本文的目的在於探討國際投資組合之風險值預測模型。有鑑於過去由多種資產組成之投資組合，因資產數量的限制，在實務上往往發生風險值估計上的困難。本文應用Engle(2002)所提出的DCC-GARCH模型推估而得的變異數共變異數矩陣，用以預測投資組合未來的市場風險值，並比較簡單移動平均法(SMA)及實務上常用的指數權數移動法(EWMA)二種變異數預測模型之預測結果。經由以七大工業國G7與台灣股價指數組成之資產組合而得之實證研究發現，利用DCC-GARCH模型所預測出的資產組合風險值比起其他變異數模型所預測出的結果，顯然具有更高的有效性及正確性。而DCC-GARCH模型中，一般而言，在通過Kupiec PF-test之情況下，t分配模型較Normal分配模型之RMSE低，故DCC-GARCH(1,1)-t模型將是估算風險值的更好選擇。另各模型皆顯示，八國股市報酬率間相關係數與變異數呈現正向關係，亦即各國股市間之波動性高時相關性會隨之上升，此亦說明八國股市報酬率為動態之共變異數及相關係數時間序列。

The purpose of this study is to find a more effective model to forecast Value-at-Risk (VaR). Due to a portfolio usually holds numerous assets, it would be difficult to estimate the very large covariance matrix that is required to caculate VaR. In this paper, we apply the Dynamic Conditional Correlation (DCC) multivariate GARCH model, proposed by Engle (2002), to estimate the future market risk. We also use two other variance-covariance forecast models, such as SMA and EWMA to compare the results. Through a portfolio composed of eight indices from the G7 (America, Canada, UK, France, Germany, Italy, Japan) and Taiwan stock markets, the findings imply that the VaR calculated from DCC multivariate GARCH model has better accuracy and efficiency. Moreover, among DCC models which pass the Kupiec PF test in backtesting, we examine RMSE for capital efficiency and find that t distribution performs better than normal distribution. Thus this study recommends DCC- GARCH(1,1)-t model to be the best option in computing VaR on equity portfolio. In addition, all the results indicate that the correlation and covariance of returns move in the same direction. That is correlations increase during times when the volatility of market is large.

目  錄
第一章 緒論..................................1
第一節 研究動機..............................1
第二節 研究目的..............................3
第三節 研究架構..............................4
第四節 研究流程..............................6
第二章 理論基礎與文獻回顧....................7
第一節 風險值的意義及概念....................7
第二節 風險值之估算方法......................9
第三節 國外相關文獻.........................11
第四節 國內相關文獻.........................15
第三章 研究方法.............................19
第一節 單根檢定.............................19
第二節 ARCH效果檢定.........................23
第三節 波動性預測計量模型...................25
第四節 風險值的評價方式與預測績效...........37
第四章 實證結果與實證分析...................40
第一節 資料來源與處理.......................40
第二節 八國股價指數基本統計量分析...........41
第三節 單根檢定.............................44
第四節 ARCH效果檢定.........................47
第五節 固定相關係數檢定.....................48
第六節 風險值之估計.........................49
第七節 投資組合共變異數及相關係數分析.......58
第五章 結論.................................68
參考文獻....................................69
表 目 錄
【表3-4-1】 Kupiec（1995）檢定法之臨界值	38
【表4-2-1】八國股價指數基本統計量	43
【表4-2-2】八國股價指數報酬率基本統計量	43
【表4-3-1】八國股價指數時間序列資料之單根檢定(水準項)	45
【表4-3-2】八國股價指數日報酬率時間序列資料之之單根檢定(差分項)	46
【表4-4-1】八國報酬率ARCH效果檢定	47
【表4-5-1】八國報酬率模型殘差項之固定相關係數矩陣 	48
【表4-5-2】八國報酬率殘差項之固定相關係數檢定	49
【表4-6-1】多頭部位估計1天之風險值穿透情形及RMSE比較表	51
【表4-6-2】空頭部位估計1天之風險值穿透情形及RMSE比較表	51
【表4-6-3】多頭部位估計10天之風險值穿透情形及RMSE比較表	54
【表4-6-4】空頭部位估計10天之風險值穿透情形及RMSE比較表	54
【表4-7-1】三模型(SMA、EWMA及DCC-GARCH)之投資組合波動度比較表	59
【表4-7-2】八國報酬率SMA模型之相關係數矩陣的平均值與標準差	60
【表4-7-3】八國報酬率EWMA模型之相關係數矩陣的平均值與標準差	62
【表4-7-4】八國報酬率DCC-GARCH(1,1)模型之相關係數矩陣的平均值與標準差	63
【表4-7-5】投資組合中八國股市報酬率間最大及最小相關係數	65
【表4-7-6】八國股市報酬率間相關係數平均值與標準差之關係	65
【表4-7-7】八國股市報酬率間相關係數與變異數之關係	66
 
