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Minimizing loss probability bounds for portfolio selection

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  • Gotoh, Jun-ya
  • Takeda, Akiko

Abstract

In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. These bounds are obtained under a nonparametric assumption of underlying return distribution by modifying the so-called generalization error bounds for the support vector machine, which has been developed in the field of statistical learning. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value-at-risk (VaR) or conditional value-at-risk (CVaR) while the denominator is any norm of portfolio vector. Depending on the parameter values in the model, the derived formulations can result in a nonconvex constrained optimization, and an algorithm for dealing with such a case is proposed. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR-based fractional programming model outperforms the empirical probability minimization.

Suggested Citation

  • Gotoh, Jun-ya & Takeda, Akiko, 2012. "Minimizing loss probability bounds for portfolio selection," European Journal of Operational Research, Elsevier, vol. 217(2), pages 371-380.
    • Handle: RePEc:eee:ejores:v:217:y:2012:i:2:p:371-380
    DOI: 10.1016/j.ejor.2011.09.012
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    References listed on IDEAS

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    Cited by:

    1. Jun-Ya Gotoh & Keita Shinozaki & Akiko Takeda, 2013. "Robust portfolio techniques for mitigating the fragility of CVaR minimization and generalization to coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 13(10), pages 1621-1635, October.
    2. Smimou, K., 2014. "International portfolio choice and political instability risk: A multi-objective approach," European Journal of Operational Research, Elsevier, vol. 234(2), pages 546-560.
    3. Wong, Man Hong & Zhang, Shuzhong, 2014. "On distributional robust probability functions and their computations," European Journal of Operational Research, Elsevier, vol. 233(1), pages 23-33.
    4. Dmitry B. Rokhlin, 2020. "Relative utility bounds for empirically optimal portfolios," Papers 2006.05204, arXiv.org.
    5. Takano, Yuichi & Gotoh, Jun-ya, 2023. "Dynamic portfolio selection with linear control policies for coherent risk minimization," Operations Research Perspectives, Elsevier, vol. 10(C).

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