追蹤穩定成長目標線的投資組合最佳化模型

Abstract

本論文研究如何建立一個投資組合用來追蹤穩定成長的目標線。我們將這個目標線追蹤問題建構成混合整數非線性數學規劃模型。由於用以追蹤目標線的投資組合，經過一段時間後其追蹤效能可能未如預期，本論文提出調整投資組合的數學規劃模型。這些模型中除了考量實務中的交易成本，亦考慮限制放空股票，所以將期貨加入投資組合中作為避險部位。最後，以台灣股票市場與期貨交易市場作為實證研究對象，探討投資組合建立與調整的表現，亦分析不同成長率設定之目標線與期貨投資比重上限對投資組合價值的影響。

This thesis studies how to construct a tracking portfolio for the benchmark of a stable growth rate. This tracking problem can be formulated as a mixed-integer nonlinear programming model. Since the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical programming model to rebalance the tracking portfolio. These models not only consider the transaction cost but also take into account of the limitation of shorting a stock; thus the tracking portfolio will include a futures position as a hedging position. Finally, an empirical study will be performed by using the data from the Taiwan stock market and the futures market to explore the performance of the proposed models. We will analyze how the different benchmark settings and the futures position limits will affect the value of the tracking portfolio.

誌謝................................................. iv\r\n摘要.................................................. v\r\nAbstract............................................ vi\r\n目錄................................................ vii\r\n表目錄............................................. viii\r\n圖目錄............................................... ix\r\n\r\n第一章 緒論........................................... 1\r\n 1.1 研究動機....................................... 1\r\n 1.2 研究目的與架構.................................. 3\r\n\r\n第二章 文獻回顧........................................ 4\r\n 2.1 資產配置....................................... 4\r\n 2.2 指數追蹤....................................... 6\r\n\r\n第三章 數學模型探討..................................... 8\r\n 3.1 資產配置的數學模型............................... 8\r\n 3.2 指數追蹤的數學模型.............................. 18\r\n\r\n第四章 建立與調整追蹤目標線投資組合的數學模型............... 34\r\n 4.1 建立投資組合的數學模型........................... 34\r\n 4.2 調整投資組合的數學模型........................... 39\r\n\r\n第五章 實證研究........................................ 43\r\n 5.1 不同時段投資組合的績效表現分析..................... 44\r\n 5.2 調整投資組合的績效表現分析........................ 51\r\n 5.3 不同目標報酬率與期貨比重上限對投資組合績效表現的影響... 55\r\n\r\n第六章 結論與建議...................................... 62\r\n\r\n參考文獻.............................................. 64\r\n\r\n附錄 附表............................................. 66