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 PRIMARY ROLE of the capital market is allocation of ownership of the economy's capital stock. In general terms, the ideal is a market in which prices provide accurate signals for resource allocation: that is, a market in which firms can make production-investment decisions, and investors can choose among the securities that represent ownership of firms' activities under the assumption that security prices at any time "fully reflect" all available information. A market in which prices always "fully reflect" available information is called "efficient."
This paper reviews the theoretical and empirical literature on the efficient markets model. After a discussion of the theory, empirical work concerned with the adjustment of security prices to three relevant information subsets is considered. First, weak form tests, in which the information set is just historical prices, are discussed. Then semi-strong form tests, in which the concern is whether prices efficiently adjust to other information that is obviously publicly available (e.g., announcements of annual earnings, stock splits, etc.) are considered. Finally, strong form tests concerned with whether given investors or groups have monopolistic access to any information relevant for price formation are reviewed.' We shall conclude that, with but a few exceptions, the efficient markets model stands up well.
Though we proceed from theory to empirical work, to keep the proper historical perspective we should note to a large extent the empirical work in this area preceded the development of the theory. The theory is presented first here in order to more easily judge which of the empirical results are most relevant from the viewpoint of the theory. The empirical work itself, however, will then be reviewed in more or less historical sequence.
Finally, the perceptive reader will surely recognize instances in this paper where relevant studies are not specifically discussed. In such cases my apologies should be taken for granted. The area is so bountiful that some such injustices are unavoidable. But the primary goal here will have been accomplished if .a coherent picture of the main lines of the work on efficient markets is presented, along with an accurate picture of the current state of the arts.
• Research on this project was supported by a grant from the National Science Foundation. I am indebted to Arthur Laffer, Robert Aliber, Ray Ball, Michael Jensen, James Lorie, Merton
Miller, Charles Nelson, Richard Roll, William Taylor, and Ross Watts for their helpful comments.
•• University of Chicago-Joint Session with the Econometric Society.
1. The distinction between weak and strong form tests was first suggested by Harry Roberts.

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II.

THE THEORY OF EFFICIENT MARKETS

A. Expected Return or "Fair Game" Models

The definitional statement that in an efficient market prices "fully reflect': available information is so general that it has no empirically testable implications. To make the model testable, the process of price formation must be specified in more detail. In essence we must define somewhat more exactly what is meant by the term "fully reflect."
One possibility would be to posit that equilibrium prices (or expected returns) on securities are generated as in the "two parameter" Sharpe [40]Lintner [24, 25] world. In general, however, the theoretical models and especially the empirical tests of capital market efficiency have not been this specific. Most of the available work is based only on the assumption that the conditions of market equilibrium can (somehow) be stated in terms of expected returns. In general terms, like the two parameter model such theories would posit that conditional on some relevant information set, the equilibrium expected return on a security is a function of its "risk." And different theories would differ primarily in how "risk" is defined.
All members of the class of such "expected return theories" can, however, be described notation ally as follows:
E(PJ,t+llcI>t)

= [1 + E(rJ,t+l!cI>t)]PJt,

(1)

where E is the expected value operator; PJt is the price of security j at time t;
PJ,t+l is its price at t + 1 (with reinvestment of any intermediate cash income from the security); rJ.t+l is the one-period percentage return (PJ,t+l - PJt)/ pJt; cI>t is a general symbol for whatever set of information is assumed to be
"fully reflected" in the price at t; and the tildes indicate that PJ,t+l and rJ,t+l are random variables at t.
The value of the equilibrium expected return E(rJ.t+llcI>t) projected on the basis of the information cI>t would be determined from the particular expected return theory at hand. The conditional expectation notation of (1) is meant to imply, however, that whatever expected return model is assumed to apply, the information in cI>t is fully utilized in determining equilibrium expected returns. And this is the sense in which cI>t is "fully reflected" in the formation of the price pJt.
But we should note right off that, simple as it is, the assumption that the conditions of market equilibrium can be stated in terms of expected returns elevates the purely mathematical concept of expected value to a status not necessarily implied by the general notion of market efficiency. The expected value is just one of many possible summary measures of a distribution of returns, and market efficiency per se (i.e., the general notion that prices "fully reflect" available information) does not imbue it with any special importance.
Thus, the results of tests based on this assumption depend to some extent on its validity as well as on the efficiency of the market. But some such assumption is the unavoidable price one must pay to give the theory of efficient markets empirical content.
The assumptions that the conditions of market equilibrium can be stated

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in terms of expected returns and that equilibrium expected returns are formed on the basis of (and thus "fully reflect") the information set t have a major empirical implication-they rule out the possibility of trading systems based only on information in t that have expected profits or returns in excess of equilibrium expected profits or returns. Thus let
Xj,t+1 = pj,t+1 - E(pj,t+11eJ>t).

