Modified Estimators of the Expected Shortfall

Abstract

The coherent risk measure Expected Shortfall is popularly considered as an alternative to Value-at-Risk. We briefly review all existing parametric and non-parametric methods to estimate Expected Shortfall. The historical method is considered as the best method of estimation for the Expected Shortfall, though it has a serious disadvantage of over-estimation in the presence of outliers in the return data. In this article, we propose two non-parametric estimators of Expected Shortfall which are robust to outliers. We estimate the Expected Shortfall corresponding to daily returns of some of the selected assets and indices of the Indian (BSE and NSE) and foreign stock markets (NYSE and LSE). The backtesting procedure boasts in confirming that the proposed non-parametric estimators are the best alternatives to the historical method in avoiding over-estimation of Expected Shortfall.