hard · FRM Part 2 Operational Risk

Why is this approach fundamentally flawed for operational risk severity, and what is the correct principle?

1. For subexponential severities, value-at-risk can be super-additive in the tail, so summing stand-alone VaRs need not even be an upper bound; a correlation-based haircut can understate capital, and aggregation must instead be done by convolving the cell distributions (e.g., via a dependence structure on the aggregate losses) before reading the 99.9% quantile.
2. VaR is always subadditive, so summing stand-alone VaRs is conservative and the correlation haircut is harmless; the only flaw is operational inefficiency from double-counting, not a capital-adequacy concern.
3. Operational losses are thin-tailed once frequency is included, so the Gaussian correlation framework from market risk applies directly and the proposed method is in fact correct.
4. The flaw is that the seven Basel cells are perfectly correlated by regulation, so any diversification benefit is prohibited and the only valid number is the simple sum with zero haircut, irrespective of the severity distribution's tail behavior.

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