Session Topic: Stock Market Price Behavior Efficient Capital Markets

Home , Market (economics), Random walk hypothesis

SESSION TOPIC: STOCK MARKET PRICE BEHAVIOR

SESSION CHAIRMAN: BURTON G. MALKIEL

EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK*

EUGENE F. FAMA**

I. INTRODUCTION THE PRIMARYROLE of the capital market is allocation of ownership of the economy'scapital stock. In generalterms, the ideal is a marketin whichprices provideaccurate signals for resourceallocation: that is, a marketin which firmscan make production-investmentdecisions, and investorscan choose among the securitiesthat representownership of firms'activities under the assumptionthat securityprices at any time "fullyreflect" all available information.A marketin whichprices always "fullyreflect" available informationis called "efficient." This paper reviewsthe theoreticaland empiricalliterature on the efficient marketsmodel. After a discussionof the theory,empirical work concerned withthe adjustmentof securityprices to threerelevant information subsets is considered.First, weak formtests, in which the informationset is just historicalprices, are discussed.Then semi-strongform tests, in whichthe concernis whetherprices efficiently adjust to otherinformation that is obviously publiclyavailable (e.g., announcementsof annual earnings,stock splits, etc.) are considered.Finally, strong form tests concerned with whethergiven in- vestorsor groupshave monopolisticaccess to any informationrelevant for price formationare reviewed.'We shall concludethat, with but a few ex- ceptions,the efficient markets model stands up well. Though we proceed fromtheory to empiricalwork, to keep the proper historicalperspective we shouldnote to a large extentthe empiricalwork in thisarea precededthe development of thetheory. The theoryis presentedfirst here in orderto more easily judge whichof the empiricalresults are most relevantfrom the viewpoint of the theory.The empiricalwork itself, however, will thenbe reviewedin moreor less historicalsequence. Finally,the perceptivereader will surelyrecognize instances in thispaper whererelevant studies are not specificallydiscussed. In such cases my apol- ogies shouldbe taken forgranted. The area is so bountifulthat some such injusticesare unavoidable.But the primarygoal here will have been ac- complishedif a coherentpicture of the main lines of the work on efficient marketsis presented,along withan accuratepicture of the currentstate of the arts. * Researchon thisproject was supportedby a grantfrom the NationalScience Foundation. I am indebtedto ArthurLaffer, Robert Aliber, Ray Ball, MichaelJensen, James Lorie, Merton Miller,Charles Nelson, Richard Roll, WilliamTaylor, and Ross Wattsfor their helpful comments. ** Universityof Chicago-JointSession with the EconometricSociety. 1. The distinctionbetween weak and strongform tests was firstsuggested by HarryRoberts. 383 384 The Journalof Finance II. THE THEORY OF EFFICIENT MARKETS A. ExpectedReturn or "Fair Game" Models The definitionalstatement that in an efficientmarket prices "fully reflect" available informationis so generalthat it has no empiricallytestable implications.To make the model testable,the processof price formationmust be specifiedin more detail. In essence we must definesomewhat more exactly whatis meantby the term"fully reflect." One possibilitywould be to posit that equilibriumprices (or expectedreturns) on securitiesare generatedas in the "two parameter"Sharpe [40]- Lintner[24, 25] world.In general,however, the theoreticalmodels and es- pecially the empiricaltests of capital marketefficiency have not been this specific.Most of the availablework is based onlyon the assumptionthat the conditionsof marketequilibrium can (somehow) be stated in termsof expectedreturns. In generalterms, like the two parametermodel such theories wouldposit that conditional on somerelevant information set, the equilibrium expectedreturn on a securityis a functionof its "risk."And differenttheories woulddiffer primarily in how "risk"is defined. All membersof the class of such "expectedreturn theories" can, however, be describednotationally as follows:

E(gj,t+,I|@t) =[I + E(r-,t+1|0t) ]pjtl 1 whereE is the expectedvalue operator;pit is theprice of securityj at timet; pj,t+iis its priceat t + 1 (withreinvestment of any intermediatecash income fromthe security); ri,t+iis the one-periodpercentage return (pi,t+l - pjt)/ pjt; (Dtis a generalsymbol for whatever set of informationis assumedto be "fully reflected"in the price at t; and the tildes indicate that pj,t+i and r,t+i are randomvariables at t. The value of the equilibriumexpected return E(rj,t+llijt) projectedon the basis of theinformation iJt would be determinedfrom the particular expected returntheory at hand. The conditionalexpectation notation of (1) is meant to imply,however, that whatever expected return model is assumedto apply, the informationin 1t is fullyutilized in determiningequilibrium expected returns.And thisis the sensein which 1t is "fullyreflected" in the formation of the price pjt. But we shouldnote rightoff that, simple as it is, the assumptionthat the conditionsof marketequilibrium can be statedin termsof expectedreturns elevatesthe purelymathematical concept of expectedvalue to a status not necessarily implied by the general notion of market efficiency.The expected value is just one of many possible summarymeasures of a distributionof returns,and marketefficiency per se (i.e., thegeneral notion that prices "fully reflect"available information) does not imbueit withany specialimportance. Thus, the resultsof testsbased on thisassumption depend to some extenton its validityas well as on the efficiencyof the market.But some such assumption is the unavoidableprice one must pay to give the theoryof efficient marketsempirical content. The assumptionsthat the conditionsof marketequilibrium can be stated EfficientCapital Markets 385 in termsof expectedreturns and thatequilibrium expected returns are formed on thebasis of (and thus"fully reflect") the informationset (Dthave a major empiricalimplication-they rule out the possibilityof tradingsystems based onlyon informationin (Dt thathave expectedprofits or returnsin excess of equilibriumexpected profits or returns.Thus let Xj,t+l - Pj,t+l - E(pj,t+1I4Dt). (2) Then

E (:j',t+lJ4t) =?0 (3) which,by definition,says thatthe sequence {xjt} is a "fairgame" with respect to the informationsequence {@t}. Or, equivalently,let zjt+l =rj,t+l - E(rj t+lt), (4) then E(Zjt+i141t) y, (5) so thatthe sequence {zjt} is also a "fairgame" with respect to theinformation sequence {41}. In economic terms,xJ,t+i is the excess market value of security j at time t + 1: it is the differencebetween the observedprice and the expectedvalue of the price thatwas projectedat t on the basis of the information(Dt. And similarly,zj,t+l is the returnat t + 1 in excess of the equilibriumexpected returnprojected at t. Let

a(1(t) [al(QDt), a2(2Dt), . . ., a1((Dt)] be any tradingsystem based on 1?t whichtells the investor the amountsaj ((It) of fundsavailable at t thatare to be investedin each of the n available securities.The totalexcess market value at t + 1 thatwill be generatedby such a systemis n

Vt+ a((Dt) [rj,t+l-E(rj,t+llt)], j=1Ejj which,from the "fairgame" propertyof (5) has expectation, n E (Vt+lIDt) Z cj((

2. Though we shall sometimesrefer to the model summarizedby (1) as the "fair game" model, keep in mind that the "fair game" propertiesof the model are implicationsof the assumptionsthat (i) the conditionsof market equilibriumcan be stated in terms of expected returns,and (ii) the information(Pt is fully utilized by the market in formingequilibrium expected returnsand thus currentprices. The role of "fair game" models in the theory of efficientmarkets was first recognized and studied rigorouslyby Mandelbrot r27] and Samuelson [38]. Their work will be discussedin more detail later. 386 The Journalof Finance B. Tke SubmartingaleModel Supposewe assumein (1) thatfor all t and (Dt E("',t+1Ilt) > Pit, orequivalently, E(i,t+1iDt) > 0. (6) This is a statementthat the price sequence{pit} forsecurity j followsa sub- martingalewith respectto the informationsequence Ol?t},which is to say nothingmore than that the expected value of nextperiod's price, as projected on thebasis of theinformation (Dt, is equal to or greaterthan the current price. If (6) holds as an equality (so thatexpected returns and price changesare zero), thenthe price sequence follows a martingale. A submartingalein priceshas one importantempirical implication. Consider theset of "one securityand cash" mechanicaltrading rules by whichwe mean systemsthat concentrate on individualsecurities and thatdefine the conditions underwhich the investorwould hold a givensecurity, sell it short,or simply hold cash at any timet. Then the assumptionof (6) that expectedreturns conditionalon (Dt are non-negativedirectly implies that such tradingrules based onlyon the informationin Ct cannothave greaterexpected profits than a policyof alwaysbuylng-and-holding the securityduring the futureperiod in question. Tests of such rules will be an importantpart of the empirical evidenceon theefficient markets model.8

C. The Random Walk Model In the early treatmentsof the efficientmarkets model, the statementthat the currentprice of a security"fully reflects"available informationwas assumedto implythat successiveprice changes (or moreusually, successive one-periodreturns) are independent.In addition,it was usuallyassumed that successivechanges (or returns)are identicallydistributed. Together the two hypothesesconstitute the randomwalk model.Formally, the modelsays f(rj,t+?ItDt)= f(rj,t+?), (7) whichis the usual statementthat the conditionaland marginalprobability distributionsof an independentrandomn variable are identical.In addition, the densityfunction f mustbe the same forall t.4

3. Note thatthe expected profitability of "one securityand cash" tradingsystems vis-'a-vis buy- and-holdis not ruledout by the generalexpected return or "fairgame" efficient markets model. The latterrules out systemswith expectedprofits in excessof equilibriumexpected returns, but sincein principleit allowsequilibriunm expected returns to be negative,holding cash (whichalways hag zero actual and thusexpected return) may have higherexpected return than holdingsome security. And negativeequilibriumn expected returns for some securitiesare quite possible.For example, in the Sharpe[40]-Lintner [24, 25] model (whichis in turna naturalextension of the portfolio modelsof Markowitz[30] and Tobin [43]) theequilibrium expected return on a securitydepends on the extentto whichthe dispersionin the security'sreturn distribution ig relatedto dispersion in the returnson all othersecurities. A securitywhose returns on averagemove oppositeto the generalmarket is particularlyvaluable in reducingdispersion of portfolioreturns, and so its equilibriumexpected return may well be negative. 4. The terminologyis loose.Prices will only followa randomwalk if pricechanges are independent,identically distributed; and even then we shouldsay "randomwalk with drift"since expectedprice changescan be non-zero.If one-periodreturns are independent,identically dis. tributed,prices will not followa randomwalk sincethe distributionof pricechanges will depend EfficientCapital Markets 387 Expression(7) of coursesays muchmore than the general expected return modelsummarized by (1). For example,if we restrict(1) by assumingthat theexpected return on securityj is constantover time, then we have E(,j,t+1|f't)= E(rj,t+?). (8) This says thatthe mean of the distributionof rj,t+lis independentof the informationavailable at t, t, whereasthe randomwalk modelof (7) in addi- tionsays that the entiredistribution is independentof CF.5 We argue later that it is best to regardthe randomwalk model as an extensionof the generalexpected return or "fair game" efficientmarkets modelin the sense of makinga moredetailed statement about the economic environment.The "fair game" modeljust says that the conditionsof market equilibriumcan be statedin termsof expectedreturns, and thusit says little about the detailsof the stochasticprocess generating returns. A randomwalk arises withinthe contextof such a model when the environmentis (fortu- itously)such that the evolutionof investortastes and the processgenerating new informationcombine to produceequilibria in whichreturn distributions repeatthemselves through time. Thus it is not surprisingthat empiricaltests of the "randomwalk" model thatare in fact testsof "fair game" propertiesare morestrongly in support of themodel than tests of theadditional (and, fromthe viewpoint of expected returnmarket efficiency, superfluous) pure independenceassumption. (But it is perhapsequally surprisingthat, as we shall soon see, the evidenceagainst theindependence of returnsover time is as weak as it is.) D. Market ConditionsConsistent with Efficiency Before turningto the empiricalwork, however, a few words about the marketconditions that might help or hinderefficient adjustment of pricesto informationare in order.First, it is easy to determinesufficient conditions for capital marketefficiency. For example,consider a marketin which (i) there are no transactionscosts in tradingsecurities, (ii) all available informationis costlesslyavailable to all marketparticipants, and (iii) all agree on the implicationsof currentinformation for the currentprice and distributionsof futureprices of each security.In sucha market,the current price of a security obviously"fully reflects" all available information. But a frictionlessmarket in whichall informationis freelyavailable and investorsagree on its implicationsis, of course,not descriptive of marketsmet in practice.Fortunately, these conditions are sufficientfor market efficiency, but not necessary.For example,as long as transactorstake account of all

