Risk Management and the Optimal Combination of Equity Market Factors

Managing the intertemporal risk of optimally constructed multifactor portfolios adds to performance. The increases in Sharpe ratios are in addition to the utility that investors gain from controlling how much active risk they are exposed to over time. We derive a simple closed-form formula for security weights in optimal multifactor portfolios with an active-risk target. We test the risk control of five well-known factors—value, momentum, small size, low beta, and profitability—and the optimal multifactor portfolio. Our empirical research was carried out on the large-capitalization US equity market for 1966 through 2019. We conclude that for the equity market, more active factors are better than fewer if each subportfolio is “pure” as to factor, anchored to the benchmark, and combined on the basis of forecastable risks. Our portfolio construction methodology allows for transparent performance attribution and replication of the process in other markets and time periods.Disclosure: The authors report no conflicts of interest. Editor’s Note This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the authors thanked the two anonymous reviewers in their acknowledgments.Submitted 18 November 2019Accepted 9 April 2020 by Stephen J. Brown.