Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test

In this paper, 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 (1962-1985) and for all sub-periods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are largely due to the behavior of small stocks, they cannot be ascribed to either the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk cannot be interpreted as supporting a mean-reverting stationary model of asset prices, but is more consistent with a specific nonstationary alternative hypothesis.

[1]  H. Barger.  The General Theory of Employment, Interest and Money , 1936, Nature.

[2]  J. Keynes,et al.  The General Theory of Employment, Interest and Money. , 1936 .

[3]  J. Keynes.  GENERAL THEORY OF EMPLOYMENT INTEREST. , 1961 .

[4]  B. Mandlebrot.  The Variation of Certain Speculative Prices , 1963 .

[5]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[6]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[7]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[8]  Dennis E. Logue,et al.  Foundations of Finance. , 1977 .

[9]  Myron S. Scholes,et al.  Estimating betas from nonsynchronous data , 1977 .

[10]  J. Hausman.  Specification tests in econometrics , 1978 .

[11]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[12]  M. C. Jensen.  Some Anomalous Evidence Regarding Market Efficiency , 1978 .

[13]  Jean-Marie Dufour.  Rank Tests for Serial Dependence , 1981 .

[14]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[15]  R. Shiller,et al.  The Use of Volatility Measures in Assessing Market Efficiency , 1980 .

[16]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[17]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[18]  K. J. Cohen,et al.  Friction in the trading process and the estimation of systematic risk , 1983 .

[19]  R. Roll,et al.  A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market , 2008 .

[20]  Stephen J. Taylor.  Estimating the Variances of Autocorrelations Calculated from Financial Time Series , 1984 .

[21]  Jean-Marie Dufour,et al.  Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness , 1985 .

[22]  H. White,et al.  Nonlinear Regression with Dependent Observations , 1984 .

[23]  J. Poterba,et al.  The Persistence of Volatility and Stock Market Fluctuations , 1984 .

[24]  J. Harrison,et al.  Continuous Price Processes in Frictionless Markets Have Infinite Variation , 1984 .

[25]  H. White.  Asymptotic theory for econometricians , 1985 .

[26]  R. Shiller,et al.  Testing the Random Walk Hypothesis: Power Versus Frequency of Observation , 1985 .

[27]  Donald B. Keim,et al.  Predicting returns in the stock and bond markets , 1986 .

[28]  L. Summers.  Does the Stock Market Rationally Reflect Fundamental Values , 1986 .

[29]  K. French,et al.  Stock return variances: The arrival of information and the reaction of traders , 1986 .

[30]  John Y. Campbell,et al.  Are Output Fluctuations Transitory? , 1986 .

[31]  K. French,et al.  Expected stock returns and volatility , 1987 .

[32]  J. Huizinga.  An empirical investigation of the long-run behavior of real exchange rates , 1987 .

[33]  P. Phillips.  Regression Theory for Near-Integrated Time Series , 1988 .

[34]  A. Craig MacKinlay,et al.  The Size and Power of the Variance Ratio Test in Finite Samples: a Monte Carlo Investigation , 1988 .

[35]  John H. Cochrane,et al.  How Big Is the Random Walk in GNP? , 1988, Journal of Political Economy.

[36]  A. Lo,et al.  The Size and Power of the Variance Ratio Test in Finite Samples: a Monte Carlo Investigation , 1988 .

[37]  A. Craig MacKinlay,et al.  Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test , 1988 .

[38]  E. Fama,et al.  Permanent and Temporary Components of Stock Prices , 1988, Journal of Political Economy.