The Limits to Stock Return Predictability∗

We examine predictive return regressions from a new angle. We ask what observable univariate properties of returns tell us about the “predictive space” that defines the true predictive model: the triplet ¡ λ,R2 x, ρ ¢ , where λ is the predictor’s persistence, R2 x is the predictive R-squared, and ρ is the "Stambaugh Correlation" (between innovations in the predictive system). When returns are nearly white noise, and the variance ratio slopes downwards, the predictive space can be tightly constrained. Data on real annual US stock returns suggest limited scope for even the best possible predictive regression to out-predict the univariate representation, particularly over long horizons.