Modelling Asset Correlations of Revolving Loan Defaults in South Africa

Muteba Mwamba, John Weirstrass and Mhlophe, Bongani (2019): Modelling Asset Correlations of Revolving Loan Defaults in South Africa.

Abstract

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 systemic risk. Therefore, we recommend that the capital levels be raised to match the capital levels determined in this study.

• Item Type: MPRA Paper
• Language: English
• Keywords: asset correlation, Vasicek distribution, Beta distribution, BCBS, economic capital, credit card defaults
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G3 - Corporate Finance and Governance

References

Bank for International Settlements (BIS) (2001). History of the Basel Committee and its membership, Basel, Switzerland, March 2001.

Basel Committee for Bank Supervision (BCBS) (1988). International convergence of capital measurement and capital standards, Basel, Switzerland.

BCBS. (2005). An explanatory note on the Basel II IRB risk weight functions, Basel, Switzerland.

BCBS. (2006). International Convergence of Capital Measurement and Capital Standards: A Revised Framework Comprehensive Version, Bank of International Settlements, June.

Bell, K. (2007). Poll: Mortgage is 1st payment priority, credit cards last, Available from: https://www.creditcards.com/credit-card-news/bill-pay-priorities- 1276.php

Bellotti, T. & Crook, J. (2012). Asset Correlations for Credit Card Defaults, Applied Financial Economics, 22:2, 87-95, DOI: 10.1080/09603107.2011.603689

Bieri, D.S. (2008). The Basel Process and Financial Stability. Bank for International Settlements, November.

Botha, M. & Van Vuuren, G. (2010). Implied Asset Correlation in Retail Loan Portfolios. Journal of Risk Management in Financial Institutions 3: 1–18.

Brown, R.J. (2005). Connecting the CDF and the PDF. Available from: http://demonstrations.wolfram.com/ConnectingTheCDFAndThePDF/

Bystrom, H. (2011). An Alternative Way of Estimating Asset Values and Asset Value Correlations, The Journal of Fixed Income 21: 30–38. doi:10.3905/jfi.2011.21.2.030.

Carver, L. (2014). Basel securitisation rules revisions criticised. Available from: https://www.risk.net/regulation/2325630/basel-securitisation-rules-revisions-criticised

Chernih, A. Vanduffel, S. & Henrard, L. (2006). Asset correlations: a literature review and analysis of the impact of dependent loss given defaults, Available from: https://pdfs.semanticscholar.org/abca/71f0bd5434d132761fe8d79875e8d6642c3a.pdf

Experian. (2017). Experian Consumer Credit Default Index. Available from: http://www.experian.co.za/consumer-information/default.html

Chummun, B.Z (2017). Mobile microinsurance and financial inclusion: the case of developing African countries. Africagrowth Agenda Journal Vol.2017, July September 2017:Pp 12-16

Gehrig, T. & Iannino, M.C. (2017). Did the Basel Process of Capital Regulation Enhance the Resiliency of European Banks?, CEPR Discussion Paper No. DP11920. Available at SSRN: https://ssrn.com/abstract=2937771

GUP, B. E. (2003). Basel II creates an uneven playing field. Available from: http://images.to.camcom.it/f/tofinanza/I_/I_64.pdf

Guttler, A. & Liedtke, H.G. (2007). Calibration of Internal Rating Systems: The Case of Dependent Default Events, Kredit und Kapital, 40, 527-552

Hansen, M., van Vuuren, G. and Ramadurai, K. (2008). Basel II Correlation Values - An Empirical Analysis of EL, UL and the IRB Model, Credit Market Research Financial Institutions Special Report, Fitch Ratings.

Hill, J. C. (2012). Basel I, Basel II and Solvency II, In: Risk Management and Financial Institutions. Hoboken: John Wiley & Sons Inc., pp. 257-284 Lang, J. (2009). Economic Capital – a common currency of risk, Available from: http://ozrisk.net/2009/04/20/economic-capital-a-common-currency-of-risk

LASTRA, R. M. (2004). Risk-Based Capital Requirements and Their Impact upon the Banking Industry: Basel II and CAD iii. Journal of Financial Regulation and Compliance 12: 225–239. doi:10.1108/13581980410810803.

