Random Walks in Stock Market Prices FOR MANY YEARS economists, statisticians, and teach- ers of finance have been interested in developing and testing models of stock price behavior. One important model that has evolved from this research is the theory of random walks. This theory casts serious doubt on many other methods for describing and predicting stock price behavior methods that have considerable popularity outside the academic world.
For example, we shall see later that if the random walk theory is an accurate description of reality, then the various “technical” or “chartist” procedures for pre- dicting stock prices are completely without value. – In general the theory of random walks raises chal- lenging questions for anyone who has more than a passing interest in understanding the behavior of stock prices. Unfortunately, however, most discussions of the theory have appeared in technical academic journals and in a form which the non-mathematician would usually find incomprehensible.
This article describes, briefly and simply, the theory of random walks and some of the important issues it raises concerning the work of market analysts. To preserve brevity some aspects of the theory and its implications are omitted. More complete (and also more technical) discussions of the theory of random walks are available elsewhere; hopefully the introduction provided here will encourage the reader to examine one of the more rigorous and lengthy works listed at the end of this article. Common Techniques for Predicting Stock Market Prices
In order to put the theory of random walks into perspective we first discuss, in brief and general terms, the two approaches to predicting stock prices that are commonly espoused by market professionals. These are ( 1 ) “chartist” or “technical” theories and (2) the theory of fundamental or intrinsic value analysis. The basic assumption of all the chartist or technical theories is that history tends to repeat itself, i. e. , past patterns of price behavior in individual securities will tend to recur in the future.
Thus the way to predict stock prices (and, of course, increase one’s potential Eugene F. Fama is Assistant Professor of Finance, Graduate School of Business, The University of Chicago. The author is indebted to his colleagues William Alberts, David Green, Merton Miller, and Harry Roberts for their helpful comments and criticisms. This article has been reprinted as paper No. 16 in the current series of Selected Papers of the Graduate School of Business, The University of Chicago. SEPTEMBER-OCTOBER by Elugene F. Fama ains) is to develop a familiarity with past patterns of price behavior in order to recognize situations of likely recurrence. Essentially, then, chartist techniques attempt to use knowledge of the past behavior of a price series to predict the probable future behavior of the series. A statistician would characterize such techniques as as- suming that successive price changes in individual securities are dependent. That is, the various chartist theories assume that the sequence of price changes prior to any given day is important in predicting the price change for that day. The techniques of the chartist have always been sur- rounded by a certain degree of mysticism, however, and as a result most market professionals have found them suspect. Thus it is probably safe to say that the pure chartist is relatively rare among stock market analysts. Rather the typical analyst adheres to a technique known as fundamental analysis or the intrinsic value method. The assumption of the fundamental analysis approach is that at any point in time an individual security has an intrinsic value (or in the terms of the economist, an equilibrium price) which depends on the earning poten- tial of the security.
The earning potential of the security depends in turn on such fundamental factors as quality of management, outlook for the industry and the econ- omy, etc. Through a careful study of these fundamental factors the analyst should, in principle, be able to determine whether the actual price of a security is above or below its intrinsic value. If actual prices tend to move toward intrinsic values, then attempting to determine the in- trinsic value of a security is equivalent to making a pre- diction of its future price; and this is the essence of the predictive procedure implicit in fundamental analysis.
The Theory of Random Walks Chartist theories and the theory of fundamental analysis are really the province of the market profes- sional and to a large extent teachers of finance. His- torically, however, there has been a large body of academic people, primarily economists and statisticians, who adhere to a radically different approach to market analysis-the theory of random walks in stock market prices. The remainder of this article will be devoted to a discussion of this theory and its major implications. *Probably the best known example of the chartist ap- proach to predicting stock prices is the Dow Theory. 1965 55