Random Walks: Reality or Myth - Comment
Michael C. Jensen
Harvard Business School; Social Science Electronic Publishing (SSEP), Inc.; National Bureau of Economic Research (NBER); European Corporate Governance Institute (ECGI)
Financial Analysts Journal, November-December 1967
A considerable amount of statistical investigation of security price movements by economists and statisticians indicates that successive changes in security prices are (for all practical purposes) independent random variables. That is, all the statistical evidence indicates that future security price changes cannot be predicted by using the past price series. This has become known as the theory of random walks. It implies that the trading rules and security selection procedures long advocated by "technical" analysts or "chartists", which are based solely on past price movements, will not be useful in aiding the investor to increase his returns. The technical analysts have responded to the evidence presented by the academicians by claiming their models and theories are not really captured by these statistical tests. Alexander (1961; 1964) and Fama and Blume (1966) have examined the returns earned by various "filter" rules for selecting securities which purportedly capture the essence of many technical theories. The evidence indicates these trading rules are not able to consistently earn returns superior to those of a simple buy and hold policy. Thus, the results of these studies also support the random walk hypothesis.
Robert Levy (1966; 1967) has recently tested a number of additional trading rules based on technical theories. Some of his results seem to be inconsistent with the theory of random walks. In particular Levy's article, "Random Walks: Reality or Myth" (1967) contains interesting results regarding the returns earned by several mechanical stock market trading rules in the five-year period October 1960 to October 1965.
Levy calculates the returns earned by a number of variations of his trading rules and finds these returns generally higher than the returns earned on a "random selection policy." Commenting on these results Levy states: "The evidence above conclusively proves that technical stock analysis could have produced greater-than-random profitability at less-than-random risk for the 1960-1965 period." On this basis he concludes that "...the theory of random walks has been refuted." Unfortunately, his results do not completely support these strongly worded statements. His results have not refuted the random walk hypothesis and indeed they are subject to criticism on a number of points. It is the purpose of this "Comment" to point out and clarify some of the issues not adequately treated by Levy.
Number of Pages in PDF File: 23Accepted Paper Series
Date posted: December 17, 2002
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