Exuberance Embedded in the Process of Mean Reversion of Extreme Stock Returns

Abstract

This study finds evidence of mean reversion for the 228 highest and 136 lowest monthly rolling annual returns, identified by a rolling equality test over a 125-year period. The distribution of returns in processes of mean reversion further suggests the dominance of optimistic speculations over pessimistic selling. That is, probabilities for market exuberance—returns remaining positive after the stock market reaches a peak or reverting to positive after the stock market hits a low point—are higher than those for either market corrections (returns becoming negative after the market peaks) or market anxiety (returns remaining negative after the market troughs). The results also indicate that positive returns demonstrate higher persistency than negative returns.