Compensation, Incentives, and the Duality of Risk Aversion and Riskiness

The common folklore that giving options to agents will make them more willing to take risks is false. In fact, no incentive schedule will make all expected utility maximizers more or less risk averse. This paper finds simple, intuitive, necessary and sufficient conditions under which incentive schedules make agents more or less risk averse. The paper uses these to examine the incentive effects of some common structures such as puts and calls, and it briefly explores the duality between a fee schedule that makes an agent more or less risk averse, and gambles that increase or decrease risk. WITH THE GROWING INTEREST in executive compensation and agency problems, there is a folklore about the relation between the shape of the fee schedule received by an agent and the agent’s attitudes toward risk that deserves further study. As an illustration, many authors take it for granted that giving options to executives makes them more willing to take risks. DeFusco, Johnson, and Zorn (1990, p. 618), for example, note that “The asymmetric payoffs of call options make it more attractive for managers to undertake risky projects.” In fact, contrary to their intuition, my intuition, and that of most observers, without further conditions on utility functions beyond monotonicity and risk aversion, this is not correct. Surprisingly, it is not the case that a convex compensation schedule makes an agent more willing to take risks, that is, less risk averse; nor does a concave compensation schedule make an agent more risk averse. The common folklore clearly has its genesis in the observation from option pricing theory that an increase in the volatility of an option makes it more valuable (see, e.g., Haugen and Senbet (1981), Smith and Watts (1982), and Smith and Stultz (1985)). This is, however, not the same as making the option more desirable to a risk-averse investor. One clear problem with the intuition of folklore is that compensation schedules move the evaluation of any given gamble to a different part of the domain of the original utility function where the utility function can have greater or lesser risk aversion. For example, suppose that an option grant is part of an incentive package that raises base compensation. With such an incentive compensation package, the agent assesses risk from the vantage point of being wealthier, and an agent can have a very different ∗Ross is with the Sloan School, MIT. I thank my colleagues at MIT whose comments aided me in writing this paper, the referees whose comments improved it, and the participants in the seminar at NYU, and, particularly Jennifer Carpenter and Anna Pavlova. All errors are my own.