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The Journal of Portfolio Management

The Journal of Portfolio Management

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Article

Minimum-Variance Portfolio Composition

Roger Clarke, Harindra de Silva and Steven Thorley
The Journal of Portfolio Management Winter 2011, 37 (2) 31-45; DOI: https://doi.org/10.3905/jpm.2011.37.2.031
Roger Clarke
is the chairman of Analytic Investors, LLC, in Los Angeles, CA. rclarke@aninvestor.com
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  • For correspondence: rclarke@aninvestor.com
Harindra de Silva
is the president of Analytic Investors, LLC, in Los Angeles, CA. hdesilva@aninvestor.com
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  • For correspondence: hdesilva@aninvestor.com
Steven Thorley
is the H. Taylor Peery professor of finance at Brigham Young University in Provo, UT. steven.thorley@byu.edu
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  • For correspondence: steven.thorley@byu.edu
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Abstract

Empirical studies document that equity portfolios constructed to have the lowest possible risk have surprisingly high average returns. Clarke, de Silva, andThorley 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 remains has market betas below an analytically specified threshold beta. The ratio of portfolio beta to threshold beta dictates the portion of ex ante portfolio variance that is market-factor related. The authors 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.

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The Journal of Portfolio Management: 37 (2)
The Journal of Portfolio Management
Vol. 37, Issue 2
Winter 2011
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Minimum-Variance Portfolio Composition
Roger Clarke, Harindra de Silva, Steven Thorley
The Journal of Portfolio Management Jan 2011, 37 (2) 31-45; DOI: 10.3905/jpm.2011.37.2.031

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Minimum-Variance Portfolio Composition
Roger Clarke, Harindra de Silva, Steven Thorley
The Journal of Portfolio Management Jan 2011, 37 (2) 31-45; DOI: 10.3905/jpm.2011.37.2.031
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  • Article
    • Abstract
    • PORTFOLIO STATISTICS AND COVARIANCE MATRIX ESTIMATION
    • MINIMUM-VARIANCE PORTFOLIO SECURITY WEIGHTS FOR THE SINGLE-INDEX MODEL
    • CROSS-SECTIONAL EXAMINATION OF SECURITY RISK AND WEIGHTS
    • TEMPORAL DYNAMICS AND DECOMPOSITION OF EX ANTE PORTFOLIO RISK
    • SUMMARY AND CONCLUSIONS
    • Appendix
    • ENDNOTES
    • REFERENCES
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