Aversion to the variability of pay and optimal incentive contracts

In a moral hazard setting with a performance additive in effort and a symmetrically distributed noise term, I show that compensation contracts which are convex in performance are suboptimal when the agent has mean-variance preferences. With step contracts, I show that sticks are more efficient than carrots: an exogenously given lower bound on payments is binding at the optimum. Intuitively, the variance of the agent's pay conditional on a high effort should be as low as possible, while it should be as high as possible conditional on a low effort. From an ex ante perspective, which is relevant for effort inducement, this maximizes the rewards associated to high effort, and the punishments associated to low effort. These results call into question the widespread use of stock-options and contracts with rewards-like features to provide incentives to risk averse executives.