Abstract
M.Com.
This study uses the aggregate balance sheet and income statement of South African banks to implement a risk aggregation model that aggregates credit, market and operational risks with the aim of generating total risk estimates using both Value at Risk (VaR) and Expected Shortfall (ES) as risk measures. The results are thereafter used to determine the supplemental Pillar II economic capital required in order to maintain the capital adequacy of the South African banking industry. We first model the return distributions due to credit and market risk using a multivariate risk factors sensitivity model, with the macroeconomic risk factors’ dynamics modelled through an asymmetric GARCH (generalize Autoregressive Conditional Heteroskedasticity) model designed by Baba, Engle, Kraft and Krona (1990) (i.e. BEKK). Operational risk losses are assumed to follow a lognormal distribution. The Gaussian copula and t-copulas are then used to aggregate the three loss distributions (i.e. credit, market and operational risk distributions). The total risk given by copulas is compared to the total risk calculated through the less complex simple additive and variance-covariance methods. Our results suggest that the South African banking sector’s Pillar I regulatory capital as at end of December 2015 should be supplemented by an amount of approximately 52 billion ZAR when using as a benchmark the Gaussian copula risk aggregation model measured through the ES metric at 99.9% confidence level. These results suggest that the Pillar 2A capital requirement imposed by the SARB should double from the current maximum of 2% to 4%.