Evaluation of the South African equity markets in a value-at-risk framework

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 dissertation focuses on the evaluation of the South African equity markets in a Value-at-Risk framework. Value-at- Risk is estimated on five 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, Student t-distribution and Extreme Value Theory and backtesting was performed under each distribution assumption. The results of these distributions are compared and discussed.