This paper examines the impact of option compensation on managerial risk appetite. It analyzes the dynamic investment problem of a risk-averse manager who is compensated with a call option on the assets he controls. The study shows that the manager's optimal policy results in either a deep in-the-money or deep out-of-the-money option. As the asset value approaches zero, volatility increases, but option compensation does not necessarily lead to greater risk-seeking behavior. In some cases, the manager's optimal volatility is lower than it would be if he were trading his own account. Additionally, giving the manager more options leads to a reduction in asset volatility.
Managers with convex compensation schemes play a significant role in financial markets. This paper solves the optimal dynamic investment policy for a risk-averse manager paid with a call option on the assets he controls. The study focuses on how option compensation affects the manager's risk appetite when he cannot hedge the option position.
The convexity of the option makes the manager avoid payoffs that are likely to be near the money. Under the optimal policy, the manager either significantly outperforms his benchmark or incurs severe losses. Furthermore, in examples of optimal trading strategies, asset volatility goes to infinity as asset value goes to zero.
However, 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 portfolio of options and outside wealth.
Giving the manager more options increases the volatility of his personal portfolio. To offset this, he reduces the volatility of the underlying asset portfolio.
An explicit example of the investment problem solved here is that of a portfolio manager paid with a share of the positive profits of the fund, net of a benchmark, like the incentive fee of a hedge fund. However, the essence of the problem solved here appears in many other contexts. For instance, a corporate manager who controls firm leverage or asset volatility and holds executive stock options that he cannot hedge faces a similar investment problem. The investment problem of shareholders of a levered firm resembles the problem solved here if the firm is privately held. Although the complete, continuous-time market modeled here is less appropriate for a corporate manager than for a fund manager, corporate managers do have the ability to manage firm risk dynamically by using forward contracts, swaps, and other derivatives.
In someThis paper examines the impact of option compensation on managerial risk appetite. It analyzes the dynamic investment problem of a risk-averse manager who is compensated with a call option on the assets he controls. The study shows that the manager's optimal policy results in either a deep in-the-money or deep out-of-the-money option. As the asset value approaches zero, volatility increases, but option compensation does not necessarily lead to greater risk-seeking behavior. In some cases, the manager's optimal volatility is lower than it would be if he were trading his own account. Additionally, giving the manager more options leads to a reduction in asset volatility.
Managers with convex compensation schemes play a significant role in financial markets. This paper solves the optimal dynamic investment policy for a risk-averse manager paid with a call option on the assets he controls. The study focuses on how option compensation affects the manager's risk appetite when he cannot hedge the option position.
The convexity of the option makes the manager avoid payoffs that are likely to be near the money. Under the optimal policy, the manager either significantly outperforms his benchmark or incurs severe losses. Furthermore, in examples of optimal trading strategies, asset volatility goes to infinity as asset value goes to zero.
However, 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 portfolio of options and outside wealth.
Giving the manager more options increases the volatility of his personal portfolio. To offset this, he reduces the volatility of the underlying asset portfolio.
An explicit example of the investment problem solved here is that of a portfolio manager paid with a share of the positive profits of the fund, net of a benchmark, like the incentive fee of a hedge fund. However, the essence of the problem solved here appears in many other contexts. For instance, a corporate manager who controls firm leverage or asset volatility and holds executive stock options that he cannot hedge faces a similar investment problem. The investment problem of shareholders of a levered firm resembles the problem solved here if the firm is privately held. Although the complete, continuous-time market modeled here is less appropriate for a corporate manager than for a fund manager, corporate managers do have the ability to manage firm risk dynamically by using forward contracts, swaps, and other derivatives.
In some