Does Option Compensation Increase Managerial Risk Appetite?

This paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls. Under the manager’s optimal policy, the option ends up either deep in or deep out of the money. As the asset value goes to zero, volatility goes to infinity. However, the option compensation does not strictly lead to greater risk seeking. Sometimes, the manager’s optimal volatility is less with the option than it would be if he were trading his own account. Furthermore, giving the manager more options causes him to reduce volatility. MANAGERS WITH CONVEX COMPENSATION SCHEMES play an important role in financial markets. This paper solves for the optimal dynamic investment policy for a risk averse manager paid with a call option on the assets he controls. The paper focuses on how the option compensation impacts the manager’s appetite for risk when he cannot hedge the option position. On one hand, the convexity of the option makes the manager shun payoffs that are likely to be near the money. Under the optimal policy, the manager either significantly outperforms his benchmark or else incurs severe losses. Furthermore, in examples of optimal trading strategies, asset volatility goes to infinity as asset value goes to zero. Yet option compensation does not strictly lead to greater risk seeking. As asset value grows large, or if the evaluation date is far away, the manager moderates asset risk. For example, if the manager has constant relative risk aversion ~CRRA!, asset volatility converges to the Merton constant as asset value goes to infinity. In some situations, the manager actually chooses a lower asset volatility than he would if he were investing on his own, because the leverage inherent in his option magnifies his exposure to the asset volatility. In addition, with all constant or decreasing absolute risk averse utility functions from the hyperbolic absolute risk averse ~HARA! class, giving the manager more options causes him to reduce asset volatility. In the CRRA case, for example, the manager targets a fixed volatility for his personal * Department of Finance, Stern School of Business, New York University. I thank Franklin Allen, Suleyman Basak, Philip Dybvig, Edwin Elton, Sanford Grossman, Bruce Grundy, Kose John, Ioannis Karatzas, Richard Kihlstrom, Anthony Lynch, René Stulz ~the editor!, David Yermack, and an anonymous referee for helpful comments and suggestions. THE JOURNAL OF FINANCE • VOL. LV, NO. 5 • OCT. 2000