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

Lo, Andrew W., and A. Craig MacKinlay, “Stock Market Prices do not Follow Random Walks:  Evidence from a Simple Specification Test,” The Review of Financial Studies, Vol 1 No 1 (1988), 41-66.

Most tests of the efficient market hypothesis have assumed that common stock returns follow a random walk.  However, some papers, including this one, have presented evidence against the random walk hypothesis.

Methods & Data:  Lo & Mackinlay use weekly return data from September 6, 1962 to December 26, 1985.  The test relies on the characteristic of a random walk whereby the variance between increments is linear in the interval between increments.  In other words, the variance of monthly observations should be about four times the variance of weekly observations.


  • The random walk hypothesis is rejected for weekly stock market returns.
  • The rejection is especially strong for small stocks, but is not entirely explained by infrequent trading or time-variation in volatility.
  • Weekly stock returns do not appear to be mean-reverting.
  • This does not mean the market is not efficient, but it does indicate that the random-walk model is not correct.