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Short sales in Log-robust portfolio management

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  • Kawas, Ban
  • Thiele, Aurélie

Abstract

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case portfolio wealth over that set in a one-period setting. The degree of the manager's aversion to ambiguity is incorporated through a single, intuitive parameter, which determines the size of the uncertainty set. The presence of short-selling requires the development of problem-specific techniques, because the optimization problem is not convex. In the case where assets are independent, we show that the robust optimization problem can be solved exactly as a series of linear programming problems; as a result, the approach remains tractable for large numbers of assets. We also provide insights into the structure of the optimal solution. In the case of correlated assets, we develop and test a heuristic where correlation is maintained only between assets invested in. In computational experiments, the proposed approach exhibits superior performance to that of the traditional robust approach.

Suggested Citation

  • Kawas, Ban & Thiele, Aurélie, 2011. "Short sales in Log-robust portfolio management," European Journal of Operational Research, Elsevier, vol. 215(3), pages 651-661, December.
  • Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:651-661
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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.
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    3. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    4. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    5. Lagos, Guido & Espinoza, Daniel & Moreno, Eduardo & Vielma, Juan Pablo, 2015. "Restricted risk measures and robust optimization," European Journal of Operational Research, Elsevier, vol. 241(3), pages 771-782.

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