Efficient Algorithms for Computing Risk Parity Portfolio Weights

Journal of Investing, vol. 21, no. 3, Fall 2012, pp. 150-163.

Posted: 26 Jul 2012 Last revised: 30 Dec 2016

Denis B. Chaves

The Vanguard Group, Inc.

Jason C. Hsu

Rayliant Global Advisors; Research Affiliates, LLC; University of California, Los Angeles - Anderson School of Business

Feifei Li

Research Affiliates, LLC

Omid Shakernia

Research Affiliates, LLC

Date Written: July 1, 2012

Abstract

This article presents two simple algorithms to calculate the portfolio weights for a risk parity strategy, where asset class covariance information is appropriately taken into consideration to achieve “true” equal risk contribution. Previous implementations of risk parity either used a naïve 1/vol solution, which ignores asset class correlations, or computed “true” risk parity weights using relatively complicated optimizations to solve a quadratic minimization program with nonlinear constraints. The two iterative algorithms presented require only simple computations and quickly converge to the optimal solution. In addition to the technical contribution, the authors compute the parity in portfolio “risk allocation” using the Gini coefficient, and confirm that portfolio strategies with parity in “asset class allocation” can actually have high concentration in its “risk allocation.”

Keywords: risk parity, asset allocation, portfolio management

Suggested Citation

Chaves, Denis B. and Hsu, Jason C. and Li, Feifei and Shakernia, Omid, Efficient Algorithms for Computing Risk Parity Portfolio Weights (July 1, 2012). Journal of Investing, vol. 21, no. 3, Fall 2012, pp. 150-163.. Available at SSRN: https://ssrn.com/abstract=2117303 or http://dx.doi.org/10.2139/ssrn.2117303

Denis Biangolino Chaves (Contact Author)

The Vanguard Group, Inc. ( email )

100 Vanguard Blvd
Malvern, PA 19355
United States

Jason C. Hsu

Rayliant Global Advisors ( email )

Hong Kong

Research Affiliates, LLC ( email )

620 Newport Center Dr
Suite 900
Newport Beach, CA 92660
United States

HOME PAGE: http://www.jasonhsu.org

University of California, Los Angeles - Anderson School of Business

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

Feifei Li

Research Affiliates, LLC ( email )

620 Newport Center Dr
Ste 900
Newport Beach, CA 92660
United States
949-325-8753 (Phone)
949-325-8953 (Fax)

HOME PAGE: http://researchaffiliates.com/index.htm

Omid Shakernia

Research Affiliates, LLC ( email )

620 Newport Center Dr
Suite 900
Newport Beach, CA 92660
United States

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