Prudence and the Convexity of Compensation Contracts

In a standard principal-agent model, we derive a new condition that relates the structure of the optimal contract to the agent's risk preferences: The optimal contract is more convex than the likelihood ratio of the performance measure if and only if the coefficient of absolute prudence is larger than twice the coefficient of absolute risk aversion. This condition trades off the effect of the contract's shape on incentives and risk sharing, and shows that the outcome depends on the relative importance of the agent's risk aversion and prudence. With CRRA utility, this condition is satisfied if and only if relative risk aversion is less than one