Top-Down Versus Bottom-Up Approaches in Risk Management

Abstract

Banks and other financial institutions face the necessity to merge the economic capital for credit risk, market risk, operational risk and other risk types to one overall economic capital number to assess their capital adequacy in relation to their risk profile. Beside just adding the economic capital numbers or assuming multivariate normality, the top-down and the bottom-up approach have been emerged recently as more sophisticated methods for solving this problem. In the top-down approach, copula functions are employed for linking the marginal distributions of profit and losses resulting from different risks. In contrast, in the bottom-up approach, different risk types are modelled and measured simultaneously in one common framework. Thus, there is no need for a later aggregation of risk-specific economic capital numbers. In this paper, these two approaches are compared with respect to their ability to predict loss distributions correctly. We find that the top-down approach can underestimate the true risk measures for lower investment grade issuers. The accuracy of the marginal loss distributions, the employed copula function, and the loss definitions have an impact on the performance of the top-down approach. Unfortunately, given limited access to times series data of market and credit risk loss returns, it is rather difficult to decide which copula function an adequate modelling approach for reality is.