Asymmetric GARCH Value-at-Risk of SPY

VaR is more applicable as a financial management tool to control risk. Since the GARCH model is proved to be the useful and more accurate model in estimating VaR, in this paper, we employ the asymmetric GARCH models including the innovation-rotated GJR GARCH and the innovation-shifted NA GARCH models with different mean equations in comparison with symmetric GARCHM model to find out a more appropriate GARCH method in estimating VaR of SPY portfolio as the representative of the also popular investment tool, ETF. We gathered the latest 1800 daily information of SPY portfolio performance and divided into two groups to fit the models and get the VaR estimates under each confidence level we chose. Our major findings contain several aspects that first we prove that GARCH model is useful and efficient since all VaR forecasts fall into the safe range in terms of the regulation by Basel Accord. Specifically, asymmetric GARCH model outperforms the symmetric one, and GJR-GARCH as the representative of rotated GARCH model has better performance than NA-GARCH as that of shifted GARCH model. Among GJR-GARCH model with different mean equations, ARMA(1,1)-GJR GARCHM(1,1) has the most outstanding result in risk control by the fewest violation number it has, and we also conduct analysis through indicators other than violation number used as a standard mainly employed by Basel Accord to have more objective and thorough confirmation that ARMA(1,1)-GJR GARCHM(1,1) is the best fitted model to SPY portfolio in estimating VaR.