圖 目 錄
【圖4-2-1】 各國股價指數時間序列圖	42
【圖4-6-1】 SMA模型之風險值(預測一天)模型	52
【圖4-6-2】 EWMA模型之風險值(預測一天)模型	52
【圖4-6-3】 DCC-GARCH模型之風險值(預測一天)模型	53
【圖4-6-4】 SMA模型之風險值(預測十天)模型	55
【圖4-6-5】 EWMA模型之風險值(預測十天)模型	55
【圖4-6-6】 DCC-GARCH模型之風險值(預測十天)模型	56
【圖4-7-1】 三模型(SMA、EWMA及DCC-GARCH)之投資組合波動度	58
【圖4-7-2】 法國與義大利股價指數日報酬率之走勢圖(相關係數最高者)	60
【圖4-7-3】 臺灣與美國股價指數日報酬率之走勢圖(相關係數最低者)	61
【圖4-7-4】 八國報酬率SMA模型之最大及最小相關係數圖	61
【圖4-7-5】 八國報酬率EWMA模型之最大及最小相關係數圖	62
【圖4-7-6】八國報酬率DCC-GARCH(1,1)模型之最大及最小相關係數圖	63

一、國內文獻
1.洪瑞成，(2002)，風險值之探討-對稱與不對稱波動GARCH模型之應用，淡江大學財務金融研究所碩士論文。
2.許傑翔，(2004)，多變量財務時間數列模型之風險值計算，東吳大學商用數學系碩士論文。
3.張維敉，(2002)，金融危機與風險外溢─DCC模型之應用，國立中央大學財務金融研究所碩士論文。
4.周業熙，(2002)，GARCH-type模型在VaR之應用，東吳大學經濟學系碩士論文。
5.謝家和，(1999)，風險值之衡量-多元變數GARCH模型之應用，暨南國際大學國際企業學系碩士論文。
6.高櫻芬，(2002)，風險值之衡量-多變量GARCH模型之應用，經濟論文叢刊第30輯第3期。
7.蔡維溢，(1997)，市場風險控管：Value at Risk—Orthogonal Garch的運用，國立台灣大學財務金融研究所碩士論文。
8.郭秋怡，(1999)，風險值運用在國內銀行資本適足性的研究，國立中央大學財務管理研究所碩士論文。
9.陳炎信，(1999)，考慮極端事件之VaR風險管理模式，銘傳大學金融研究所碩士論文。
10.盧陽正，(2000)，「考量厚尾分配誤差修正之風險值拔靴複製估計--以亞洲新興股市投資組合為實證」，證券市場發展季刊，第12卷第2期。
11.周裕峰，(2001)，結合波動性時間序列模式與極端值理論之風險值評估模式，銘傳大學金融研究所碩士論文。