Then
E(XJ,t+11t)

=

(2)

°

(3)

which, by definition, says that the sequence {xu} is a "fair game" with respect to the information sequence {d. Or, equivalently, let
Zj,t+l

= rj,t+1 -

E(rj,t+1/t),

then
E(iJ,t+1jeJ>t)

(4)

= 0,

(5)

so that the sequence {zjd is also a "fair game" with respect to the information sequence {eJ>}.
In economic terms, Xj,t+1 is the excess market value of security j at time
1: it is the difference between the observed price and the expected value t of the price that was projected at t on the basis of the information t. And similarly, Zj,t+l is the return at t
1 in excess of the equilibrium expected return projected at 1. Let

+

+

u(t)

= [U1(t), U2(t), ... , un(t)]

be any trading system based on t which tells the investor the amounts Uj(t) of funds available at t that are to be invested in each of the n available securities. The total excess market value at t
1 that will be generated by such a system is

+

n

Vt+ 1

=L

Uj(t) [rj,t+1 - E(rj,t+11t)],

j~l

which, from the "fair game" property of (5) has expectation, n E(Vt+ 1/t)

=

L

Uj(t)E(iJ,t+11t)

= 0.

j=l

The expected return or "fair game" efficient markets model" has other important testable implications, but these are better saved for the later discussion of the empirical work. Now we turn to two special cases of the model, the submartingale and the random walk, that (as we shall see later) play an important role in the empirical literature.
2. Though we shall sometimes refer to the model summarized by (1) as the "fair game" model, keep in mind that the "fair game" properties of the model are implications of the assumptions that
(i) the conditions of market equilibrium can be stated in terms of expected returns, and (ii) the information t is fully utilized by the market in forming equilibrium expected returns and thus current prices,
The role of "fair game" models in the theory of efficient markets was first recognized and studied rigorously by Mandelbrot [27] and Samuelson [38]. Their work will be discussed in more detail later.

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B. The Submartingale Model
Suppose we assume in (1) that for all t and C»t
E(PJ.t+l/C»t) ;::: Pjt, or equivalently, E(i'J.t+l!C»t);::: O.

(6)

This is a statement that the price sequence {Pjt} for security j follows a submartingale with respect to the information sequence {C»t}, which is to say nothing more than that the expected value of next period's price, as projected on the basis of the information C»t, is equal to or greater than the current price.
If (6) holds as an equality (so that expected returns and price changes are zero), then the price sequence follows a martingale.
A submartingale in prices has one important empirical implication. Consider the set of "one security and cash" mechanical trading rules by which we mean systems that concentrate on individual securities and that define the conditions under which the investor would hold a given security, sell it short, or simply hold cash at any time t. Then the assumption of (6) that expected returns conditional on cI>t are non-negative directly implies that such trading rules based only on the information in cI>t cannot have greater expected profits than a policy of always buying-and-holding the security during the future period in question. Tests of such rules will be an important part of the empirical evidence on the efficient markets model,"

C. The Random Walk Model
In the early treatments of the efficient markets model, the statement that the current price of a security "fully reflects" available information was assumed to imply that successive price changes (or more usually, successive one-period returns) are independent. In addition, it was usually assumed that successive changes (or returns) are identically distributed. Together the two hypotheses constitute the random walk model. Formally, the model says f(rJ.t+llcI>t) f(rJ.t+l),
(7)

=

which is the usual statement that the conditional and marginal probability distributions of an independent random variable are identical. In addition, the density function f must be the same for all t.4
3. Note that the expected profitability of "one security and cash" trading systems vis-a-vis buyand-hold is not ruled out by the general expected return or "fair game" efficient markets model.
The latter rules out systems with expected profits in excess of equilibrium expected returns, but since in principle it allows equilibrium expected returns to be negative, holding cash (which always has zero actual and thus expected return) may have higher expected return than holding some security. And negative equilibrium expected returns for some securities are quite possible. For example, in the Sharpe [40]-Lintner [24, 25] model (which is in tum a natural extension of the portfolio models of Markowitz [30] and Tobin [43]) the equilibrium expected return on a security depends on the extent to which the dispersion in the security's return distribution is related to dispersion in the returns on all other securities. A security whose returns on average move opposite to the general market is particularly valuable in reducing dispersion of portfolio returns, and so its equilibrium expected return may well be negative.
4. The terminology is loose. Prices will only follow a random walk if price changes are independent, identically distributed; and even then we should say "random walk with drift" since expected price changes can be non-zero. If one-period returns are independent, identically distributed, prices will not follow a random walk since the distribution of price changes will depend