on the pricelevel. But thoughrigorous terminology is usuallydesirable, our loose use of terms shouldnot cause confusion;and our usage followsthat of the efficientmarkets literature. Note also thatin the randomwalk literature,the informationset (t in (7) is usuallyassumed to include only the past returnhistory, rj,t, rj t-1 . . . 5. The randomwalk modeldoes not say, however,that past informationis of no value in assessingdistributions of futurereturns. Indeed since returndistributions are assumedto be stationarythrough time, past returnsare the bestsource of such information.The randomwalk modeldoes say, however, that the sequence (or theorder) of thepast returnsis of no consequence in assessingdistributions of futurereturns. 388 The Journalof Finance available information,even large transactionscosts that inhibitthe flowof transactionsdo not in themselvesimply that when transactions do take place, priceswill not "fullyreflect" available information.Similarly (and speaking, as above, somewhatloosely), the marketmay be efficientif "sufficientnum- bers" of investorshave readyaccess to available information.And disagreementamong investors about the implicationsof giveninformation does not in itselfimply market inefficiency unless there are investorswho can consistently make betterevaluations of available informationthan are implicitin market prices. But thoughtransactions costs, information that is not freelyavailable to all investors,and disagreementamong investors about the implicationsof given informationare notnecessarily sources of marketinefficiency, they are potential sources.And all threeexist to someextent in real worldmarkets. Measur- ing theireffects on theprocess of priceformation is, of course,the majorgoal of empiricalwork in thisarea.

III. THE EVIDENCE All the empiricalresearch on the theoryof efficientmarkets has been concerned with whetherprices "fully reflect"particular subsets of available information.Historically, the empiricalwork evolved more or less as follows. The initialstudies were concerned with what we call weak formtests in which theinformation subset of interestis just past price (or return)histories. Most of theresults here come from the random walk literature.When extensive tests seemedto supportthe efficiencyhypothesis at thislevel, attention was turned to semi-strongform tests in whichthe concern is thespeed of priceadjustment to other obviouslypublicly available information(e.g., announcementsof stock splits,annual reports,new securityissues, etc.). Finally,strong form testsin whichthe concernis whetherany investoror groups (e.g., managementsof mutualfunds) have monopolisticaccess to any informationrelevant forthe formationof priceshave recentlyappeared. We reviewthe empirical researchin moreor less thishistorical sequence. First, however,we should note that what we have called the efficient marketsmodel in the discussionsof earliersections is the hypothesisthat securityprices at any pointin time "fullyreflect" all available information. Thoughwe shall argue thatthe modelstands up ratherwell to the data, it is obviouslyan extremenull hypothesis.And, like any otherextreme null hy- posthesis,we do not expectit to be literallytrue. The categorizationof the testsinto weak, semi-strong, and strongform will servethe usefulpurpose of allowingus to pinpointthe level of informationat whichthe hypothesis breaks down.And we shall contendthat thereis no importantevidence against the hypothesisin the weak and semi-strongform tests (i.e., prices seem to effi- cientlyadjust to obviouslypublicly available information),and only limited evidenceagainst the hypothesisin the strongform tests (i.e., monopolistic access to informationabout prices does notseem to be a prevalentphenomenon in the investmentcommunity). EfficientCapital Markets 389 A. Weak Form Tests of the EfficientMarkets Model 1. RandomWalks and Fair Games: A Little HistoricalBackground As notedearlier, all of the empiricalwork on efficientmarkets can be con- sideredwithin the contextof the general expectedreturn or "fair game" model,and muchof the evidencebears directlyon the special submartingale expectedreturn model of (6). Indeed, in the early literature,discussions of the efficientmarkets model were phrasedin termsof the even more special randomwalk model,though we shall arguethat most of theearly authors were in factconcerned with more general versions of the "fair game" model. Some of theconfusion in the earlyrandom walk writingsis understandable. Researchon securityprices did not beginwith the developmentof a theory of price formationwhich was thensubjected to empiricaltests. Rather,the impetusfor the developmentof a theorycame fromthe accumulationof evidence in the middle 1950's and early 1960's that the behaviorof common stockand otherspeculative prices could be well approximatedby a random walk. Faced withthe evidence,economists felt compelled to offersome ratio- nalization.What resultedwas a theoryof efficientmarkets stated in termsof randomwalks, but usuallyimplying some moregeneral "fair game" model. It was notuntil the work of Samuelson[38] and Mandelbrot[27] in 1965 and 1966 that the role of "fair game" expectedreturn models in the theory of efficientmarkets and the relationshipsbetween these models and thetheory of randomwalks were rigorouslystudied.6 And thesepapers came somewhat afterthe major empiricalwork on randomwalks. In the earlierwork, "theoretical"discussions, though usually intuitively appealing, were alwayslacking in rigorand ofteneither vague or ad hoc. In short,until the Mandelbrot- Samuelsonmodels appeared, there existed a large body of empiricalresults in searchof a rigoroustheory. Thus, thoughhis contributionswere ignored for sixty years, the firststate- mentand testof the randomwalk modelwas thatof Bachelier[3] in 1900. But his "fundamentalprinciple" for the behaviorof priceswas that specula- tionshould be a "fairgame"; in particular,the expectedprofits to the specu- lator should be zero. With the benefitof the moderntheory of stochastic processes,we knownow that the process implied by thisfundamental principle is a martingale. AfterBachelier, research on thebehavior of securityprices lagged until the

6. Basing their analyses on futurescontracts in commoditymarkets, Mandelbrot and Samuelson show that if the price of such a contractat time t is the expected value at t (given information t) of the spot price at the terminationof the contract,then the futuresprice will follow a martingalewith respectto the informationsequence {jt); that is, the expected price change from period to period will be zero, and the price changes will be a "fair game." If the equilibriumexpected returnis not assumed to be zero, our more general "fair game" model, summarizedby (1), is obtained. But though the Mandelbrot-Samuelsonapproach certainly illuminates the process of price formationin commoditymarkets, we have seen that "fair game" expected returnmodels can be derived in much simplerfashion. In particular,(1) is just a formalizationof the assumptionsthat the conditions of market equilibrium can be stated in terms of expected returns and that the information t is used in formingmarket prices at t. 390 The Journalof Finance comingof the computer.In 1953 Kendall [21] examinedthe behaviorof weeklychanges in nineteenindices of Britishindustrial share prices and in spot prices for cotton (New York) and wheat (Chicago). Afterextensive analysisof serial correlations,he suggests,in quite graphicterms: The serieslooks like a wanderingone, almost as ifonce a weekthe Demon of Chance drewa randomnumber from a symetricalpopulation of fixeddispersion and added it to thecurrent price to determinethe next week's price [21, p. 13]. Kendall's conclusionhad in fact been suggestedearlier by Working[47], thoughhis suggestionlacked the force provided by Kendall's empiricalresults. And theimplications of theconclusion for stock market research and financial analysiswere laterunderlined by Roberts [36]. But thesuggestion by Kendall,Working, and Robertsthat series of speculativeprices may be well describedby randomwalks was based on observation. None of theseauthors attempted to providemuch economic rationale for the hypothesis,and, indeed, Kendall feltthat economists would generally reject it. Osborne [33] suggestedmarket conditions,similar to those assumed by Bachelier,that would lead to a randomwalk. But in his model,independence of successiveprice changes derives from the assumptionthat the decisionsof investorsin an individualsecurity are independentfrom transactionto transaction-whichis littlein the way of an economicmodel. Whenevereconomists (prior to Mandelbrotand Samuelson) triedto provide economicjustification for the randomwalk, their argumentsusually implieda "fairgame." For example,Alexander [8, p. 200] states: If onewere to startout with the assumption that a stockor commodityspeculation is a "fairgame" with equal expectationof gainor loss or, moreaccurately, with an expectationof zerogain, one would be wellon theway to picturingthe behavior of speculativeprices as a randomwalk. There is an awarenesshere that the "fairgame" assumptionis not sufficient to lead to a randomwalk, but Alexandernever expands on the comment. Similarly,Cootner [8, p. 232] states: If any substantialgroup of buyersthought prices were too low,their buying would forceup theprices. The reversewould be truefor sellers. Except for appreciation due to earningsretention, the conditional expectation of tomorrow'sprice, given today's price,is today'sprice. In sucha world,the only price changes that would occur are those that result from newinformation. Since there is no reasonto expectthat information to be non-randomin appearance,the period-to-period price changes of a stockshould be random movements,statistically independent of one another. Thoughsomewhat imprecise, the last sentenceof thefirst paragraph seems to pointto a "fair game" modelrather than a randomwalk.' In this light,the secondparagraph can be viewedas an attemptto describeenvironmental con- ditionsthat would reduce a "fair game" to a randomwalk. But the specifica- tionimposed on theinformation generating process is insufficientfor this purpose; one would, for example,also have to say somethingabout investor

7. The appropriateconditioning statement would be "Given the sequenceof historicalprices." EfficientCapital Markets 391 tastes. Finally,lest I be accused of criticizingothers too severelyfor am- biguity,lack of rigorand incorrectconclusions, By contrast,the stock markettrader has a much more practical criterionfor judgingwhat constitutesimportant dependence in successiveprice changes.For his purposesthe randomwalk modelis valid as long as knowledgeof the past behavior of the seriesof pricechanges cannot be used to increaseexpected gains. More specifically,the independenceassumption is an adequate descriptionof realityas long as theactual degreeof dependencein the seriesof pricechanges is not sufficientto allow the past historyof the seriesto be used to predictthe futurein a way whichmakes expectedprofits greater than they would be under a naive buy-and hold model [10, p 35]. We know now, of course,that this last conditionhardly requires a random walk. It will in factbe metby the submartingalemodel of (6). But one shouldnot be too hard on the theoreticalefforts of the earlyem- piricalrandom walk literature.The argumentswere usually appealing; where theyfell short was in awarenessof developmentsin the theoryof stochastic processes.Moreover, we shall now see thatmost of the empiricalevidence in the randomwalk literaturecan easilybe interpretedas testsof moregeneral expectedreturn or "fair game" models.8 2. Tests of MarketEfficiency in theRandom Walk Literature As discussed earlier,"fair game" models imply the "impossibility"of varioussorts of tradingsystems. Some of therandom walk literaturehas been concernedwith testing the profitability of such systems.More of the literature has, however,been concernedwith tests of serial covariancesof returns.We shall now show that,like a randomwalk, the serial covariancesof a "fair game" are zero, so that thesetests are also relevantfor the expectedreturn models. If Xt is a "fair game," its unconditionalexpectation is zero and its serial covariancecan be writtenin generalform as:

E (it+r iit) xtE (it+rIxt) f(xt)dxt, xt wheref indicatesa densityfunction. But if Xt is a "fairgame,"

E (5Et+ lxt) = 0.