二、國外文獻： 
1.Akgiray, V., (1989),“Conditional Heteroskedasticity in Time Series of Stock Returns：Evidence and Forecasts,” Journal of Business, Vol. 62, pp.54-80.
2.Alexander, C. O., and C. T. Leigh, (1997), “On the Covariance Matrices Used in Value at Risk Models,” Journal of Derivatives, Vol. 4, pp.50-62.
3.Bera, Anil K. and Sangwhan Kim, (1996), “Testing Constancy of Correlation with an Application to International Equity Returns,” University of Illinois at Urbana-Champaign, CIBER Working Paper 96-107.
4.Billio, Pelizzon, (2000), “Value-at-Risk: a multivariate switching regime approach,” Journal of Empirical Finance, Vol. 7, pp.531-554.
5.Bollerslev, T., (1986), “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, Vol. 31, pp.307-327.
8.Bollerslev, T., Engle, R. F., and Wooldridge, J. M., (1988), “A Capital- Asset Pricing Model with Time-Varying Covariances,” Journal of Political Economy, Vol. 96, pp.116-131.
9.Bollerslev, T., (1990), “Modeling the Coherence in Short-Run Nominal Exchange Rates Generalized ARCH,” Review of Economics and Statistics, Vol. 70, pp.498-505.
10.Burns, P., (2002), “The Quality of Value at Risk via Univariate GARCH,” Burns Statistics, October/10, pp.1-19.
11.Colm, K. and A. J. Patton., (2000), “Multivariate GARCH Modeling of Exchange Volatility Transmission in the European Monetary System,” The Financial Review, Vol. 41, pp.29-48.
12.Dickey, D. and W. Fuller, (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, Vol. 74, pp.427-431. 
13.Dickey, D. A and W. A. Fuller, (1981), “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, Vol. 49(4), pp.1057-1072.
14.Engle, R. F., (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation,” Econometirca, Vol. 50, pp.987-1008.
15.Engle, R. and B. Yoo., (1987), “Forecasting and Testing in Cointegrated Systems,” Journal of Econometrics, Vol. 35, pp.143-159.
16.Engle, R. F. and V. K. NG, (1993), “Measuring and Testing The Impact of News on Volatility,” Journal of Finance, Vol. 48, pp.1749-1178.
17.Engle, R. F. and K. F. Kroner, (1995), “Multivariate simultaneous generalized ARCH,” Econometric Theory, Vol. 11, pp.122-150.
18.Engle, R. F., (2001), “Dynamic Conditional Correlation - A simple class of multivariate GARCH models.” Department of Economics, University of California, San Diego.
19.Engle, R. F. and K. Sheppard, (2001), “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH,” discussion paper, University of California, San Diego.
20.Engle, R. F. , (2002), “Dynamic conditional correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models,” Journal of Business and Economic Statistics, Vol. 20(3), pp.339-350.
21.Fama, E. F., (1965), “The Behavior of Stock Market Prices,” Journal of Business, Vol. 38, pp.34-105.
22.Giot, P. and S. Laurent, (2003), “Value-at-Risk for long and short trading positions,” Applied Econometrics, Vol. 18, pp.641-663.
23.Goorbergh, R.V.D. and P. Vlaar, (1999), “Value-at-Risk Analysis of Stock Returns Historical Simulation, Variance Techniques or Tail Index Estimation,” DNB Staff Reports 40, Netherlands Central Bank.
24.Granger, C. W. J. and P. Newbold, (1974), “Superious Regressions in Econometrics,” Journal of Econometrics, Vol. 12, pp.111-120.
25.Hendricks, D., (1996), “Evaluation of ‘Value-at-Risk’ Models Using Historical Data,” Economic Policy Review, Federal Reserve Bank of New York, 2, April, pp.39-69.
26.Jorion, P., (1996), Value at Risk: the New Benchmark for Controlling Derivatives Risk, Irwin Professional Publishing, Chicago. 
27.Jorion, P., (2000), Value-at-Risk, 2nd edition, McGraw-Hill, N.Y.
28.J. P. Morgan and Reuters, (1996), RiskMetrics-Technical Document, 4th ed., J.P. Morgan.
29.Kupiec, P. H., (1995), “Techniques for Verifying the Accuracy of Risk Measurement Models,” Journal of Derivatives, Vol. 3, pp.73-84.
30.Longin, F. and B. Solnik, (1995), “Is the Correlation in International Equity Returns Constant：1960–1990?,” Journal of International Money and Finance, Vol. 14(1), pp.3-26.
31.Mandelbrot, B., (1963), “The variation of certain speculative prices,” Journal of Business, Vol. 36, pp.394-419.
32.Mandelbrot, B., (1967), “The Variation of Some Other Speculative Prices,” Journal of Business, Vol. 40, pp.393-413.
33.Phillips, P., (1986), “Understanding Spurious Regressions,” Journal of Econometrics, Vol. 33, pp.311-340.
34.Phillips, P. and P. Perron, (1988), “Testing for a Unit Root in Time Series Regression,” Biometrika, Vol. 75, pp.334-346.
35.Said, S. and D. Dickey, (1984), “Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order,” Biometrika, Vol. 71, pp.599-607.
36.Tse, Y. K., (2000), “A test for constant correlations in a multivariate garch model,” Journal of Econometrics, Vol. 98, pp.107-127.
37.Tsui, A. K. and Q. Yu, (1999), “Constant conditional correlation in a bivariate garch model: Evidence from the stock market in China,” Mathematics and Computers in Simulation, Vol. 48, pp.503-509.
38.Wang, P. and P. Wang, (2001), “Equilibrium Adjustment, Basis Risk and Risk Transmission in Spot and Forward Foreign Exchange Markets,” Applied Financial Economics, Vol. 11, pp.127-136.
39.Wong, M. C. S. and W. Y. Cheng and C. Y. P. Wong, (2002), “Market Risk Management of Banks: Implications from the Accuracy of Value-at-Risk Forecasts,” Journal of Forecasting, Vol. 21, pp.27-38.