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Expression (7) of course says much more than the general expected return model summarized by (1). For example, if we restrict (1) by assuming that the expected return on security j is constant over time, then we have
E(rj.t+ll~t) = E(rj,t+l)'
(8)
This says that the mean of the distribution of rj,t+l is independent of the information available at t, t, whereas the random walk model of (7) in addition says that the entire distribution is independent of t. 6
We argue later that it is best to regard the random walk model as an extension of the general expected return or "fair game" efficient markets model in the sense of making a more detailed statement about the economic environment. The "fair game" model just says that the conditions of market equilibrium can be stated in terms of expected returns, and thus it says little about the details of the stochastic process generating returns. A random walk arises within the context of such a model when the environment is (fortuitously) such that the evolution of investor tastes and the process generating new information combine to produce equilibria in which return distributions repeat themselves through time.
Thus it is not surprising that empirical tests of the "random walk" model that are in fact tests of "fair game" properties are more strongly in support of the model than tests of the additional (and, from the viewpoint of expected return market efficiency, superfluous) pure independence assumption. (But it is perhaps equally surprising that, as we shall soon see, the evidence against the independence of returns over time is as weak as it is.)

D. Market Conditions Consistent with Efficiency
Before turning to the empirical work, however, a few words about the market conditions that might help or hinder efficient adjustment of prices to information are in order. First, it is easy to determine sufficient conditions for capital market efficiency. For example, consider a market in which (i) there are no transactions costs in trading securities, (ii) all available information is costlessly available to all market participants, and (iii) all agree on the implications of current information for the current price and distributions of future prices of each security. In such a market, the current price of a security obviously "fully reflects" all available information.
But a frictionless market in which all information is freely available and investors agree on its implications is, of course, not descriptive of markets met in practice. Fortunately, these conditions are sufficient for market efficiency, but not necessary. For example, as long as transactors take account of all on the price level. But though rigorous terminology is usually desirable, our loose use of terms should not cause confusion; and our usage follows that of the efficient markets literature.
Note also that in the random walk literature, the information set c;l)t in (7) is usually assumed to include only the past return history, rj,t, rj,t_l' ...
S. The random walk model does not say, however, that past information is of no value in assessing distributions of future returns. Indeed since return distributions are assumed to be stationary through time, past returns are the best source of such information. The random walk model does say, however, that the sequence (or the order) of the past returns is of no consequence in assessing distributions of future returns.

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available information, even large transactions costs that inhibit the flow of transactions do not in themselves imply that when transactions do take place, prices will not "fully reflect" available information. Similarly (and speaking, as above, somewhat loosely), the market may be efficient if "sufficient numbers" of investors have ready access to available information. And disagreement among investors about the implications of given information does not in itself imply market inefficiency unless there are investors who can consistently make better evaluations of available information than are implicit in market prices. But though transactions costs, information that is not freely available to all investors, and disagreement among investors about the implications of given information are not necessarily sources of market inefficiency, they are potential sources. And all three exist to some extent in real world markets. Measuring their effects on the process of price formation is, of course, the major goal of empirical work in this area.

III.

THE EVIDENCE

All the empirical research on the theory of efficient markets has been concerned with whether prices "fully reflect" particular subsets of available information. Historically, the empirical work evolved more or less as follows.
The initial studies were concerned with what we call weak form tests in which the information subset of interest is just past price (or return) histories. Most of the results here come from the random walk literature. When extensive tests seemed to support the efficiency hypothesis at this level, attention was turned to semi-strong form tests in which the concern is the speed of price adjustment to other obviously publicly available information (e.g., announcements of stock splits, annual reports, new security issues, etc.). Finally, strong form tests in which the concern is whether any investor or groups (e.g., managements of mutual funds) have monopolistic access to any information relevant for the formation of prices have recently appeared. We review the empirical research in more or less this historical sequence.
First, however, we should note that what we have called the efficient markets model in the discussions of earlier sections is the hypothesis that security prices at any point in time "fully reflect" all available information.
Though we shall argue that the model stands up rather well to the data, it is obviously an extreme null hypothesis. And, like any other extreme null hyposthesis, we do not expect it to be literally true. The categorization of the tests into weak, semi-strong, and strong form will serve the useful purpose of allowing us to pinpoint the level of information at which the hypothesis breaks down. And we shall contend that there is no important evidence against the hypothesis in the weak and semi-strong form tests (i.e., prices seem to efficiently adjust to obviously publicly available information), and only limited evidence against the hypothesis in the strong form tests (Le., monopolistic access to information about prices does not seem to be a prevalent phenomenon in the investment community).

