The Multifactor Risk-Return Tradeoff

Abstract

The multifactor risk-return tradeoff (MF-RRT) is severely understudied relative to the market. In contrast to mixed evidence for the market, we find that the MF-RRT is strongly positive when appropriately accounting for factor covariances. Our multifactor risk model (i) shows that covariances contribute more to variation in factor returns than variances and (ii) performs at least as well in predicting multiple factors as benchmark models that are specifically designed to predict a single factor, both in-and out-of-sample. Consistent with a positive MF-RRT, conditional multifactor alphas for a large set of anomalies are indistinguishable from unconditional alphas. Our results are largely overlooked in recent literature on factor return predictability and volatility-timing and important for practitioners that rely on conditional moments for their asset allocation.

Keywords: Factor Models, Unconditional versus Conditional Tests, Multifactor Return Predictability, Variance and Covariance Risk