Expected Shortfall
Quantitative Finance glossary · Quantitative Finance
Definition
ES_α = mathbbE[L mid L ≥ VaR_α] — expected loss conditional on exceeding VaR at confidence α (also called CVaR, Conditional VaR, Tail VaR). Unlike VaR, ES satisfies the subadditivity axiom ρ(X + Y) ≤ ρ(X) + ρ(Y), making it a coherent risk measure (Artzner et al. 1999) — diversification cannot increase risk under ES. Basel FRTB (Fundamental Review of the Trading Book) replaced VaR with 97.5% ES as the standard market-risk capital metric in 2019.
Expected Shortfall in plain English
Imagine you want to know how bad a really bad day for your investments could be. A common measure (VaR) just draws a line — 'you'll lose at least this much on your worst days' — but it stays silent about how catastrophic those worst days actually get. Expected Shortfall fixes that: it's the AVERAGE loss on the bad days beyond that line, so it tells you the depth of the disaster, not just where it starts. It also has a fairness property VaR lacks — combining two portfolios can never make ES look riskier than the two separately, which matches common sense that diversifying shouldn't be punished — and that's exactly why global banking rules switched to ES (at a 97.5% confidence level) for measuring trading risk.
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