Optimal consumption, portfolio Selection, and the value and incentive effects of executive stock Options

Abstract

In this paper, we study the value and incentive effects of u11tra<led stock options to risk-averse, undiversified executives using a continuous-time, intertemporal consumption and portfolio-selection framework. The executive's employment income consists of cash pay, restricted stock and option grants. The executive takes his or her compensation and initial wealth as given and maximizes the expected intertemporal utility of consumption by opt imally allucatiug disposable wealth between current consumption a nd future investments. Any unconsumed disposable wealth is invested in the riskfree asset and the market portfolio. Consumption must be financed by the executive's cash pay, accumulated cash holdings and other marketable investments. The value of the untraded option is derived from the Euler equation following the determination of optimal consumption and portfolio-selection rules. A closed-form solution is obtained under certain restrictive assumptions.