CVaR (Conditional VaR)

While VaR says 'you won't lose more than X on 95% of days,' CVaR asks 'but on those worst 5% of days, how much do you lose on average?' If VaR is $1,000, CVaR might show the average loss in that worst 5% is actually $1,800 — a fuller picture of how bad the bad days really get.

CVaR (also called Expected Shortfall) is calculated by first finding the VaR threshold — the loss level not expected to be exceeded at a chosen confidence level, such as 95% — then averaging the losses in the scenarios that fall beyond that threshold. Where VaR only reports the cutoff, CVaR quantifies how severe a breach of that cutoff tends to be. Because it accounts for the full severity of tail outcomes rather than stopping at one point on the distribution, CVaR is considered more conservative and better behaved mathematically than VaR — it satisfies subadditivity, meaning a diversified portfolio's CVaR can never exceed the sum of its parts' CVaRs. It's especially useful for return distributions with fat tails, where VaR alone can understate how bad the worst outcomes really are.

CVaR = E[Loss | Loss > VaR]