IMPLEMENTING A ROBUST RISK MODEL FOR SOUTH AFRICAN EQUITY MARKETS: A PEAK‐OVER‐THRESHOLD APPROACH

Abstract This paper implements a market risk model for the South African equity market using daily returns of the Johannesburg Stock Exchange All Share Index. Firstly, we separate positive returns from negative returns and model them using the peak‐over‐threshold (POT) method in order to compute the downside as well as upside risk measures separately. We thereafter compute the value‐at‐risk (VAR) and the expected shortfall (ES) estimates corresponding to upside and downside risks. We bootstrap these risk measures and compute their standard errors and confidence intervals (CIs) to see whether they fall inside these CIs. Secondly, we compute out‐sample forecasts of VAR estimates using the POT method and the generalised autogressive conditional heteroscedasticity process. Three backtesting methodologies are employed: the unconditional and conditional coverage tests and the counting of number of exceptions according to Basel II green zone. We find that all our VAR and ES estimates are well inside their CIs and that at lower quantiles, parametric ES estimates are equal to POT‐ES estimates, although the difference between the two is more pronounced at higher quantiles (99% or higher). Furthermore, our market risk model falls into the Basel II green zone, as it produces fewer exceptions in out‐sample space.