Coherent Risk Measures as Alternatives to VaR

Summary

The document asks how to respond when realized losses exceed a value-at-risk limit more often than the model allows. It raises possible actions such as changing the VaR simulation approach, applying an additional capital factor, or switching to expected shortfall. The answer points to coherent risk measures as a broader family of alternatives that retain useful risk-measure properties while addressing shortcomings associated with VaR.

It lists monotonicity, sub-additivity, homogeneity, and translation invariance as the defining properties, and identifies conditional value-at-risk as an example. The response is brief and conceptual: it does not give a model-validation procedure, explain how to diagnose why exceedances occur, or prescribe a regulatory or capital response. Thus it introduces a class of alternatives rather than resolving whether a particular VaR model should be recalibrated, replaced, or supplemented.

Key ideas

• Frequent VaR exceedances prompt a review of the risk model and its assumptions.
• Coherent risk measures are characterized by monotonicity, sub-additivity, homogeneity, and translation invariance.
• Conditional value-at-risk is given as an example of a coherent measure and an alternative to VaR.
• The answer does not specify an operational response or explain how to diagnose exceedance causes.

Tags

# What would be an alternative if the VaR model is not acceptable?


# What would be an alternative if the VaR model is not acceptable?












Assume we have a VaR model wich says : the lost should not exceed X for more 3 days and we come up with more days where the lost exceeded X, what is usually done for the VaR model ?

Do we switch to Monte Carlo VaR ? Do we keep the same VaR and add a security factor in the computing the required capital ? Do we switch to excepcted shortfall ?

## Answer by vonjd (score 3, accepted)

https://quant.stackexchange.com/a/10478

In general I would answer your question in the following way: Alternatives to VaR which share most of its helpful properties but not its shortcomings are the so called coherent risk measures. They have the following properties:

- monotonicity

- sub-additivity

- homogeneity and

- translational invariance

One example would be the conditional value-at-risk.

You can find more on Wikipedia:

- coherent risk measures

- conditional value-at-risk

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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