Statistical Methods in Finance 2018

Abstract

Modified Expected Shortfall : A Coherent Risk Measure for Elliptical Family of Distributions

by Deepak Jadhav

The Modified Expected Shortfall risk measure proposed in Jadhav et al. (2013) intended to eliminate the effect of exceptionally high returns. It provides a balanced risk measure, valued higher than the Value-at-Risk, but, lesser than the Expected Shortfall, based on shrinkage parameter a. However, it is not a coherent risk measure. In this article, we prove that the Modified Expected Shortfall is a coherent risk measure under univariate and multivariate elliptical family of distributions. The Modified Expected Shortfall performs better than the Expected Shortfall and found to be lower in magnitude. Backtesting results support the Modified Expected Shortfall.

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