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Quantification of VaR: A Note on VaR Valuation in the South African Equity Market

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  • Lesedi Mabitsela

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa)

  • Eben Maré

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa)

  • Rodwell Kufakunesu

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa)

Abstract

The statistical distribution of financial returns plays a key role in evaluating Value-at-Risk using parametric methods. Traditionally, when evaluating parametric Value-at-Risk, the statistical distribution of the financial returns is assumed to be normally distributed. However, though simple to implement, the Normal distribution underestimates the kurtosis and skewness of the observed financial returns. This article focuses on the evaluation of the South African equity markets in a Value-at-Risk framework. Value-at-Risk is estimated on four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE TOP40 index and the S & P 500 index. The statistical distribution of the financial returns is modelled using the Normal Inverse Gaussian and is compared to the financial returns modelled using the Normal, Skew t-distribution and Student t-distribution. We then estimate Value-at-Risk under the assumption that financial returns follow the Normal Inverse Gaussian, Normal, Skew t-distribution and Student t-distribution and backtesting was performed under each distribution assumption. The results of these distributions are compared and discussed.

Suggested Citation

  • Lesedi Mabitsela & Eben Maré & Rodwell Kufakunesu, 2015. "Quantification of VaR: A Note on VaR Valuation in the South African Equity Market," JRFM, MDPI, vol. 8(1), pages 1-24, February.
    • Handle: RePEc:gam:jjrfmx:v:8:y:2015:i:1:p:103-126:d:45910
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    References listed on IDEAS

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    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    3. Schaumburg, Julia, 2012. "Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4081-4096.
    4. Bhattacharyya, Malay & Madhav R, Siddarth, 2012. "A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns," MPRA Paper 54189, University Library of Munich, Germany.
    5. Tina Hviid Rydberg, 2000. "Realistic Statistical Modelling of Financial Data," International Statistical Review, International Statistical Institute, vol. 68(3), pages 233-258, December.
    6. repec:adr:anecst:y:2000:i:60:p:10 is not listed on IDEAS
    7. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    8. repec:hum:wpaper:sfb649dp2010-009 is not listed on IDEAS
    9. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    10. Longin, Francois, 2005. "The choice of the distribution of asset returns: How extreme value theory can help?," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 1017-1035, April.
    11. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    13. Schaumburg, Julia, 2010. "Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory," SFB 649 Discussion Papers 2010-009, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    15. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    16. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    17. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    18. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    19. Huisman, R. & Koedijik, K.G. & Pownall, R.A.J., 1998. "VaR-x: Fat Tails in Financial Risk Management," Papers 98-54, Southern California - School of Business Administration.
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    Cited by:

    1. Zi-Yi Guo, 2017. "Heavy-tailed Distributions and Risk Management of Equity Market Tail Events," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 31-41.

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