### Abstract

Abstract: Denote the loss return on the equity of a financial institution as X and that of the entire market as Y . For a given very small value of p > 0, the marginal expected shortfall (MES) is defined as E(X | Y > QY (1−p)), where QY (1−p) is the (1−p)-th quantile of the distribution of Y . The MES is an important factor when measuring the systemic risk of financial institutions. For a wide nonparametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when p ↓ 0, as the sample size n → ∞. Since we are in particular interested in the case p = O(1=n), we use extreme value techniques for deriving the estimator and its asymptotic behavior. The finite sample performance of the estimator and the adequacy of the limit theorem are shown in a detailed simulation study. We also apply our method to estimate the MES of three large U.S. investment banks.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 28 |

Volume | 2012-080 |

Publication status | Published - 2012 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2012-080 |

### Keywords

- Asymptotic normality
- extreme values
- tail dependence

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## Cite this

Cai, J., Einmahl, J. H. J., de Haan, L. F. M., & Zhou, C. (2012).

*Estimation of the Marginal Expected Shortfall: The Mean when a Related Variable is Extreme*. (CentER Discussion Paper; Vol. 2012-080). Econometrics.