本研究以Koenker與Bassett（1978）提出的分量迴歸（Quantile Regression）導入風險值模型，經Markowitz投資組合理論篩選出最佳的外匯投資組合，日圓、美元、新加坡幣及里亞爾。比較GARCH、tGARCH、EGARCH及多變量CCC-GARCH在傳統變異–共變數法之風險值估計能力與加入分量迴歸後的差異；另外，比較個別外匯風險值與投資組合風險值。並以Kupeic和Christofferson二種回溯測試方法檢定風險值模型績效。
實證結果發現，VaR.tGARCH（1, 1）模型算出的每日外幣報酬率風險值較其他模型低，估計能力最差。分量迴歸結合單變量GARCH所算出的個別外匯風險值十分接近，平均較VaR.GARCH-type高，經回溯測試後，加入分量迴歸能夠做出準確的估計，充分展現不需任何分配假設即能捕捉金融資產厚尾、峰態及自我相關的特性。投資組合風險值模型回溯測試結果顯示，適當的投資組合確實能有效降低風險，同時VaR.QR.CCC-GARCH模型在外匯投資組合的績效明顯優於VaR.CCC-GARCH 模型。

We applied quantile regression proposed by Koenker and Bassett (1978) to value at risk model in this study. After selecting the best foreign exchange portfolio by Markowitz's portfolio theory, the JPY, USD, SGD and SAR was selected. We compared GARCH, tGARCH, EGARCH and multivariate CCC-GARCH in traditional variance-covariance method with quantile regression to estimating value at risk. And using two kinds of back-testing which includes Kupeic and Christofferson test the performance of value at risk models. 
Empirical results, VaR.tGARCH (1, 1) model worst estimated the daily foreign return of value at risk. Combining quantile regression with GARCH-type to calculate the value at risk of individual foreign exchange is very close, where the average is higher than VaR.GARCH-type. After back-testing, adding quantile regression indeed is able to make accurate estimation. It fully shows that without any assumption of distribution surely capture fat-tail, kurtosis and correlation of financial assets characteristics. The back-testing results of portfolio's value at risk models show that the appropriate portfolio can actually reduce risk, while VaR.QR.CCC-GARCH model perform better than VaR.CCC-GARCH model in this foreign exchange portfolio.

目　錄
第一章　緒論　1
第一節　研究背景與動機　1
第二節　研究目的　3
第三節　研究架構與流程　4
第二章　理論介紹及文獻回顧　5
第一節　風險值　5
第二節　文獻回顧　11
第三章　研究方法　17
第一節　Markowitz投資組合　17
第二節　波動性估計　20
第三節　分量迴歸　28
第四節　風險值模型　31
第五節　回溯測試　36
第四章　實證結果與分析　39
第一節　資料選取與說明　39
第二節　基本統計分析　43
第三節　風險值模型結果分析　46
第四節　回溯測試結果　54
第五章　結論與建議　59
第一節　結論　59
第二節　研究限制與建議　60
參考文獻　61

表　目　錄
表2-1　風險值估計方法比較表　10
表4-1　外匯初步篩選排行計分　41
表4-2　外匯投資組合最適投資權重　41
表4-3　滿足不同風險偏好時之風險、報酬率及投資比重　42
表4-4　外幣價格的敘述統計量　43
表4-5　外幣相關系數　44
表4-6　單根檢定　45
表4-7　風險值水準－日幣　46
表4-8　風險值水準－美元　48
表4-9　風險值水準－新加坡幣　49
表4-10　風險值水準－里亞爾　50
表4-11　變異－共變數投資組合風險值　52
表4-12　回溯測試500天－日幣　54
表4-13　回溯測試500天－美元　55
表4-14　回溯測試500天－新加坡幣　56
表4-15　回溯測試500天－里亞爾　56
表4-16　回溯測試500天－投資組合風險值　57
表4-17　外幣個別風險值總和V.S.投資組合風險值　58

圖　目　錄
圖4-1　風險性資產組合之效率前緣　42
圖4-2　考慮風險偏好下之最適投資組合　42
圖4-3　外幣價格走勢　44
圖4-4　日幣投資期間內之風險值變化　47
圖4-5　美元投資期間內之風險值變化　48
圖4-6　新加坡幣投資期間內之風險值變化　50
圖4-7　里亞爾投資期間內之風險值變化　51
圖4-8　投資組合投資期間內風險值變化　52
圖4-9　共變數與顯著水準（常態分配值）及投資組合風險值的關係　53

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