以GARCH模型衡量投資組合的波動性風險- 台灣股票市場為例

Abstract

投資人若瞭解並事前掌握股票報酬率波動性，較能作出正確的投資決策。為瞭解股票報酬率的波動性，本論文首先採用單變量GARCH (Generalized Autoregressive Conditional Heteroskedasticity)或TGARCH (Threshold GARCH)模型來計算各支股票報酬率的變異數；而後將單變量GARCH模型擴充至多變量Constant Correlation GARCH 或Orthogonal GARCH模型，以建構一隨時間變化的共變異數矩陣；最後再應用「熵權重法」求得投資組合中各支股票的權重，並計算出不同信賴水準下投資組合的風險值。本論文於模型建構、推導時發現，使用Orthogonal GARCH模型時，因考慮到所有主成份的影響，較能精確地衡量出每日的風險值；而使用Constant Correlation GARCH模型時，因假設各股間的相關係數不變，可能會造成風險值低估的現象。在數值計算方面，本論文於MSCI中挑選數支股票進行投資組合之風險值估算，結果發現利用Orthogonal GARCH模型來衡量投資組合的風險值較應用Constant Correlation GARCH模型來得精確、有效。

Investors can make appropriate decisions if they can grasp and control volatility of the stock return rate in advance. The objective of this research is to find an appropriate VaR (Value at Risk) model that can estimate the time-varying volatility of a portfolio. When developing the VaR model, the portfolio return covariance matrix is a key factor. This matrix contains two parts. The first part consists of a univariate GARCH model and an asymmetric GARCH model called TGARCH. And the second part consists of a simplified multivariate GARCH model which, in turn, can be a Constant Correlation GARCH model or an Orthogonal GARCH model. The former is then incorporated into the latter part to generate four different time-varying covariance matrices. The other factor affecting a VaR model are weights of the stocks invested. Entropy weighting method is used to obtain weights of stocks in the portfolio. Finally, covariance matrices and weights are used to compute VaR under different confidence levels. It is found that, considering all principal components, a VaR model can provide more accurate estimation if the Orthogonal GARCH model is employed. On the other hand, the assumption that stock correlation matrix is constant under Constant Correlation GARCH model may underestimate VaRs. The above proposed VaR model is used to analyze a few selected common stocks from Taiwan equity market. The forecasting results of VaR models are compared with the actual return of portfolio to examine the appropriateness of the proposed model. It is found that the VaR model under Orthogonal GARCH model gives us more accurate result than that under Constant Correlation GARCH model.