Optimal Executive Compensation Schemes

This note uses stochastic dominance to help decision makers who are expected utility maximizers choose between risky investments with minimal knowledge of the decision maker's utility function. More specifically, we employ second-order stochastic dominance. It is argued that for two risky investments X and Y, investment Y has second-order stochastic dominance over investment X if investment Y is less risky and has at least as high a mean return than investment X (that is, investors with increasing and concave utility functions) prefer a second-order stochastically dominant investment to a dominated investment. We consider two alternative executive compensation plans. First, under a proportional compensation plan, the executive receives a fixed proportion of the unknown stock price. Second, under the executive stock option plan, the executive receives an out-of-the-money call option on the company's underlying stock with the same expiration date as the proportional compensation plan. We prove by using the method of second order stochastic dominance, that a wealth seeking risk-averse executive would prefer an executive stock option to a compensation scheme which pays a fixed proportion of the stock price, regardless of the underlying stock price distribution