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.
Highlights
Value-at-Risk (VaR) is defined as the worst expected loss over a given period at a specified confidence level [1]
The VaR and ES estimates obtained under the Normal Inverse Gaussian (NIG), Skew t, Normal and t-distribution assumption for a one-day holding period at 99% confidence level are shown in Tables 4 and 5, respectively
The NIG predicts that losses in the interval 15% to 20% will occur once every 8.3 years, the Skew t and t-distribution predicts that losses for the same interval will occur once every 5.7 years and 4.7 years respectively
Summary
Value-at-Risk (VaR) is defined as the worst expected loss over a given period at a specified confidence level [1]. Parametric VaR assumes that financial returns are modelled using a statistical distribution (e.g., Normal and Student t-distribution). The introduction of VaR as the market risk measure has seen a number of empirical studies being done to find alternative distributions to the Normal distribution. These studies include application of the Student t-distribution The graphs and some of the tables are presented in the last five pages of this article
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