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。

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.

第一章  緒論	                         1
第一節  研究背景與動機	                1
第二節  研究目的	                         5
第三節  研究架構與流程	                6
第二章  理論與相關文獻	                8
第一節  風險值理論與相關文獻	       8
第二節  Markowitz 投資組合理論與相關文獻   11
第三節  極值理論與相關文獻	                12
第四節  動態極值理論與相關文獻	       15
第三章　研究方法	                         17
第一節　研究流程	                         17
第二節  Markowitz 投資組合模型	       18
第三節  Chow Test 之應用	                20
第四節  風險值模型	                         22
第四章  實證結果與分析	                33
第一節  研究資料	                         33
第二節  最適投資權重	                36
第三節  敘述統計分析與Chow檢定	       40
第四節  次貸風暴前風險值估計結果	       43
第五節  次貸風暴後風險值估計結果	       51
第五章　結論與建議	                         59
第一節　結論	                         59
第二節　建議	                         61
參考文獻	                                  62

表目錄
頁次
表1 臺灣50權重前20大個股................................................................................34
表2 20檔個股在效率前緣下之投資權重................................................................37
表3 最適投資權重 ....................................................................................................38
表4 變數之敘述統計量表 ........................................................................................40
表5 GPD門檻值與模型參數對應表........................................................................44
表6 風險值(VaR)與預期損失表(ES) .......................................................................45
表7 殘差敘述統計量................................................................................................46
表8 GARCH-GPD門檻值和模型參數對應表.........................................................48
表9 風險值(VaR)與預期損失表(ES) .......................................................................48
表10 各模型回溯測試檢定結果..............................................................................50
表11 GPD門檻值與模型參數對應表......................................................................52
表12 風險值(VaR)與預期損失表(ES) .....................................................................53
表13 殘差敘述統計量..............................................................................................54
表14 GARCH-GPD門檻值和模型參數對應表.......................................................56
表15 風險值(VaR)與預期損失表(ES) .....................................................................56
表16 各模型回溯測試檢定結果..............................................................................58
附表1 2002年 7 月1日至2012 年 11 月30日複迴歸分析...............................69
附表2 2002年 7 月1日至2012 年 11 月30日複迴歸ANOVA.........................69
附表3 2002年 7 月1日至2008年 9月15日複迴歸分析...................................70
附表4 2002年 7 月1日至2008年 9月15日複迴歸ANOVA ............................70
附表5 2008年 9月16日至2012年 11月30日複迴歸分析................................71
附表6 2008年 9月16日至2012年 11月30日複迴歸ANOVA.........................71

圖目錄
頁次
圖1研究方法流程.....................................................................................................17
圖2 POT法示意圖.....................................................................................................26
圖3投資組合效率前緣.............................................................................................36
圖4最適風險投資組合.............................................................................................38
圖5台灣加權指數時間序列.....................................................................................41
圖6損失資料之平均餘額函數.................................................................................43
圖7損失資料之Hill Plot...........................................................................................44
圖9 殘差資料之Hill Plot..........................................................................................47
圖10損失資料之平均餘額函數...............................................................................51
圖11損失資料之Hill Plot.........................................................................................52
圖12殘差資料之平均餘額函數...............................................................................55
圖13殘差資料之Hill Plot.........................................................................................55

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