Conditional Value-at-Risk (CVaR)

VaR tells you the loss threshold you should not exceed on, say, 95% of days, but it says nothing about how bad things get on the worst 5%. CVaR fills that gap: it is the average of all losses beyond the VaR threshold. Two portfolios can share the same VaR and yet have very different CVaRs if one has a much fatter tail.

CVaR is usually estimated by historical simulation, a parametric (Gaussian) assumption, or Monte Carlo. It is identical to Expected Shortfall, and unlike plain VaR it is a coherent risk measure: combining two portfolios never produces a CVaR worse than the sum of the parts, which makes it well behaved for optimization.