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系統識別號 U0002-2406201313554700
中文論文名稱 利用GARCH-EVT估計投資組合風險值-臺灣50指數為例
英文論文名稱 Applying GARCH-EVT to Estimate the Portfolio's Value at Risk- The Case of TSEC Taiwan 50 Index
校院名稱 淡江大學
系所名稱(中) 財務金融學系碩士班
系所名稱(英) Department of Banking and Finance
學年度 101
學期 2
出版年 102
研究生中文姓名 翁銘志
研究生英文姓名 Ming-Chih Weng
學號 600530462
學位類別 碩士
語文別 中文
口試日期 2013-06-22
論文頁數 71頁
口試委員 指導教授-李沃牆
共同指導教授-吳典明
委員-李沃牆
委員-池秉聰
委員-張淑華
中文關鍵字 GARCH-EVT  極值理論  GARCH模型  風險值 
英文關鍵字 GARCH-EVT  Extreme value theory  GARCH model  VaR 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 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
參考文獻 一、 中文文獻:
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. 邱臙珍、莊益源、林文昌、徐嘉彬,(2003),「靜態與動態風險值模型績效之比較」,證券市場發展季刊,第15 卷,第4 期,頁107~159。
3. 郭秋榮,(2009),「全球金融風暴之成因、對我國影響及因應對策之探討」,經濟研究,第9期,頁59-89。
4. 康景翔(2008),國內股票投資組合之風險值評估-以台灣50 指數成份股為例,中原大學國際貿易學系碩士論文。
5. 楊奕農(2009),「時間序列分析:經濟與財務上之應用」,臺北市:雙葉書廊公司。

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