Stock market Prices Do Not Follow random Walks Evidence from a simple Specification Test Andrew W. lo Craig MacKinlay University of Pennsylvania In tbis article we test the random walk bypotbesis ance estimators derived from data sampled at dif ferent frequencies. Tbe random walk model is strongly rejected forthe entire sample period (1962- 1985)and for all subperiods for a variety ofaggre- gate returns indexes and size-sorted portfolios. largely to ior of small stocks, tbey cannot be attributed con pletely to tbe effects of infrequent trading or time- ying volatilities. Moreover, tbe rejection of tbe random walk for weekly returns does not support a mean-reverting model of asset prices ince Keynes's(1936)now famous pronouncement that most investors' decisions" can only be taken as a result of animal spirits--of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of benefits multiplied by quantitative proba bilities, 'a great deal of research has been devoted xamining the efficiency of stock market price forma tion. In Fama's(1970)survey, the vast majority of those studies were unable to reject the" efficient markets This paper has benefited considerably from the suggestions of the editor Michae and the referee. We thank Cliff Ball, Don Keim, Whitney K Newe rsity, Ohio State University, Princeton University, Stanford UCLA ya havi Vinjamuri for preparing the manu Grant No. SES-8520054), and the u gratefully acknowledged. Any errors are of course our own. Address reprint quests to Andrew Lo, Department of Finance, Wharton School, University of Pennsylvania, Philadelphia, PA 19104 al Studies 1988 ber 1, pp. 41-66. c 1988 The Revi nancial Studies00219398/88/5904013$150 41