Risk Parity, Maximum Diversification, and Minimum Variance: An Analytic Perspective

Posted: 1 Jan 2012 Last revised: 21 Nov 2013

See all articles by Roger G Clarke

Roger G Clarke

Ensign Peak Advisors

Harindra de Silva

Analytic Investors, Inc.

Steven Thorley

BYU Marriott School of Business

Date Written: June 1, 2012


Analytic solutions to Risk Parity, Maximum Diversification, and Minimum Variance portfolios provide useful perspectives about their construction and composition. Individual asset weights depend on both systematic and idiosyncratic risk in all three risk-based portfolios, but systematic risk eliminates many investable assets in long-only constrained Maximum Diversification and Minimum Variance portfolios. On the other hand, all investable assets are included in Risk Parity portfolios, and idiosyncratic risk has little impact on the magnitude of the weights. The algebraic forms for optimal asset weights derived in this paper yield generalizable properties of risk-based portfolios, in contrast to empirical simulations that employ a specific set of historical returns, proprietary risk models, and multiple constraints. The analytic solutions reveal precisely how the various kinds of predicted risk impact the relative magnitude of security weights under each type of risk-based portfolio construction.

Keywords: Minimum Variance, Maximum Diversification, Risk Parity, Risk-Based, Portfolio Construction

JEL Classification: G11

Suggested Citation

Clarke, Roger G and de Silva, Harindra and Thorley, Steven, Risk Parity, Maximum Diversification, and Minimum Variance: An Analytic Perspective (June 1, 2012). Journal of Portfolio Management, Vol. 39, No. 3, pp. 39-53 (Spring 2013).. Available at SSRN: https://ssrn.com/abstract=1977577 or http://dx.doi.org/10.2139/ssrn.1977577

Roger G Clarke

Ensign Peak Advisors ( email )

60 East South Temple
4th Floor
Salt Lake City, UT 84111
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)

BYU Marriott School of Business ( email )

616 TNRB
Brigham Young University
Provo, UT 84602
United States
801-378-6065 (Phone)
801-378-5984 (Fax)

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