We develop a framework for estimating expected returns---a <i>predictive system</i>---that allows predictors to be imperfectly correlated with the conditional expected return. When predictors are imperfect, the estimated expected return depends on past returns in a manner that hinges on the correlation...

The standard regression approach to modeling return predictability seems too restrictive in one way but too lax in another. A predictive regression models expected returns as an exact linear function of a given set of predictors but does not exploit the likely economic property that innovations...

A pre-specified set of nine prominent U.S. equity return anomalies produce significant alphas in Canada, France, Germany, Japan, and the U.K. All of the anomalies are consistently significant across these five countries, whose developed stock markets afford the most extensive data. The anomalies...