The existence of insurance, futures markets, and stock markets indicates the importance of risk aversion in economics. In spite of this, there are few studies which attempt to estimate the degree of an agent' s risk aversion (see Friend and Blume 1975).1 Any study which seeks to quantify risk aversion, regardless of the setting, must necessarily resort to indirect measures. In this article We construct a model in which it is rational for an agent with constant absolute risk aversion to select the more risky of two investments if and only if his wealth is small. This paradoxical behavior is induced by the presence of discounting and a bankruptcy constraint, and it bodes ill for the empirical resolution of the controversial assumption of risk-averse agents. *This research was partially supported by the National Science Foundation through grant SOC-7808985. 1. This gap is especially significant given the continued controversy regarding the nature of the objective function when agents must produce in an uncertain environment. Some (see Sandmo 1971) have assumed that firms maximize expected utility where utility is a strictly concave function of profits. The model based on the strict concavity assumption gives rise to implications that are quite different from those flowing from expected profit maximization. For example, fixed costs affect output decisions. One objection to this model asserts that firms with strictly concave (or strictly convex) utility functions will not survive when confronted with risk-neutral competitors. In the long run, the average profits of the risk-averse firms will be smaller than those of the risk-neutral firm. Moreover, there will be a tendency for them to disappear or be acquired by risk neutral entrepreneurs (see, e.g., Gould 1976). Furthermore, the demise of the risk-averse entrepreneur will be beneficial for stockholders who will want each firm in their diversified portfolio to maximize expected profits. On the other hand, if there are perfect markets, then Fisher separation obtains and the firm's goal is profit maximization which, empirically, is indistinguishable from a linear utility function. (The empirical work on efficient markets starts with the assumption of perfect capital markets.) This problem continues to be the subject of theoretical inquiry (see Radner 1974).