We develop a model that clarifies how to measure CEO incentive strength and how to reconcile the enormous differences in pay sensitivities between executives in large and small firms. The crucial parameter is shown to be the elasticity of CEO productivity with respect to firm size. We find that CEO marginal products rise significantly with firm size (confirming Rosen's conjecture that CEOs of large firms have a "chain letter" effect on firm performance), and overall CEO incentives are roughly constant, or decline slightly, with firm size. We employ a multitask model to discuss implications for the design of control systems.

ABSTRACT We empirically analyze the dynamics of executives' pay‐to‐performance sensitivities. Option pay‐to‐performance sensitivities become weaker as options fall underwater, often leading to pressures to reprice options or restore pay‐to‐performance sensitivity in other ways. Building a detailed data set on executives' portfolios of stock and options, we find that the responsiveness of pay‐to‐performance sensitivities (created by all executive holdings of stock and options) to changes in stock price is large. The elasticity of pay‐to‐performance sensitivities with respect to stock price decreases is about 0.7 and is larger for high‐option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies offset declines in option pay‐to‐performance sensitivities is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock‐price‐induced pay‐to‐performance sensitivity declines. Option repricings are inconsequential in this regard, despite the attention they have attracted. In looking at positive returns, we find the reverse: higher returns both directly increase pay‐to‐performance sensitivities and lead to larger option grants, which raise pay‐to‐performance sensitivities further. Thus, option grants to executives tend to be largest following large stock price increases or large stock price decreases.

We employ a certainty-equivalence framework to analyze the cost, value and pay/performance sensitivity of non-tradable options held by undiversified, risk-averse executives. We derive “executive value” lines, the risk-adjusted analogues to Black–Scholes lines. We show that distinguishing between “executive value” and “company cost” provides insight into many issues regarding stock option practice including: executive views about Black–Scholes values; tradeoffs between options, restricted stock and cash; exercise price policies; option repricings; early exercise policies and decisions; and the length of vesting periods. It also leads to reinterpretations of both cross-sectional facts and longitudinal trends in the level of executive compensation.

Although exercise prices for executive stock options can be set either below or above the grant-date market price, in practice virtually all options are granted at the money. We offer an economic rationale for this apparent puzzle, by showing that pay-to-performance incentives for risk-averse undiversified executives are typically maximized by setting exercise prices at (or near) the grant-date market price. We provide an operationally useful alternative to Black-Scholes (1973) for the purpose of both valuing executive stock options and measuring the incentives created by options. Our framework has implications not only for exercise-price policies, but also for indexed options, option repricings, exchanges of cash for stock-based compensation, and the design of bonus plans.