Maximal predictability under long-term mean reversion

I analyse the relationship between two stylized empirical facts for stock returns: Unconditional long-term mean reversion and predictability by variables such as the dividend-price ratio or the short-term interest rate. In particular, I show that if one imposes that returns satisfy long-term mean reversion, this implies an upper bound on the predictive regression R-square. If a predictive regression is intended as a motivational building block for theoretical modelling, and the R-square bound is violated, one should recognize that the implied returns process violate long-term mean reversion. Empirical results show that the proposed bound is binding for several leading predictors.