Modified Expected Shortfall: A New Robust Coherent Risk Measure

Abstract

The coherent risk measure expected shortfall is a popular alternative to value-at-risk. However, the estimated value may miscommunicate the actual risk, especially when huge losses are present in the return series. This may force the financial institution to keep extra capital to meet the requirement set by the regulators. We propose a new robust coherent risk measure called modified expected shortfall, which quantifies the authentic risk of a portfolio. In comparison with the expected shortfall, the magnitude of the suggested risk measure is found to be lower. We propose non-parametric estimators of the modified expected shortfall and establish their statistical properties such as consistency and asymptotic normality.