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

This paper examines the efficiency of stock based compensation by valuing stock and options from the executive's point of view. Companies give compensation in the form of stock in order to align incentives by providing a link between executive wealth and the stock price performance of the company. However, it requires the executive to be exposed to firm-specific risk, and thus hold a less than fully diversified portfolio. Since firm-specific risk is not priced, this leads to the executive placing less value on the options than their cost to the company, given by their market value. We propose a continuous time, utility maximisation model to value the executive's com- pensation. We endogenise allocation of the executive's non-option wealth as the executive may invest in the market portfolio. Executives trade the market portfolio to adjust exposure to market risk, but are subject to firm-specific risk for incentive purposes. By distinguishing between these two types of risks, we are able to examine the effect of stock volatility, firm-specific risk, market risk and the correlation between the stock and the market, on the value to the executive and incentives. We can prove that there is a negative relationship between firm-specific risk and value, if volatility is fixed. However, the value may increase or decrease with firm-specific risk if market risk is fixed. The same ambiguous relationship is found if we consider value as a function of volatility, so executives will not always aim to increase the volatility of the stock price. Just as the value of the compensation to the executive is overstated in a Black Scholes model, the Black Scholes model also exaggerates the incentives for the executive to increase the stock price. We address the question of how the company can maximise incentives (for a given cost) and show that if stock compensation replaces cash remuneration, it is optimal to compensate with stock, rather than options.