Expected shortfall (ES)

The average loss on the occasions when Value at Risk is breached — the question VaR refuses to answer. Sub-additive, so diversification can never appear to add risk, which is why bank capital rules moved to it from VaR.

Where Expected shortfall is explained in depth

The definition above is the short version. These pages put it to work, in the order they use it most:

• Risk Measures
• Value at Risk vs. Stress Testing
• The Arithmetic of Drawdowns

Calculators that compute it

• Value at Risk & expected shortfall

Terms this definition uses

• Diversification

The whole glossary