A post-crisis investigation in to the performance of GARCH-based historical & analytical value-at-risk on the FTSE

Abstract

This paper is an investigation into the performance of GARCH-based VaR models on the South African FTSE/JSE Top 40 Index. Specifically, this paper investigates whether stability has returned to the VaR measure following its poor performance during the latest global financial crisis (2007). GARCH models are used in both an analytic and historical approach for modeling 1%, 2.5% and 5% daily VaR for a three year backtest period (2010-2012). Four distributions are used: the normal, generalised error, t-distribution and the skewed t-distribution. A particular question asked by this paper, is whether the data from the latest financial crisis (2007) should be used in estimating VaR in a post-crisis market. To investigate this, all models are re-estimated using data that has the financial crisis and/or high volatility period removed, then the results across the two data sets are compared. The take away point from this research is that the volatility-clustering mechanism inherent in every GARCH model is capable of producing accurate VaR estimates in a post-downturn/lower-volatility market even when the data on which the model was estimated contains financial downturn/volatile data. There is strong evidence suggesting stability has returned to this measure - however caution remains over using over-simplified models.