The Limits to Stock Return Predictability

We examine predictive return regressions from a new angle. We ask what observ-able univariate properties of returns tell us about the “predictive space ” that defines the predictive model: the triplet λ,R2x, ρ, where λ is the predictor’s persistence, R2x 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 of long-horizon returns slopes downwards we show that the predictive space can be quite tightly constrained. Data on real annual US stock returns suggest there is is very limited scope for even the best possible predictive regression to out-predict the univariate representation, particularly over long horizons