The Behavior of Stock-Market Prices TORIo Eugene f fama The Journal of Business, Vol 38, No. 1. Jan, 1965), pp. 34-105 Stable url: http://links.jstor.org/sici?sici=0021-9398%28196501%2938903a1%03c34%03atbosp%3e2.0.c0%3b2-6 The Journal of Business is currently published by The University of Chicago Press Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://wwwjstor.org/journals/ucpress.html Each copy of any part of a jSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jStOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor. org http://www」]stor.or Thu Apr2709.03:012006
THE BEHAVIOR OF STOCK-MARKET PRICES* EUGENE F FAMA I. INTRODUCTION havior will tend to recur in the future JoR many years the following ques- Thus, if through careful analysis of price tion has been a source of continuing charts one develops an understanding controversy in both academic and of these patterns, this can be used to business circles: To what extent can the predict the future behavior of prices an past history of a common stocks price in this way increase expected gains be used to make meaningful predictions By contrast the theory of random concerning the future price of the stock? walks says that the future path of the price level of a security is no more pre- Answers to this question have been po, dictable than the path of a series of vided on the one hand by the varie chartist theories and on the other hand cumulated random numbers. In statisti by the theory of random walks al terms the theory says that successive Although there are many different price changes are independent, identical- chartist theories, they all make the same ly distributed random variables. Most basic assumption. That is, they all as- simply this implies that the series of price sume that the past behavior of a securi- changes has no memory, that is, the ty's price is rich in information concern- past cannot be used to predict the future ng its future behavior. History repeats in any meaningful way itself in that"patterns"of past price be-,. The purpose of this paper will be to This study has profited from the criticisms, underlying the random-walk model and ggestions, and technical assistance of many dif- then to test the model's empirical validi ratitude to professors William Alberts, lawrence ty. The main conclusion will be that the Fisher, Robert Graves, James Lorie, Merton Miller, data seem to present consistent and ate School of Business, University of Chicago. I wish strong support for the model. This im- pecially to thank Professors Miller and Roberts for plies, of course, that chart reading roviding not only continuous intellectual stimula- though perhaps an interesting pastime, ading the v is of no real value to the stock market in Many of the ideas in this t of the vestor. This is an extreme statement and work of Benoit Mandelbrot of the IBM Watson Re- the chart reader is certainly free to take ritten work of Dr Mandelbrot many exception We suggest, however, that nce the empirical evidence produced by Work on this paper was supported in part by this and other studies in support of the funds from a grant by the Ford Foundation to Graduate School of Business of the University of random-walk model is now so volumi Chicago, and in part by funds granted to the Center nous, the counterarguments of the chart time was provided by the 7094 Computation Center force if they are not equally well supp s for Research in Security, Prices of the School by the reader will be completely lacking University of Chica ed by empirical work f Assistant professor of finance, Graduate School I The Dow Theory of course, is the best known of Business, University of Chicage example of a chartist theory
BEHAVIOR OF STOCK-MARKET PRICES II. THEORY OF RANDOM WALKS one is trying to solve. For example, some IN STOCK PRICES one who is doing statistical work in the The theory of random walks in stock stock market may wish to decide whether actually involves two separate dependence in the series of successive hypotheses: (1)successive price changes price changes is sufficient to account for are independent, and (2)the price some particular property of the distribu- changes conform to some probability bon of price changes. If the actual de- distribution. We shall now examine each pendence in the series is not sufficient to of these hypotheses in detail account for the property in question, the the independence hypothesi quate description of reality. In statistical termsindependence means By contrast the stock market trader that the probability distribution for the has a much more practical criterion for price change during time period t is inde- judging what constitutes important de his purposes the random walk model is during previous time periods. That is, valid as long as knowledge of the past knowledge of the sequence of price changes behavior of the series of price changes leading up to time period t is of no help in assessing the probability distribution cannot be used to increase expected gains for the price change during time period More specifically, the independence as- Now in fact we can probably never reality as long as the actual degree of hope to find a time series that is charac- dependence in the series of price changes terize ed by perfect independence. Thus, is not sufficient to allow the past history strictly speaking, the random walk the- of the series to be used to predict the ory cannot be a completely accurate de- future in a way which makes expected scription of reality. For practical pur- profits greater than they would be under poses, however, we may be willing to a naive buy-and-hold model accept the independence assumption of Dependence that is important from the model as long as the dependence in the trader 's point of view need not be im the series of successive price changes rtant from a statistical point of view, not above some "minimum acceptable, and conversely dependence which is im- level portant for statistical purposes need not What constitutes a" minimum accept. be important for investment purposes. able"level of dependence depends, of For exanple, we may know that on alter course, on the particular problem that nate days the price of a security always increases by e and then decreases by e From a statistical point of view knowl Pr(!=xJ*L1,2t-g,.)=Pr(ac=x), edge of this dependence would be impor tant information since it tells us quite a where the term on the right of the equality sig the unconditional probability that the bit about the shape of the distribution during time t will take the value a, of price changes. For trading purposes, term on the left is the conditional pr the price change will take the value however, as long as e is very small, this on the knowledge that previous price perfect, negative, statistical dependence the values xt-1,at-2, etc. is unimportant. Any profits the trader
