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Interpreting VaR-Equivalent Volatility as an Implied Normal Scale

Article Quant Q&A · Author: TheEditingify
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Summary

VaR-equivalent volatility (VeV) is interpreted as the volatility scale that would produce the specified value-at-risk under a particular normal-return assumption. The answer describes it as an equivalent parameter obtained by inverting the VaR formula, rather than as a separate, directly observed measure of market variability. Under the stated setup, returns are modeled with a normal distribution whose mean includes a negative half-variance adjustment over the time horizon, and whose variance grows with that horizon.

This interpretation is conditional on the assumed distribution and the VaR convention used in the inversion. VeV therefore expresses a VaR result in volatility-like terms, but it does not establish that actual returns are normal or that their tails are accurately represented by the model. The brief response points to a fuller derivation elsewhere but provides no empirical example or discussion of how the measure performs when return distributions depart from the assumption.

Key ideas

  • VeV is the normal volatility scale implied by a VaR value under the specified model.
  • It is calculated by inverting a VaR formula rather than measuring volatility directly from returns.
  • The stated return model includes a horizon-dependent mean adjustment and variance.
  • Interpreting VeV depends on the distributional and VaR assumptions used in the calculation.

Tags

VolatilityRisk managementStatistics
Full text
# VaR equivalent volatility meaning


# VaR equivalent volatility meaning












I have a hard time with interpreting VeV. I mean - I see its just standard deviation derived from Cornish-Fischer VaR, but I don't really know how to interpret it. The formula for VeV is:

```
VeV = sqrt(3.842-2*VaR-1.96)/sqrt(T)
```

Do you have any ideas? :)

Thanks in advance

## Answer by AdB (score 3)

https://quant.stackexchange.com/a/44982

VeV is simply the scale parameter $\sigma$ such that the returns follow the $N(-\dfrac{1}{2} \sigma T, \sigma^2T)$ distribution and is obtained by inverting the VaR formula under this assumption.

Have a look at this question where the full derivation of VeV is covered.

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.