Modelling Asset Correlations of Revolving Loan Defaults in South Africa

This paper examines the extraction of the empirical asset correlation for three datasets of monthly defaults on loans and credit cards obtained from the SARB from February 2006 to January 2017. The study makes use of the Beta and Vasicek distributions over a static period of time, as well as a rolling period of time. However two different calculation approaches (mode and percentile) are used for the Vasicek distribution assumption. We first use these three distinct calculation approaches to empirically estimate the asset correlation over a static period of time and compare them to the BCBS (Basel Committee for Bank Supervision) prescribed asset correlations. The computed empirical asset correlations are thereafter used to determine the economic capital and compare it to the economic capital determined using the BCBS prescribed asset correlations. Secondly, we use these three distinct calculation approaches to empirically estimate the asset correlation over a rolling five-year period and compare them to the BCBS’ prescribed asset correlations. For both the static and five-year rolling empirical asset correlations, we show that the BCBS’ prescribed asset correlations are much higher than the empirical asset correlations for the South African loans dataset. However, the opposite is found for both the credit card default and writeoff datasets which had higher empirical asset correlations. The economic capital charge calculated using the computed empirical asset correlations is lower than the economic capital calculated using the BCBS’ prescribed asset correlations for the South African loans dataset, while the opposite result is found for both the credit card default and write-off datasets. This result implies that the BCBS’ prescribed asset correlation is not as conservative as intended for South African bank specific credit cards and that the required capital charge stipulated by the BCBS is not sufficient to cover unexpected losses. This may have dire consequences to the South African banking system through ...