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Technical Note—Ranking Distributions When Only Means and Variances Are Known

Author

Listed:
  • Alfred Müller

    (Department Mathematik, Universität Siegen, 57072 Siegen, Germany)

  • Marco Scarsini

    (Dipartimento di Economia e Finanza, Luiss University, 00197 Roma, Italy)

  • Ilia Tsetlin

    (INSEAD, Singapore, Singapore 138676)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

Consider a choice between two random variables, for which only means and variances are known. Is it possible to rank them by putting some constraints on risk preferences? We provide such a ranking by bounding how much marginal utility can change. Such bounds enable us to rank all distributions with given means and variances by first-order almost-stochastic dominance. We show how our results can be used to compare a risky project and a sure payoff and also provide a new connection between the Sharpe and Omega ratios from finance.

Suggested Citation

  • Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2022. "Technical Note—Ranking Distributions When Only Means and Variances Are Known," Operations Research, INFORMS, vol. 70(5), pages 2851-2859, September.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:5:p:2851-2859
    DOI: 10.1287/opre.2020.2072
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