8. Our briefhistorical review is meant only to provide perspective,and it is, of course,somewhat incomplete.For example, we have ignored the importantcontributions to the early random walk literaturein studies of warrants and other options by Sprenkle, Kruizenga, Boness, and others. Much of this early work on options is summarizedin [8]. 9. More generally,if the sequence {xj is a fair game with respect to the informationsequence {(Dt}, (i.e., E(Xt+1?It) = 0 for aH Pt); then xt is a fair game with respect to any Vt that is a subset of (t (i.e., E(xt+? I t) = 0 for all 't). To show this, let (P = (Vt, V"t). Then, using Stieltjes integrals and the symbol F to denote cumulative distinctionfunctions, the conditional expectation

, % dF E(xt+ll,t)= f xt+dF(xt+i t1e, = f[f xt+dF(xt+1I4t) ] (O)- bt Xtt+ (Pt Xt.+1 392 The Journalof Finance From this it followsthat for all lags, the serial covariancesbetween lagged valuesof a "fairgame" variableare zero.Thus, observationsof a "fairgame" variableare linearlyindependent.10 But the "fair game" model does not necessarilyimply that the serial covariancesof one-periodreturns are zero. In the weak formtests of this modelthe "fair game" variableis

zj,t -rj,t- E(r-j,tIrj,t_j,rj,t-2, . . .). (Cf. fn.9) (9) But the covariancebetween, for example, rit and rj,t+iis E( rFj,t+j-E(r'j,t+j)] [r-jt-E(r'jt)]) - [rjt-E(rjt)] [E(rj,t+lIrjt)-E(rj,t?i)]f(rjt)drjt, rjt and (9) does not implythat E(rj,t+?irjt) E(ij,t+1): In the "fair game" efficientmarkets model, the deviationof the returnfor t + 1 fromits conditionalexpectation is a "fair game" variable,but the conditionalexpectation itselfcan dependon the returnobserved for t.1' In the randomwalk literature,this problemis not recognized,since it is assumed that the expected return(and indeed the entire distributionof returns)is stationarythrough time. In practice,this implies estimating serial covariancesby takingcross productsof deviationsof observedreturns from the overallsample mean return. It is somewhatfortuitous, then, that this pro- cedure,which represents a rathergross approximation from the viewpointof the generalexpected return efficient markets model, does not seem to greatly affectthe resultsof the covariancetests, at least forcommon stocks.'2

But the integralin bracketsis just E(xt?iI |t) which by the "fair game" assumptionis 0, so that E(xt?+l 't) = 0 for all Vt C t. 10. But thoughzero serial covariancesare consistentwith a "fair game," they do not imply such a process. A "fair game" also rules out many types of non linear dependence. Lhus using argu- mentssimilar to those above, it can be shown that if x is a "fair game," E(xtxt+l . . . xt+r) = 0 for all -r,which is not implied by E(Xtxt+T) = 0 for all T. For example, considera three-period case where x must be either? 1. Suppose the process is xt+2 = sign (xtxt+?), i.e., i xt Xt+l Xt+2 ? + e +

- ?

If probabilitiesare uniformlydistributed across events,

E(xt?21xt+l) = E(xt+2Ixt) .= E(xt+llxt) = E(xt+2) = E(xt+?) = E(xt) = 0, so that all pairwise serial covariances are zero. But 'the process is not a "fair game," since E(Xt?2lXt+?, xt) & 0, and knowledgeof (xt+i, Xt) can be used as the basis of a simple "system" with positive expected profit. 11. For example,suppose the level of one-periodreturns follows a martingaleso that

E(fijt+1?rjt, rj,t_1 ... ) = rjt. Then covariances between successive returns will be nonzero (though in this special case first differencesof returnswill be uncorrelated). 12. The reason is probably that for stocks, changes in equilibrium expected returns for the EfficientCapital Markets 393 TABLE 1 (from [10]) First-orderSerial CorrelationCoefficients for One-, Four-, Nine-, and Sixteen-Day Changes in Loge Price DifferencingInterval (Days) Stock One Four Nine Sixteen Allied Chemical .017 .029 -.091 -.118 Alcoa .118* .095 -.112 -.044 AmericanCan -.087* -.124* -.060 .031 A. T. & T. -.039 -.010 -.009 -.003 AmericanTobacco .111* -.175* .033 .007 Anaconda .067* -.068 -.125 .202 BethlehemSteel .013 -.122 -.148 .112 Chrysler .012 .060 -.026 .040 Du Pont .013 .069 -.043 -.055 Eastman Kodak .025 -o.006 -.053 -.023 GeneralElectric .011 .020 -.004 .000 General Foods .061* -.005 -.140 -.098 General Motors -.004 -.128* .009 -.028 Goodyear -.123* .001 -.037 .033 InternationalHarvester -.017 -.068 -.244* .116 InternationalNickel .096* .038 .124 .041 InternationalPaper .046 .060 -.004 -.010 JohnsManville .006 -.068 -.002 .002 Owens Illinois -.021 -.006 .003 -.022 Procter& Gamble .099* -.006 .098 .076 Sears .097* -.070 -.113 .041 StandardOil (Calif.) .025 -.143* -.046 .040 StandardOil (N.J.) .008 -.109 -.082 -.121 Swift & Co. -.004 -.072 .118 -.197 Texaco .094* -.o53 -.047 -.178 Union Carbide .107* .049 -.101 .124 United Aircraft .014 -.190* -.192* -.040 U.S. Steel .040 -.006 -.056 .236* Westinghouse -.02 7 -.097 -.137 .067 Woolworth .028 -.033 -.112 .040 * Coefficientis twice its computedstandard error. For example,Table 1 (taken from[10]) showsthe serial correlationsbe- tweensuccessive changes in the naturallog of price for each of the thirty stocksof theDow JonesIndustrial Average, for time periods that vary slightly fromstock to stock,but usuallyrun from about theend of 1957 to September 26, 1962. The serialcorrelations of successivechanges in loge priceare shown fordifferencing intervals of one, four,nine, and sixteendays.13 common differencingintervals of a day, a week, or a month,are trivial relativeto other sources of variation in returns.Later, when we consider Roll's work [37], we shall see that this is not true for one week returnson U.S. GovernmentTreasury Bills. 13. The use of changes in loge price as the measure of returnis common in the random walk literature.It can be justifiedin several ways. But for currentpurposes, it is sufficientto note that for price changesless than fifteenper cent,the change in loge price is approximatelythe percentage price change or one-periodreturn. And for differencingintervals shorter than one month,returns in excess of fifteenper cent are unusual. Thus [10] reportsthat for the data of Table 1, tests carried out on percentage or one-period returnsyielded results essentiallyidentical to the tests based on changes in loge price. 394 The Journalof Finance The resultsin Table 1 are typicalof thosereported by othersfor tests based on serial covariances.(Cf. Kendall [21], Moore [31], Alexander[1], and the resultsof Grangerand Morgenstern[17] and Godfrey,Granger and Morgenstern[16] obtainedby meansof spectralanalysis.) Specifically,there is no evidenceof substantiallinear dependence between lagged price changes or returns.In absoluteterms the measuredserial correlations are alwaysclose to zero. Lookinghard, though, one can probablyfind evidence of statistically"significant"linear dependencein Table 1 (and again thisis trueof resultsre- portedby others). For the daily returnseleven of the serial correlationsare morethan twice their computed standard errors, and twenty-twoout of thirty are positive.On theother hand, twenty-one and twenty-fourof the coefficients forthe four and nineday differencesare negative.But withsamples of thesize underlyingTable 1 (N- 1200-1700observations per stockon a daily basis) statistically"significant" deviations from zero covarianceare not necessarily a basis forrejecting the efficientmarkets model. For the resultsin Table 1, the standarderrors of the serial correlationswere approximatedas (1/ (N-i) )'/2,which for the daily data impliesthat a correlationas small as .06 is morethan twice its standarderror. But a coefficientthis size impliesthat a linearrelationship with the laggedprice change can be used to explainabout .36% of the variationin the currentprice change,which is probablyinsig- nificantfrom an economicviewpoint. In particular,it is unlikelythat the small absolutelevels of serial correlationthat are always observedcan be used as the basis of substantiallyprofitable trading systems.'4 It is, of course,difficult to judge what degreeof serial correlationwould implythe existenceof tradingrules with substantialexpected profits. (And indeedwe shall soon have to be a littlemore precise about whatis impliedby "substantial"profits.) Moreover, zero serialcovariances are consistentwith a "fairgame" model,but as notedearlier (fn. 10), thereare typesof nonlinear dependencethat imply the existenceof profitabletrading systems, and yet do not implynonzero serial covariances.Thus, formany reasons it is desirable to directlytest the profitability of varioustrading rules. The firstmajor evidence on tradingrules was Alexander's[1, 2]. He testsa varietyof systems,but the most thoroughlyexamined can be decribedas follows:If the price of a securitymoves up at least y%7,buy and hold the securityuntil its price moves downat least y%' froma subsequenthigh, at whichtime simultaneously sell and go short.The shortposition is maintained untilthe price rises at least y%oabove a subsequentlow, at whichtime one coversthe short position and buys.Moves less thany% in eitherdirection are 14. Given the evidenceof Kendall [21], Mandelbrot[28], Fama [10] and othersthat large pricechanges occur much more frequently than would be expectedif the generatingprocess were Gaussian,the expression(1/(N-1))'/2 understatesthe samplingdispersion of the serialcorrelation coefficient,and thusleads to an overstatementof significancelevels. In addition,the fact that sampleserial correlations are predominantlyof one sign or the otheris not in itselfevidence of lineardependence. If, as thework of King [23] and Blume [7] indicates,there is a marketfactor whose behavioraffects the returnson all securities,the samplebehavior of this marketfactor maylead to a predominanceof signsof one typein theserial correlations for individual securities, even thoughthe populationserial correlationsfor both the marketfactor and the returnson individualsecurities are zero.For a moreextensive analysis of theseissues see [10]. EfficientCapital Markets 395 ignored.Such a systemis calleda y% filter.It is obviouslya "one securityand cash" tradingrule, so that the resultsit producesare relevantfor the sub- martingaleexpected return model of (6). Afterextensive tests using daily data on price indicesfrom 1897 to 1959 and filtersfrom one to fiftyper cent, and aftercorrecting some incorrect presumptionsin theinitial results of [1] (see fn.25), in his finalpaper on the subject,Alexander concludes: In fact,at thispoint I shouldadvise any readerwho is interestedonly in practical results,and whois nota floortrader and so mustpay commissions,to turn to other sourceson howto beatbuy and hold. The restof this article is devotedprincipally to a theoreticalconsideration of whetherthe observedresults are consistentwith a randomwalk hypothesis [8], p. 351). Later in the paper Alexanderconcludes that thereis some evidencein his resultsagainst the independenceassumption of the randomwalk model.But marketefficiency does not requirea randomwalk, and fromthe viewpointof thesubmartingale model of (6), theconclusion that the filters cannot beat buy- and-holdis supportfor the efficientmarkets hypothesis. Further support is providedby Fama and Blume [13] who comparethe profitability of various filtersto buy-and-holdfor the individualstocks of the Dow-JonesIndustrial Average.(The data are thoseunderlying Table 1.) But again, lookinghard one can findevidence in the filtertests of both Alexanderand Fama-Blumethat is inconsistentwith the submartingaleef- ficientmarkets model, if thatmodel is interpretedin a strictsense. In particular, the resultsfor very small filters (1 per centin Alexander'stests and .5, 1.0, and 1.5 per centin the testsof Fama-Blume) indicatethat it is possible to devisetrading schemes based on veryshort-term (preferably intra-day but at most daily) price swingsthat will on average outperformbuy-and-hold. The averageprofits on individualtransactions from such schemesare minis- cule, but theygenerate transactions so frequentlythat over longerperiods and ignoringcommissions they outperformbuy-and-hold by a substantial margin.These resultsare evidenceof persistenceor positivedependence in very short-termprice movements.And, interestingly,this is consistentwith the evidencefor slightpositive linear dependencein successivedaily price changesproduced by theserial correlations.15

