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.
