Before revision:  We present extensions of this result for the case of convex or co-monotone coherent risk measures. Under this perspective, we propose a specific formulation that generates, from any coherent measure, a generalized deviation based on the dispersion of results worse than it, which leads to a very interesting risk measure. Moreover, we present some examples of risk measures that lie in our proposed class .
After revision:  We present extensions of this result for the case of convex or co-monotone risk measures, conform the properties of the two components .