利用GARCH-EVT估計投資組合風險值－臺灣50指數為例

本研究運用Markowitz (1952) 的平均數-變異數模型(Mean-Variance Model)來對臺灣50指數成份股進行篩選，藉此建構最適投資組合。再利用變異數¬-共變異數法(Variance-Covariance Method)、CCC-GARCH、DCC-GARCH、EVT與McNeil and Frey (2000)提出的GARCH-EVT模型等五種方法，分別對次貸風暴發生前後兩段期間，評估所建構投資組合之風險值。接著以Gerlach et al. (2011)運用比率、McAleer and da Veiga (2008)提出穿透的絕對誤差(Absolute Deviation, AD)和Kupiec (1995)提出的概似比檢定( Likelihood Ratio Test, LR test )評估風險值模型的準確性。由實證結果可知次貸危機發生後，風險值與預期損失顯著增加。回溯測試結果顯示，在金融風暴發生前，EVT模型與GARCH-EVT模型皆可準確預測風險值；在金融風暴後，GARCH-EVT模型表現最佳，將可用做一般投資人及金融機構決策時之參考。

關鍵字

GARCH-EVT ；極值理論； GARCH模型；風險值

並列摘要

With the ferment of liberalization and globalization in financial markets,investor faces more investment opportunity and investment risk simultaneously. Therefore, it is an important and focus topic for investor to utilize her limited funds to select optimal investment portfolio and adopt suitable risk measure method to evaluate risk and further control risk. This thesis first adopts Markowitz’s Mean-Variance approach to select the best target stock portfolio from TSEC Taiwan 50 index ,and the study applies Variance-Covariance Method,CCC-GARCH, DCC-GARCH and GARCH-EVT model which McNeil (2000) proposed to evaluate Value at Risk(hence VaR). On the other hand, the study applies Likelihood Ratio Test which Kupiec (1995)proposed, Violation Rate, VRate/α and Absolute Deviation(AD) to evaluate the accuracy of VaR model. The empirical results demonstrate the VaR and Expected Shortfall increasing after financial crisis . By backing tests, before financial crisis, EVT model and GARCH-EVT model can correctly forecast VaR. Moreover, after financial crisis, GARCH-EV model is more precise to forecast VaR than other models. Compared with traditional linear structure, nonlinear structure are relatively correct on VaR forecasting.

並列關鍵字

GARCH-EVT ； Extreme value theory ； GARCH model ； VaR

參考文獻

1. 林楚雄、高子荃與邱瓊儀(2006)，「結合GARCH模型與極值理論的風險值模型」，管理學報，第22卷，第4期，頁133-54。

2. Bali, T. G. (2003), “An Extreme Value Approach to Estimating Volatility and Value at Risk, ”The Journal of Business,Vol.76, No.1, pp.83-108.

3. Balkema, A. A., and L. De Haan (1974),“Residual Life Time at Great Age,” The Annals of Probability, ” Vol.2, No. 5, pp.792-804.

4. Bera, A. K. and S. Kim (1996),“Testing Constancy of Correlation with an Application to International Equity Returns,” Mimeo,Center for International Business Education and Research (CIBER) working paper,pp.96-107.

5. Billio, M., M. Caporin, and M. Gobbo. (2006), “Flexible Dynamic Conditional Correlation Multivariate GARCH Models forAsset Allocation,” Applied Financial Economics Letters, Vol.2,No. 2, pp.123-130.

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利用GARCH-EVT估計投資組合風險值－臺灣50指數為例

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