Risk Aggregation, Tail Risk, Correlation : Capital Allocation Efficiency and Regulator-Set Standard Models for Bank Capital

In modern frameworks for financial regulation such as Basel III, IV as well as Solvency II, financial institutions are regulated to maintain a certain level of capital to prepare for potential future losses. In this paper, we take the perspective of a regulator who designs regulatory capital principles to calculate the amount of capital required for financial institutions bearing risks.We review the implications for regulatory capital requirement resulting from the risk model and risk classes aggregation approaches in the Standardised Approach (SA) and Simplified Standard Approach (SSA) frameworks of the FRTB. We highlight a number of significant issues for the efficiency of regulatory capital allocation in the banking sector, as a result of the risk measure implementation framework and adopted risk aggregation methods in the SSA. In particular, we show that risk aggregation turns out to be inconsistent with a coherent-type of risk measure, which would be a necessary condition for a “coherent” capital allocation rule implementation (such as the Euler rule). Moreover, we reckon that aggregating risk classes by adding up stand-alone risk measures (e.g., assuming perfect correlation across risk classes) can induce large overestimates of capital requirements within the SSA framework. According to the Basel Committee of Banking Supervision estimates banks that are likely to adopt the SA approaches are expected to reckon an average increase in regulatory capital of 30 (SA banks) and 58 percent (SSA banks), while IMA banks' average capital requirement increase is limited to 20 percent.We argue, based on some recent academic studies and modeling evidence on financial risk, that the implied excess capital as a result of assuming perfect correlation across risk classes in the SSA framework cannot be convincingly justified by appealing to a generic quest for prudent regulatory capital fixing rule, (perhaps) anchored into some (vaguely specified) concept of “model risk”, whose technical apparatus needs some effective expedient to be pragmatically implemented in a (simplified) risk model approach. Sure enough, model uncertainty is a vital component of the current challenges in risk measurement, and therefore the regulator should design risk measures encouraging well-understood prudent decisions over (less understood) risky ones. From this perspective robust regulation should be a desirable goal. To achieve such an objective, simple – but not simpler – rules are needed