Evolutionary Foundation for Heterogeneity in Risk Aversion

We examine the evolutionary basis for risk aversion with respect to aggregate risk. We study populations in which agents face choices between aggregate risk and idiosyncratic risk. We show that the choices that maximize the long-run growth rate are induced by a heterogeneous population in which the least and most risk-averse agents are indifferent between taking an aggregate risk and obtaining its linear and harmonic mean for sure, respectively. Moreover, approximately optimal behavior can be induced by a simple distribution according to which all agents have constant relative risk aversion, and the coefficient of relative risk aversion is uniformly distributed between zero and two.