Minimum Variance Portfolio Composition

Roger G Clarke

Analytic Investors, Inc.

Harindra de Silva

Analytic Investors, Inc.

Steven Thorley

Marriott School of Management, BYU

June 1, 2010

Journal of Portfolio Management, Vol. 37, No. 2, pp. 31-45 (Winter 2011)

Empirical studies document that equity portfolios constructed to have the lowest possible risk have surprisingly high average returns. We derive an analytic solution for the long-only minimum variance portfolio under the assumption of a single-factor covariance matrix. The equation for optimal security weights has a simple and intuitive form that provides several insights on minimum variance portfolio composition. While high idiosyncratic risk can lead to a low security weight, high systematic risk takes the large majority of investable securities out of long-only solutions. The relatively small set of securities that remain have market betas below an analytically specified threshold beta. The math also shows that the ratio of portfolio beta to the threshold beta dictates the portion of ex-ante portfolio variance that is market-factor related. We verify and illustrate the portfolio mathematics using historical data on the U.S. equity market and explore how the single-factor analytic results compare to numerical optimization under a generalized covariance matrix. The analytic and empirical results of this study suggest that minimum variance portfolio performance is largely a function of the long-standing empirical critique of the traditional CAPM that low beta stocks have relatively high average returns.

Keywords: Portfolio Theory, Mean Variance Optimization, Market Model, Idiosyncratic Risk

JEL Classification: G11

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Date posted: February 10, 2010 ; Last revised: November 21, 2013

Suggested Citation

Clarke, Roger G and de Silva, Harindra and Thorley, Steven, Minimum Variance Portfolio Composition (June 1, 2010). Journal of Portfolio Management, Vol. 37, No. 2, pp. 31-45 (Winter 2011). Available at SSRN: https://ssrn.com/abstract=1549949 or http://dx.doi.org/10.2139/ssrn.1549949

Contact Information

Roger G Clarke
Analytic Investors, Inc. ( email )
700 So. Flower St., Suite 2400
Los Angeles, CA 90017
United States
Harindra De Silva
Analytic Investors, Inc. ( email )
555 West 5th Street
50th Floor
Los Angeles, CA 90013
United States
213-688-3015 (Phone)
213-688-8856 (Fax)
Steven Thorley (Contact Author)
Marriott School of Management, BYU ( email )
616 TNRB
Brigham Young University
Provo, UT 84602
United States
801-378-6065 (Phone)
801-378-5984 (Fax)
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