Variance as a proxy for risk: the case of the binomial distribution

SUMMARY In a recent review of stochastic dominance, Levy has observed that there are (to date) three cases in which a meanpreserving increase in variance leads to the unequivocal reduction in the welfare of all risk averse individuals. These cases are defined by expected utility functions which have a quadratic von Neumann-Morgenstem utility function, a normal distribution or a log-normal distribution. This paper adds a fourth case to Levy's list of three by employing Sproule's mean-preserving transformation of the Bernoulli distribution and the Fu and Sproule generalization of the binomial distribution.