Performance measure skewness and the structure of CEO compensation: Theory and evidence

While research has analyzed how the structure of incentive pay relates to the dispersion of the performance measure distribution, as measured by its variance or volatility, we examine how it relates to the asymmetry of the distribution, as measured by its skewness. In contrast to the variance, skewness affects the relative informativeness of high and low performance about the agent's effort, which determines the relative efficiency of providing rewards and punishments for incentive purposes. Therefore, skewness is an important determinant of compensation convexity, which is determined by the relative holdings of stock and options. Consistent with our analytical and numerical results, we find that the skewness of expected earnings is negatively associated with the convexity of CEO compensation. Our results are economically significant, robust to alternative specifications, and do not appear to be driven by reverse causality. In addition, we find that earnings skewness is negatively associated with total CEO compensation and that this association is driven by lower options-based compensation. These findings are consistent with CEOs preferring positively skewed performance metrics. Overall, we provide theoretical, numerical, and empirical evidence suggesting that skewness is a more important determinant of the convexity and structure of CEO compensation than volatility.