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 fully cancel out, leaving q_CF ≈ q_norm overall.
- The q_CF will actually be less negative, reflecting a claimed diversification benefit from fat tails.
- The q_CF will be more negative (larger in absolute value), leading to a higher VaR than the normal assumption.
- The Cornish-Fisher expansion technically applies only to Expected Shortfall (ES) figures, and never to Value at Risk (VaR).
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