VaR, Coherent Risk Measures, and Desk-Level Sensitivities

Summary

The document contrasts coherent risk measures with Value at Risk (VaR), a widely used metric that can fail sub-additivity. Under a normal return distribution, VaR is sub-additive, but that property is not assured when the distribution departs from normality. The response therefore mentions Conditional Value at Risk (CVaR) as another measure with sub-additivity, while noting that institutions may use proprietary models.

A second answer describes practice at small and mid-sized German banks: VaR is commonly used for overall bank steering, while traders use portfolio or desk sensitivities such as delta, gamma, vega, basis point value, and duration. This illustrates that aggregate risk oversight and day-to-day position management can rely on different measures. The observations are not a universal survey of financial institutions, and the document offers no comparative performance evidence or detailed implementation guidance. Risk measurement choices depend on institutional models and the intended level of control.

Key ideas

• VaR can violate sub-additivity, although it is sub-additive under a normal distribution assumption.
• CVaR is presented as a sub-additive alternative to VaR.
• Financial institutions may rely on proprietary risk models.
• VaR may support overall bank steering while sensitivities guide desk and portfolio management.

Tags

# Ways most financial institutions measure risk


# Ways most financial institutions measure risk












Does most financial institutions measure risks in terms of https://en.wikipedia.org/wiki/Coherent_risk_measure? Or are they using other/newer theoretical tools?

## Answer by Martin Vesely (score 2, accepted)

https://quant.stackexchange.com/a/53444

For example VaR, one of most widely used measure, is not coherent measure because it does not satisfy always sub-additivity property. However, under asumption of a normal distribution, VaR is sub-additive measure.

Since we cannot be sure whether normality assumption is satisfied, we have to combine VaR with other measures, for example CVaR which is sub-additive.

To be more concrete is difficult because each bank/financial institution has its own proprietary models.

## Answer by simzoor (score 3)

https://quant.stackexchange.com/a/53450

I can confirm that for most small/mid sized banks in Germany, VaR is the most popular risk metric out there. While VaR is used for overall bank steering, banks (i.e. traders) use sensitivities (Delta, Gamma, Vega, BPV, Duration etc.) for desk/portfolio steering.

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.