Lee, S.C., Lin, C.T. & Yang, C.K. (2011). The asymmetric Behavior and Procyclical Impact of Asset Correlations, Journal of Banking & Finance 35: 2559–2568. doi:10.1016/j.jbankfin.2011.02.014.

Martin, L. (2013). Analysis of the IRB asset correlation coefficient with an application to a credit portfolio, Master’s thesis, Uppsala Universitet, 2013.

MFMA. (2004). No. 56 of 2003: Local Government: Municipal Finance Management Act, 2003, Vol. 464 Cape Town 13 February 2004 No. 26019.

Miu, P. & Ozdemir, B. (2006). Basel Requirement of Downturn LGD: Modeling and Estimating PD and LGD Correlations, Journal of Credit Risk 2: 43–68.

Moody’s Analytics. (2013). The Impact of Electronic Payments on Economic Growth. Available from: https://usa.visa.com/dam/VCOM/download/corporate/media/moodyseconomy- white-paper-feb-2013.pdf

Nachane, D. M., Ray, P. and Ghosh, S. (2005). The new Basel capital accord: rationale design and tentative implications for India. Available from: https://mpra.ub.unimuenchen.de/17426/1/MPRA_paper_17426.pdf

National Treasury. (2018). Treasury’s Response To The Vbs Mutual Bank Matter, National Treasury Media statement.

Newscientist. (2009). The credit crunch: What happened? Available from: https://www.newscientist.com/article/dn16783-the-credit-crunch-what-happened/

Nyaundi, D.N. (2015). The effects of capital adequacy requirements on liquidity of commercial banks in Kenya, Master’s thesis, University of Nairobi

Padayachee, V. (2012). Global economic recession: effects and implications for South Africa at a time of political challenges. Claves de la Economia Mundial, University of KwaZulu-Natal.

Resti, A. (2016). Banks’ internal rating models - time for a change? The "system of floors" as proposed by the Basel Committee. Available from: http://www.europarl.europa.eu/committees/en/ECON/home.html

Rosch, D. & Scheule, H. (2004). Forecasting Retail Portfolio Credit Risk, The Journal of Risk Finance, Vol. 5 Issue: 2, pp.16-32, https://doi.org/10.1108/eb022983

Santos, J.A.C. (2001). Bank capital regulation in contemporary banking theory: A review of the literature, Financial Markets, Institutions & Instruments, Bank for International Settlements", Basel, Switzerland, Vol. 10(2), pp. 41-84.

Santucci, L. (2016). What Happened to the Revolving Credit Card Balances of 2009?, FRB of Philadelphia Payment Cards Center Discussion Paper No. 16-1. Available at SSRN: https://ssrn.com/abstract=2783652

Sharma, J.K. (2010). Measures of Central Tendency: Mode. In: D Pandey (ed.) Fundamentals of Business Statistics, pp. 104–108. New Delhi: Dorling Kindersley.

Smit, W. & Van Vuuren, G. (2009). Determining the fair level of economic capital for credit and market risk in commercial banks, Master’s thesis, North-West University

Stoffberg, H.J. & Van Vuuren, G. (2015). Asset correlations in single factor credit risk models: an empirical investigation, Applied Economics, 48:17, 1602-1617, DOI: 10.1080/00036846.2015.1103040.

Tjiane, K.N. & Van Heerden, C. (2015). Curatorship of banks as a measure to rescue failing banks, Master’s thesis, University of Pretoria

Van Dyk, F. (2018). Basel III: An Overview of the safer ‘safety net’, Available from: http://financialmarketsjournal.co.za/oldsite/13thedition/printedarticles/basel3.htm

Vasicek, O. (1987). Probability of loss on loan portfolio, Available from: http://www.kmv.com

Vasicek, O. (1991). Limiting loan loss probability distribution, Available from: http://www.kmv.com

Vasicek, O.A. (2002). The Distribution of Loan Portfolio Value, Risk 15: 160–162.

Venter, K. (2017). Bank supervision forms: BA200, Available from: http://wwwapp.resbank.co.za/sarbdata/ifdata/periods.asp?type=BA200

Wolfram Research, (2009). Beta Distribution. Available from: http://mathworld.wolfram.com/BetaDistribution.html