medium · Frm Part 2 Market Risk
A bank is using the Cornish-Fisher expansion to adjust its VaR for non-normal skewness (S) and excess kurtosis (K).
If a portfolio has negative skewness (S < 0) and positive excess kurtosis (K > 0), how will the Cornish-Fisher adjusted quantile (q_CF) compare to the standard normal quantile (q_norm)?
- The skewness and kurtosis effects will cancel each other out, leaving q_CF ≈ q_norm.
- The q_CF will be less negative, reflecting the 'diversification benefit' of fat-tailed assets.
- The q_CF will be more negative (larger in absolute value), leading to a higher VaR than the normal assumption.
- The Cornish-Fisher expansion only applies to Expected Shortfall (ES), not to Value at Risk (VaR).
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