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Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions

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  • George C. Philippatos

    (Pennsylvania State University)

  • Nicolas Gressis

    (Indiana University)

Abstract

Conditions of equivalence are established among the following portfolio selection criteria: (1) Mean-Variance (E-V), (2) Second-Degree Stochastic Dominance (SSD), and (3) Mean-Entropy (E-H), for portfolios whose returns are characterized by-Uniform, Normal, and Lognormal probability distributions. We also assume that all portfolios derive from the same family of distributions and consider only the cases where the cumulative density functions intersect. In comparing the three selection criteria, under the three posited probability distributions, we utilize a combination of mathematical and graphical analyses. It is concluded that the three efficiency criteria are equivalent for uniformly and normally distributed portfolio returns. For lognormally distributed portfolio returns, the SSD criterion is optimal. Its efficiency, however, is sufficient but not necessary to establish efficiency for E-V and E-H. On the other hand, given the empirical similarities between E-V and SSD derived portfolios, and the close correspondence between the E-V and E-H criteria, the potential use of E-H becomes more appealing because of its distribution free nature.

Suggested Citation

  • George C. Philippatos & Nicolas Gressis, 1975. "Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions," Management Science, INFORMS, vol. 21(6), pages 617-625, February.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:6:p:617-625
    DOI: 10.1287/mnsc.21.6.617
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    Cited by:

    1. Daniel Chiew & Judy Qiu & Sirimon Treepongkaruna & Jiping Yang & Chenxiao Shi, 2019. "The predictive ability of the expected utility-entropy based fund rating approach: A comparison investigation with Morningstar ratings in US," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-22, April.
    2. Colin Beardsley & John R. O'Brien, 2005. "The Financial Services Reform Act 2001: Impact on Systemic risk in Australia," ICMA Centre Discussion Papers in Finance icma-dp2005-12, Henley Business School, University of Reading.
    3. Qing Ding & Lingxiu Dong & Panos Kouvelis, 2007. "On the Integration of Production and Financial Hedging Decisions in Global Markets," Operations Research, INFORMS, vol. 55(3), pages 470-489, June.
    4. Lindner, Thomas & Puck, Jonas, 2024. "Information distance: Conceptual development and empirical tests of a novel measure of cross-national distance," Journal of International Management, Elsevier, vol. 30(2).
    5. Berman, Oded & Sanajian, Nima & Wang, Jiamin, 2017. "Location choice and risk attitude of a decision maker," Omega, Elsevier, vol. 66(PA), pages 170-181.

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