Choices, Values, and Frames

INTRODUCTION

Economists pervasively explain widespread risk aversion by the realistic assumption that people generally have diminishing marginal utility of wealth. Indeed, diminishing marginal utility of wealth probably explains much of our aversion to large-scale financial risk: We dislike vast uncertainty in lifetime wealth because the marginal value of a dollar when we are poor is higher than when we are rich.

Within the expected-utility framework, the concavity of the utility-of-wealth function is not only sufficient to explain risk aversion - it is also necessary: Diminishing marginal utility of wealth is the sole explanation for risk aversion. Unfortunately, it is an utterly implausible explanation for appreciable risk aversion, except when the stakes are very large. Any utility-of-wealth function that does not predict absurdly severe risk aversion over very large stakes predicts negligible risk aversion over modest stakes.

Arrow (1971, p. 100) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positive-expected-value bet. That is, expected-utility maximizers are arbitrarily close to risk neutral when stakes are arbitrarily small. Although most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for very small stakes but for quite sizable and economically important stakes as well. Diminishing marginal utility of wealth is not a plausible explanation of people's aversion to risk on the scale of $10, $100, $1,000, or even more.