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

Author

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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. 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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