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The relationship between CEO compensation and firm performance is a field of intense theoretical and empirical research. The purpose of this study is to gain additional insights into the nature of this relationship by examining empirically the relatively unexplored areas of its non-linearity. The findings of this study show strong evidence that supports the view that the relationship between executive compensation and firm performance is non-linear and asymmetric. Additionally, the structure of asymmetry is found to be dependent upon the measure of performance. Convexity characterizes the asymmetry of the relationship between executive compensation and market returns, while concavity distinguishes the asymmetry of the relationship between executive compensation and accounting returns.