Conditional value at risk
The average loss across those worst scenarios that fell beyond the value-at-risk threshold. It answers not where the line is, but how bad things get past it.
Formula
CVaR_{\alpha} = \mathbb{E}\left[L \mid L > VaR_{\alpha}\right]Losses are averaged only over scenarios worse than the chosen threshold. The confidence level is set in advance and is not part of the resulting figure.
How to read the number
Unlike value at risk it accounts for the shape of the tail: two portfolios with the same threshold can differ several times over in what lies behind it.
When the metric lies
It is estimated from the thinnest part of the sample, so the answer depends heavily on the length of history and on whether a genuine crash ever made it into the data.
Also known as: expected shortfall, cvar