Modeling heavy-tailed returns in emerging markets: With an application to the Taiwan Stock Index and its futures

This thesis focuses on two topics in financial risk management: optimal hedge ratios and portfolio value-at-risk (VaR). The empirical analysis is based on the daily return series for the Taiwan stock market index and two associated futures contracts. The sample period for the daily data covers 1998 to 2001. In Chapter 2, we examine optimal hedging of equity positions on the Taiwan Stock Exchange (TSE) with the Taiwan Futures Exchange (TAIFEX) contract for the TSE stock index. The empirical results show that the EGARCH residuals of the heavy-tailed return series are well represented by tail probability models in the generalized Pareto family. We use the fitted generalized Pareto distributions and a bivariate normal copula to construct a joint distribution of the returns for the hedged portfolio. The optimal hedge ratios are determined under the minimum lower partial moment criterion for various target returns and degrees of risk aversion. As in other studies, the optimal hedge ratio increases from -1 as the hedger becomes more risk averse. Although this result is contrary to the behavior of risk averse hedgers under maximum expected utility, we prove the claim made by Lien and Tse (2001) that the result may occur under the minimum lower partial moment criterion. In Chapter 3, we develop a method for modeling the joint distribution of asset returns and for estimating the portfolio VaR. This method combines the empirical distribution function, GP model, normal copula, and Monte Carlo simulation. We compare the estimates from the proposed method to outcomes from three alternatives, the variance-covariance method, historical simulation, and Jorion's method. The VaR estimates are computed for portfolios based on the value of the TSE index and the associated futures contracts traded on the Taiwan Futures Exchange (TAIFEX) and the Singapore International Monetary Exchange (SIMEX). We use the VaR estimates to evaluate the performance of speculative, fully hedged, equally hedged, and optimally hedged portfolios. The empirical analysis shows that (1) SIMEX appears to be a better hedging option than TAIFEX, (2) VaR cannot be qualified as a coherent risk measure but it is an overall acceptable risk measure when the target tail probability is not less than five percent, (3) the VaR non-subadditivity property can be aggravated in the portfolio case, but the severity of the problem can be lessened if our new method is employed, and (4) the optimal hedge strategy dominates the full hedge or unhedged strategies under the VaR risk measure.