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| Title: | 資產分類數限制下的投資組合最佳化模型
Portfolio optimization models with restricting the number of asset category |
| Authors: | 廖得勳
Liao, Der Shiun |
| Contributors: | 劉明郎
廖得勳
Liao, Der Shiun |
| Keywords: | 投資組合
限制類股數
混合整數線性規劃
portfolio
stock category restriction
mixed-integer linear programming |
| Date: | 2011 |
| Issue Date: | 2012-04-12 14:11:55 (UTC+8) |
| Abstract: | 本論文研究股票分類與否對投資組合報酬有無差別，因此以目標規畫方式提出兩個混合整數線性規劃模型建立投資組合。在考量市場風險上，兩模型的差別在於一個是單股比重的限制，另一個是類股數目的限制。兩模型中均考慮交易數量為整數與實務中的交易成本，且採用了0-1決策變數，決定股票及類股的選取與否。並以台灣股票市場作為實證研究對象，探討兩模型投資組合在市場不同走勢下的表現，同時也觀察股票分類後，探討選幾個類股數會有較佳的績效，並分析投資組合建立後多久應該進行調整。
This thesis studies the effect of return of a portfolio while restricting the number of asset category. Two mixed-integer linear programming models are proposed by using the goal programming technique. In consideration of the risk, the difference between these two models is that one focuses on a single stock restriction, and the other is on the asset category restriction. The integer restriction and transaction cost are included in the model while using binary decision variable to indicate the selection of an asset and the selection a category. Finally, an empirical study will be presented by applying to Taiwan’s stock market. The performances of these two models are discussed. Moreover, the best number of category in the portfolio and the best timing of rebalance are also investigated.
誌謝 iv
摘要 v
Abstract vi
目錄 vii
表目錄 viii
圖目錄 ix
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的與架構 3
第二章 文獻回顧 4
第三章 數學模型探討 8
3.1 Markowitz 的模型 8
3.2 Konno與Yamazaki的模型 10
3.3 Speranza 的模型 13
3.4 Young的模型 16
3.5 Xia等之投資組合模型 18
第四章 價值成長的投資組合數學規劃模型 19
4.1 建立價值成長的投資組合模型 19
4.2 股票分類限制下的價值成長投資組合模型 23
第五章 實證研究 28
5.1 探討模型A在不同期間的表現 29
5.2 透過模型B觀察市場類股輪動變化 32
5.3 探討模型B在不同期間的表現 39
5.4 探討模型B(二類)的效用期 46
第六章 結論與建議 49
參考文獻 51
附表 53 |
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Konno, H. and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37, 519-531 (1991).
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Speranza, M. G., Linear programming models for portfolio optimization, Finance 14, 107-123 (1993).
Xia, Y., B. Liu, S. Wang and K. K. Lai, A model for portfolio selection with order of expected returns, Computers & Operations Research 27, 409-422 (2000).
Young, M. R., A minimax portfolio selection rule with linear programming solution, Management Science 44, 673-683 (1998).
王靜亮，成長基金的最佳化模型，國立政治大學應用數學系碩士論文，民國96年。
朱志達，超越指數績效的投資組合最佳化模型，國立政治大學應用數學系碩士論文，民國99年。 |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
98972006
100 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0098972006 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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