Optimal CEO Compensation when Managers are Loss Averse

In our paper Sticks or Carrots? Optimal CEO Compensation when Managers are Loss Averse, which was recently accepted for publication in the Journal of Finance, we analyze a simple contracting model where the manager is loss averse and explore to what extent its predictions are consistent with salient features of observed compensation contracts. In particular, we suggest a new approach to explaining the almost universal presence of stock options by assuming that manager’s preferences exhibit loss aversion as described by Kahneman and Tversky. More specifically, on the basis of experimental evidence they argue that choices under risk exhibit three features: (i) reference dependence, where agents do not value their final wealth levels, but evaluate outcomes relative to some benchmark or reference level; (ii) loss aversion, which adds the notion that losses (measured relative to the reference level)loom larger than gains; (iii) diminishing sensitivity, so that individuals become progressively less sensitive to incremental gains and incremental losses.

We develop a stylized principal-agent model with a loss-averse agent and show how it can be calibrated to individual CEO data. In the first part of the paper, we consider piecewise linear contracts that consist of fixed salary, stock and one option grant. We find that the loss aversion model can explain observed contracts very well if the manager’s reference wage is low, i.e. not much higher than last year’s fixed salary and bonus. The model then predicts realistic option holdings and salaries.

In the second part of the paper, we derive, analyze, and calibrate the optimal nonlinear contract. It turns out that the optimal contract features two regions: First, above a certain critical stock price, it is increasing and convex and pays out at least the reference wage. In the second region below this critical stock price, compensation falls discontinuously to a lower bound, a feature that is reminiscent of performance-related dismissals. The intuition for this drop is that a loss-averse CEO is risk-loving whenever her pay falls below her reference wage. Therefore, whenever the contract pays off below the reference wage, it can only pay the lowest possible wage, because any intermediate payoff can be improved upon by a lottery over more extreme payoffs. If the reference wage is low, the optimal contract features a low dismissal probability and is dominated by the region where the contract is increasing and convex. This shape can be approximated with high salaries and positive stock and option holdings that we observe in practice.

Optimal risk sharing implies that the contract is more high-powered where the risk-tolerance of the CEO is higher, so the fast increase of risk-tolerance leads to optimal contracts that are convex. By contrast in the risk-aversion model, risk-tolerance is mainly determined by the agent’s wealth and therefore increases only slowly with increasing payouts. As a consequence, the shape of the optimal risk-aversion contract is dominated by a second effect: the decreasing marginal utility that makes it more effective to provide incentives at low payout levels. This incentive effect by itself results in a concave contract. The incentive effect is also present in the loss-aversion model, but is dominated by the risk-tolerance effect.

The ability to quantitatively disentangle the importance of these effects for individual CEO compensation contracts is an advantage of our calibration approach. A noteworthy cross-sectional implication of our model is that CEOs with a higher reference wage have less performance-related pay, but they are attracted to firms with better corporate governance standards where they have a higher probability of being fired.

The full paper is available for download here.