THE JOURNAL OF BUSINESS may hope to make from it would be with the random-walk hypothesis. In washed away in transactions costs order to justify this statement, however, In Section V of this paper we shall be it will be necessary now to discuss more concerned with testing independence fully the process of price determination from the point of view of both the statis- in an intrinsic-value-random-walk mar tician and the trader at this point, how- ket ever, the next logical step in the develop- Assume that at any point in time ment of a theory of random walks in there exists, at least implicitly, an intrin stock prices is to consider market situa- sic value for each security. The intrinsic tions and mechanisms that are consistent value of a given security depends on the with independence in successive price earnings prospects of the company which hanges. The procedure will be to con- in turn are related to economic and po- sider first the simplest situations and litical factors some of which are peculiar then to successively introduce complica- to this company and some of which affect other companies as well. s We stress. however, that actual mar 2. MARKET SITUATIONS CONSISTENT ket prices need not correspond to intrin- sic values. In a world of uncertaintSas55 Independence of successive price trinsic values are not known exac changes for a given security may simply Thus there can always be disagreemer reflect a price mechanism which is totally among individuals, and in this way ad litical events. That is, stock prices may Henceforth uncertainty e 3 unrelated to real-world economic and po- tual prices and intrinsic values of randomly generated noise, where by concerning intrinsic values will emer be just the accumulation of many bits noise in this case we mean psychological the market under the general heading of“ noise”in and other factors peculiar to different In addition. intrinsic values can them- the types selves change across time as a result of of bets"they are willing to place on either new information or trend. New in different companies Even random walk theorists, however, the success of a current research and de would find such a view of the market un- velopment project, a change in manage- appealing. Although some people may be ment, a tariff imposed on the industry's primarily motivated by whim, there are product by a foreign country, an increase many individuals and institutions that in industrial production or any other seem to base their actions in the market actual or anticipated change in a factor painstaking) of economic and politica/ which is likely to affect the companys circumstances. That is, there are many 3 We can think of intrinsic values in either of two ways. First, perhaps they just cur ities have conventions for e ting the worth of a security "intrinsic values"which depend on eco- by relating it to various factors which affect nomic and political factors that affect in- values may actually represe dividual companies lve from The existence of intrinsic values for some dynamic general equ vlew one individual securities is not inconsistent takes
BEHAVIOR OF STOCK-MARKET PRICES On the other hand, an anticipated however, the assumptions upon which long-term trend in the intrinsic value of the Bachelier-Osborne model is built are a given security can arise in the following rather extreme. There is no strong reason way. Suppose we have two unlevered to expect that each individuals estimates companies which are identical in all re- of intrinsic values will be independent spects except dividend policy. That is, of the estimates made by others (i.e. both companies have the same current noise may be generated in a dependent and anticipated investment opportuni- fashion). For example, certain individ ties, but they finance these opportunities uals or institutions may be opinion lead- in different ways. In particular, one com- ers in the market. That is, their actions pany pays out all of its current earnings may induce people to change their opin as dividends and finances new invest- ions concerning the prospects of a given ment by issuing new common shares. company. In addition there is no strong The other company, however, finances reason to expect successive bits of new new investment out of current earnings information to be generated independ- and pays dividends only when there is ently across time. For example, goo money left over. Since shares in the two news may tend to be followed more often a ompanies are subject to the same degree by good news than by bad news, and bad risk, we would expect their expected news may tend to be followed more often ates of returns to be the same. This will by bad news than by good news. Thus be the case, however, only if the shares there may be dependence in either the payout have a higher expected rate of generating new information, and price increase than do the shares of the may in turn lead to dependence in suc- igh-payout company. In this case the cessive price changes trend in the price level is just part of the Even in a situation where there are expected return to equity. Such a trend dependencies in either the information is not inconsistent with the random-walk or the noise generating process, however, it is still possible that there are offsetting pendence assumption of the random walk produce independence in price changes model was proposed first, in a rather for individual common stocks. For ex- much later but more explo] and then ample, let us assume that there are many vague fashion, by Bachelier itly by Os- sophisticated traders in the stock market borne[42]. The argument runs as follows: and that sophistication can take two If successive bits of new information forms: (1)some traders may be much arise independently across time, and if better at predicting the appearance of noise or uncertainty concerning intrinsic new information and estimating its ef values does not tend to follow any con- fects on intrinsic values than others sistent pattern, then successive price while (2)some may be much better at changes in a common stock will be inde- doing statistical analyses of price be pendent havior. Thus these two types of sophis- As with many other simple models, ticated traders can be roughly thought 4 A trend in the price level, of course, corresponds to a non-zero mean in the distribution of price 5 A lengthy and rigorous justification for these statements is given by Miller and Modigliani [40]