Equal Risk Bounding Is Better than Risk Parity for Portfolio Selection

Journal of Global Optimization, DOI: 10.1007/s10898-016-0477-6.

Posted: 23 Mar 2014 Last revised: 27 Mar 2018

See all articles by Francesco Cesarone

Francesco Cesarone

University of Rome III - Department of Business Studies

Fabio Tardella

Faculty of Economics - Sapienza University of Rome

Date Written: October 24, 2016


Risk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification for portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. This alternative approach, called Equal Risk Bounding (ERB), requires the solution of a nonconvex quadratically constrained optimization problem. The ERB approach, while starting from different requirements, turns out to be strictly linked to the RP approach. Indeed, when short selling is allowed, we prove that an ERB portfolio is actually an RP portfolio with minimum variance. When short selling is not allowed, there is a unique RP portfolio and it contains all assets in the market. In this case, the ERB approach might lead to the RP portfolio or it might lead to portfolios with smaller variance that do not contain all assets, and where the risk contributions of each asset included in the portfolio is strictly smaller than in the RP portfolio. We define a new riskiness index for assets that allows to identify those assets that are more likely to be excluded from the ERB portfolio. With these tools we then provide an exact method for small size nonconvex ERB models and a very efficient and accurate heuristic for larger problems of this type. In the case of a common constant pairwise correlation among all assets, a closed form solution to the ERB model is obtained and used to perform a parametric analysis when varying the level of correlation. The practical advantages of the ERB approach over the RP strategy are illustrated with some numerical examples. Computational experience on real-world and on simulated data confirms accuracy and efficiency of our heuristic approach to the ERB model also in comparison with some state-of-the-art local and global optimization codes.

Keywords: Portfolio optimization, Risk diversification, Risk Parity, Non-convex quadratically constrained optimization, Nonlinear 0–1 optimization

JEL Classification: C6, G1

Suggested Citation

Cesarone, Francesco and Tardella, Fabio, Equal Risk Bounding Is Better than Risk Parity for Portfolio Selection (October 24, 2016). Journal of Global Optimization, DOI: 10.1007/s10898-016-0477-6., Available at SSRN: https://ssrn.com/abstract=2412559 or http://dx.doi.org/10.2139/ssrn.2412559

Francesco Cesarone (Contact Author)

University of Rome III - Department of Business Studies ( email )

Via Silvio D'Amico 77
Rome, Rome 00145

HOME PAGE: http://www.francescocesarone.com/

Fabio Tardella

Faculty of Economics - Sapienza University of Rome ( email )

Via del Castro Laurenziano, 9
Roma, Rome 00161

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