Undoubtedly there is enforced or assumed sub-additivity in the standard solvency capital reserve formula (SCR) – equation (1) on the picture. The SCR metric by line, geo-admin unit, peril, risk factor is a value at risk metric. By definition value at risk metrics are not guaranteed to be sub-additive. They are not guaranteed to be super-additive either. The relationship between the accumulated total SCR and the sum of the component SCR(s) is empirical and theoretically unknown. Still the standard SCR formula guarantees sub-additivity – equation (2). If the risk factors are guaranteed independent or very well-known and measured dependent in physical and economic laws such as geography, (in)dependence in catastrophe perils, financial diversification, this should be safe and acceptable. Still this practical practitioner view will not agree with the purist mathematician’s view of the modeling world. The latter will require the construction of a multivariate probabilistic distribution or copula – equation (3) from the marginal distributions of all risk factors – equations (5). Only from the combined aggregate distribution of all risk factors in the portfolio one could then coherently measure the portfolio SCR, and since it is a value at risk type metric, it is not guaranteed to be sub or super-additive. It is an empirical and scenario based relationship. The standard formula also guarantees that a back-allocated single risk factor SCR (i.e. component SCR) is less than the same stand-alone SCR – equation 4. The economists will immediately see the benefits of diversification and market scale. However the true coherent back-allocated SCR from the joint distribution is not that easy to compute, and it is certainly not guaranteed to behave predictably versus the stand-alone SCR.
Category: Climate/natural disasters: Disaster risk, Earthquakes, Floods/storms
Location: Montreal, QC, Canada