hard · FRM Part 2 Operational Risk

Which statement best identifies the reason the SLA is biased here and the direction of the bias?

1. The SLA omits the mean-aggregate offset entirely; because the body of this compound Poisson-lognormal loss distribution contributes a genuine positive shift, the SLA thus understates true 99.9% VaR by roughly the full expected aggregate annual loss.
2. The SLA is asymptotically exact only as αto1 for subexponential severities, but at finite λ and high σ it should be corrected upward by adding the mean of the aggregate loss, λ,e^μ+σ^2/2, which the first-order SLA drops.
3. The SLA overstates the true 99.9% VaR because it attributes the entire capital charge to a single extreme loss, whereas genuine diversification benefit across the λ= 20 expected annual events lowers the aggregate quantile by a factor tied to √(λ).
4. The SLA is essentially unbiased for any subexponential severity distribution once α= 99.9% is reached, so the reviewer's concern is mistaken; the apparent capital gap here is merely an artifact of computing F^-1 in log-dollar space rather than in raw dollars.

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