1
$\begingroup$

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}

$\endgroup$

1 Answer 1

1
$\begingroup$

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

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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