Markov Chains and Regression toward the Mean.

Using the theory of stationary Markov chains, the authors uncover a previously unknown property of the behavior of betas. Specifically, if the cross-sectional distribution of betas is stationary over time, then the set of firms that remain in an arbitrarily chosen beta interval between one period and the next will not regress toward the mean. This surprising result occurs in spite of the well-known fact that the set of all the firms in the interval will exhibit the regression tendency. The authors' empirical tests indicate that betas behave in remarkable accordance with this prediction. Copyright 1991 by MIT Press.