Testing for mean-coherent regular risk spanning

Coherent risk measures have received considerable attention in therecent literature. Coherent regular risk measures form an importantsubclass: they are empirically identifiable, and, when combined withmean return, they are consistent with second order stochastic domi-nance. As a consequence, these risk measures are natural candidatesin a mean-risk trade-off portfolio choice. In this paper we developa mean-coherent regular risk spanning test and related performancemeasure. The test and the performance measure can be implementedby means of a simple semi-parametric instrumental variable regres-sion, 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.