本文的目的在於探討不同投資權重的國際投資組合分配。有鑑於一般在研究時，通常會假設投資組合為相同權重之投資組合，然而此一假設往往與實際情況有出入。本文應用Engle and Kroner（1995）提出的多變量GARCH模型之BEKK表示法建構條件共變異矩陣，進而求出配適後非等權投資權重，建立一與等權投資組合相同預期報酬條件下的最小變量投資組合，進而與等權投資組合作比較。經由以NASDAQ指數、英鎊對美元及NYMEX輕原油期貨組成之資產組合而得之實證研究發現，在相同預期報酬條件下的最小變量投資組合較等權投資組合具有波動性群聚的現象及具有高狹峰的分配特性，而在衡量風險的能力亦較等權投資組合為佳。

The purpose of this article is to discuss the different weighted investment in international investment portfolio allocation. Due to equal weighted investment portfolio is the first assumption in risk forecasting in ordinary investment portfolio model research, however this assumption often differ from real situation. 
This article applies BEKK express constructive condition in same variables matrix of multi-variables GARCH model from Engle and Kroner (1995) and get the un-equal investment weighted to establish an adjusted un-equal investment portfolio allocation, and then compare to the equal weighted investment portfolio allocation.
The real examination researches discover that through the assets combination of NASDAQ index, British Pound vs. US dollar and NYMEX light crude oil futures portfolio, the adjusted un-equal weighted investment portfolio has the phenomenon of volatility grouping and the character of high narrow peak allocation compare to the equal weighted investment allocation, so it has better ability in forecasting the risks than the equal weighted investment portfolio.

目  錄
第一章 緒論	1
第一節 研究動機	1
第二節 研究目的	2
第三節 研究架構	4
第四節 研究流程	5
第二章 理論基礎與文獻回顧	6
第一節 理論基礎	6
第二節 國外相關文獻	9
第三節 國內相關文獻	11
第三章 研究方法	15
第一節 資料檢定	15
第二節 風險值衡量	19
第二節 以風險值為設限條件投資組合權重	27
第四章 實證結果與實證分析	29
第一節 資料來源與期間	29
第二節 資料處理	29
第三節 基本統計量分析	30
第四節 單根檢定	31
第五節 ARCH效果檢定	33
第六節 等權投資組合與配適後非等權投資組合之建立	34
第七節 風險值之估計	36
第五章 結論	38
參考文獻	39
表 目 錄
【表4.1】三資產基本統計量	30
【表4.2】三資產報酬率基本統計量	30
【表4.3】ADF單根檢定法之單根檢定（水準項）	32
【表4.4】PP單根檢定法之單根檢定（水準項）	32
【表4.5】ADF單根檢定法之單根檢定（差分項）	32
【表4.6】PP單根檢定法之單根檢定（差分項）	33
【表4.7】三資產指數報酬率ARCH效果檢定	34
【表4.8】等權與非等權分配的基本統計量	35
【表4.9】等權與非等權分配的風險值	37

圖 目 錄
【圖4.1】等權與非等權分配的變異數曲線圖	36

ㄧ、國外文獻
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.
Burns P. (2002), “The Quality of Value at Risk via Univariate GARCH,” Burns Statistics, October/10, pp.1-19.
Bensalah(2002), “Asset Allocation Using Extreme Value Theory, ” Working Papers  02-20, Bank of Canada.
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.
Colm K. and A. J. Patton(2000), “Multivariate GARCH Modeling of Exchange Volatility Transmission in the European Monetary System,” Financial Review, Vol. 41, pp.29-48.
Campbell R., Ronald H. and K. Koedijk（2001）, “Optimal portfolio selection in a Value-at-Risk framework”, Journal of Banking and Finance, Vol. 25, pp.1789-1804.
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.
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.
Engle R. F.(1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation,” Econometirca, Vol. 50, pp.987-1008.
Engle R. F. and K. F. Kroner(1995), “Multivariate simultaneous generalized ARCH,” Econometric Theory, Vol. 11, pp.122-150.
Engle R. and B. Yoo(1987), “Forecasting and Testing in Cointegrated Systems,” Journal of Econometrics, Vol. 35, pp.143-159.
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.
Granger C. W. J. and P. Newbold (1974), “Superious Regressions in Econometrics,” Journal of Econometrics, Vol. 12, pp.111-120
Hendricks D. (1996), “Evaluation of ‘Value-at-Risk’ Models Using Historical Data,” Economic Policy Review, Federal Reserve Bank of New York , Vol. 2, pp.39-69.
Jorion P.(1996), Value at Risk: the New Benchmark for Controlling Derivatives Risk,  Irwin Professional Publishing, Chicago.
Jorion P.(2000), Value-at-Risk, 2nd edition, McGraw-Hill, N.Y.

J. P. Morgan and Reuters (1996), RiskMetrics-Technical Document, 4th ed., J.P. Morgan.
Lucas A. and P. Klaassen (1998), “Extreme returns, downside risk, and optimal asset allocation, ” Journal of Portfolio Management ,Vol. 25 , 71-79. 
Luc B. and L. Sebastien (2005), “A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models,”Journal of Business and Economic Staistics,Vol. 23,pp.346-354.
Mandelbrot B. (1967), “The Variation of Some Other Speculative Prices,” Journal of Business, Vol. 40, pp.393-413.
Madura J. and W. Reiff (1985), “A Hedge Strategy for International Portfolios”, Journal of Portfolio Management, pp.70-74。
Phillips P. (1986), “Understanding Spurious Regressions,” Journal of Econometrics, Vol. 33, pp.311-340.
Phillips P. and P. Perron (1988), “Testing for a Unit Root in Time Series Regression,” Biometrika, Vol. 75, pp.334-346.
Said S. and D. Dickey (1984), “Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order,” Biometrika, Vol. 71, pp.599-607.
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

二、國內文獻
李吉元（2003），風險值限制下最適資產配置，成功大學財務金融研究所碩士論文。
李命志、李彥賢及張智超（2005），原油價格風險值之估計-拔靴法的應用，金融風險管理季刊 ，第一卷第二期，2005年。
黃小菁（2005），DCC多變量GARCH模型之風險值計算－G7及臺灣等八國股市投資組合之實證研究，淡江大學財務金融研究所碩士論文。
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。
洪慶昇（2004），不同風險預測模式之投資組合績效比較-以國際資產配置為例，樹德科技大學金融保險研究所碩士論文。
陳建銘（2002），厚尾分配、極值理論與最適資產配置，東吳大學經濟研究所碩士論文。
張揖平、洪明欽及李雪真（2004），GARCH模型之選擇權風險值計算-以台灣加權股價指數選擇權為例，風險管理學報，第六卷第三期，2004年。
廖丁輝（2003），風險估計-跳躍模型之應用，淡江大學財務金融研究所碩士論文。