Abstract
This study examines the extraction of the empirical asset correlation for three datasets using both the Beta and Vasicek distributions over a static period of time, as well as a rolling period of time. The computed empirical asset correlations are thereafter used to determine the economic capital. The first two datasets relate to a sample of credit card accounts from a South African bank1 . The first dataset contains monthly defaulted data which spans nine years (i.e February 2006-September 2015) and was calculated by taking yearly cohorts of actual defaulted customers as a percentage of open, performing customers at the beginning of each yearly cohort. The second dataset spans ten years (i.e January 2007-May 2017) and was calculated by taking the actual monthly write-off amount as a percentage of the monthly total exposure on the balance sheet. The third dataset contains data for all loans issued in South Africa2 which spans some nine years of monthly data (i.e June 2008- January 2017). This data was collected from the SARB (Venter, 2017) by dividing the monthly impaired advances by the monthly total exposure on the balance sheet. Two distributions have been selected for this study, the Beta and Vasicek distributions, 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 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 systemic risk. Therefore, we recommend that the capital levels be raised to match the capital levels determined in this study.
M.Com. (Financial Economics)