15. Though strictlyspeaking, such tests of pure independence are not directly relevant for expected returnmodels, it is interestingthat the conclusionthat very short-termswings in prices persist slightlylonger than would be expected under the martingalehypothesis is also supported by the resultsof non-parametricruns tests applied to the daily data of Table 1. (See [10], Tables 12-15.) For the daily price changes,the actual number of runs of price changes of the same sign is less than the expectednumber for 26 out of 30 stocks.Moreover, of the eightstocks for which the actual numberof runs is more than two standard errorsless than the expected number,five of the same stocks have positive daily, first order serial correlationsin Table 1 that are more than twice theirstandard errors.But in both cases the statistical"significance" of the resultsis largely a reflectionof the large sample sizes. Just as the serial correlationsare small in absolute terms (the average is .026), the differencesbetween the expected and actual number of runs on average are only three per cent of the total expected number. On the other hand, it is also interestingthat the runs tests do not support the suggestionof slight negative dependencein four and nine day changes that appeared in the serial correlations. In the runs tests such negative dependencewould appear as a tendencyfor the actual number of runs to exceed the expectednumber. In fact, for the four and nine day price changes, for 17 and 396 The Journalof Finance But whenone takesaccount of even the minimumtrading costs thatwould be generatedby small filters,their advantage over buy-and-holddisappears. For example,even a floortrader (i.e., a personwho ownsa seat) on the New York Stock Exchangemust pay clearinghousefees on his tradesthat amount to about .1 per cent per turnaroundtransaction (i.e., sales plus purchase). Fama-Blumeshow that because small filtersproduce such frequenttrades, theseminimum trading costs are sufficientto wipe out theiradvantage over buy-and-hold. Thus thefilter tests, like theserial correlations, produce empirically notice- able departuresfrom the strictimplications of the efficientmarkets model. But, in spiteof any statisticalsignificance they might have, froman economic viewpointthe departuresare so small that it seems hardlyjustified to use themto declare the marketinefficient.

3. OtherTests of Independencein the Random Walk Literature It is probablybest to regardthe randomwalk model as a special case of themore general expected return model in thesense of makinga moredetailed specificationof the economicenvironment. That is, thebasic modelof market equilibriumis the "fair game" expectedreturn model, with a randomwalk arisingwhen additionalenvironmental conditions are such that distributions of one-periodreturns repeat themselvesthrough time. From this viewpoint violationsof thepure independence assumption of therandom walk modelare to be expected.But whenjudged relativeto the benchmarkprovided by the randomwalk model,these violations can provideinsights into the natureof the marketenvironment. For example,one departurefrom the pure independenceassumption of the randomwalk modelhas been notedby Osborne[34], Fama ([10], Table 17 and Figure8), and others.In particular,large daily price changes tend to be followedby large daily changes.The signsof the successorchanges are ap- parentlyrandom, however, which indicates that the phenomenonrepresents a denialof therandom walk modelbut notof themarket efficiency hypothesis. Nevertheless,it is interestingto speculatewhy the phenomenonmight arise. It may be that when importantnew informationcomes into the marketit cannot always be immediatelyevaluated precisely.Thus, sometimesthe initialprice will overadjustto the information,and othertimes it will under- adjust.But sincethe evidence indicates that the price changes on days follow- ingthe initial large change are randomin sign,the initial large change at least representsan unbiasedadjustment to theultimate price effects of theinformation,and tlhisis sufficientfor the expectedreturn efficient markets model. Niederhofferand Osborne [32] documenttwo departuresfrom complete randomnessin commonstock price changesfrom transaction to transaction. First,their data indicatethat reversals(pairs of consecutiveprice changes of oppositesign) are fromtwo to threetimes as likelyas continuations(pairs of consecutiveprice changes of the same sign). Second, a continuationis

18 of the 30 stocks in Table 1 the actual number of runs is less than the expected number.Indeed, runs tests in general show no consistentevidence of dependencefor alnydifferencing interval longer than a day, which seems especiallypertinent in light of the commentsin footnote14. EfficientCapital Markets 397 slightlymore frequent after a precedingcontinuation than aftera reversal. Thatis, let (+I++) indicatethe occurrence of a positiveprice change, given twopreceding positive changes. Then the events(+?++) and (-I---) areslightly more frequent than (+1+-) or ( _|+).1B Niederhofferand Osborneoffer explanations for these phenomena based on themarket structure of the New York Stock Exchange (N.Y.S.E.). In particular,there are threemajor typesof ordersthat an investormight place in a givenstock: (a) buy limit (buy at a specifiedprice or lower), (b) sell limit(sell at a specifiedprice or higher),and (c) buy or sell at market(at thelowest selling or highestbuying price of anotherinvestor). A book of unexecutedlimit orders in a givenstock is keptby thespecialist in thatstock onthe floor of the exchange.Unexecuted sell limitorders are, of course,at higherprices than unexecutedbuy limit orders. On both exchanges,the smallestnon-zero price change allowed is Y8 point. Supposenow thatthere is morethan one unexecutedsell limitorder at the lowestprice of any such order.A transactionat this price (initiatedby an orderto buy at market'7)can onlybe followedeither by a transactionat the sameprice (if thenext market order is to buy) or by a transactionat a lower price(if the next marketorder is to sell). Consecutiveprice increasescan usuallyonly occurwhen consecutive market orders to buy exhaustthe sell limitorders at a givenprice.'8 In short,the excessivetendency toward re- versalfor consecutive non-zero price changescould resultfrom bunching of unexecutedbuy and sell limitorders. The tendencyfor the events (+ ++) and (- -) to occurslightly more frequentlythan (+?+-) and (-I-+) requiresa moreinvolved explanation whichwe shall not attemptto reproducein full here.In brief,Niederhoffer and Osbornecontend that the higherfrequency of (+|++) relativeto (+I+-) arises froma tendencyfor limit orders "to be concentratedat integers(26, 43), halves (26X2, 43'2), quarters and odd eighthsin descending orderof preference."'9The frequencyof the event (+I++), whichusually requiresthat sell limitorders be exhaustedat at least twoconsecutively higher prices(the last of whichis relativelymore frequentlyat an odd eighth), moreheavily reflects the absenceof sell limitorders at odd eighthsthan the event(+?+-), whichusually implies that sell limitorders at onlyone price havebeen exhaustedand so moreor less reflectsthe average bunchingof limitorders at all eighths. But thoughNiederhoffer and Osbornepresent convincing evidence of sta-

16.On a transactionto transactionbasis, positive and negativeprice changes are about equally likely.Thus, under the assumptionthat price changes are random,any pair of non-zerochanges shouldbe as likelyas any other,and likewisefor triplets of consecutivenon-zero changes. 17.A buy limitorder for a priceequal to or greaterthan the lowestavailable sell limitprice is effectivelyan order to buy at market,and is treatedas suchby thebroker. 18.The exceptionis whenthere is a gap of morethan IX betweenthe highestunexecuted buy limitand the lowestunexecuted sell limitorder, so that marketorders (and new limitorders) canbe crossedat intermediateprices. 19.Their empiricaldocumentation for this claim is a few samplesof specialists'books for selecteddays, plus the observation[34] thatactual trading prices, at least forvolatile high priced stocks,seem to be concentratedat integers,halves, quarters and odd eighthsin descendingorder. 398 The Journalof Finance tisticallysignificant departures from independencein price changes from transactionto transaction,and thoughtheir analysis of theirfindings presents interestinginsights into the process of marketmaking on the majorexchanges, the types of dependenceuncovered do not implymarket inefficiency. The best documentedsource of dependence,the tendencytoward excessive reversals in pairs of non-zeroprice changes,seems to be a directresult of the abilityof investorsto place limitorders as well as ordersat market,and this negativedependence in itselfdoes notimply the existenceof profitabletrading rules. Similarly,the apparenttendency for observedtransactions (and, by implication,limit orders) to be concentratedat integers,halves, even eighths and odd eighthsin descendingorder is an interestingfact about investor behavior,but in itselfis not a basis on whichto concludethat the marketis inefficient.20 The Niederhoffer-Osborneanalysis of marketmaking does, however,point clearlyto the existenceof marketinefficiency, but withrespect to strongform testsof the efficientmarkets model. In particular,the list of unexecutedbuy and sell limitorders in the specialist'sbook is importantinformation about the likelyfuture behavior of prices,and thisinformation is only available to the specialist.When the specialistis asked for a quote, he gives the prices and can give the quantitiesof the highestbuy limit and lowest sell limit orderson his book,but he is preventedby law fromdivulging the book's full contents.The interestedreader can easilyimagine situations where the structure of limitorders in the book could be used as the basis of a profitable tradingrule.2' But therecord seems to speak foritself: It shouldnot be assumedthat these transactions undertaken by thespecialist, and in whichhe is involvedas buyeror sellerin 24 per centof all marketvolume, are necessarilya burden to him.Typically, the specialist sells above his last purchase on 83 per centof all his sales,and buysbelow his last sale on 81 per centof all his purchases( [3 2 ], p. 908). Thus it seemsthat the specialisthas monopolypower over an importantblock of information,and, not unexpectedly,uses his monopolyto turn a profit. And this,of course,is evidenceof marketinefficiency in the strong form sense. The importanteconomic question, of course,is whetherthe marketmaking

