Risk – Reward Representations of Expected Utility Theory

Abstract

For each individual with von Neumann and Morgernstern’s preferences and for each gamble that can take negative values yet has positive expected value we calculate separately the reservation values of the losses and of the gains of the gamble and denote those values by risk and reward, respectively. In this paper we show the connection between these numbers and the certainty equivalent of a gamble, explain how the (risk, reward) pair paints a richer picture about the risk and return characteristics of that gamble to that individual than the one obtained from the (risk premium, expected value) profile, and argue that the resulting risk measure is a more accurate measure of risk of loss than those that arise from strict considerations of first and second order stochastic dominance.

Keywords: Expected Utility Theory, Riskiness measures

JEL Classification: D81, G00, G22, G32