Kim, Myung Jig, Charles R. Nelson, and Richard Startz, “Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence,” The Review of Economic Studies, Vol 58, No 3 (1991), 515-528.
Background: In the 1970s and -80s, stock returns were thought to follow a random walk. Researchers in the late 1980s began to question this view, and used a variance ratio method to show that autocorrelation did exist in stock returns. Define the “variance ratio” as the return over K periods divided by the product of the return over one period and K. If returns follow a random walk, this ratio must equal 1.
However, this assumption is not borne out by the data. The variance ratio is higher than 1 for periods shorter than a year (positive autocorrelation) and is less than one for periods longer than a year (negative autocorrelation). A common interpretation of this negative autocorrelation over longer periods is to say that returns are mean-reverting.
Fama & French’s approach is to regress the returns from period t to t+k on the return from period t-1 to t:
In this model, a negative beta indicates mean-reversion, and a zero beta, a random walk. This model is also better suited to predicting future returns
Purpose: This paper re-examines the data and finds no evidence of mean reversion after WWII. Stock returns in the post-war period are actually mean-averting, meaning that disturbances are too persistent to support a mean-reversion theory. Furthermore, indicators of post-WWII mean-aversion are as statistically significant as indicators of mean-reversion for the whole 1926-1986 period. The comparison of pre- and post-war returns do not support the random-walk hypothesis, but point to a fundamental change occurring at the end of the war.
Method: Use statistical methods that do not assume returns are normally distributed.
- Returns are only mean-reverting pre-WWII.
- Post-war returns are, if anything, mean-averting.
- The change may have accompanied the resolution of uncertainties surrounding the duration of the Great Depression, the outcome of WWII, and fears of another post-war depression.