Abstract
The conventional wisdom about convexity is that positive convexity is good, and more is better. Paradoxically, while defensible in theory, this maxim has been found to fail in practice. In this paper, the relationship of convexity to the assumption of parallel shifts is explored, and new convexity measures are developed to reflect nonparallel shifts. These new measures can differ dramatically from the traditional values, providing insight into when convexity does not have to be good and when it does.