Non-parametric approach to VaR for portfolios in the South African equity market

M.Com. (Economics)Abstract: 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