]MKT-0.08-0.030.00-0.05[-4.28][-2.12][0.07][-1.96]SMB-0.03-0.00-0.03-0.00[-1.20][-0.21][-1.12][-0.06]HML-0.11-0.030.04-0.08[-4.13][-1.27][1.33][-2.26]UMDnet0.130.120.12[7.79][4.74][5.24]SUEnet0.220.200.25[5.54][3.72][4.19]adj.-R2(%)5.734.623.740.2Whilepricemomentum'snetperformanceisinsidethespanofthenetearningsmomentumfactors,PanelBshowsthatSUEnetisoutsidethespanofUMDnetandCAR3net.SUEnetearnedhighlysignicantreturnsoverthesample(test-statisticof3.40)evenafteraccountingfortransactioncosts,andhadahighlysignicantalpharelativetothethreeFamaandFrenchfactorsandtheothertwomomentumfactors.Thisnetperformancewaspositive,butnotstatisticallysignicant,overthelatehalfofthesample,covering19years.PanelCshowsthatCAR3,whichismoreexpensivetotradethanSUE,andsufferedgreaterperformancedeteriorationovertime,generatedstatisticallysignicantnetreturnsoverthewholesample,butcompletelyinsignicantnetreturnsoverthesecondhalfofthesample.ItsabnormalreturnsrelativetotheFamaandFrenchfactorsandtheothertwomomentumstrategieswerealsoinsignicantoverthewholesample,suggestingthatinpracticeCAR3doesnotsignicantlyimprovetheopportunitysetforinvestorsalreadytradingSUE.35 A.1.AportfolioperspectiveAnotherwaytoquantifythepotentialvalueofmomentumstrategiestorealinvestorsistoconsiderthepotentialSharperatiosthatcouldhavebeenachievedusingthestrategies.TableA2reportstheportfolioweightsinexpostmean-varianceefcientportfoliosofvariouscombinationsofthemomentumstrategiesandthethreeFamaandFrenchfactors.PanelAprovidesfullsampleresults.TherstfourspecicationsshowthatallthreeofthemomentumstrategieshavereasonablyhighSharperatiosoverthesample,thoughthisisclearlyhighestforSUEnet,whichistheonlymomentumstrategythatrealizesahighernetSharperatiooverthesamplethanthe0.48deliveredbythemarket.TheyalsoshowthataccesstoallthreemomentumstrategieshardlyimprovestheSharperatiooverthatavailablefromSUEnetalone(0.57vs.0.55).ThelastvespecicationsshowthataddinganyofthemomentumstrategiestotheopportunitysetofaninvestoralreadytradingthethreeFamaandFrenchfactorsyieldssignicantSharperationimprovements(from0.81tofrom0.98to0.16),butthatincludingpricemomentumandthestrategybasedonCAR3againyieldonlymarginalimprovementsabovethoserealizedfromaddingSUEalone(1.19vs1.16).PanelBandCshowconsistentsubsampleresults,andsuggestthatifanythingtheseconclusionshavestrengthenedovertime.36 TableA2Ex-postmean-varianceefcientportfoliosThistablegivesweightsintheex-postmean-varianceefcientportfolioforvariouscombinationsofthenetoftransactioncostmomentumfactors(UMDnet,SUEnet,andCAR3net)andtheFamaandFrenchfactors(MKT,SMB,andHML),aswellastherealizedannualSharperatios(S.R.)oftheseportfolios.ThefullsamplecoversJanuary1975throughDecember2012,withthedatesdeterminedbythedatarequirementsformakingtheSUEandCAR3strategies.TheearlyandlatesamplesareJanuary1975throughDecember1993andJanuary1994throughDecember2012,respectively.Strategyweightinex-postMVEportfolioandportfolioSharperatio(1)(2)(3)(4)(5)(6)(7)(8)(9)PanelA:FullsampleresultsUMDnet1.00-0.030.190.00SUEnet1.000.700.420.31CAR3net1.000.330.420.16MKT0.280.230.160.170.15SMB0.240.160.160.130.14HML0.480.420.260.280.24S.R.0.330.550.410.570.810.981.161.021.19PanelB:Earlysample(1/75–12/93)resultsUMDnet1.000.010.240.02SUEnet1.000.520.470.34CAR3net1.000.460.480.17MKT0.270.170.120.130.10SMB0.190.150.110.120.10HML0.540.440.310.270.27S.R.0.590.870.750.971.091.341.641.391.69PanelC:Latesample(1/94–12/12)resultsUMDnet1.00-0.030.17-0.00SUEnet1.000.950.420.33CAR3net1.000.080.390.12MKT0.320.290.210.210.20SMB0.240.150.160.130.14HML0.450.390.210.280.21S.R.0.180.340.190.340.580.690.840.710.8537 