Asymmetric mean reversion of stock returns

This study investigates asymmetric mean reversion in the real returns of large- and small-cap US stocks for one- to ten-year periods. The return distributions are estimated with 1,000 random block bootstraps of 240-month returns from 1926-2017. Large-cap stock returns show significant asymmetric mean reversion in all periods, although they have symmetric mean reversion in only five of ten periods. Returns in nine periods are significantly negatively related to previous returns in multiple periods and asymmetric mean reversion produces higher adjusted R-squares than symmetric mean reversion for eight periods. Small-cap stock returns over all periods have significant negative relationships with previous returns in all periods. Asymmetric mean reversion provides greater explanatory power than symmetric mean reversion for nine periods. The highest adjusted R-squares of asymmetric mean reversion in small-cap stock returns for different periods range between 7.35% and 30.25%, higher than the range of 0.79% to 26.29% for symmetric mean reversions.