# 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

• Usually you can write $VaR = q \sqrt(\sigma^2 T)$ and then you invert the formula and solve for $\sigma^2$ (=VEV). In the PRIIP context they use a bit of more assumptions and that's why the constants are different – Ric Apr 7 at 17:33
• The answer given below is a good reference to an earlier question. However, in case you might over see this: the formula quoted by you is wrong (don't worry, you copied it correctly, it is wrong in the regulation of PRIIPs). You will discover this when solving the quadratic equation which appears starting from the VaR. In particular, the 97.5 quantile (-1.96) needs to be outside the square root but stays together in the numerator together with the square root. So it is: $VEV = \frac{\sqrt{(1.96)^2 \cdot VaR}-1.96}{\sqrt{T}}$ – Fokko Apr 9 at 10:54

## 1 Answer

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.