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 in- formation.A marketin whichprices always "fullyreflect" available informa- tionis 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 con- cernis 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 implica- tions.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 expectedre- turns) 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 ex- pectedreturns. In generalterms, like the two parametermodel such theories wouldposit that conditional on some relevantinformation 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 the informationiJt 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., the generalnotion 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 assump- tion 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 secu- rities.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((<Dt)E(!j,t+1[(Dt) = 0. j=l The expectedreturn or "fair game" efficientmarkets model2 has other importanttestable implications, but these are bettersaved for the later dis- cussionof theempirical work. Now we turnto two special cases of themodel, the submartingaleand the randomwalk, that (as we shall see later) play an importantrole in the empiricalliterature. 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 the efficientmarkets model.8 C. The Random Walk Model In the early treatmentsof the efficientmarkets model, the statementthat the