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Modelling Asset Correlations of Revolving Loan Defaults in South Africa

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Modelling Asset Correlations of Revolving Loan Defaults in South Africa COPYRIGHT AND CITATION CONSIDERATIONS FOR THIS THESIS/ DISSERTATION o Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. o NonCommercial — You may not use the material for commercial purposes. o ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. How to cite this thesis Surname, Initial(s). (2012). Title of the thesis or dissertation (Doctoral Thesis / Master’s Dissertation). Johannesburg: University of Johannesburg. Available from: http://hdl.handle.net/102000/0002 (Accessed: 22 August 2017). Modelling asset correlations of revolving loan defaults in South Africa by BONGANI MHLOPHE MINOR DISSERTATION Submitted in partial fulfillment of the requirements for the degree MAGISTER COMMERCII in FINANCIAL ECONOMICS in the FACULTY OF ECONOMICS AND ECONOMETRICS at the UNIVERSITY OF JOHANNESBURG SUPERVISOR: Professor J.W. Muteba Mwamba December 18, 2019 Dedication I would like to dedicate this dissertation to our Lord and Saviour Jesus Christ for granting me the intellectual ability to be able to embark on this journey. I would also like to dedicate this work to my wife, Thandi Mataboge, and my son, Simnikiwe Mhlophe, for being patient with me and supporting me throughout the late nights spent away from them. In closing, I would also like to thank my grandmother, aunt and siblings for the words of encouragement and, lastly, my late parents. 1 Acknowledgments I would like to give thanks to the following people/institutions: • My employer, for providing the finance for my Master’s degree. • Bank X and the SARB for providing me with the data for the research. • Professor J.W. Muteba Mwamba, my supervisor, for guiding and providing me with support throughout this journey. 2 Contents 1 Introduction1 Background................................... 3 The BCBS................................. 6 The Basel Capital Accords........................ 8 The introduction of Basel I as a first attempt at capital regu- lation .......................... 8 The introduction of Basel II as a replacement to Basel I . 9 The Basel III Accord: "A global regulatory framework for more resilient banks and banking systems" . 16 The South African Economic Landscape ................... 19 The South African Credit Card Landscape . 21 Problem statement and objectives ....................... 22 Dissertation Outline .............................. 24 2 Literature Review 25 3 Methodology 34 3.1 The Methodology and Parameter estimations . 34 3.1.1 The ASRF approach: The mathematics behind the model . 34 3.1.2 Distributions ........................... 35 3.1.2.1 The Beta Distribution . 35 3.1.2.1.1 Empirical extraction of the asset correlation based on the beta distribution . 37 3.1.2.2 Vasicek distribution . 39 3.1.2.2.1 Empirical extraction of the asset correlation based on the Mode approach of the Vasicek distribution . 40 3.1.2.2.2 Empirical extraction of the asset correlation based on the Percentile approach of the Va- sicek distribution . 42 4 Empirical analysis 44 4.1 Data used in the study .......................... 44 4.2 Empirical results ............................. 46 5 Conclusions, Research Limitations and Recommendations for Fu- ture Investigations 60 5.1 Conclusion ................................. 60 5.2 Limitations ................................ 62 3 5.3 Recommendations............................. 62 References 64 4 List of Tables 1.1 Basel II Capital Calculation Approaches . 12 1.2 Asset correlations descriptions ...................... 16 1.3 The extent of bank failures in South Africa post democracy . 20 4.1 Asset classes for our data and their Basel II asset classification . 45 4.2 LGD data for the banks that participated in the BCBS’ 5th Quanti- tative Impact study ............................ 46 4.3 Credit Card Empirical correlations compared to Basel II correlations 50 4.4 Comparison of the South African commercial loans empirical asset correlations and the BCBS-specified asset correlations . 51 4.5 Comparison of Bank X’s Credit Card Capital Charge (Relative to Basel Capital Charges .......................... 52 4.6 Comparison of South African Commercial Loans Ratio of the Capital charge (Relative to the ratio of the Basel Capital Charge) . 53 5.1 The average asset correlation determined using the default data . 60 5.2 The average asset correlation determined using the write-off data . 61 5.3 A presentation of the correlation results based on publications . 61 5 List of Figures 1.1 The loss distribution that contains a total loss at the 99:9th percentile. Source: Stoffberg & van Vuuren, 2015 . 13 4.1 (a) The cumulative, and (b) the density function for Credit Card Actual Default Rate losses from February 2006 to September 2015. 47 4.2 (a) The cumulative, and (b) the density function for Credit Card Write-Off data from January 2007 to May 2017. 48 4.3 (a) The cumulative, and (b) the density function for the South African Commercial Loans from June 2008 - December 2016. 49 4.4 A comparison of the empirical asset correlations compared to Basel specified asset correlations using the actual default data . 50 4.5 A comparison of the empirical asset correlations compared to Basel specified asset correlations using the Write-Off data . 50 4.6 South African commercial loans empirical correlations compared to Basel II correlations ........................... 52 4.7 Comparison of Bank X’s Credit Cards Ratio of the Capital charge (Relative to the ratio of the Basel Capital Charge) . 52 4.8 Comparison of South African Commercial Loans Ratio of the Capital charge (Relative to the ratio of the Basel Capital Charge) . 54 4.9 A comparison of the five-year rolling empirical asset correlations to the Basel specified rolling asset correlations for the South African commercial loans data .......................... 56 4.10 A comparison of the five-year rolling empirical asset correlations to the Basel specified rolling asset correlations for Bank X’s credit card default data ................................ 56 4.11 A comparison of the 5-year rolling empirical asset correlations to the Basel specified rolling asset correlations for Bank X’s Credit Card Write-off Data. .............................. 58 6 Abbreviations ASRF Asymptotic Single Risk Factor BCBS Basel Committee on Banking Supervision BIS Bank of International Settlements CDF Cumulative Density Function EAD Exposure at Default IRB Internal ratings-based LCR Liquidity Coverage Ratio LGD Loss Given Default NSFR Net Stable Funding Ratio PD Probability of Default PDF Probability Density Function RWA Risk-weighted assets SA Standardised Approach SARB South African Reserve Bank 7 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 con- tains 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 calcu- lated 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 distribu- tions, however two different calculation approaches (mode and percentile) are used for the Vasicek distribution assumption. We first use these three distinct calcula- tion 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 empiri- cally 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 write- off 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
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