20. Niederhofferand Osborneoffer little to refutethis conclusion. For example([32], p. 914): Althoughthe specificproperties reported in thisstudy have a significancefrom a statisticalpoint of view,the readermay well ask whetheror not theyare helpfulin a practicalsense. Certain tradingrules emerge as a resultof our analysis.One is thatlimit and stop ordersshould be placed at odd eights,preferably at Y8 forsell ordersand at /8 forbuy orders.Another is to buy whena stockadvances through a barrierand to sell whenit sinksthrough a barrier. The first"trading rule" tells the investorto resisthis innateinclination to place ordersat integers, but ratherto placesell ordersI/8 below an integerand buy ordersI/8 above. Successfulexecution of the ordersis thenmore likely, since the congestionof ordersthat occurat integersis avoided. But the cost of thissuccess is apparent.The second"trading rule" seemsno morepromising, if indeedit can evenbe translatedinto a concreteprescription for action. 21. See, forexample, ([32], p. 908). But it is unlikelythat anyone but the specialistcould earn substantialprofits from knowledge of the structureof unexecutedlimit orders on the book. The specialistmakes tradingprofits by engagingin many transactions,each of whichhas a small averageprofit; but forany othertrader, including those with seats on the exchange,these profits wouldbe eatenup by commissionsto the specialist. EfficientCapital Markets 399 functionof the specialistcould be fulfilledmore economicallyby some non- monopolisticmechanism.22 4. DistributionalEvidence At this date the weightof the empiricalevidence is such that economists would generallyagree thatwhatever dependence exists in series of historical returnscannot be used to make profitablepredictions of the future.Indeed, forreturns that cover periods of a day or longer,there is littlein the evidence thatwould cause rejectionof the strongerrandom walk model,at least as a goodfirst approximation. Rather,the last burningissue of the randomwalk literaturehas centered on the natureof the distributionof price changes (which,we should note immediately,is an importantissue for the efficientmarkets hypothesis since thenature of thedistribution affects both the types of statisticaltools relevant fortesting the hypothesisand the interpretationof any resultsobtained). A model implyingnormally distributed price changes was firstproposed by Bachelier [3], who assumedthat price changesfrom transaction to transaction are independent,identically distributed random variables with finite variances.If transactionsare fairlyuniformly spread across time,and if the numberof transactionsper day,week, or monthis verylarge, then the Central LimitTheorem leads us to expectthat theseprice changeswill have normal or Gaussian distributions. Osborne [33], Moore [31], and Kendall [21] all thoughttheir empirical evidencesupported the normalityhypothesis, but all observedhigh tails (i.e., higherproportions of large observations)in theirdata distributionsvis-a-vis what would be expectedif the distributionswere normal.Drawing on these findingsand someempirical work of his own,Mandelbrot [28] thensuggested that these departuresfrom normality could be explainedby a moregeneral formof the Bacheliermodel. In particular,if one does not assume that distributionsof price changesfrom transaction to transactionnecessarily have finitevariances, then the limitingdistributions for price changesover longer differencingintervals could be any memberof the stable class, whichincludes the normalas a special case. Non-normalstable distributionshave higher tails thanthe normal, and so can accountfor this empirically observed feature of distributionsof price changes.After extensive testing (involving the data fromthe stocksin Table 1), Fama [10] concludesthat non-normalstable distributionsare a betterdescription of distributionsof daily returnson common stocks than the normal.This conclusionis also supportedby the empiricalwork of Blume [7] on commonstocks, and it has been extendedto U.S. GovernmentTreasury Bills by Roll [37]. Economistshave, however,been reluctantto accept theseresults,2" primar-

22. With moderncomputers, it is hard to believe that a more competitiveand economical systemwould not be feasible.It does not seem technologicallyimpossible to replacethe entire floorof theN.Y.S.E. witha computer,fed by manyremote consoles, that kept all the booksnow keptby the specialists,that could easily make theentire book on any stockavailable to anybody (so that interestedindividuals could then competeto "make a market"in a stock) and that carriedout transactionsautomatically. 23. Some have suggestedthat the long-tailedempirical distributions might result from processes 400 The Journalof Finance ily because of the wealthof statisticaltechniques available for dealingwith normalvariables and the relativepaucity of such techniquesfor non-normal stable variables.But perhapsthe biggestcontribution of Mandelbrot'swork has been to stimulateresearch on stable distributionsand estimationpro- ceduresto be appliedto stablevariables. (See, forexample, Wise [46], Fama and Roll [15], and Blattbergand Sargent[6], amongothers.) The advance of statisticalsophistication (and the importanceof examiningdistributional assumptionsin testingthe efficientmarkets model) is well illustratedin Roll [37], as compared,for example, with the early empirical work of Mandelbrot [28] and Fama [10]. 5. "Fair Game" Models in the TreasuryBill Market Roll's work is novel in otherrespects as well. Comingafter the efficient marketsmodels of Mandelbrot[27] and Samuelson[38], it is the firstweak formempirical work that is consciouslyin the "fair game" ratherthan the randomwalk tradition. More important,as we saw earlier,the "fair game" properties of thegeneral expectedreturn models apply to zjt= rjt- E(fjtjDt_j). (10) For data on commonstocks, tests of "fair game" (and randomwalk) pro- pertiesseem to go well whenthe conditionalexpected return is estimatedas theaverage return for the sample of data at hand.Apparently the variation in commonstock returnsabout theirexpected values is so large relativeto any changesin the expectedvalues that the lattercan safelybe ignored.But, as Roll demonstrates,this result does not hold forTreasury Bills. Thus, to test the "fair game" model on TreasuryBills requiresexplicit economic theory forthe evolution of expectedreturns through time. Roll uses threeexisting theories of theterm structure (the pureexpectations hypothesisof Lutz [26] and two marketsegmentation hypotheses, one of whichis the familiar"liquidity preference" hypothesis of Hicks-[18] and Kessel [22 ]) forthis purpose.24 In his modelsrnt is the rateobserved from the termstructure at periodt forone week loans to commenceat t + j - 1, and can be thoughtof as a "futures"rate. Thus rj+i,t-i is likewisethe rate on thatare mixturesof normaldistributions with different variances. Press [35], forexample, suggests a Poissonmixture of normalsin whichthe resultingdistributions of pricechanges have long tails but finitevariances. On the otherhand, Mandelbrot and Taylor[29] showthat other mixtures of normalscan stilllead to non-normalstable distributionsof pricechanges for finitedifferencing intervals. If, as Press'model would imply, distributions of pricechanges are long-tailedbut have finite variances,then distributions of pricechanges over longerand longerdifferencing intervals should be progressivelycloser to the normal.No such convergenceto normalitywas observedin [101 (thoughadmittedly the techniquesused weresomewhat rough). Rather,except for originand scale, the distributionsfor longerdifferencing intervals seem to have the same "high-tailed" characteristicsas distributins for shorter differencing intervals, which is as wouldbe expectedif the distributionsare non-normalstable. 24. As notedearly in our discussions,all availabletests of marketefficiency are implicitlyalso testsof expectedreturn models of marketequilibrium. But Roll formulatesexplicitly the economic modelsunderlying his estimatesof expectedreturns, and emphasizesthat he is simultaneously testingeconomic models of the termstructure as well as marketefficiency. EfficientCapital Markets 401 one week loans to commenceat t + j -1, but observedin thiscase at t - 1. Similarly,Lit is theso-called "liquidity premium" in rjt; thatis rjt E((ro,t+j_iIIt) + Ljt. In words,the one-week"futures" rate for period t + j - 1 observedfrom the termstructure at t is theexpectation at t of the "spot" rate fort + j -1 plus a "liquiditypremium" (which could, however, be positiveor negative). In all threetheories of the termstructure considered by Roll, the conditionalexpectation required in (10) is of the form - E(r"j,tPt_1) rj+?,tl + E(LjtJI~t-L)- Lj+L,t-.. The threetheories differ only in the values assignedto the "liquiditypremiums."For example,in the"liquidity preference" hypothesis, investors must always be paid a positivepremium for bearinginterest rate uncertainty,so that the Lit are alwayspositive. By contrast,in the "pure expectations"hypothesis,all liquiditypremiums are assumedto be zero,so that

i( tJOt-:tL) - rj+L,t -L. Afterextensive testing, Roll concludes(i) thatthe twomarket segmentation hypothesesfit the data betterthan the pure expectationshypothesis, with perhapsa slightadvantage for the "liquiditypreference" hypothesis, and (ii) thatas faras his testsare concerned,the market for Treasury Bills is effcient. Indeed, it is interestingthat when the best fittingterm structure model is used to estimatethe conditional expected "futures" rate in (10), the resulting variablezjt seems to be seriallyindependent! It is also interestingthat if he simplyassumed that his data distributionswere normal,Roll's resultswould notbe so stronglyin supportof theefficient markets model. In thiscase taking accountof the observedhigh tails of the data distributionssubstantially af- fectedthe interpretationof the results.25 6. Tests of a Multiple SecurityExpected ReturnModel Though the weak formtests supportthe "fair game" efficientmarkets model,all of the evidenceexamined so far consistsof what we mightcall "single securitytests." That is, the price or returnhistories of individual securitiesare examinedfor evidence of dependencethat might be used as the basis of a tradingsystem for that security.We have not discussedtests of whethersecurities are "appropriatelypriced" vis-a-vis one another. But to judge whetherdifferences between average returns are "appropriate" an economictheory of equilibriumexpected returns is required.At the mo- ment,the only fully developed theory is thatof Sharpe [40] and Lintner[24,

25. The importanceof distributionalassumptions is also illustratedin Alexander'swork on trading rules. In his initial tests of filtersystems [1], Alexander assumed that purchases could always be executed exactly (rather than at least) y% above lows and sales exactly y% below highs. Mandelbrot [281 pointed out, however, that though this assumption would do little harm with normally distributedprice changes (since price series are then essentiallycontinuous), with non- normal stable distributionsit would introducesubstantial positive bias into the filterprofits (since with such distributionsprice series will show many discontinuities). In his later tests [2], Alexander does indeed find that taking account of the discontinuities(i.e., the presence of large price changes) in his data substantiallylowers the profitabilityof the filters. 402 The Journalof Finance 25] referredto earlier.In this model (which is a directoutgrowth of the mean-standarddeviation portfolio models of investorequilibrium of Mar- kowitz[30] and Tobin [43]), theexpected return on securityj fromtime t to t+ 1 is - E(f,t+1j1t) = rf,t+l + [E(Fm,t+lfDt) rf,t+l co]C(j,to,y rm,t+4lDt) (11) whererf,t+1 is the returnfrom t to t + 1 on an asset thatis risklessin money terms; rm,t+1is the returnon the "marketportfolio" m (a portfolioof all investmentassets witheach weightedin proportionto the total marketvalue of all its outstandingunits); 02(rm,t+110t) is thevariance of the returnon m; cov (rij,t+i, rm,t+:Lit)is the covariance between the returnson j and m; and the appearanceof lIt indicatesthat the various expectedreturns, variance and covariance,could in principledepend on 'Dt. ThoughSharpe and Lintner derive(11) as a one-periodmodel, the resultis givena multiperiodjustifica- tion and interpretationin [11]. The modelhas also been extendedin (12) to the case wherethe one-periodreturns could have stable distributionswith infinitevariances. In words,(11) says thatthe expected one-period return on a securityis the one-periodriskless rate of interestrf,t+1 plus a "riskpremium" that is propor- tional to cov(rij,t+i,rm,t+ilDt)/6(rm t+11100. In the Sharpe-Lintnermodel each investorholds some combinationof the risklessasset and the market portfolio,so that,given a mean-standarddeviation framework, the riskof an individualasset can be measuredby its contributionto the standarddeviation of the returnon the market portfolio.This contributionis in fact cov (rj,t+i, rm,t+l r(t)/I(imst+it) *26 The factor [E(r-m,t+,ifDt)- rf,t+1]/0(rm,t+1j@I t), whichis the same forall securities,is thenregarded as the marketprice of risk. Publishedempirical tests of the Sharpe-Lintnermodel are notyet available, thoughmuch work is in progress.There is some publishedwork, however, which,though not directedat the Sharpe-Lintnermodel, is at least consistent withsome of its implications.The statedgoal of thiswork has been to determinethe extentto whichthe returnson a givensecurity are relatedto the returnson othersecurities. It started (again) with Kendall's [21] finding thatthough common stock price changes do notseem to be seriallycorrelated, thereis a high degreeof cross-correlationbetween the simultaneousreturns of differentsecurities. This line of attack was continuedby King [23] who (usingfactor analysis of a sampleof monthlyreturns on sixtyN.Y.S.E. stocks forthe period1926-60) foundthat on averageabout 50% of the varianceof an individualstock's returnscould be accountedfor by a "marketfactor" whichaffects the returnson all stocks,with "industry factors" accounting for at mostan additional10%'o of the variance.

