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Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test

  • Andrew W. Lo, A. Craig MacKinlay

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.

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Article provided by Society for Financial Studies in its journal Review of Financial Studies.

Volume (Year): 1 (1988)
Issue (Month): 1 ()
Pages: 41-66

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Handle: RePEc:oup:rfinst:v:1:y:1988:i:1:p:41-66
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  1. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
  2. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," NBER Working Papers 1462, National Bureau of Economic Research, Inc.
  3. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
  4. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  5. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  6. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
  7. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
  8. Pierre Perron & Robert J. Shiller, 1984. "Testing the Random Walk Hypothesis: Power Versus Frequency of Observation," Cowles Foundation Discussion Papers 732, Cowles Foundation for Research in Economics, Yale University.
  9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  10. Andrew W. Lo & Craig A. MacKinlay, . "A Simple Specification Test of the Random Walk Hypothesis," Rodney L. White Center for Financial Research Working Papers 13-87, Wharton School Rodney L. White Center for Financial Research.
  11. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November.
  12. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
  13. Donald B. Keim & Robert F. Stambaugh, . "Predicting Returns in the Stock and Bond Markets," Rodney L. White Center for Financial Research Working Papers 15-85, Wharton School Rodney L. White Center for Financial Research.
  14. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
  15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  16. Cohen, Kalman J. & Hawawini, Gabriel A. & Maier, Steven F. & Schwartz, Robert A. & Whitcomb, David K., 1983. "Friction in the trading process and the estimation of systematic risk," Journal of Financial Economics, Elsevier, vol. 12(2), pages 263-278, August.
  17. Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, vol. 57(3), pages 353-65, July.
  18. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  19. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  20. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
  21. Robert J. Shiller, 1980. "The Use of Volatility Measures in Assessing Market Efficiency," NBER Working Papers 0565, National Bureau of Economic Research, Inc.
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