Expected Shortfall
From Open Risk Manual
Definition
Expected Shortfall (ES) is a Risk Measure used in the context of Quantitative Risk Management of Market Risk or Credit Risk in a Portfolio Management context. The "expected shortfall at level " is the Expected Loss experienced in the portfolio in the worst of scenarios.
ES is an alternative to Value at Risk that is addressing some widely criticized attributes of VaR as a risk measure. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), and expected tail loss (ETL).
Formula
If is a Random Variable expressing the Risk Distribution of a portfolio at some future time and then we define the expected shortfall as
where is the Value at Risk.
References