26. That is, coy rm Crm = (rjt+i ,t+ilt)/o ,t+iI1,t) (Yrm,t+iI,Dd. EfficientCapital Markets 403 For our purposes,however, the work of Fama, Fisher,Jensen, and Roll [14] (henceforthFFJR) and the more extensivework of Blume [7] on monthlyreturn data is morerelevant. They test the following "market model," originallysuggested by Markowitz[30]: r,t+i = aj + ijrM,t+1 + ij,t+ (12) wherera,t+1 is the rate of returnon securityj formonth t, rm,t+iis the cor- respondingreturn on a marketindex M, aj and ij are parametersthat can vary fromsecurity to security,and uj,t+l is a randomdisturbance. The tests of FFJR and subsequentlythose of Blumeindicate that (12) is well specified as a linear regressionmodel in that (i) the estimatedparameters aj and ij remainfairly constant over long periodsof time (e.g., the entirepost-World War II periodin thecase of Blume), (ii) rM,t+1and the estimatedufj,t+,, are close to seriallyindependent, and (iii) the uj,t+i seem to be independentof rM,t+1. Thus the observedproperties of the"market model" are consistentwith the expectedreturn efficient markets model, and, in addition,the "marketmodel" tellsus somethingabout theprocess generating expected returns from security to security.In particular,

E(r- t+c) = aj + PjE(riM,t+1). (13) The questionnow is to what extent(13) is consistentwith the Sharpe- Lintnerexpected return model summarizedby (11). Rearranging(11) we obtain

E(r-j,t+1J|t) aj((Dt)+ (3j((Dt)E(rim,t+i1|Dt), (14) where,noting that the risklessrate rf,t+1is itselfpart of the informationset t, we have

aj(@Dt) rf,t+l[ P-j (Dt)], (15) and Pj( D) =cov (r'jja,~rm t+11(Dt) ( 16)

Withsome simplifyingassumptions, (14) can be reducedto (13). In particular, if the covarianceand variancethat determineWj(Ct) in (16) are the same forall t and Dt, thenPjf(Dt) in (16) correspondsto Pj in (12) and (13), and the least squares estimateof Pj in (12) is in fact just the ratio of the samplevalues of the covarianceand variancein (16). If we also assumethat rf,t+1is thesame forall t, and thatthe behaviorof the returnson themarket portfoliom are closelyapproximated by the returnson some representative indexM, we will have come a longway towardequating (13) and (11). In- deed, the onlymissing link is whetherin the estimatedparameters of (12) ajrf(I S) (17) Neither FFJR nor Blume attack this question directly,though some of Blume's evidenceis at least promising.In particular,the magnitudesof the 404 The Journalof Finance estimated`j are roughlyconsistent with (17) in the sense that the estimates are alwaysclose to zero (as theyshould be withmonthly return data).27 In a sense, though,in establishingthe apparentempirical validity of the "marketmodel" of (12), both too muchand too littlehave been shownvis- a-vis theSharpe-Lintner expected return model of (11). We knowthat during thepost-World War II periodone-month interest rates on risklessassets (e.g., governmentbills withone monthto maturity)have not been constant.Thus, if expectedsecurity returns were generatedby a versionof the "market model"that is fullyconsistent with the Sharpe-Lintnermodel, we would,ac- cordingto (15), expectto observesome non-stationarityin the estimatesof aj. On a monthlybasis, however,variation through time in one-periodriskless interestrates is probablytrivial relative to variationin otherfactors affecting monthlycommon stock returns,so that more powerfulstatistical methods wouldbe necessaryto studythe effectsof changesin the risklessrate. In any case, since the workof FFJR and Blume on the "marketmodel" was not concernedwith relating this model to the Sharpe-Lintnermodel, we can onlysay thatthe resultsfor the formerare somewhatconsistent with the implicationsof the latter.But the resultsfor the "marketmodel" are, after all, just a statisticaldescription of thereturn generating process, and theyare probably somewhatconsistent with other models of equilibriumexpected returns.Thus the onlyway to generatestrong empirical conclusions about the Sharpe-Lintnermodel is to testit directly.On the otherhand, any alternative modelof equilibriumexpected returns must be somewhatconsistent with the "marketmodel,' giventhe evidencein its support. B. Tests of MartingaleModels of the Semi-strongForm In general,semi-strong form tests of efficientmarkets models are concerned with whethercurrent prices "fullyreflect" all obviouslypublicly available information.Each individualtest, however, is concernedwith the adjustment of securityprices to one kind of informationgenerating event (e.g., stock splits,announcements of financialreports by firms,new securityissues, etc.). Thus each testonly brings supporting evidence for the model,with the idea thatby accumulatingsuch evidencethe validityof the modelwill be "estab- lished." In fact,however, though the available evidenceis in supportof the efficient marketsmodel, it is limitedto a few major typesof informationgenerating events.The initialmajor work is apparentlythe study of stocksplits by Fama,

27. With least squares applied to monthlyreturn data, the estimateof (X in (12) is

aj = rj,t - jrm,t, where the bars indicate sample mean returns.But, in fact, Blume applies the market model to the wealth relativesRjt = 1 + rjt and RMt = 1 + rmt.This yields preciselythe same estimate of ,1 as least squares applied to (12), but the interceptis now

a'J=Rjt- 3jRMt = 1 + rJt-3j(1 + rMt) = 1- pj + aj

Thus what Blume in fact finds is that for almost all securities, j'j + 3j 1, which implies that ctj is close to 0. EfficientCapital Markets 405 Fisher,Jensen, and Roll (FFJR) [14], and all the subsequentstudies summarizedhere are adaptationsand extensionsof the techniquesdeveloped in FFJR. Thus, this paper will firstbe reviewedin some detail,and thenthe otherstudies will be considered.

1. Splits and the Adjustmentof Stock Prices to New Information Since the onlyapparent result of a stocksplit is to multiplythe number of sharesper shareholderwithout increasing claims to real assets,splits in them- selves are not necessarilysources of new information.The presumptionof FFJR is that splits may oftenbe associatedwith the appearanceof more fundamentallyimportant information. The idea is to examinesecurity returns aroundsplit dates to see firstif thereis any "unusual"behavior, and, if so, to what extentit can be accountedfor by relationshipsbetween splits and othermore fundamental variables. The approachof FFJR to theproblem relies heavily on the"market model" of (12). In thismodel if a stocksplit is associatedwith abnormal behavior, thiswould be reflectedin the estimatedregression residuals for the months surroundingthe split. For a givensplit, define month 0 as themonth in which theeffective date of a splitoccurs, month 1 as themonth immediately following the split month,month -1 as the monthpreceding, etc. Now definethe averageresidual over all splitsecurities for month m (wherefor each security mis measuredrelative to the splitmonth) as N u N'1 wherefUjm is thesample regression residual for security j in monthm and N is thenumber of splits.Next, define the cumulativeaverage residual Um as m

Um i Uk. k=-29 The averageresidual um can be interpretedas the average deviation(in monthm relativeto split months)of the returnsof split stocks fromtheir normalrelationships with the market.Similarly, Um can be interpretedas the cumulativedeviation (from month -29 to monthm). Finally,define u+, u;, U+ and Um as the averageand cumulativeaverage residuals for splitsfollowed by"increased" (+) and "decreased"(-) dividends.An "increase"is a case wherethe percentagechange in dividendson the splitshare in the year after thesplit is greaterthan the percentagechange for the N.Y.S.E. as a whole, whilea "decrease"is a case of relativedividend decline. The essenceof theresults of FFJR are thensummarized in Figure1, which showsthe cumulativeaverage residualsUr U+ and U- for -29 ` m 30. The sampleincludes all 940 stock splitson the N.Y.S.E. from1927-59, wherethe exchangewas at least fivenew sharesfor four old, and wherethe securitywas listedfor at least twelvemonths before and afterthe split. For all threedividend categories the cumulativeaverage residualsrise in 406 The Journalof Finance the 29 monthsprior to the split,and in factthe averageresiduals (not shown here) are uniformlypositive. This cannotbe attributedto thesplitting process, sincein onlyabout ten per centof thecases is thetime between the announce- mentand effectivedates of a splitgreater than fourmonths. Rather, it seems thatfirms tend to splittheir shares during "abnormally" good times-thatis, duringperiods when the prices of theirshares have increasedmore than would

U m o.44 , , , , , ' ' ' ' '

0.33 -

0.22

0.11

o t

-29 25-20_15-10_50 5 10 15 20 25 30 Monthrelative to split--m

FIGURE la Cumulative average residuals-all splits.

u- u m + m 10.44 , , , , ,T o.~~~~~~~~~44

0.33 ~0.33

. - 0.22 0.22 . .

0.11 0.11 _. o:i

0 --20 -29 25 -2 10 15 20 25 30 ~-29 -loO0 1 0 3 15-10 _50 5 -25 -15 5 5 1015 20523 Monthrelative to split--m Month relative to Split--m

FIGURE lb FiGuRE lc Cumulative average residuals for dividend Cumulativeaverage residualsfor dividend "increases." "decreases." EfficientCapital Markets 407 be impliedby theirnormal relationships with generalmarket prices, which itselfprobably reflects a sharp improvement,relative to the market,in the earningsprospects of thesefirms sometime during the years immediatelypre- cedinga split.28 Afterthe split month there is almostno furthermovement in Un, thecumu- lativeaverage residual for all splits.This is striking,since 71.5 per cent (672 out of 940) of all splitsexperienced greater percentage dividend increases in theyear afterthe splitthan the averagefor all securitieson the N.Y.S.E. In lightof this,FFJR suggestthat when a splitis announcedthe marketinter- prets this (and correctlyso) as a signal thatthe company'sdirectors are probablyconfident that future earnings will be sufficientto maintaindividend paymentsat a higherlevel. Thus the largeprice increasesin the monthsim- mediatelypreceding a splitmay be due to an alterationin expectationscon- cerningthe futureearning potential of the firm,rather than to any intrinsic effectsof thesplit itself. If thishypothesis is correct,return behavior subsequent to splitsshould be substantiallydifferent for the cases wherethe dividendincrease materializes than forthe cases whereit does not. FFJR argue thatin factthe differences are in the directionsthat would be predicted.The fact that the cumulative averageresiduals for the "increased"dividends (Figure lb) driftupward but onlyslightly in the year afterthe split is consistentwith the hypothesisthat whenthe split is declared,there is a priceadjustment in anticipationof future dividendincreases. But thebehavior of theresiduals for stock splits associated with "decreased" dividendsoffers even strongerevidence for the split hypothesis.The cumulativeaverage residuals for these stocks (Figure lc) rise in the fewmonths before the split,but thenfall dramaticallyin the fewmonths afterthe split when the anticipateddividend increase is not forthcoming. When a year has passed afterthe split,the cumulativeaverage residual has fallento about whereit was fivemonths prior to thesplit, which is about the earliesttime reliable information about a split is likelyto reach the market. Thus by the timeit becomesclear that the anticipateddividend increase is not forthcoming,the apparenteffects of the split seem to have been wiped away, and the stock'sreturns have revertedto theirnormal relationship with marketreturns. Finally,and mostimportant, although the behavior of post-splitreturns will be verydifferent depending on whetheror notdividend "increases" occur, and in spite of the fact that a large majorityof split securitiesdo experience dividend "increases,"when all splits are examinedtogether (Figure la), subsequentto thesplit there is no netmovement up or downin thecumulative

28. It is importantto note, however,that as FFJR indicate,the persistentupward driftof the cumulativeaverage residualsin the monthspreceding the split is not a phenomenonthat could be used to increase expected tradingprofits. The reason is that the behavior of the average residuals is not representativeof the behavior of the residuals for individual securities.In months prior to the split, successivesample residuals for individual securitiesseem to be independent.But in most cases, there are a few months in which the residuals are abnormally large and positive. The months of large residuals differfrom security to security,however, and these differencesin timing explain why the signs of the average residuals are uniformlypositive for many months preceding the split. 408 The Journalof Finance averageresiduals. Thus, apparentlythe marketmakes unbiased forecasts of the implicationsof a split forfuture dividends, and theseforecasts are fully reflectedin theprices of thesecurity by theend of thesplit month. After con- siderablymore data analysisthan can be summarizedhere, FFJR conclude that theirresults lend considerablesupport to the conclusionthat the stock marketis efficient,at least withrespect to its abiliyto adjust to theinforma- tionimplicit in a split.

