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

The 'Modified Expected Shortfall' is a risk measure proposed by Jadhav et al. (J. Risk 16, 69-83, 2013) is not a coherent risk measure in general. In this paper, we prove that 'Modified Expected Shortfall' is a coherent risk measure under univariate and multivariate elliptical families of distributions. The Modified Expected Shortfall performs better than the Expected Shortfall and is found to be lower in magnitude. Backtesting results support the superiority of Modified Expected Shortfall when compared with the Expected Shortfall.