Conditional value at risk
What is Conditional value at risk?
Conditional value at risk estimates the average loss in outcomes that are worse than the value-at-risk threshold at a stated horizon and confidence level.
What conditional value at risk means
If ten-day 97.5% VaR marks the loss threshold for the worst 2.5% of modeled outcomes, conditional VaR averages the losses within that tail. It therefore addresses a central limitation of VaR by describing severity after the threshold has been crossed rather than reporting only where the tail begins.
How it is calculated
Historical expected shortfall averages observed or weighted scenario losses beyond the selected percentile. Parametric and Monte Carlo methods estimate the same tail expectation from modeled distributions or simulated paths. The portfolio must be revalued consistently, especially for options. Results depend heavily on tail observations, scenario generation, horizon, confidence, and liquidity assumptions.
Example
A portfolio has one-day 97.5% VaR of $4 million and conditional VaR of $6.5 million. The model places the boundary of its worst 2.5% of days at $4 million, while their average loss is estimated at $6.5 million. Individual losses can still be far larger than the conditional VaR figure.
How to interpret it
State whether the measure is reported as a positive loss, negative return, or percentage, and identify its horizon and confidence level. Compare it with VaR to understand tail severity. A large gap can indicate fat tails, nonlinear exposure, or concentrated scenarios. Review the actual scenarios contributing most to the average rather than relying only on the aggregate.
Limitations
Tail estimates are statistically uncertain because few observations lie beyond a high confidence threshold. Historical methods inherit the sample's omissions, while parametric methods inherit distribution assumptions. Conditional VaR does not identify the worst possible loss and may exclude liquidity, default, or path-dependent effects unless they are modeled explicitly.
Practical checklist
Use a transparent confidence level and horizon, inspect the scenarios within the tail, and test sensitivity to data windows and weighting. Reconcile nonlinear valuations and risk-factor coverage. Pair expected shortfall with stress tests, reverse stresses, drawdown, liquidity, and concentration analysis. Where it supports a limit, specify model-change governance and prevent improvements caused only by changing assumptions.
Also known as: CVaR, expected shortfall, average value at risk
Sources and further reading
- Minimum capital requirements for market risk, Basel Committee on Banking Supervision