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Combining factors in a multi-factor portfolio using forecast risk management can add substantially to returns. Backtesting showed such a strategy over 54 years earned annualized returns of 10.79%, vs. 7.77% for a similar non-risk-managed portfolio.


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.

About the Author(s)

Roger G. Clarke

Roger Clarke is chairman of the board of Analytic Investors, Inc., an investment management firm, and serves as president of Ensign Peak Advisors, Inc. He is currently on the editorial board of the Journal of Portfolio Management and the Journal of Investment Management and previously served on the editorial board of the Financial Analysts Journal. Dr. Clarke has authored numerous articles and papers relating to quantitative investment management and is the recipient of three Graham and Dodd Scrolls from CFA Institute. He holds a BA degree in physics and an MBA degree from Brigham Young University, and an MS degree in economics and a PhD degree in finance from Stanford University.

Harindra de Silva PhD, CFA
Image of Steven Thorley
Steven Thorley CFA

Steven Thorley, CFA, is the H. Taylor Peery Professor of Finance at the BYU Marriott School of Business. He received his PhD in financial economics from the University of Washington and holds numerous awards for academic excellence, including the Marriott School Outstanding Faculty Award. While on academic leaves from BYU, Professor Thorley has served as the interim Research Director for Analytic Investors, a factor-based fund based in Los Angeles, and for Ensign Peak Advisors in Salt Lake City. His journal publications have been presented at academic and professional seminars around the world and cited in the Wall Street Journal and other financial periodicals.

Professor Thorley is an associate editor of the Financial Analysts Journal. He teaches investments in the MBA program at the Marriott School and acts in a consulting capacity for Analytic Investors. He is currently on the investment committees for Intermountain Healthcare, Deseret Mutual Benefit Administrators, and Brigham Young University.