### Abstract

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.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 1 |

Volume | 2005-99 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2005-99 |

### Keywords

- portfolio choice
- coherent risk
- spanning test

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## Cite this

Melenberg, B., & Polbennikov, S. Y. (2005).

*Testing for Mean-Coherent Regular Risk Spanning*. (CentER Discussion Paper; Vol. 2005-99). Econometrics.