本研究的主要目的在於開發並檢測新的風險值測量工具，使得一般投資人與機構投資人能有效率的評估投資組合所暴露的風險，進而管控投資組合的風險，在能承擔的風險水準下尋求最大的獲利。本研究利用台灣證券交易市場中金融股價指數與電子股價指數當作樣本資產，原始資料取自「TEJ台灣經濟新報資料庫」，資料型態為日資料，研究期間為1995年1月7日至2007年6月23日，共3266筆資料。本研究延伸了Wong and Li（2001）、Lanne and Saikkonen（2003）與柯婷玲（2004）的單變量MAR-GARCH 模型，在考慮資產間共變異的特性下，建議以多變量MAR-GARCH之波動估算模型，並進一步利用該模型估計應用至預測投資組合的風險值。
根據實證結果發現，傳統雙變量GARCH模型僅在99%信賴水準下通過檢定，樣本外的檢定效果並非十分理想，而本研究所發展出的雙變量-MAR-GARCH由於考量到結構轉變的特性，發現Lanne and Saikkonen雙變量-MAR-GARCH模型樣本外在95%信賴水準與99%信賴水準下皆通過檢定，且Wing and Li雙變量-MAR-GARCH模型樣本外則全部通過檢定，由此可知雙變量-MAR-GARCH模型有效的修正了傳統雙變量GARCH模型沒有考慮到結構轉換的問題，雙變量-MAR-GARCH模型確實有著較佳的預估風險能力。
因此，根據實證發現，多變量MAR-GARCH模型 不但能考慮到投資組合可能處於不同狀態，對不同狀態下的模型進行估計，多變量的設定更能有效的捕捉投資組合中資產間的共變異特性，相較於傳統雙變量GARCH模型，以及單變量MAR-GARCH模型，多變量MAR-GARCH模型確實能有著較佳的預估風險能力。

This thesis mainly develops and tests new VaR measurement model, multi-variables MAR-GARCH model, for investors to estimate the risk of portfolio efficiently. With this new model, investors can maximize the profits under the control of portfolio risk.
Wong and Li(2001) and Lanne and Saikkonen(2003) introduce single-variable MAR-GARCH model. In nowadays, VaR measurement only for single-asset is inappropriate. Under considering the covariance structure of portfolio assets, we urge multi-variables MAR-GARCH model to estimate the portfolio VaR.
The data we used are collected form Taiwan TEJ database, which include Financial index and Electronic index in Taiwan stock market from 1995/1/7 to 2007/6/23. We use equal weights of these two assets to form a studying portfolio. With in-sample and out-sample test, the empirical results show that multi-variables MAR-GARCH model not only take state-variable into consideration, but also estimate parameters within different states. The multi-variable modeling can capture the covariance between portfolio assets in different sate. Comparing to traditional bi-variate GARCH model and single-variable MAR-GARCH model, multi-variables MAR-GARCH model indeed have better predict ability to estimate the VaR of portfolio in our empirical evidence.

目錄
第一章 緒論……1
第一節 研究動機與目的……1
第二節 文章架構與研究流程……4
第二章 相關文獻探討與理論基礎……5
第一節 單變量MAR模型相關文獻……5
第二節 單變量MAR-ARCH模型相關文獻……6
第三節 單變量MAR-GARCH模型相關文獻……7
第四節 多變量MAR-GARCH模型……8
第五節 風險值相關文獻……10
第三章 研究設計……13
第一節 資料來源與基本性質探索……13
第二節 雙變量-MAR-GARCH 模型……16
第三節 投資組合風險值估算……20
第四節 模型檢定……21
第四章 實證結果分析與探討……22
第一節 資料來源與處理……22
第二節 統計檢定……22
第三節 模型估計與分析……26
第五章 結論……35

表目錄

表1 金融與電子股價指數報酬率基本統計量……22
表2 金融與電子股價指數報酬率常態性檢定……23
表3 金融股價指數報酬率單根檢定……23
表4 電子股價指數報酬率單根檢定……23
表5 金融與電子股價指數報酬率ARCH效果檢定……24
表6 投資組合報酬率基本統計量……25
表7 各模型參數估計值(K=2)……26
表8 各模型參數估計值(K=3)……27
表9 （樣本內3006筆）投資組合報酬率超出模型估計風險值次數……31
表10（樣本內3006筆）不同風險值模型的Proportion of Failure test統計量……31
表11（樣本外250筆）投資組合報酬率超出模型估計風險值次數……34
表12（樣本外250筆）不同風險值模型的Proportion of Failure test 統計量……34

圖目錄

圖1 金融股價指數……14
圖2 金融股價指數報酬率……14
圖3 電子股價指數……14
圖4 電子股價指數報酬率……14
圖5 投資組合報酬率……25
圖6 （樣本內3006筆）投資組合報酬率與不同顯著水準下利用傳統雙變量-GARCH模型所計算之投資組合風險值……29
圖7 （樣本內3006筆K=2）投資組合報酬率與不同顯著水準下利用Wong and Li雙變量MAR-GARCH模型所計算之投資組合風險值……29
圖8 （樣本內3006筆K=2）投資組合報酬率與不同顯著水準下利用Lanne and Saikkonen雙變量-MAR-GARCH模型所計算之投資組合風險值……29
圖9 （樣本內3006筆K=3）投資組合報酬率與不同顯著水準下利用Wong and Li雙變量MAR-GARCH模型所計算之投資組合風險值……30
圖10（樣本內3006筆K=3）投資組合報酬率與不同顯著水準下利用Lanne and Saikkonen雙變量-MAR-GARCH模型所計算之投資組合風險值……30
圖11（樣本外250筆）投資組合標準差預測值與投資組合報酬率在不同顯著水準下利用傳統雙變量-MAR-GARCH所計算之投資組合風險值……32
圖12（樣本外250筆K=2）投資組合標準差預測值與投資組合報酬率在不同顯著水準下利用Wong and Li雙變量-MAR-GARCH所計算之投資組合風險值……32
圖13（樣本外250筆K=2）投資組合標準差預測值與投資組合報酬率在不同顯著水準下利用Lanne and Saikkoneni雙變量-MAR-GARCH所計算之投資組合風險值……32
圖14（樣本外250筆K=3）投資組合標準差預測值與投資組合報酬率在不同顯著水準下利用Wong and Li雙變量-MAR-GARCH所計算之投資組合風險值……33
圖15（樣本外250筆K=3）投資組合標準差預測值與投資組合報酬率在不同顯著水準下利用Lanne and Saikkoneni雙變量-MAR-GARCH所計算之投資組合風險值……33

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