PRIIPs KID: if VaR (Return Space) < -1, how to compute VEV (VaR-equivalent volatility)?

Question

The PRIIPs regulation does not specify how to compute the VaR-equivalent volatility if $VaR_{Return Space} < -1$. What would you do in the following case?

I have the following moments from the historical daily log-returns of a stock:

$M1 = 0.0019$ (Mean)

$\sigma = 0.0378$ (Standard Deviation)

$\mu_1 = 0.9201$ (Skewness)

$\mu_2 = 12.068$ (Excess Kurtosis)

Assume

$T = 1$ (asset’s holding period in years)

$N = 256$ (number of trading periods in days)

Then, the Cornish-Fisher VaR
 is: \begin{eqnarray} VaR_{Return Space} &=& \sigma \sqrt{N} * (− 1.96 + 0.474 * \mu_1/\sqrt{N} - 0.0687 * \mu_2/N + 0.146* \mu_{1}^2/N) − 0.5 \sigma^2 N \\ &=& -1.3534 \end{eqnarray}

Given that $VaR_{Return Space}$ is below - 1, which of these two VEVs would be the correct one:

(1) Simply apply the formula and obtain: \begin{eqnarray} VEV &=& (\sqrt{3.842-2*VaR_{Return Space}}-1.96)/\sqrt{T} \\ &=& \sqrt{3.842-2*(-1.3534)}-1.96 \\ &=& 0.5990 \end{eqnarray}

(2) Since an investor cannot lose more than the initial investment, put a floor to $VaR_{Return Space} = -1$ and get \begin{eqnarray} VEV &=& \sqrt{3.842-2*(-1)}-1.96 \\ &=& 0.4570 \end{eqnarray}

Answer 1

I glimpsed at the regulation: In Annex II, part 1, no 11 and 12, they define the return as log-returns, see screenshot:

Hence, I'd argue that you should use your calculation 1.