Expected Shortfall: A Natural Coherent Alternative to Value at Risk

TLDR

Expected shortfall is defined as the average of the worst losses at a fixed confidence level, naturally arising from portfolio return samples. The paper examines the coherence properties of expected shortfall as a risk measure and compares alternative representations suitable for different regulatory contexts. The authors compare several alternative representations of expected shortfall, highlighting which are more appropriate for specific regulatory purposes.

Abstract

We discuss the coherence properties of expected shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the ‘average of the 100% worst losses’ in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes (J.E.L.: G20, C13, C14).