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A. Weak Form Tests of the Efficient Markets Model

1. Random Walks and Fair Games: A Little Historical Background
As noted earlier, all of the empirical work on efficient markets can be considered within the context of the general expected return or "fair game" model, and much of the evidence bears directly on the special submartingale expected return model of (6). Indeed, in the early literature, discussions of the efficient markets model were phrased in terms of the even more special random walk model, though we shall argue that most of the early authors were in fact concerned with more general versions of the "fair game" model.
Some of the confusion in the early random walk writings is understandable.
Research on security prices did not begin with the development of a theory of price formation which was then subjected to empirical tests. Rather, the impetus for the development of a theory came from the accumulation of evidence in the middle 1950's and early 1960's that the behavior of common stock and other speculative prices could be well approximated by a random walk. Faced with the evidence, economists felt compelled to offer some rationalization. What resulted was a theory of efficient markets stated in terms of random walks, but usually implying some more general "fair game" model.
It was not until the work of Samuelson [38] and Mandelbrot [27] in 1965 and 1966 that the role of "fair game" expected return models in the theory of efficient markets and the relationships between these models and the theory of random walks were rigorously studied." And these papers came somewhat after the major empirical work on random walks. In the earlier work, "theoretical" discussions, though usually intuitively appealing, were always lacking in rigor and often either vague or ad hoc. In short, until the MandelbrotSamuelson models appeared, there existed a large body of empirical results in search of a rigorous theory.
Thus, though his contributions were ignored for sixty years, the first statement and test of the random walk model was that of Bachelier [3] in 1900.
But his "fundamental principle" for the behavior of prices was that speculation should be a "fair game"; in particular, the expected profits to the speculator should be zero. With the benefit of the modern theory of stochastic processes, we know now that the process implied by this fundamental principle is a martingale.
After Bachelier, research on the behavior of security prices lagged until the
6. Basing their analyses on futures contracts in commodity markets, Mandelbrot and Samuelson show that if the price of such a contract at time t is the expected value at t (given information
t) of the spot price at the termination of the contract, then the futures price will follow a martingale with respect to the information sequence {t}; that is, the expected price change from period to period will be zero, and the price changes will be a "fair game." If the equilibrium expected return is not assumed to be zero, our more general "fair game" model, summarized by (1), is obtained.
But though the Mandelbrot-Samuelson approach certainly illuminates the process of price formation in commodity markets, we have seen that "fair game" expected return models can be derived in much simpler fashion. In particular, (1) is just a formalization of the assumptions that the conditions of market equilibrium can be stated in terms of expected returns and that the information t is used in forming market prices at t.

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coming of the computer. In 1953 Kendall [21] examined the behavior of weekly changes in nineteen indices of British industrial share prices and in spot prices for cotton (New York) and wheat (Chicago). After extensive analysis of serial correlations, he suggests, in quite graphic terms:
The series looks like a wandering one, almost as if once a week the Demon of Chance drew a random number from a symetrical population of fixed dispersion and added it to the current price to determine the next week's price [21, p. 13].
Kendall's conclusion had in fact been suggested earlier by Working [47], though his suggestion lacked the force provided by Kendall's empirical results.
And the implications of the conclusion for stock market research and financial analysis were later underlined by Roberts [36].
But the suggestion by Kendall, Working, and Roberts that series of speculative prices may be well described by random walks was based on observation.
None of these authors attempted to provide much economic rationale for the hypothesis, and, indeed, Kendall felt that economists would generally reject it.
Osborne [33] suggested market conditions, similar to those assumed by
Bachelier, that would lead to a random walk. But in his model, independence of successive price changes derives from the assumption that the decisions of investors in an individual security are independent from transaction to transaction-which is little in the way of an economic model.
Whenever economists (prior to Mandelbrot and Samuelson) tried to provide economic justification for the random walk, their arguments usually implied a "fair game." For example, Alexander [8, p. 200] states:
If one were to start out with the assumption that a stock or commodity speculation is a "fair game" with equal expectation of gain or loss or, more accurately, with an expectation of zero gain, one would be well on the way to picturing the behavior of speculative prices as a random walk.
There is an awareness here that the "fair game" assumption is not sufficient to lead to a random walk, but Alexander never expands on the comment.
Similarly, Cootner [8, p. 232] states:
If any substantial group of buyers thought prices were too low, their buying would force up the prices. The reverse would be true for sellers. Except for appreciation due to earnings retention, the conditional expectation of tomorrow's price, given today's price, is today's price.
In such a world, the only price changes that would occur are those that result from new information. Since there is no reason to expect that information to be non-random in appearance, the period-to-period price changes of a stock should be random movements, statistically independent of one another.
Though somewhat imprecise, the last sentence of the first paragraph seems to point to a "fair game" model rather than a random walk," In this light, the second paragraph can be viewed as an attempt to describe environmental conditions that would reduce a "fair game" to a random walk. But the specification imposed on the information generating process is insufficient for this purpose; one would, for example, also have to say something about investor
7. The appropriate conditioning statement would be "Given the sequence of historical prices."