2. OtherStudies of Public Announcements Variantsof the methodof residualanalysis developed in [14] have been used by othersto studythe effects of differentkinds of publicannouncements, and all of thesealso supportthe efficientmarkets hypothesis. Thus usingdata on 261 majorfirms for the period 1946-66, Ball and Brown [4] applythe methodto studythe effects of annualearnings announcements. They use theresiduals from a timeseries regression of theannual earnings of a firmon theaverage earnings of all theirfirms to classifythe firm'searnings fora givenyear as having"increased" or "decreased"relative to the market. Residualsfrom regressions of monthlycommon stock returns on an indexof returns(i.e., themarket model of (12)) are thenused to computecumulative average returnresiduals separately for the earningsthat "increased,"and thosethat "decreased." The cumulativeaverage return residuals rise through- out the year in advance of the announcementfor the earnings"increased" category,and fall for the earnings"decreased" category.29 Ball and Brown [4, p. 175] concludethat in factno morethan about ten to fifteenpercent of theinformation in theannual earnings announcement has not been anticipated by the monthof the announcement. On themacro level, Waud [45] has used themethod of residualanalysis to examinethe effectsof announcementsof discountrate changesby Federal ReserveBanks. In this case the residualsare essentiallyjust the deviations of the daily returnson the Standardand Poor's 500 Index fromthe average daily return.He findsevidence of a statisticallysignificant "announcement effect"on stockreturns for the firsttrading day followingan announcement, but the magnitudeof the adjustmentis small,never exceeding .5%. More interestingfrom the viewpointof the efficientmarkets hypothesis is his conclusionthat, if anything,the marketanticipates the announcements(or informationis somehowleaked in advance). This conclusionis based on the non-randompatterns of the signs of average returnresiduals on the days immediatelypreceding the announcement. Furtherevidence in supportof the efficientmarkets hypothesis is provided in the workof Scholes [39] on large secondaryofferings of common stock (ie., large underwrittensales of existingcommon stocks by individuals and institutions)and on newissues of stock.He findsthat on averagesecon- daryissues are associatedwith a declineof betweenone and two per centin thecumulative average residual returns for the corresponding common stocks. Since the magnitudeof the price adjustmentis unrelatedto the size ofthe

29. But the commentof footnote28 is againrelevant here. EfficientCapital Markets 409 issue, Scholesconcludes that the adjustmentis not due to "sellingpressure" (as is commonlybelieved), but ratherresults from negative information implicitin the factthat somebody is tryingto sell a largeblock of a firm'sstock. Moreover,he presentsevidence that the value of the informationin a secon- darydepends to some extenton the vendor;somewhat as wouldbe expected, by far the largestnegative cumulative average residuals occur where the vendoris the corporationitself or one of its officers,with investmentcom- paniesa distantsecond. But the identityof the vendoris not generallyknown at the time of the secondary,and corporateinsiders need only reporttheir transactionsin theirown company's stock to theS.E.C. withinsix days aftera sale. By thistime the market on averagehas fullyadjusted to the information in the secondary,as indicatedby the fact that the average residualsbehave randomlythereafter. Note, however,that though this is evidencethat prices adjust efficientlyto public information,it is also evidencethat corporateinsiders at least some- timeshave importantinformation about theirfirm that is not yet publicly known.Thus Scholes' evidencefor secondarydistributions provides support forthe efficientmarkets model in the semi-strongform sense, but also some strong-formevidence against the model. Though his resultshere are only preliminary,Scholes also reportson an applicationof the methodof residualanalysis to a sample of 696 new issues of commonstock during the period 1926-66.As in the FFJR studyof splits, thecumulative average residuals rise in themonths preceding the new security offering(suggesting that new issues tend to come after favorablerecent events)30but behave randomlyin the monthsfollowing the offering(indicat- ingthat whatever information is containedin thenew issue is on averagefully reflectedin the priceof the monthof the offering). In short,the available semi-strongform evidence on the effectof various sortsof publicannouncements on commonstock returnsis all consistentwith the efficientmarkets model. The strongpoint of the evidence,however, is its consistencyrather than its quantity; in fact, few differenttypes of public informationhave been examined,though those treatedare among the ob- viouslymost important. Moreover, as we shall now see, the amountof semi- strongform evidence is voluminouscompared to the strongform tests that are available.

C. StrongForm Tests of the EfficientMarkets Models The strongform tests of the efficientmarkets model are concernedwith whetherall available informationis fullyreflected in pricesin the sense that no individualhas higherexpected trading profits than othersbecause he has monopolisticaccess to someinformation. We wouldnot, of course,expect this modelto be an exact descriptionof reality,and indeed,the precedingdiscus- sions have alreadyindicated the existenceof contradictoryevidence. In particular,Niederhoffer and Osborne [32] have pointedout that specialistson the N.Y.S.E. apparentlyuse theirmonopolistic access to informationconcern-

30. Footnote 28 is again relevanthere. 410 The Journalof Finance ing unfilledlimit orders to generatemonopoly profits, and Scholes' evidence [39] indicatesthat officers of corporationssometimes have monopolisticaccess to informationabout theirfirms. Since we alreadyhave enoughevidence to determinethat the modelis not strictlyvalid, we can nowturn to otherinteresting questions. Specifically, how far down throughthe investmentcommunity do deviationsfrom the model permeate?Does it pay for the averageinvestor (or the averageeconomist) to expend resourcessearching out little knowninformation? Are such ac- tivitieseven generally profitable for various groups of market"professionals"? More generally,who are the people in the investmentcommunity that have access to "special information"? Though this is a fascinatingproblem, only one grouphas been studiedin any depth-the managementsof open end mutualfunds. Several studiesare available (e.g., Sharpe [41, 42] and Treynor[44]), but the most thorough are Jensen's[19, 20], and our commentswill be limitedto his work.We shall firstpresent the theoreticalmodel underlying his tests,and thengo on to his empiricalresults. 1. TheoreticalFramework In studyingthe performance of mutualfunds the major goals are to deter- mine (a) whetherin generalfund managers seem to have access to special informationwhich allows themto generate"abnormal" expected returns, and (b) whethersome fundsare betterat uncoveringsuch special information thanothers. Since thecriterion will simplybe the abilityof fundsto produce higherreturns than some normwith no attemptto determinewhat is re- sponsiblefor the high returns,the "special information"that leads to high performancecould be eitherkeener insight into the implicationsof publicly available informationthan is implicitin marketprices or monopolisticaccess to specificinformation. Thus the testsof theperformance of the mutualfund industryare not strictlystrong form tests of the efficientmarkets model. The major theoretical(and practical) problemin using the mutualfund industryto test the efficientmarkets model is developinga "norm"against whichperformance can be judged.The normmust represent the resultsof an investmentpolicy based on the assumptionthat prices fullyreflect all available information.And if one believesthat investors are generallyrisk averse and so on averagemust be compensatedfor any risksundertaken, then one has theproblem of findingappropriate definitions of riskand evaluatingeach fundrelative to a normwith its chosenlevel of risk. Jensenuses the Sharpe [40]-Lintner[24, 25] model of equilibriumex- pectedreturns discussed above to derivea normconsistent with these goals. From (14)-(16), in thismodel the expectedreturn on an asset or portfolioj fromt to t + 1 is

E(r'j,t?l 10t) rf,t+l [1 - (Dt))] + E (rm,t+1ikt)Pj(3t), (18) wherethe various symbols are as definedin SectionIII. A. 6. But (18) is an ex ante relationship,and to evaluateperformance an ex post normis needed. EfficientCapital Markets 411 One way the lattercan be obtainedis to substitutethe realizedreturn on the marketportfolio for the expectedreturn in (18) withthe result3' E(rij,t+,(Dt, rm,t+,) rf,t+l [1 - 3j((Dt)] + rm,t+,(j(QDt). (9) Geometrically,(19) says that within the contextof the Sharpe-Lintner model,the expected return on j (giveninformation (Dt and thereturn rm,t?l on the marketportfolio) is a linearfunction of its risk rm p(34Q>) - COV (irj,t+1, as indicatedin Figure2. Assumingthat the value of (3j(Dt) is somehowknown, or can be reliablyestimated, if j is a mutualfund, its ex post performance fromt to t + 1 mightnow be evaluatedby plottingits combinationof realized returnrj,t+l and riskin Figure2. If (as forthe point a) the combinationfalls above theexpected return line (or, as it is morecommonly called, the "market line"), it has donebetter than would be expectedgiven its level of risk,while if (as forthe point b) it fallsbelow the line it has done worse. r

E(ib,t?1lit,rn ,t+1)------

b,t+------

m,t+IL

a,tR%+1 t rm,t+1-

o - - - .

? Paia( t) PM(1t PO t) 04t)

FIGURE 2 PerformanceEvaluation Graph Alternatively,the marketline shows the combinationsof returnand risk providedby portfoliosthat are simplemixtures of the risklessasset and the marketportfolio m. The returnsand risks forsuch portfolios(call themc) are r =,t+l arf,t+l + (1 -0rM,t+1 (z1)) cv ( )mta (rcst(" ,t+1, rm,"m,t+1! t t) l|acocov ? t Pt+l| (3~QD~)(D)=coy0 ( (1a) r'm, + l, rm,mt+1IlI )t a O2(irm,t+ 11t) -adrm,t+ij(Dt)1-

