90 Cents of Every “Pay-for-Performance” Dollar are Paid for Luck

It is well-known that CEOs are sometimes rewarded for luck. The classic example is that of oil company CEOs whose compensations increase with the price of oil (Bertrand and Mullainathan 2001). This has been show to hold for other factors that are both outside the control of the manager, and observable to the boards who grant compensation, yet rarely adjust it for these factors. My paper is an attempt to estimate the magnitude of the pay-for-luck component in option-based compensation. How much of the “pay-for-performance” compensation is actually paid for luck? The answer to this question depends on the ratio between the manager’s talent, T, defined as her ability to increase the firm’s average return, and the inherent “noise” in the stock’s returns, as measured by the standard deviation of returns, σR. We develop an analytical expression for the proportion of option-based compensation that constitutes pay-for-luck as a function of the ratio σR ∕ T. We show that this proportion grows very quickly with σR ∕ T. For the empirically estimated parameters the pay-for-luck component exceeds 90% of the compensation. This result is robust, and stems from the fundamental fact that chance plays a dominant role in determining firm performance.