Expected Shortfall

Expected Shortfall (ES, also called Conditional VaR or CVaR) is the average loss conditional on the loss exceeding VaR:

If a $95\%$ VaR is 1M USD and the average loss on the worst $5\%$ of days is 2M USD, then $95\%$ ES is 2M USD.

ES has two big advantages over VaR. It captures tail magnitude — large losses don't all look the same. And it's a coherent risk measure: it satisfies subadditivity ($\text{ES}(A + B) \le \text{ES}(A) + \text{ES}(B)$), so combining portfolios never increases total risk. VaR can fail this property in extreme cases.

Basel III is gradually migrating from VaR to ES for market-risk capital requirements. In practice, both are reported and stress-tested side by side.