BAdditionaltablesTableA3Fama-MacBethregressionsamonglarge,small,andmicrocapstocksThetablereportsresultsofFama-MacBeth(1973)regressionsofindividualmonthlystockreturnsontopastperformance,measuredovertheprecedingyearskippingthemostrecentmonth(r2;12),andrms'mostrecentearningssurprises,measuredusingbothstandardizedunexpectedearnings(SUE)andthecumulativethreedayabnormalreturnsaroundthemostrecentearningsannouncement(CAR3).Regressionsincludecontrolsforothervariablesknowntopredictcrosssectionalvariationinexpectedreturns,thelogofrms'marketcapitalizations(ln(ME)),thelogofrms'book-to-marketratios(ln(B/M)),grossprotability(GP/A,whereGPisrevenuesminuscostofgoodssoldandAisassets),andstocks'priormonthreturns(r2;12).Independentvariablesaretrimmedattheoneand99%levels.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Fullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelA:Largecapstocks(aboveNYSEmedianmarketcapitalization)r2;120.510.320.830.590.200.05[2.13][1.33][3.02][2.12][0.50][0.12]SUE0.080.060.090.04[4.48][4.41][4.72][1.68]CAR33.463.185.121.25[7.12][7.10][7.77][2.14]ln(ME)-0.09-0.11-0.11-0.15-0.16-0.03-0.06[-2.29][-2.66][-2.73][-2.69][-2.77][-0.58][-1.11]ln(B/M)0.300.230.280.390.410.200.15[3.59][2.69][3.57][3.38][3.61][1.72][1.38]GP/A0.810.600.690.970.840.650.53[4.48][3.19][3.78][3.82][3.23][2.52][2.10]r0;1-3.02-3.17-3.70-4.62-5.52-1.41-1.89[-5.26][-4.89][-6.33][-6.32][-7.44][-1.62][-2.12]38 TableA3continuedFullsample1/75–12/931/94–12/12(1)(2)(3)(4)(5)(6)(7)PanelB:Smallcapstocks(NYSEdeciles3-5)r2;120.600.111.050.380.16-0.16[2.81][0.49][4.61][1.49][0.45][-0.44]SUE0.180.170.240.10[8.21][8.99][9.13][3.83]CAR35.175.077.152.99[10.5][10.8][9.62][5.52]ln(ME)-0.04-0.09-0.11-0.06-0.10-0.02-0.11[-0.62][-1.26][-1.39][-0.72][-1.02][-0.22][-0.95]ln(B/M)0.370.250.290.470.450.280.13[4.06][2.70][3.19][4.14][3.88][1.92][0.92]GP/A0.820.540.540.870.630.770.45[4.70][3.00][3.05][3.76][2.69][2.94][1.69]r0;1-3.15-4.08-4.30-4.82-6.43-1.49-2.17[-6.32][-7.49][-8.37][-7.70][-9.61][-1.95][-2.87]PanelC:Microcapstocks(NYSEdeciles1and2)r2;120.61-0.010.77-0.020.450.01[2.72][-0.03][3.49][-0.08][1.16][0.02]SUE0.450.440.550.34[20.5][21.0][17.0][13.3]CAR36.226.266.376.15[16.3][16.7][10.7][13.3]ln(ME)-0.18-0.19-0.18-0.30-0.27-0.07-0.09[-2.61][-2.47][-2.39][-3.55][-2.66][-0.62][-0.81]ln(B/M)0.460.280.290.440.260.480.32[6.18][3.36][3.79][4.66][2.47][4.16][2.88]GP/A0.880.880.850.840.830.910.88[6.19][5.81][5.70][4.50][4.10][4.28][3.97]r0;1-5.20-7.08-7.18-7.17-9.69-3.24-4.66[-10.8][-13.8][-14.3][-12.3][-14.8][-4.36][-6.46]39 TableA4SUEandCAR3strategies'underlyingportfoliosThistablereportstheaveragemonthlyexcessreturnsoftheportfoliosunderlyingtheearningsmomentumfactorsSUEandCAR3,andresultsoftime-seriesregressionsoftheexcessreturnstotheseportfoliosontothethreeFamaandFrenchfactors,MKT,SMB,andHML,andthepricemomentumfactor,UMD.Theportfoliosareconstructedusingeitherlargeorsmallcapitalizationstocks,denedasthosewithaboveandbelowmedianNYSEmarketcapitalization,andholdstocksrankedinthehighestorlowest30%bytheearningssurprisemeasure,alsousingNYSEbreaks.Returnsarevalue-weighted.