Linear Factor Models and the Estimation of Expected Returns

Abstract

Linear factor models of asset pricing imply a linear relationship between expected returns of assets and exposures to one or more sources of risk. We show that exploiting this linear relationship leads to statistical gains of up to 31% in variances when estimating expected returns on individual assets over historical averages. When the factors are weakly correlated with assets, i.e. β's are small, and the interest is in estimating expected excess returns, that is risk premiums, on individual assets rather than the prices of risk, the Generalized Method of Moment estimators of risk premiums does lead to reliable inference, i.e. limiting variances suffer from neither lack of identification nor unboundedness. If the factor model is misspecified in the sense of an omitted factor, we show that factor model based estimates may be inconsistent. However, we show that adding an alpha to the model capturing mispricing only leads to consistent estimators in case of traded factors. Moreover, our simulation experiment documents that using the more precise estimates of expected returns based on factor models rather than the historical averages translates into significant improvements in the out-of-sample performances of the optimal portfolios.