VAR Analysis for SEMDEX Market Index: Fat Tails and Conditional Asymmetries in Return Innovations

Abstract

This paper performs a comparative study between the symmetric GARCH(1,1) and asymmetric EGARCH(1,1) models under six distributional assumptions to estimate the 99% one-day-ahead Value-at-Risk (VaR) for SEMDEX market index. The SEMDEX market index is an index of prices of all listed shares on the Stock Exchange of Mauritius Ltd. The dataset consists of daily SEMDEX returns from January 2000 to November 2015. The study employs three symmetric distributions which are the normal, the fat-tailed Student’s-t and GED distributions, and three asymmetric distributions which are the skewed Student’s-t, the skewed GED and the reparametrised Johnson SU (JSU) distributions. The VaR forecasting accuracy of the different combinations of GARCH processes and innovation distributions is assessed using the Kupiec’s test. The assessment concludes that the normal distribution is not appropriate to model the 99%-VaR. Overall, the Kupiec’s test shows that the leptokurtic or skewed innovation specifications produce correct VaR exceedances. The GARCH(1,1) outperforms the EGARCH(1,1), which concludes that VaR forecasting procedure requires a simple GARCH structure and a non-normal underlying distribution. The most performant combinations are the JSU-GARCH(1,1) and the Skewed GED-GARCH(1,1). The findings hence conclude that employing a skewed and leptokurtic distribution improves the VaR forecasting accuracy of GARCH processes. Being most performant in capturing the negative tail events in the SEMDEX data, they forecast accurately the 99%-VaR.