AW-lo(1988)-Stock-Market-Prices-Do-Not-Follow-Rand

TheSocietyforFinancialStudiesStockMarketPricesdonotFollowRandomWalks:EvidencefromaSimpleSpecificationTestAuthor(s):AndrewW.LoandA.CraigMacKinlaySource:TheReviewofFinancialStudies,Vol.1,No.1(Spring,1988),pp.41-66Publishedby:OxfordUniversityPress.Sponsor:TheSocietyforFinancialStudies.StableURL::11/12/200908:09YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableat://=oup.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,[e-mail]udiesandOxfordUniversityPressarecollaboratingwithJSTORtodigitize,preserveandextendaccesstoTheReviewofFinancialStudies.(1962-1985)andforallsubperiodsforavarietyofaggre-gatereturnsindexesandsize-sortedportfolios.Althoughtherejectionsareduelargelytothebehav-iorofsmallstocks,theycannotbeattributedcom-pletelytotheeffectsofinfrequenttradingortime-varyingvolatilities.Moreover,therejectionoftherandomwalkforweeklyreturnsdoesnotsupportamean-revertingmodelofassetprices.SinceKeynes's(1936)nowfamouspronouncementthatmostinvestors'decisionscanonlybetakenasaresultofanimalspiritsofaspontaneousurgetoactionratherthaninaction,andnotastheoutcomeofaweightedaverageofbenefitsmultipliedbyquantitativeproba-bilities,agreatdealofresearchhasbeendevotedtoexaminingtheefficiencyofstockmarketpriceforma-tion.InFama's(1970)survey,thevastmajorityofthosestudieswereunabletorejecttheefficientmarketsThispaperhasbenefitedconsiderablyfromthesuggestionsoftheeditorMichaelGibbonsandthereferee.WethankCliffBall,DonKeim,WhitneyK.Newey,PeterPhillips,JimPoterba,KrishnaRamaswamy,BillSchwert,andseminarparticipantsatMIT,theNBER-FMMEProgramMeeting(November1986),NorthwesternUniversity,OhioStateUniversity,PrincetonUniversity,StanfordUniversity,UCLA,UniversityofChicago,UniversityofMichigan,UniversityofPennsylvania,UniversityofWesternOntario,andYaleUniversityforhelpfulcomments.WearegratefultoStephanieHogue,ElizabethSchmidt,andMad-haviVinjamuriforpreparingthemanuscript.ResearchsupportfromtheGee-wax-TerkerResearchPrograminInvestments,theNationalScienceFoundation(GrantNo.SES-8520054),andtheUniversityofPennsylvaniaResearchFundisgratefullyacknowledged.Anyerrorsareofcourseourown.AddressreprintrequeststoAndrewLo,DepartmentofFinance,WhartonSchool,UniversityofPennsylvania,Philadelphia,PA19104.TheReviewofFinancialStudies1988,Volume1,number1,pp.41-66.?)1988TheReviewofFinancialStudies0021-9398/88/5904-013$1.5041TheReviewofFinancialStudies/Spring,1988hypothesisforcommonstocks.Althoughseveralseeminglyanomalousdeparturesfrommarketefficiencyhavebeenwelldocumented,'manyfinan-cialeconomistswouldagreewithJensen's(1978a)beliefthatthereisnootherpropositionineconomicswhichhasmoresolidempiricalevidencesupportingitthantheEfficientMarketsHypothesis.Althoughapreciseformulationofanempiricallyrefutableefficientmar-ketshypothesismustobviouslybemodel-specific,historicallythemajorityofsuchtestshavefocusedontheforecastabilityofcommonstockreturns.Withinthisparadigm,whichhasbeenbroadlycategorizedastherandomwalktheoryofstockprices,fewstudieshavebeenabletorejecttherandomwalkmodelstatistically.However,severalrecentpapershaveuncoveredempiricalevidencewhichsuggeststhatstockreturnscontainpredictablecomponents.Forexample,KeimandStambaugh(1986)findstatisticallysignificantpredictabilityinstockpricesbyusingforecastsbasedoncertainpredeterminedvariables.Inaddition,FamaandFrench(1987)showthatlongholding-periodreturnsaresignificantlynegativelyseriallycorrelated,implyingthat25to40percentofthevariationoflonger-horizonreturnsispredictablefrompastreturns.Inthisarticleweprovidefurtherevidencethatstockpricesdonotfollowrandomwalksbyusingasimplespecificationtestbasedonvarianceesti-mators.Ourempiricalresultsindicatethattherandomwalkmodelisgenerallynotconsistentwiththestochasticbehaviorofweeklyreturns,especiallyforthesmallercapitalizationstocks.However,incontrasttothenegativese