# Negative VaR equivalent Volatility (VEV) and its meaning?

Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?

## 1 Answer

You can attain negative VEV if the "loss" measured at the 2.5% percentile is actually a gain.

I build you a product where you lose all capital with 1% measured probability and pay you a coupon with the proceeds.

Under VEV, it will attain a MRM of 1 (I.e. cash-like)

• I have a product, where are acutally no possible losses, i.e. the return is limited below through its initial value. Does it mean that products with no possible losses have a negative VEV? – SinusK Jun 18 '18 at 20:44
• If the undiscounted return is even slightly positive at 2.5% ptile, then yes you get a negative VeV. If it is zero return then you get a zero VEV I think – James Spencer-Lavan Jun 18 '18 at 20:56
• @James Spencer-Lavan. The PRIIPS regulations specify that the mean return used when calculating the VEV is 0.0. Hence, whilst I accept that a product such as yours could be constructed to have a negative VEV if you ignore that constraint, I think the PRIIPS VEV would always be >=0 (see pp. 6 & 7 @ ec.europa.eu/transparency/regdoc/rep/3/2017/EN/…) – Tim Wilding Jun 19 '18 at 14:33
• The mean return of the underlying asset is either zero (If stress scenario) or risk neutral (or historical drift depending upon your views) for the other scenarios. But the MRM is always calculated off cashflows, not asset returns. So it is actually very easy to end up with negative VEV; you only need to solve for a measured probability of any loss being less than 2.5%. Sell a vanilla put at maturity for lower and lower strike; initially MRM will increase as conditional loss increases, then it falls to MRM 1 when loss probability less than 2.5% – James Spencer-Lavan Jun 19 '18 at 15:12