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.PortfoliossortedSUEPortfoliossortedonCAR3LowHighHLLowHighHLPanelA:LargecapstrategiesMean(re/0.490.760.270.500.760.26[2.13][3.73][2.77][2.11][3.37][2.95]-0.110.130.24-0.080.130.21[-1.98][2.80][2.69][-1.49][2.54][2.39]MKT1.060.97-0.091.061.02-0.04[83.0][90.5][-4.36][89.8][88.0][-2.21]SMB-0.10-0.19-0.09-0.03-0.020.02[-5.27][-12.4][-3.20][-2.02][-1.12][0.56]HML0.030.03-0.00-0.04-0.07-0.04[1.81][1.99][-0.09][-2.08][-4.15][-1.19]UMD-0.080.100.18-0.110.030.14[-6.12][9.96][9.01][-9.46][2.96][7.44]PanelB:SmallcapstrategiesMean(re/0.611.520.910.521.320.80[2.08][5.54][9.69][1.64][4.37][12.7]-0.250.550.79-0.360.380.74[-4.51][9.05][10.3][-6.74][7.83][13.0]MKT1.041.050.011.121.10-0.02[82.3][76.3][0.69][91.5][98.0][-1.41]SMB0.930.78-0.151.010.93-0.08[51.5][39.6][-5.99][57.6][57.7][-4.35]HML0.290.24-0.040.090.100.01[15.0][11.7][-1.58][4.98][5.80][0.33]UMD-0.27-0.010.26-0.23-0.100.13[-21.9][-0.47][15.3][-19.9][-9.30][10.6]40 TableA5Conditionalpriceandearningsmomentumstrategyperformance,alternateconstructionThistablepresentsresultsoftime-seriesregressionsoftheform:ytDC000XtC"twheretheytarethemonthlyexcessreturnstoeitherUMD(specicationsoneandtwo),theearningsmomentumfactorSUE(specicationsthreeandfour),thepricemomentumfactorconstructedtobeneutralwithrespecttoearningsmomentumUMDjSUE(specicationsveandsix),andtheearningsmomentumfactorconstructedtobeneutralwithrespecttopricemomentumSUEjr2;12(specicationssevenandeight).Explanatoryfactorsaretakenfromthesamesetofstrategies.TheconditionalfactorsareconstructedsimilartoUMD,butsortstocksontheprimarysortingcharacteristic(r2;12orSUE)fromamongstocksmatchedontheothercharacteristic.Theinitialmatchselectstriplesofstocksmatchedontheconditioningvariable,whichyieldssimilarnamediversicationtothatobtainedfromaunivariatetertilesort.Explanatoryfactorsaretakenfromthesamesetofstrategies.ThesamplecoversJanuary1975throughDecember2012.dependentvariableyDUMDyDSUEyDUMDjSUEyDSUEjr2;12(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)0.640.290.040.590.150.010.25-0.15-0.030.430.200.17[3.03][4.09][0.57][7.14][2.14][0.12][1.77][-3.26][-0.58][8.42][4.75][5.08]UMDjSUE1.401.430.31[61.0][67.1][20.2]SUEjr2;120.561.031.18[9.30][17.6][27.3]UMD0.640.70-0.14[61.0][60.8][-16.1]SUE-0.290.390.59[-9.74][17.6][27.4]adj.-R2(%)89.190.840.568.789.191.040.562.141 TableA6Conditionalstrategies'underlyingportfoliosThistablereportstheaveragemonthlyexcessreturnsoftheportfoliosunderlyingtheconditionalmomentumfactorsUMDjSUEandSUEjr2;12,andresultsoftime-seriesregressionsoftheexcessreturnstotheseportfoliosontothethreeFamaandFrenchfactors,MKT,SMB,andHML,andthepricemomentumfactor,UMD.Theportfoliosareconstructedusingeitherlargeorsmallcapitalizationstocks,denedasthosewithaboveandbelowmedianNYSEmarketcapitalization,andholdstocksrankedhighestorlowestbytheprimarysortingcharacteristic(r2;12orSUE)fromamonggroupsofsevenstocksmostcloselymatchedontheothercharacteristic.Returnsarevalue-weighted.