Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test Andrew W.Lo A.Craig MacKinlay University of Pennsylvania In this article we test the random walk bypotbesis for weekly stock market returns by comparing vari- ance estimators derived from data sampled at dif- ferent frequencies.The random walk model is strongly rejected for the entire sample period (1962- 1985)and for all subperiods for a variety of aggre- gate returns indexes and size-sorted portfolios. Altbougb the rejections are due largely to the bebav- ior of small stocks,they cannot be attributed com- pletely to the effects of infrequent trading or time- varying volatilities.Moreover,the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices. Since 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 to examining 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 Michael Gibbons and the referee.We thank Cliff Ball,Don Keim,Whitney K.Newey Peter Phillips,Jim Poterba,Krishna Ramaswamy,Bill Schwert,and seminar participants at MIT,the NBER-FMME Program Meeting(November 1986), Northwestern University,Ohio State University,Princeton University,Stanford University,UCLA,University of Chicago,University of Michigan,University of Pennsylvania,University of Western Ontario,and Yale University for helpful comments.We are grateful to Stephanie Hogue,Elizabeth Schmidt,and Mad- havi Vinjamuri for preparing the manuscript.Research support from the Gee- wax Terker Research Program in Investments,the National Science Foundation (Grant No.SES-8520054),and the University of Pennsylvania Research Fund is gratefully acknowledged.Any errors are of course our own.Address reprint requests to Andrew Lo,Department of Finance,Wharton School,University of Pennsylvania.Philadelphia,PA 19104. Tbe Review of Financial Studies 1988,Volume 1,number 1,pp.41-66. @1988 The Review of Financial Studies 0021-9398/88/5904-013 $1.50 41