Linear Factor Models and the Estimation of Expected Returns

Abstract:

This paper focuses on analyzing the properties of expected return estimators on individual assets implied by the linear factor models of asset pricing, i.e., the product beta and lambda. We provide the asymptotic properties of factor-model-based expected return estimators under the following set-ups: 1) when the underlying model is correct, 2) when some of the priced risk factors are omitted, and 3) when factors with small betas are present in the underlying model. Moreover, we analyze the role of traded, non-traded, and mimicking factors in the estimation of expected returns. We find that using factor-model-based risk premium estimates leads to precision gains of up to 31% when compared to the 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 cannot be corrected. Finally, inference about expected returns, unlike inference on factor prices, does not suffer from a small-beta bias. The more precise factor-model-based estimates of expected returns translate into significant improvements in out-of-sample performance of optimal portfolios.