medium · FRM Part 2 Market Risk
A risk manager is using the Cornish–Fisher expansion to adjust a 99% VaR. The sample has a standard deviation of 2%, negative skewness of -0.5, and excess kurtosis of 2.0. Compared to a standard Normal VaR calculation (z = -2.326), the Cornish-Fisher adjusted quantile (q_CF) will be:
- Unchanged because the Normal distribution is the limit of the expansion.
- Equal to the Expected Shortfall (ES) of the Normal distribution.
- Further in the tail (more negative), increasing the VaR.
- Closer to the mean, decreasing the VaR.
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