Assessing tail-related risk for heteroscedastic return series of Asian emerging equity markets : a thesis presented in partial fulfillment of the requirements for Master of Business Studies at Massey University

Abstract

High degrees of leptokurtosis, heteroscedasticity and asymmetries in return series are the common features of Asian emerging equity markets, especially during the financial crisis. Thus, strengthening risk management with improved risk measures becomes increasingly important. According to the Basle Committee on Banking Supervision, the value at risk (VaR) should be calculated at the 99% confidence level or above with daily data. In the context of Asian equity markets, the use of the estimated conditional variance of market returns as the sole measure of market risk may result in serious underestimation of the true risk caused by tail events. Therefore, this research focuses on the tail-related risk measure of nine Asian index returns within the framework of extreme value theory. It employs the generalized extreme value (GEV) and the generalized Pareto distribution (GPD) approaches combined with AR(l)-GARCH(m, s) filtering of the return data. The VaR performances under different distributions with different volatility filtering are compared, and the estimated conditional and unconditional expected shortfalls based on the GPD are reported. The important findings include the following. (1) The nine heteroscedastic index returns indeed follow heavy-tailed distributions rather than the normal distribution. (2) Both the GPD and GEV distributions of daily returns are asymmetric between local maxima (right tail) and local minima (left tail). (3) The results of the GEV approach are somewhat sensitive to the block length chosen, while the GPD approach, with the thresholds determined much less arbitrarily, can avoid equivocalness with the GEV method. (4) The reported results indicate that the VaR based on the extreme value theory at high quantiles (above 99%) is more accurate than the VaR based on the normal distribution.