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tastes. Finally, lest I be accused of criticizing others too severely for ambiguity, lack of rigor and incorrect conclusions,
By contrast, the stock market trader has a much more practical criterion for judging what constitutes important dependence in successive price changes. For his purposes the random walk. model is valid as long as knowledge of the past behavior of the series of price changes cannot be used to increase expected gains. More specifically, the independence assumption is an adequate description of reality as long as the actual degree of dependence in the series of price changes is not sufficient to allow the past history of the series to be used to predict the future in a way which makes expected profits greater than they would be under a naive buy-and hold model
[10, p 35].

We know now, of course, that this last condition hardly requires a random walk. It will in fact be met by the submartingale model of (6).
But one should not be too hard on the theoretical efforts of the early empirical random walk literature. The arguments were usually appealing; where they fell short was in awareness of developments in the theory of stochastic processes. Moreover, we shall now see that most of the empirical evidence in the random walk literature can easily be interpreted as tests of more general expected return or "fair game" models,"
2. Tests of Market Efficiency in the Random Walk Literature
As discussed earlier, "fair game" models imply the "impossibility" of various sorts of trading systems. Some of the random walk literature has been concerned with testing the profitability of such systems. More of the literature has, however, been concerned with tests of serial covariances of returns. We shall now show that, like a random walk, the serial covariances of a "fair game" are zero, so that these tests are also relevant for the expected return models. If Xt is a "fair game," its unconditional expectation is zero and its serial covariance can be written in general form as:
E(XtH it)

= JXtE(Xt+ ..IXt)f(Xt)dxt,
"t

where f indicates a density function. But if Xt is a "fair game,"
E(Xt+ ../Xt) = 0. 9
8. Our brief historical review is meant only to provide perspective, and it is, of course, somewhat incomplete. For example, we have ignored the important contributions to the early random walk literature in studies of warrants and other options by Sprenkle, Kruizenga, Boness, and others.
Much of this early work on options is summarized in [8].
9. More generally, if the sequence {xt } is a fair game with respect to the information sequence
{q»t}, (I.e., E(it+ 11q»t) = 0 for all q»t); then x t is a fair game with respect to any q»'t that is a
0 for all q»'t). To show this, let q»t
(q»\, q»"t). Then, using subset of q»t (i.e., E(~+llq»'t)
Stieltjes integrals and the symbol F to denote cumulative distinction functions, the conditional expectation =

E(~+llq»;) =

fJ
4>t %t+ 1

Xt+l dF(x t+l' q»;',q»;)

=

=J[J
4>i'

x t+ 1dF(xt+ 11q»;'q»;') ]

"t+ 1

dF(q»~Iq»:).

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From this it follows that for all lags, the serial covariances between lagged values of a "fair game" variable are zero. Thus, observations of a "fair game" variable are linearly independent."
But the "fair game" model does not necessarily imply that the serial covariances of one-period returns are zero. In the weak form tests of this model the "fair game" variable is
Zj,t = rj,t - E(rj,t/rj,t-1' rj,t-2, ... ). (Cf. fn. 9)
(9)
But the covariance between, for example, rjt and rj,t+1 is
E( [rj,t+! - E(rj,t+1)] [rjt - E(rjt)])

=

f [rjt rjt

E(rjt)] [E(i-j,t+1Irjt) - E(i'j,t+d Jf(rjt)drjt,

and (9) does not imply that E(rj,t+1Irjt) = E(rj,t+1): In the "fair game" efficient markets model, the deviation of the return for t
1 from its conditional expectation is a "fair game" variable, but the conditional expectation itself can depend on the return observed for t."
In the random walk literature, this problem is not recognized, since it is assumed that the expected return (and indeed the entire distribution of returns) is stationary through time. In practice, this implies estimating serial covariances by taking cross products of deviations of observed returns from the overall sample mean return. It is somewhat fortuitous, then, that this procedure, which represents a rather gross approximation from the viewpoint of the general expected return efficient markets model, does not seem to greatly affect the results of the covariance tests, at least for common stocks.P

+

But the integral in brackets is just E(it+11