Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion

This paper analyzes optimal executive compensation by studying a continuous-time agency model where the agent controls the drift of the geometric Brownian motion firm size. In contrast to existing agency models with constant firm size setting, in our model the changing firm size generates partial incentives, analogous to awarding the agent equity shares according to her continuation payoff. Along the optimal path, necessary additional incentives are provided by the optimal contract. When the agent is as patient as investors, performance-based stock grants implement the optimal contract; we also characterize the optimal contracting with shirking for this case. Our model generates a leverage effect on the firm's equity returns, and implies that the agency problem is more severe for smaller firms. That the empirical evidence pertaining to grants-performance sensitivity shows that CEO compensation is largely based on historical performance - rather than current performance - lends support to our model