Filter Rules and Stock-Market Trading

IN THE recent literature there has been a considerable interest in the theory of random walks in stock-market prices. The basic hypothesis of the theory is that successive price changes in individual securities are independent random variables. Independence implies, of course, that the past history of a series of changes cannot be used to predict future changes in any meaningful way. What constitutes a meaningful prediction depends, of course, on the purpose for which the data are being examined. For example, the investor wants to know whether the history of prices can be used to increase expected gains. In a random-walk market, with either zero or positive drift, no mechanical trading rule applied to an individual security would consistently outperform a policy of simply buying and holding the security. Thus, the investor who must choose between the random-walk model and a more complicated model which assumes the existence of an excessive degree of either persistence (positive dependence) or reaction (negative dependence) in successive price changes, should accept the theory of random walks as the better model if the actual degree of dependence cannot be used to produce greater expected profits than a buy-and-hold policy.' On the other hand, the statistician has different though equally pragmatic notions of what constitutes an important violation of the independence assumption of the random-walk model. He will