Linear Factor Models and the Estimation of Expected Returns

This paper analyzes the properties of expected return estimators on individual assets implied by the linear factor models of asset pricing, i.e., the product of beta and lambda. We provide the asymptotic properties of factor-model-based expected return estimators, which yield the standard errors for risk premium estimators for individual assets. We show that using factor-model-based risk premium estimates leads to sizable precision gains compared to using historical averages. In the presence of omitted factors, adding an alpha to the model captures mispricing only in case of traded factors, otherwise the bias caused by misspecification is not corrected. Finally, inference
about expected returns does not suffer from a small-beta bias when factors are traded. The more precise factor-model-based estimates of expected returns translate into sizable improvements in out-of-sample performance of optimal portfolios.

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