# Mean Reversion in Stock Prices?

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:

$r_{k,t+K} = \alpha_K + \beta_Kr_{K,t} + \varepsilon_{K,t+K}$

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.

Findings:

• 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.