Pay-Performance Sensitivity and Its Relations to Firm Performance and Firm Risk in a Continuous-Time Principal-Agent Model

摘要

We study the optimal contract between risk-neutral shareholders and a power utility (CRRA) manager who controls the instantaneous rate of an output process in a continuous-time model and examine its properties and implications. We make several contributions. First, we provide a simple semi-explicit characterization of the optimal contract. This model has remained intractable using the traditional first-order approach. Second, using our characterization, we show that neither does a definite positive relation between pay-performance sensitivity (PPS) and firm performance nor does a definite negative relation between PPS and firm risk exist in our model. Both results are consistent with empirical findings and contrary to standard agency theory predictions. Third, linear contracts, I.e. restricted shares, are optimal in our model under two conditions: (a) the manager has a log-utility; and (b) there does not exist a lower bound on his compensation other than that it is nonnegative. Stock options are optimal when a positive lower bound exists. Fourth, we show that, if the manager's compensation has a positive lower bound which can be interpreted as a base payment, in general the optimal compensation consists of a cash payment plus an equity-linked component which is generally not regular stock options unless the aforementioned conditions are met. Fifth, besides the log-utility case, some explicit nonlinear optimal contracts are also obtained. Explicit optimal contracts, especially nonlinear ones, are rare in continuous-time models outside the standard class of exponential utility (CARA)-Brownian motion where the contracts are linear when the cost function is quadratic. Finally, on the methodological side, we illustrate the power of backward stochastic differential equations (BSDEs) in solving certain principal-agent problems.