Modelling Aggregate Risk of the South African Banking
Industry: An Application to Pillar II Economic Capital

Dingaan Jack Khoza and J.W. Muteba Mwamba
University of Johannesburg


In this paper, we aggregate credit, market and operational risks to determine the economic capital required by Basel regulations’ Pillar II to ensure that South African banks are sound and do not pose a threat to financial stability. We first model the return distributions due to credit and market risks using macroeconomic risk factors by applying an asymmetric GARCH model, and we fit the distribution of operational risk losses to a lognormal distribution. We thereafter aggregate these risk measures using traditional approaches (simple additive and variance-covariance) and the modern approach (copula). For the modern approach, we use the Gaussian copula and t-Copula. Our results based on aggregate balance sheet and income statement data of South African banks collected for the period 2008 to 2015 show that traditional measures over-estimate the regulatory capital by an average of 55% when compared to the modern approach. In addition, our results indicate that diversification benefits increase as one moves from less complex risk aggregation methods (i.e. simple additive and variancecovariance methods) to the more advanced forms of risk aggregation (copula).