Operational risk and the Solvency II capital aggregation formula: Implications of the hidden correlation assumptions

We analyze the Solvency II standard formula (SF) for capital risk aggregation in relation to the treatment of operational risk (OR) capital. We show that the SF implicitly assumes that the correlation between OR and the other risks is very high: a situation that seems to be at odds with both the empirical evidence and the view of most industry participants. We also show that this formula, which somehow obscures the correlation assumptions, gives different insurance companies different benefits for diversification effects in relation to OR. Unfortunately, these benefits are based on the relative weights of the six basic capital components and not on any risk-related metric. Hence, contrary to what has been claimed, the SF does give diversification benefits (although minor ones) in relation to OR. Further, since the SF does not treat the correlation between OR and the other risks explicitly, it provides no incentive to gather data regarding this effect. Given all these considerations, for the time being, we recommend the adoption of the well-known linear aggregation formula, using low-to-moderate correlation assumptions between OR and the other risks.