The Markowitz Utility Function and Some Experimental Evidence for Small Speculative Risks

Abstract

In recent article in this journal Hershey and Schoemaker [4] present some experimental evidence on choice within the domain of losses' and offer test of the hypothesis that as the potential loss increases the utility function is at first concave and then convex. As they indicate, this hypothesis regarding the shape of the utility function was first proposed by Markowitz [9] as part of broader hypothesis which specifies as well that over the domain of gains the utility function is at first convex and then concave. Thus the utility function suggested by Markowitz has three inflection points: one in the domain of losses, second at the origin (the present wealth position, i.e., neither gain nor loss) and third in the domain of gains. The Markowitz function was developed to overcome several troubling implications of the Friedman and Savage formulation [2] and yet preserve consistency with the common behavioral observation that the same individual will often buy both lottery tickets and insurance. H & S find that while the Markowitz utility function provides a good first approximation to much of the behavior observed in their experiments, it is not reliable predictor of behavior in lotteries involving only small probability of large potential loss (a probability of .01 in their experiments). While noting that the existence of another concave segment in the utility function farther out in the domain of losses could account for this subgroup of observations, their own view appears to be that substantive progress in the