31. The assumptionhere is thatthe returnr; t--l is generatedaccording to

rj,t+l = ri,t+,[l - j(Dt)] + rm,t+j0j((Dt) + Uj,t+ls and E(UJ,t+IIrm,t+,) = 0 forall rm,t+. 412 The Journalof Finance wherea is the proportionof portfoliofunds invested in the risklessasset. Thus,when 1 > a > 0 we obtainthe combinations of returnand riskalong the marketline fromrf,t+? to m in Figure 2, while when a < 0 (and underthe assumptionthat investorscan borrowat the same rate that theylend) we obtain the combinationsof returnand risk along the extensionof the line throughm. In this interpretation,the marketline representsthe resultsof a naive investmentstrategy, which the investorwho thinksprices reflectall availableinformation might follow. The performanceof a mutualfund is then measuredrelative to this naive strategy. 2. EmpiricalResults Jensenuses thisrisk-return framework to evaluatethe performance of 115 mutual fundsover the ten year period 1955-64. He argues at lengthfor measuringreturn as the nominalten year rate withcontinuous compounding (i.e., the naturallog of the ratioof terminalwealth after ten years to initial wealth) and for using historicaldata on nominalone-year rates with con- tinuouscompounding to estimaterisk. The Standardand Poor Index of 500 majorcommon stocks is used as theproxy for the market portfolio. The generalquestion to be answeredis whethermutual fund managements have any special insightsor informationwhich allows themto earn returns above the norm.But Jensenattacks the questionon severallevels. First,can the fundsin generaldo well enough to compensateinvestors for loading charges,management fees, and othercosts that mightbe avoided by simply choosingthe combinationof the risklessasset f and the marketportfolio m withrisk level comparableto thatof the fund'sactual portfolio?The answer seemsto be an emphaticno. As far as net returnsto investorsare concerned, in 89 out of 115 cases, the fund'srisk-return combination for the ten year periodis belowthe marketline forthe period, and the averageover all funds of the deviationsof ten year returnsfrom the markettime is -14.6%o. That is, on averagethe consumer'swealth after ten years of holdingmutual funds is about fifteenper centless thanif he held thecorresponding portfolios along the marketline. But theloading charge that an investorpays in buyinginto a fundis usually a pure salesman'scommission that the funditself never gets to invest.Thus one mightask whether,ignoring loading charges (i.e., assumingno such chargeswere paid by the investor),in generalfund managements can earn returnssufficiently above the normto cover all otherexpenses that are pre- sumablymore directlyrelated to the managementof the fund portfolios. Again,the answerseems to be no. Even whenloading charges are ignoredin computingreturns, the risk-returncombinations for 72 out of 115 fundsare belowthe market line, and the averagedeviation of tenyear returnsfrom the marketline is -8.9%. Finally,as a somewhatstronger test of the efficientmarkets model, one would like to knowif, ignoringall expenses,fund managementsin general showedany abilityto pick securitiesthat outperformedthe norm.Unfortu- nately,this questioncannot be answeredwith precision for individual funds since,curiously, data on brokeragecommissions are not publishedregularly. EfficientCapital Markets 413 But Jensensuggests the available evidenceindicates that the answerto the questionis again probablynegative. Specifically, adding back all otherpub- lishedexpenses of fundsto theirreturns, the risk-returncombinations for 58 out of 115 fundswere below the market line, and the averagedeviation of ten year returnfrom the line was -2.5%o. But part of this resultis due to the absence of a correctionfor brokeragecommissions. Estimating these com- missionsfrom average portfolioturnover rates for all fundsfor the period 1953-58,and addingthem back to returnsfor all fundsincreases the average deviationfrom the marketline from-2.5%o to .09%o,which still is not in- dicativeof the existenceof special informationamong mutual fund managers. But thoughmutual fund managers in generaldo not seem to have access to informationnot alreadyfully reflected in prices,perhaps there are individual fundsthat consistently do betterthan the norm, and so provideat least some strongform evidence against the efficientmarkets model. If thereare such funds,however, they escape Jensen'ssearch. For example,for individual funds,returns above the normin one subperioddo not seem to be associated withperformance above thenorm in othersubperiods. And regardlessof how returnsare measured(i.e., netor grossof loadingcharges and otherexpenses), thenumber of fundswith large positive deviations of returnsfrom the market line of Figure 2 is less than the numberthat would be expectedby chance with115 fundsunder the assumptionthat fund managements have no special talentsin predictingreturtis.32 Jensenargues that thoughhis resultsapply to only one segmentof the investmentcommunity, they are neverthelessstriking evidence in favorof the efficientmarkets model: Althoughthese results certainly do notimply that the strong form of themartingale hypothesisholds for all investorsand forall time,they provide strong evidence in supportof thathypothesis. One mustrealize that these analysts are extremelywell endowed.Moreover, they operate in thesecurities markets every day and havewide- rangingcontacts and associationsin boththe businessand financialcommunities. Thus,the fact that they are apparently unable to forecastreturns accurately enough to recovertheir research and transactions costs is a strikingpiece of evidence in favor of the strongform of the martingalehypothesis-at least as far as the extensive subsetof informationavailable to theseanalysts is concerned[20, p. 170].

IV. SUMMARY AND CONCLUSIONS The preceding(rather lengthy) analysis can be summarizedas follows.In generalterms, the theory of efficientmarkets is concernedwith whether prices at any pointin time"fully reflect" available information. The theoryonly has empiricalcontent, however, within the contextof a more specificmodel of

32. On the other hand, there is some suggestionin Scholes' [39] work on secondaryissues that mutual funds may occassionallyhave access to "special information."After corporate insiders, the next largest negative price changes occur when the secondary seller is an investmentcompany (includingmutual funds), though on average the price changes are much smaller (i.e., closer to 0) than when the seller is a corporateinsider. Moreover, Jensen'sevidence itself,though not indicative of the existenceof special information among mutual fund managers,is not sufficientlyprecise to conclude that such informationnever exists. This stronger conclusion would require exact data on unavoidable expenses (including brokeragecommissions) of portfoliomanagement incurred by funds. 414 The Journalof Ftnance marketequilibrium, that is, a model that specifiesthe nature of market equilibriumwhen prices "fullyreflect" available information.We have seen thatall of theavailable empirical literature is implicitlyor explicitlybased on the assumptionthat the conditionsof marketequilibrium can be stated in termsof expectedreturns. This assumptionis thebasis of the expectedreturn or "fair game" efficientmarkets models. The empiricalwork itselfcan be dividedinto threecategories depending on thenature of theinformation subset of interest.Strong-form tests are concernedwith whether individual investors or groupshave monopolisticaccess to any informationrelevant for price formation.One would not expectsuch an extrememodel to be an exact descriptionof the world,and it is probably best viewedas a benchmarkagainst which the importanceof deviationsfrom marketefficiency can be judged.In the less restrictivesemi-strong-form tests the informationsubset of interestincludes all obviouslypublicly available information,while in the weak form tests the informationsubset is just historicalprice or returnsequences. Weak formtests of the efficientmarket model are the most voluminous, and it seems fair to say that the resultsare stronglyin support.Though statisticallysignificant evidence for dependencein successiveprice changes or returnshas been found,some of this is consistentwith the "fair game" modeland the restdoes not appear to be sufficientto declarethe marketinefficient.Indeed, at least forprice changes or returnscovering a day or longer, thereisn't much evidence against the "fairgame" model'smore ambitious off- spring,the randomwalk. Thus, thereis consistentevidence of positive dependencein day-to-day price changesand returnson commonstocks, and the dependenceis of a formthat can be used as the basis of marginallyprofitable trading rules. In Fama's data [10] the dependenceshows up as serial correlationsthat are consistentlypositive but also consistentlyclose to zero,and as a slighttendency forobserved numbers of runsof positiveand negativeprice changes to be less thanthe numbers that would be expectedfrom a purelyrandom process. More important,the dependencealso showsup in thefilter tests of Alexander[1, 2] and thoseof Fama and Blume [13] as a tendencyfor very small filtersto produceprofits in excess of buy-and-hold.But any systems(like the filters) that attemptto turnshort-term dependence into tradingprofits of necessity generateso manytransactions that theirexpected profits would be absorbed by even the minimumcommissions (security handling fees) that floortraders on majorexchanges must pay. Thus, usinga less thancompletely strict interpretationof marketefficiency, this positive dependencedoes not seem of sufficientimportance to warrantrejection of the efficientmarkets model. Evidence in contradictionof the "fair game" efficientmarkets model for price changesor returnscovering periods longerthan a single day is more difficultto find.Cootner [9], and Moore [31] reportpreponderantly negative (but again small) serialcorrelations in weeklycommon stock returns, and this resultappears also in the fourday returnsanalyzed by Fama [10]. But it does not appear in runstests of [10], where,if anything,there is some slight indicationof positivedependence, but actually not much evidenceof any EfficientCapital Markets 415 dependenceat all. In any case, thereis no indicationthat whatever dependence existsin weeklyreturns can be used as thebasis of profitabletrading rules. Otherexisting evidence of dependencein returnsprovides interesting in- sightsinto the processof price formationin the stock market,but it is not relevantfor testingthe efficientmarkets model. For example,Fama [10] showsthat large daily price changes tend to be folowedby large changes,but of unpredictablesign. This suggeststhat importantinformation cannot be completelyevaluated immediately, but that the initialfirst day's adjustment of pricesto the informationis unbiased,which is sufficientfor the martingale model.More interestingand important,however, is the Niederhoffer-Osborne [32] findingof a tendencytoward excessive reversals in commonstock price changesfrom transaction to transaction.They explainthis as a logical result of the mechanismwhereby orders to buy and sell at marketare matched against existinglimit orders on the books of the specialist.Given the way this tendencytoward excessive reversals arises, however, there seems to be no way it can be used as thebasis of a profitabletrading rule. As theyrightly claim,their results are a strongrefutation of the theoryof randomwalks, at least as appliedto pricechanges from transaction to transaction,but theydo not constituterefutation of the economicallymore relevant"fair game" efficientmarkets model. Semi-strongform tests, in which prices are assumed to fullyreflect all obviouslypublicly available information,have also supportedthe efficient marketshypothesis. Thus Fama, Fisher,Jensen, and Roll [14] findthat the informationin stocksplits concerning the firm'sfuture dividend payments is on averagefully reflected in theprice of a splitshare at the timeof the split. Ball and Brown[4] and Scholes[39] cometo similarconclusions with respect to the informationcontained in (i) annual earningannouncements by firms and (ii) newissues and largeblock secondary issues of commonstock. Though only a few differenttypes of informationgenerating events are represented here,they are amongthe moreimportant, and the resultsare probablyin- dicativeof whatcan be expectedin futurestudies. As notedearlier, the strong-form efficient markets model, in whichprices are assumedto fullyreflect all available information,is probablybest viewedas a benchmarkagainst which deviations from market efficiency (interpreted in its strictestsense) can be judged.Two such deviationshave in factbeen observed. First,Niederhoffer and Osborne [32] point out that specialistson major securityexchanges have monopolisticaccess to informationon unexecutedlimit orders and theyuse thisinformation to generatetrading profits. This raises the questionof whetherthe "marketmaking" function of the specialist (if indeed this is a meaningfuleconomic function) could not as effectivelybe carriedout by some other-mechanism that did not implymon- opolisticaccess to information.Second, Scholes [39] findsthat, not unexpectedly,corporate insiders often have monopolisticaccess to information about theirfirms. At themoment, however, corporate insiders and specialistsare the onlytwo groupswhose monopolistic access to informationhas been documented.There is no evidencethat deviationsfrom the strongform of the efficientmarkets 416 The Journalof Finance modelpermeate down any furtherthrough the investment community. For the purposesof mostinvestors the efficient markets model seems a good first(and second) approximationto reality. In short,the evidence in supportof the efficientmarkets model is extensive, and (somewhatuniquely in economics) contradictoryevidence is sparse. Nevertheless,we certainlydo not wantto leave the impressionthat all issues are closed.The old saw, "muchremains to be done,"is relevanthere as else- where.Indeed, as is oftenthe case in successfulscientific research, now that we knowwe've been in thepast, we are able to pose and (hopefully)to answer an even moreinteresting set of questionsfor the future.In thiscase the most pressingfield of futureendeavor is the developmentand testingof modelsof marketequilibrium under uncertainty. When the processgenerating equilibriumexpected returns is betterunderstood (and assumingthat some expected returnmodel turns out to be relevant),we willhave a moresubstantial frame- workfor more sophisticated intersecurity tests of marketefficiency.

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