- 學位論文
以狀態轉換之動態相關係數模型配適最佳投資組合
An Investment Portfolio with Optima Assets Allocation Using Regime Switching for Dynamic Correlation Model
摘要
本篇論文採用Denis Pelletier (2006) 所提出的狀態轉換之動態相關係數模型，將資產報酬之相關係數分為三個狀態，以估計其共變異數矩陣。實證研究則以台灣加權股價指數中的電子、金融與保險、食品、鋼鐵指數為投資組合標的資產，利用兩階段估計法估計投資組合的共變異數矩陣，將共變異數矩陣分為標準差矩陣與相關係數矩陣分別估計。首先第一階段，利用 GARCH 模型估計標準差矩陣，第二階段，給定第一階段的估計值下，利用 RSDC 之相關係數模型並透過EM演算法估計投資組合中各資產間的相關係數矩陣，由此得到投資組合標的資產的共變異數矩陣，以進行最佳化投資組合的資產配置。 研究結果發現，在限制報酬大於目標報酬值 r0 的最小風險投資組合下，在各個狀態數的模型下，皆有最小風險會隨著目標報酬的增加而增加的結果。另外，在控制風險小於給定的風險值 v0 之最大報酬投資組合下，不同狀態數的模型，對於最佳化後的報酬有不同的結果。當投資風險 v0 放寬以後，最大投資報酬即不受狀態變數的影響，且漸漸收斂到一固定報酬。本研究之投資組合配置與未進行最佳化資產配置的投資組合比較，控制風險的最佳化資產配置確實可以達到較高的報酬。
並列摘要
This research bases on Dennis Pelletier's (2006) "Regime Switching Dynamic Correlation" (RSDC) model to estimate the covariance matrix through dividing the correlation into three regimes. The electronics, finance, food, steel & iron sector indices of the TAIEX is adopted as the investment portfolio assets in practical analysis. The covariance matrix of portfolio is estimated by a two-stage approach. The covariance matrix is decomposed into a standard deviation matrix and a correlation coefficient matrix. In the first stage, the volatility of individual asset is estimated by GARCH model. In the second stage, condition on the estimates obtained in the first stage, the correlation matrix of the investment portfolio is estimated based on the RSDC model and the EM Algorithm. Once the covariance matrix of the investment portfolio is determined, optimization method is applied to finding the optimal asset allocation and the optimal return of the investment portfolio will be evaluated accordingly. The result of this study shows that an investment portfolio having the minimum risk constraining on target return greater than a fixed value r0 will increase as r0 increased. And there is only a slight difference among the minimum risks obtained from different number of regimes. On the other hand, an investment portfolio having the maximum return constraining on the risk less than a fixed value v0 will also increase as v0 increased. But, when the restricted upper bound of investment risk v0 is small, the return of the optimum return varies for RSDC models with different number of regimes. When the restricted upper bound of investment risk v0 becomes larger, the number of regime does not affect investment return and eventually the investment return converges to a fixed value. It is also found that the optimal allocation of an investment portfolio proposed by this research will generate higher returns than an investment without optimal allocation.