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Long-only equal risk contribution portfolios for CVaR under discrete distributions

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  • Helmut Mausser
  • Oleksandr Romanko

Abstract

Portfolios in which all assets contribute equally to the conditional value-at-risk (CVaR) represent an interesting variation of the popular risk parity investment strategy. This paper considers the use of convex optimization to find long-only equal risk contribution (ERC) portfolios for CVaR given a set of equally likely scenarios of asset returns. We provide second-order conic and non-linear formulations of the problem, which yields an ERC portfolio when CVaR is both positive and differentiable at the optimal solution. We identify sufficient conditions for differentiability and develop a heuristic that obtains an approximate ERC portfolio when the conditions are not satisfied. Computational tests show that the approach performs well compared to non-convex formulations that have been proposed in the literature.

Suggested Citation

  • Helmut Mausser & Oleksandr Romanko, 2018. "Long-only equal risk contribution portfolios for CVaR under discrete distributions," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1927-1945, November.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:11:p:1927-1945
    DOI: 10.1080/14697688.2018.1434317
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    Cited by:

    1. Kim, Hyuksoo & Kim, Saejoon, 2022. "Managing downside risk of low-risk anomaly portfolios," Finance Research Letters, Elsevier, vol. 46(PB).
    2. M. D. Braga & C. R. Nava & M. G. Zoia, 2023. "Kurtosis-based risk parity: methodology and portfolio effects," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 453-469, March.
    3. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    4. da Costa, B. Freitas Paulo & Pesenti, Silvana M. & Targino, Rodrigo S., 2023. "Risk budgeting portfolios from simulations," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1040-1056.
    5. Timo Dimitriadis & Yannick Hoga, 2023. "Regressions under Adverse Conditions," Papers 2311.13327, arXiv.org, revised Jul 2024.
    6. Gilles Boevi Koumou, 2023. "Risk budgeting using a generalized diversity index," Journal of Asset Management, Palgrave Macmillan, vol. 24(6), pages 443-458, October.
    7. Giorgio Costa & Roy Kwon, 2020. "A robust framework for risk parity portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(5), pages 447-466, September.
    8. M. Bayat & F. Hooshmand & S. A. MirHassani, 2024. "Scenario-based stochastic model and efficient cross-entropy algorithm for the risk-budgeting problem," Annals of Operations Research, Springer, vol. 341(2), pages 731-755, October.

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