Incentive Contracts and Downside Risk Sharing

This paper seeks to characterize incentive compensation in a principal-agent moral hazard setting in which the principal is prudent, or downside risk averse, as many situations (such as that of a patient in hospital or a regulator dealing with food safety) suggest she should be. We show that optimal incentive pay should then be 'approximately concave' in performance, the approximation being closer the more downside risk averse the principal is compared to the agent. Limiting the agent's liability would improve the approximation, but taxing the principal would make it coarser. The notion of an approximately concave function we introduce here to describe the pay-performance relationship is relatively recent in mathematics; it is intuitive and translates into concrete empirical implications, notably for the composition of incentive pay. We also clarify which measure of prudence - among the various ones proposed in the literature - is relevant to investigate the tradeoff between downside risk sharing and incentives.