Testing for Mean-Coherent Regular Risk Spanning

Coherent risk measures have received considerable attention in the recent literature.Coherent regular risk measures form an important subclass: they are empirically identifiable, and, when combined with mean return, they are consistent with second order stochastic dominance.As a consequence, these risk measures are natural candidates in a mean-risk trade-off portfolio choice.In this paper we develop a mean-coherent regular risk spanning test and related performance measure.The test and the performance measure can be implemented by means of a simple semi-parametric instrumental variable regression, where instruments have a direct link with the stochastic discount factor.We illustrate applications of the spanning test and the performance measure for several coherent regular risk measures, including the well known expected shortfall.