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A simple SSD-efficiency test

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Abstract

A linear programming SSD-efficiency test capable of identifying a dominating portfolio is proposed. It has \(T+n\) variables and at most \(2T+1\) constraints, whereas the existing SSD-efficiency tests are either unable to identify a dominating portfolio, or require solving a linear program with at least \(O(T^2+n)\) variables and/or constraints.

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Notes

  1. Throughout the paper, we do not count the bounds on decision variables (such as \(x_j\ge 0\)) as constraints, because the linear programming algorithms can efficiently deal with such bounds. This does not make any significant difference for our linear program, because it has at most \(T+n\) such bounds.

  2. A method for treatment of ties has been outlined already in [15, Section II-C]. However, no SSD-test for the case with ties has been explicitly formulated in that paper.

  3. The set of such indices may be an empty set. Throughout the paper, we will use the convention that the minimum over an empty set is equal to \(+\infty \).

  4. The columns AT, DP, and EP indicate whether the test allows ties in the return distribution, whether the results of the test can be used to identify a dominating portfolio, and whether the solution portfolio is SSD-efficient, correspondingly.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, Leicester, UK

    Bogdan Grechuk

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  1. Bogdan Grechuk
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Correspondence to Bogdan Grechuk.

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Grechuk, B. A simple SSD-efficiency test. Optim Lett 8, 2135–2143 (2014). https://doi.org/10.1007/s11590-013-0720-8

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  • DOI: https://doi.org/10.1007/s11590-013-0720-8

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