Economics and management science share the tradition of ordering risk aversion by fitting the best expected utility (EU) model with a certain utility function to individual data, and then using the utility curvature for each individual as the sole index of risk attitude. (Cumulative) Prospect theory (CPT) has demonstrated various empirical deficiencies of EU and introduced the weighting of probabilities as an additional component to capture risk attitude. However, if utility curvature and probability weighting were strongly correlated, the utility curvature in EU alone, while not properly describing risky behavior in general, would still capture most of the variance regarding degrees of risk aversion. This study shows, however, that such a strong correlation does not exist. Though, most individuals exhibit concave utility and convex probability weighting, the two components show no correlation. Thus neglecting one component entails a loss.