Random Walk Hypothesis
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 hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying 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 probabilities,” a great deal of research has been devoted to examining the efficiency of stock market price formation. 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 Madhavi Vinjamuri for preparing the manuscript. Research support from the Geewax-Terker Research Program in
Andrew W. Lo A. Craig MacKinlay University of Pennsylvania In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying 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 probabilities,” a great deal of research has been devoted to examining the efficiency of stock market price formation. 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 Madhavi Vinjamuri for preparing the manuscript. Research support from the Geewax-Terker Research Program in