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 by construction for any distribution whatsoever, so summing stand-alone cell VaRs is inherently conservative and the correlation haircut on top is harmless; the only real flaw in the proposal is operational inefficiency from double-counting overlapping exposures, not any genuine capital shortfall for the institution overall.
3. Operational losses effectively become thin-tailed once loss frequency is folded into the aggregate distribution, so the Gaussian correlation framework long used for market-risk aggregation applies directly here as well, meaning the quant's proposed correlation-haircut aggregation method for the seven cells is in fact entirely correct exactly as proposed.
4. The real flaw is that the seven Basel event-type cells are deemed perfectly correlated by regulation itself, so any claimed diversification benefit across them is strictly prohibited, and the only valid aggregate figure is therefore the simple unadjusted sum with zero haircut applied, irrespective of each cell's severity tail behavior or shape.

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