Elicitability and Forecast Evaluation for Risk Measures

Summary

The document asks what it means for a risk measure to be elicitable, contrasting Value at Risk (VaR), described as elicitable but not coherent, with Conditional Value at Risk (CVaR), also called Expected Shortfall, described as coherent but not elicitable. The cited explanation connects elicitability to the ability to verify and compare estimation procedures using historical data, a useful property when choosing among competing risk forecasts.

The response says quantile-based measures such as VaR are elicitable and mentions conditional VaR, or CoVaR, as a possible alternative for describing one institution’s distress conditional on another’s. It offers no derivation, scoring rule, or detailed comparison of VaR, CVaR, and CoVaR, so it serves as a brief orientation rather than a full treatment. The discussion is limited to forecast evaluation and does not explain how to estimate or validate these measures in practice.

Key ideas

• Elicitability concerns whether competing estimates of a risk measure can be verified and compared using data.
• The document identifies VaR as elicitable and CVaR as coherent but not elicitable.
• Quantile-based measures, including VaR, are cited as elicitable.
• CoVaR is mentioned as a conditional measure related to another institution’s distress.
• The response gives no scoring rules or detailed practical evaluation method.

Tags

# Elicitability of risk measures


# Elicitability of risk measures












I read that CVaR (Conditional Value-at-Risk, also Expected Shortfall), satisfies coherence, but not Elicitability.

On the other hand, VaR satisfies Elicitability, but not coherence.

What is Elicitability?

## Answer by guihp (score 1, accepted)

https://quant.stackexchange.com/a/14997

From Ziegel (2013) : The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible, are called elicitable. It is known that quantile based risk measures such as value at risk are elicitable.

Better use CoVaR in fact (Value at risk conditional to other value at risk, as a conditional co-movement of another institution's distress)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.