Skip to content

Square-root scaling the whole normal VaR

When mean period loss is nonzero, multiplying the whole one-period VaR by √n generally gives the wrong aggregate.

On this page

Use the original independent model

Each of five independent identically distributed normal period losses has mean 2 and dispersion 10. The aggregate is their sum, not a compounded return. Confidence remains 95%.

Scale the two moments separately

Aggregate mean is 5×2=10 and dispersion √5×10. Correct aggregate VaR is 10+√5×10×z95≈46.780045. The mean term scales with five rather than √5.

Inspect the whole-number shortcut

One-period VaR is 2+10×z95≈18.448536. Multiplying that entire number by √5 gives approximately 41.252181. The difference comes from scaling the mean incorrectly, even though the dispersion scaling is valid under the supplied independence.

Keep the horizon model explicit

With dependent or different period losses, even the variance scaling changes. The tool performs a one-horizon calculation only. Do not use a valid independent-normal identity as a universal market-horizon rule.

Further references