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Relative Robust Portfolio Optimization with benchmark regret

Author

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  • Gonçalo Simões
  • Mark McDonald
  • Stacy Williams
  • Daniel Fenn
  • Raphael Hauser
Abstract
We extend Relative Robust Portfolio Optimization models to allow portfolios to optimize their performance when considered relative to a set of benchmarks. We do this in a minimum volatility setting, where we model regret directly as the maximum difference between our volatility and that of a given benchmark. Portfolio managers are also given the option of computing regret as a proportion of the benchmark’s performance, which is more in line with market practice than other approaches suggested in the literature. Furthermore, we propose using regret as an extra constraint rather than as a brand new objective function, so practitioners can maintain their current framework. We also look into how such a triple optimization problem can be solved or at least approximated for a general class of objective functions and uncertainty and benchmark sets. Finally, we illustrate the benefits of this approach by examining its performance against other common methods in the literature in several equity markets.

Suggested Citation

  • Gonçalo Simões & Mark McDonald & Stacy Williams & Daniel Fenn & Raphael Hauser, 2018. "Relative Robust Portfolio Optimization with benchmark regret," Quantitative Finance, Taylor & Francis Journals, vol. 18(12), pages 1991-2003, December.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:12:p:1991-2003
    DOI: 10.1080/14697688.2018.1453940
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    Citations

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    Cited by:

    1. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    3. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    4. Meade, N. & Beasley, J.E. & Adcock, C.J., 2021. "Quantitative portfolio selection: Using density forecasting to find consistent portfolios," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1053-1067.
    5. Zongrun Wang & Tangtang He & Xiaohang Ren & Luu Duc Toan Huynh, 2024. "Robust portfolio strategies based on reference points for personal experience and upward pacesetters," Review of Quantitative Finance and Accounting, Springer, vol. 63(3), pages 863-887, October.
    6. Dmitry B. Rokhlin, 2021. "Relative utility bounds for empirically optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 437-462, June.
    7. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.

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