Glossary term
Expected Shortfall (ES)
Subject: Risk Management, Risk Assessment and Quantification
Also known as: ES, Conditional VaR, CVaR, Tail VaR
Expected shortfall is the average loss on the days when losses exceed the Value at Risk threshold, so it shows how bad the worst cases are once the threshold is passed.
Explanation
Value at Risk gives a cut-off, such as the loss exceeded on 1 day in 100, but says nothing about how large losses are once that line is crossed. Expected shortfall fills the gap. It averages all losses beyond the cut-off. Two portfolios can share the same VaR while one has a far heavier tail, and only expected shortfall shows the difference. It also has a mathematical property called subadditivity: the figure for a combined portfolio never exceeds the sum of its parts, which fits the idea that diversification helps. The Basel Committee chose it over VaR for market risk capital in its Fundamental Review of the Trading Book, usually at a 97.5% confidence level. Capital sized on average tail loss reacts to extreme events that VaR passes over.
Example
Two trading books both show a one-day 97.5% VaR of 10. Book A's worst days average a loss of 12. Book B's worst days average 25, because a few huge losses sit far out in the tail. Expected shortfall separates them, and the risk team asks B's desk to cut positions.
Not to be confused with
- Value at Risk (VaR)
- VaR is the loss threshold at a chosen confidence level. Expected shortfall is the average loss beyond that threshold.