On the Relevance of Variances and Correlations for Multifactor Investors

Investors believing in diversification across multiple orthogonal risk factors should prioritize factor variances over correlations when evaluating conditional portfolio risk. This study decomposes the variance of an equally weighted multifactor portfolio into two components, average variance (AV) across and average correlation (AC) between factors, and shows that only AV predicts future multifactor risk and return over the short run, therefore supporting the idea of short-term persistence in risk and a variance-in-mean relationship uncovered only when focusing on AV. The results show robustness in various instances and caution investors to bet on a dysfunctional variance-in-mean relationship by forming a volatility-managed multifactor portfolio.