Working Paper: NBER ID: w13804
Authors: Lubos Pastor; Robert F. Stambaugh
Abstract: We develop a framework for estimating expected returns—a predictive system—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 between unexpected returns and innovations in expected returns. We find empirically that prior beliefs about this correlation, which is most likely negative, substantially affect estimates of expected returns as well as various inferences about predictability, including assessments of a predictor's usefulness. Compared to standard predictive regressions, predictive systems deliver different and more precise estimates of expected returns.
Keywords: predictive systems; expected returns; imperfect predictors
JEL Codes: G1; G11; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| unexpected returns (u) (Y30) | innovations in expected returns (w) (G19) |
| innovations in expected returns (w) (G19) | unexpected returns (u) (Y30) |
| predictors (C29) | expected returns (G17) |
| lagged returns (G17) | expected returns (G17) |
| prior beliefs about uw (D80) | estimates of expected returns (G17) |
| predictors and historical returns (G17) | expected returns (G17) |