Why is time-scaling Cornish-Fisher VaR more delicate than scaling normal VaR?

Question

AcadiFi · Accepted Answer

Cornish-Fisher VaR modifies a normal quantile using skewness and kurtosis. That is why time scaling is more delicate. Under normal independent returns, volatility scales with the square root of time and the quantile adjustment is straightforward. Once skewness and kurtosis enter, their behavior across horizons depends on distributional assumptions and aggregation rules.

Suppose Westhaven Treasury estimates one-day modified VaR for a rates portfolio using volatility, skewness, and excess kurtosis. Scaling the final one-day modified VaR by the square root of ten may look convenient, but it may not preserve the intended higher-moment adjustment. Skewness and kurtosis can decay or transform with aggregation in ways that are not captured by simple volatility scaling.

The FRM lesson is that modified VaR is only as reliable as the assumptions behind the moments. If a question assumes independent identically distributed returns with stable moments, you may be able to derive horizon adjustments. If the question gives fat tails, skew, or volatility clustering, be suspicious of naive scaling. The more the measure departs from normal VaR, the more careful you must be about horizon conversion. On the exam, also state the horizon, confidence level, data source, modeling assumption, and validation step, because those choices usually explain why two reasonable VaR answers differ materially. Practice more in our FRM question bank.

Why is time-scaling Cornish-Fisher VaR more delicate than scaling normal VaR?

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