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

Application of DCC Multivariate GARCH Model at VaR－Evidence from G7 and Taiwan's Stock Markets

黃小菁(Hsiao-Chin Huang)

指導教授 ： 李命志

淡江大學/商學院/財務金融學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00310

摘要

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。

關鍵字

風險值 ； 動態條件相關 ； 多變量GARCH ； 股票投資組合

並列摘要

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.

並列關鍵字

Value-at-Risk ； DCC ； Multivariate GARCH ； Equity Portfolio

參考文獻

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