Forex glossary
Conditional Value at Risk (CVaR)
CVaR, or expected shortfall, is the mean loss in a specified worst portion of the distribution, such as the worst 5% at a 95% confidence level. It adds tail-severity information to VaR. The estimate depends on model, sample and horizon and is not a maximum possible loss.
Illustrative example
How does it work in practice?
In 100 equally weighted hypothetical scenarios, the worst five losses are 100, 120, 140, 160 and 180 USD. Mean loss in the worst 5% is 140 USD; the largest observed loss is 180 USD.
A case to work through
Tails with different severity
Model: 20 equally weighted scenarios; the largest two losses are 90 and 210 USD; select the worst 10%.
- The worst 10% of this sample contains two scenarios.
- Their mean is (90 + 210)/2 = 150 USD.
What follows? Report the tail-selection convention with the result.
Example boundary: The sample and selected tail do not bound future losses.
A selected tail’s mean
Text description of the diagram
- Sample: 20 equally weighted scenarios.
- Worst 10%: Two losses: 90 and 210 USD.
- Tail mean: (90 + 210)/2 = 150 USD.
A useful distinction
Conditional Value at Risk (CVaR) / Value at Risk (VaR)
VaR identifies a quantile threshold; CVaR describes mean severity in a specified tail.
Check your understanding
Calculate a selected tail mean without confusing it with the maximum.
Show the answer and explanation
100 USD
(60 + 140)/2 = 100 USD.
Net results and risk measures
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Related terms
Sources and documentation
- BIS MAR10: market risk terminology
VaR at a stated horizon/confidence and expected shortfall as a tail mean.
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