Consolidating Multi-Factor Models of Systematic Risk with Regulatory Capital

Abstract: To maintain solvency intimes of severe economic downturns banks and financialinstitutions keep capital cushions that reflect the risks in the balance sheet.Broadly,how much capital that is being held is a combination of external requirementsfromregulators and internal assessments of credit risk. We discuss alternatives totheBasel Pillar II capital add-on based on multi-factor models for held capitaland howthese can be applied so that only concentration (or sector) risk affects theoutcome,even in a portfolio with prominent idiosyncratic risk. Further, the stabilityandreliability of these models are evaluated. We found that this idiosyncraticrisk canefficiently be removed both on a sector and a portfolio level and that themulti-factormodels tested converge.We introduce two new indices based on Risk Weighted Assets (RI) and EconomicCapital (EI). Both show the desired effect of an intuitive dependence on the PDand LGD. Moreover, EI shows a dependence on the inter-sector correlation. Inthesample portfolio, we show that the high concentration in one sector could be(better)justified by these methods when the low average LGD and PD of this sector weretaken into consideration.