Abstract
M.Com. (Economics)
The best measure for market risk is still a question that has remained largely unanswered. There are
a variety of different methodologies that attempt to answer this question. The goal of this study is
to assess how combining different elements of different Value at Risk (VaR) models contributes to
better estimations of the risk inherent within a portfolio, thereby resulting is a sufficient risk capital
allocation without over providing for risk that does not exist within the system. This study makes
use of three VaR models, namely Constant Volatility Portfolio VaR approach, Conditional Volatility
Single Asset VaR approach, and Conditional Volatility Portfolio VaR approach. The Constant Volatility
Portfolio VaR approach consists of using Standard Deviation in order to estimate the volatility
and the Pearson Correlation Coefficient in order to estimate how the constituents of the portfolio
interact with one another; this is constructed using a standard Variance Covariance approach. The
Conditional Volatility Single Asset VaR approach is constructed using a Historical Simulation VaR
approach, where the historical returns dataset is scaled using the most recent volatility within the
portfolio in order to give the estimation some symmetry based on what has occurred during stressed
periods. No decomposition of the portfolio is used and therefore the end of day price of the portfolio
is used to generate the returns dataset, thereby giving the portfolio a single asset appearance. The
Conditional Volatility Portfolio VaR approach uses a GARCH(1,1) process in order to estimate volatility
on a constituent based approach and then uses the Variance Covariance approach to combine the
constituent’s volatility and the correlation, which is calculated using Kendall’s Tau. In order to evaluate
the performance of each VaR model, back-testing is used. The techniques used are the Traffic Light
Test, Probability of Failure and a measure of the amount of capital that is used. The use of capital test
is designed to assess how much capital is utilised as a proportion of the underlying volatility. This
test is only useful if the calculation passes the two aforementioned tests. Using daily financial time
series of the JSE TOP40 index and the JSE DTOP index from 02 June 2008 to 14 April 2016, the VaR
calculations are generated and the back-testing is appropriately conducted. Based on the back-testing
results, it is found that the best approach was Conditional Volatility Portfolio VaR approach because
it passed both of the back-tests, as well as having the lowest capital usage figure if only a portion of
the back-testing passes are considered. It is found that the capital requirement obtained with this
methodology find that the capital number should be bound between 3.77% and 6.70% on the TOP40
and 3.82% and 6.78% on the DTOP.