Stock Based Compensation: Firm-specific risk, Efficiency and Incentives

We propose a continuous time utility maximization model to value stock and option compensation from the executive's perspective. We allow the executive to invest non-option wealth in the market and riskless asset but not in the company stock itself. This enables executives to adjust exposure to market risk, but they are subject to firm-specific risk for incentive purposes. Since the executive is risk averse, this unhedgeable firm risk leads them to place less value on the options than their cost to the company, given by their market or Black Scholes value. By distinguishing between these two types of risks, we are able to examine the effect of stock volatility, firm-specific risk, and market risk on the value to the executive. Executives do not necessarily want to increase stock volatility, as their risk aversion can outweigh the option's convexity effect. Firm-specific risk generally reduces option value, although if market risk is held fixed and the options are out-of-the-money it is possible for the reverse to hold. Generally, market risk has a positive effect on option value. An implication of the model is that the Black Scholes formula exaggerates the incentives for the executive to increase the company stock price. We examine the relationship between risk and optimal incentives, and find firm-specific risk decreases optimal incentives (regardless of which parameters are fixed) whilst market risk may decrease optimal incentives depending on other parameters. The research has implications for future design of compensation plans, in light of the recent trend towards expensing all options. The model supports the use of stock if the company can adjust cash pay when granting stock or options, and does not support the use of indexed options.