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Conditionalmomentum:ConditionalPEAD:SUEmatched,thensortedonr2;12r2;12matched,thensortedonSUELowHighHLLowHighHLPanelA:LargecapstrategiesMean(re/0.550.930.380.540.770.23[2.08][3.62][1.58][2.44][3.82][2.28]0.25-0.10-0.36-0.140.190.33[3.37][-1.23][-3.01][-2.01][2.99][3.15]MKT1.021.090.071.040.94-0.10[59.0][56.3][2.46][67.2][64.3][-4.10]SMB-0.110.090.20-0.14-0.19-0.05[-4.47][3.06][5.00][-6.29][-8.93][-1.42]HML-0.01-0.04-0.030.050.00-0.04[-0.56][-1.51][-0.72][2.00][0.21][-1.17]UMD-0.570.441.01-0.01-0.01-0.00[-34.0][23.7][38.3][-0.41][-0.68][-0.15]PanelB:SmallcapstrategiesMean(re/0.691.220.520.681.570.89[1.88][3.97][2.08][2.44][5.71][11.4]0.07-0.06-0.12-0.310.590.89[0.67][-0.83][-1.08][-5.43][8.86][11.1]MKT1.151.08-0.071.021.060.03[49.9][67.7][-2.75][79.4][69.2][1.80]SMB1.001.040.040.920.80-0.12[30.2][45.4][0.96][49.6][36.4][-4.55]HML0.120.10-0.020.290.26-0.02[3.48][4.32][-0.43][14.6][11.3][-0.86]UMD-0.780.311.09-0.14-0.110.03[-35.1][20.0][42.5][-10.9][-7.14][1.71]42 TableA7Conditionalstrategies'underlyingportfolios,alternativeconstructionThistablereportstheaveragemonthlyexcessreturnsoftheportfoliosunderlyingtheconditionalmomentumfactorsUMDjSUEandSUEjr2;12,andresultsoftime-seriesregressionsoftheexcessreturnstotheseportfoliosontothethreeFamaandFrenchfactors,MKT,SMB,andHML,andthepricemomentumfactor,UMD.Theportfoliosareconstructedusingeitherlargeorsmallcapitalizationstocks,denedasthosewithaboveandbelowmedianNYSEmarketcapitalization,andholdstocksrankedhighestorlowestbytheprimarysortingcharacteristic(r2;12orSUE)fromtriplesofstocksmostcloselymatchedontheothercharacteristic.Returnsarevalue-weighted.ThesamplecoversJanuary1975throughDecember2012,datesdeterminedbythedatarequiredtomaketheSUEandCAR3.Conditionalmomentum:ConditionalPEAD:SUEmatched,thensortedonr2;12r2;12matched,thensortedonSUELowHighHLLowHighHLPanelA:LargecapstrategiesMean(re/0.560.770.210.540.770.24[2.57][3.50][1.40][2.52][3.89][3.27]0.14-0.09-0.23-0.130.180.32[2.65][-2.13][-2.76][-3.33][4.08][4.31]MKT0.971.030.061.020.95-0.07[81.3][102.1][3.27][111.9][92.1][-4.24]SMB-0.17-0.040.13-0.12-0.18-0.06[-9.96][-2.71][4.74][-8.74][-12.0][-2.62]HML0.05-0.00-0.050.030.00-0.02[2.85][-0.02][-1.77][1.98][0.22][-0.94]UMD-0.310.280.590.00-0.01-0.01[-27.1][28.8][31.9][0.21][-0.61][-0.49]PanelB:SmallcapstrategiesMean(re/0.901.200.300.801.380.58[2.88][4.31][1.97][2.89][5.07][10.6]0.120.04-0.08-0.200.400.60[2.09][0.78][-1.21][-4.42][7.72][10.7]MKT1.101.05-0.051.031.050.01[83.8][95.6][-3.24][99.4][87.3][1.08]SMB0.890.920.040.900.81-0.09[46.9][58.4][1.60][59.9][46.9][-4.73]HML0.260.22-0.040.290.28-0.01[13.1][13.5][-1.53][18.2][15.2][-0.54]UMD-0.510.150.66-0.12-0.12-0.01[-39.9][14.6][43.8][-11.4][-10.5][-0.55]43 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