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.
Müller, Alfred; Scarsini, Marco; Tsetlin, Ilia; Winkler, Robert L.. (2022). Tehnical Note - Ranking Distributions When Only Means and Variances Are Known. OPERATIONS RESEARCH, (ISSN: 0030-364X), 70:5, 2851-2859. Doi: 10.1287/opre.2020.2072.
Tehnical Note - Ranking Distributions When Only Means and Variances Are Known
Marco Scarsini;
2022
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.
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