As from title, can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative?


The formula for VaR equivalent volatility (from here) is :

$$\frac{\sqrt{3.842 - 2 \ln{\mathrm{VaR}}} - 1.96}{\sqrt{T}}$$

which looks like this (for T=1):

VaR equivalent vol.

where the x axis is VaR.

Since VaR is bounded between 0 and 1, no you cannot have a negative VaR equivalent volatility.

Indeed, from the paper I have stated above, it is written on page 29:

"The VaR is the percentage of the amount paid that is returned to the retail investor"

Therefore, you can say something like this:

$$ \begin{align} \frac{\sqrt{3.842 - 2 \ln{\mathrm{VaR}}} - 1.96}{\sqrt{T}} &\geqslant 0 \\ 3.842 - 2 \ln{\mathrm{VaR}} &\geqslant 1.96^2 \\ - 2 \ln{\mathrm{VaR}} &\geqslant 1.96^2 - 3.842\\ - 2 \ln{\mathrm{VaR}} &\geqslant -0.0004\\ \ln{\mathrm{VaR}} &\leqslant 0.0002\\ \mathrm{VaR} &\leqslant e^{0.0002}\\ \mathrm{VaR} &\leqslant 1.00040008001\\ \end{align}$$ Implying that while $\mathrm{VaR} \leqslant 1.00040008001$, the VaR implied vol. is positive.

  • $\begingroup$ Thanks but VaR cannnot be outside the 0-1 interval if it is computed with Cornish Fisher expansion, am I right? $\endgroup$ – Thegamer23 May 11 '17 at 9:20
  • $\begingroup$ @Simons123 VaR is the probability of a loss, so if you're computing it to be outside of this integral, then you've made a mistake... $\endgroup$ – will May 11 '17 at 9:27
  • $\begingroup$ Ok I got your point but I do not agree. Actually that is because you are giving a theoretical answer. But if you take the VaR as the percentile of an historical distribution over a given horizon you might have (e.g. in a series of all positive returns) a positive VaR. $\endgroup$ – Thegamer23 May 11 '17 at 10:14
  • $\begingroup$ So is your question "If i use a flawed method to calculate VaR such that i end up with it outside of the range of actually attainable values of VaR, can this formula result in a negative VEV?" ? $\endgroup$ – will May 11 '17 at 10:18
  • $\begingroup$ Actually it is the law that requires that methodology cfr. "as defined by..." btw I agree with you $\endgroup$ – Thegamer23 May 11 '17 at 10:27

VeV under PRIIPS will be negative if the "loss" at the 2.5% cutoff is actually a gain

Imagine a product where you receive a small positive coupon C with probability 0.99, full capital loss with probability 0.01

This product will have a negative VeV and thus score MRM1


VEV can also be negative in the following case (please correct me if I'm wrong):

for a category 3 product characterized by an uconditional protection of capital, you have to calc the pV. With negative risk free rates, dfs are >1 and thus VaR as a percentage of the invested amount is >1. i.e:

Amount= 10,000 ,Residual= 145 , Risk free= -0.295% , PV= 10,011.75 , VaR [Price Space]= 1.001174886, VEV= -0.079%

Does it look OK to you?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.