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Equal Risk Bounding is better than Risk Parity for portfolio selection

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  • Francesco Cesarone

    () (Università degli Studi Roma Tre)

  • Fabio Tardella

    () (Sapienza Università di Roma)

Abstract

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.

Suggested Citation

  • Francesco Cesarone & Fabio Tardella, 2017. "Equal Risk Bounding is better than Risk Parity for portfolio selection," Journal of Global Optimization, Springer, vol. 68(2), pages 439-461, June.
  • Handle: RePEc:spr:jglopt:v:68:y:2017:i:2:d:10.1007_s10898-016-0477-6
    DOI: 10.1007/s10898-016-0477-6
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    References listed on IDEAS

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    1. Elton, Edwin J & Gruber, Martin J & Padberg, Manfred W, 1976. "Simple Criteria for Optimal Portfolio Selection," Journal of Finance, American Finance Association, vol. 31(5), pages 1341-1357, December.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. repec:dau:papers:123456789/4688 is not listed on IDEAS
    4. Bertrand, Philippe & Lapointe, Vincent, 2015. "How performance of risk-based strategies is modified by socially responsible investment universe?," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 175-190.
    5. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    6. Aneja, Yash P & Chandra, Ramesh & Gunay, Erdal, 1989. " A Portfolio Approach to Estimating the Average Correlation Coefficient for the Constant Correlation Model," Journal of Finance, American Finance Association, vol. 44(5), pages 1435-1438, December.
    7. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    8. Edwin J. Elton & Martin J. Gruber & Jonathan Spitzer, 2006. "Improved Estimates of Correlation Coefficients and their Impact on Optimum Portfolios," European Financial Management, European Financial Management Association, vol. 12(3), pages 303-318, June.
    9. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "A new method for mean-variance portfolio optimization with cardinality constraints," Annals of Operations Research, Springer, vol. 205(1), pages 213-234, May.
    10. Elton, Edwin J & Gruber, Martin J, 1973. "Estimating the Dependence Structure of Share Prices-Implications for Portfolio Selection," Journal of Finance, American Finance Association, vol. 28(5), pages 1203-1232, December.
    11. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2015. "Linear vs. quadratic portfolio selection models with hard real-world constraints," Computational Management Science, Springer, vol. 12(3), pages 345-370, July.
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    Cited by:

    1. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2020. "An optimization–diversification approach to portfolio selection," Journal of Global Optimization, Springer, vol. 76(2), pages 245-265, February.
    2. Cesarone, Francesco & Mango, Fabiomassimo & Mottura, Carlo Domenico & Ricci, Jacopo Maria & Tardella, Fabio, 2020. "On the stability of portfolio selection models," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 210-234.
    3. Justo Puerto & Moises Rodr'iguez-Madrena & Andrea Scozzari, 2019. "Location and portfolio selection problems: A unified framework," Papers 1907.07101, arXiv.org.

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