考量波動性風險下之投資組合配置-以台灣股票市場為例

Abstract

本論文主要在建構一個考量波動性風險下之最適投資組合配置模型，此模型由兩個模組所構成，模組一使用simplified multivariate GARCH模型計算資產變異數與資產間共變異數，以建構一隨時間變動的共變異數矩陣(波動性矩陣)；模組二則使用「平均數-變異數」模型與「平均數-風險值」模型，以求得具最小風險之最適投資組合配置。特別的，本論文於模組一中，分別採用Constant Correlation GARCH、Orthogonal GARCH 與PC GARCH 三種不同simplified multivariate GARCH模型，求得三種不同的共變異數矩陣；再將它們分別輸入於模組二，搭配「平均數-變異數」與「平均數-風險值」兩種投資組合管理模型，最後可求得三組不同的最適投資組合配置。在以上推導最佳化投資組合過程中，本論文發現，使用「平均數-變異數」作為投資組合管理模型時，有一封閉型的最佳解；然而使用「平均數-風險值」模型時，如果選擇一個較小的信賴水準，有時可能無法獲得最佳投資組合的解答。本論文於MSCI中挑選數支股票作為以上投資組合分析之驗證，首先應用本文所提出之最適投資組合配置模型，求得一組最佳投資組合配置，再將此最佳投資組合的績效表現與市場數個標竿結果比較，其中包括根據台灣加權股票市值再加權的投資組合、根據MSCI Taiwan市值加權的投資組合、以及台灣加權股票指數。分析與驗證的結果發現，無論使用哪一種simplified multivariate GARCH來衡量風險，利用「平均數-變異數」模型所得最佳投資組合的風險都較台灣加權股票市值再加權的投資組合與MSCI Taiwan市值加權的投資組合為低。

This thesis is aimed to construct a comprehensive model of portfolio selection under time-varying volatility. The model contains two modules. Module 1 consists of three simplified multivariate GARCH models namely Constant Correlation GARCH model, Orthogonal GARCH model and PC GARCH model respectively. Module 2 consists of a mean-variance model and a mean-VaR model. Module 1 is used to generate three different time-varying covariance matrices. Any of these matrices can be substituted into Module 2 to obtain a time-varying portfolio that minimizes the risk reflected by its volatility. It is shown that a closed-form solution exists for the optimal portfolio weights if the mean-variance model is employed. However, the optimal portfolio weight may not exist for the mean-VaR model if a small confidence level is selected. The above proposed portfolio selection model is used to analyze a few common stocks selected from Taiwan equity market. The optimal portfolio obtained from the mean-variance model is compared with benchmarks of the market such as TWEX market-value weighted portfolio, MSCI weighted portfolio and TWEX. It is found that the optimal portfolio obtained using the proposed model has the least volatility as compared to those of TWEX weighted portfolio and MSCI weighted portfolio regardless of which of the three multivariate GARCH models is used.