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題名 指數基金追蹤模型的最佳化
A Tracking Model for Index Fund Portfolio Optimization
作者 白惠琦
貢獻者 劉明郎
白惠琦
關鍵詞 指數基金
目標規劃
切面法
index fund
goal programming model
cutting plane method
日期 2002
上傳時間 9-May-2016 16:39:19 (UTC+8)
摘要 　　指數基金係提供投資者追隨市場指數成長的投資工具，且投資者僅需考量市場風險即可，其建構方式有完全複製法、分層法、抽樣法、及最佳化法。本論文使用目標規劃模型建構指數基金，此法可歸類為最佳化法。由於模型中每種股票的投資數量設為整數變數，加上控制股票種類數量的0-1變數，因此所建構的目標規劃模型為混合型整數線性規劃問題。此問題在大尺度模型時往往無法求得其最佳解，我們研究此模型的結構提出一組縮小解集合空間的合理不等式，應用切面法加入必需的不等式後再根據本模型的對偶性質發展出有效率的啟發式演算法，最後將此模型及演算法應用在模擬台灣發行量加權股價指數。
　　Index fund is an investment tool which tracks a stock-market index and thus is associated with market risk only. Its attraction to investors is low investment risk and low administrative expenses. Four different approaches to index fund construction can be classified as full replication, stratification, sampling, and optimizing respectively. In this thesis, we construct an index fund via the goal programming model with the optimizing approach. The model can be formulated as a mixed integer linear programming. The exact optimal solution can not be obtained when the model becomes large. We then develop a valid inequality and use this valid inequality to develop a cutting plane method. We also propose an efficient heuristic by adopting the dual property. Finally, an empirical study applying to the Taiwan Stock Exchange Capitalization Weighted Stock Index is given to show the efficiency of the algorithm.
謝辭
     摘要-----i
     Abstract-----ii
     目錄-----iii
     表目錄-----iv
     圖目錄-----V
     1 緒論-----1
     　　1.1 前言-----1
     　　1.2 研究目的與架構-----3
     2 文獻回顧-----6
     3 選擇投資組合的數學模型-----9
     4 指數基金的數學模型與演算法-----16
     　　4.1 追蹤誤差-----16
     　　4.2 指數基金的目標規劃模型及其對偶模型-----18
     　　4.3 演算法-----22
     　　　　4.3.1 切面法-----22
     　　　　4.3.2 啟發式演算法-----28
     　　　　4.3.3 結合切面法的啟發式演算法-----29
     5 實證研究-----30
     6 結論與建議-----39
     參考文獻-----41
     附錄 附表-----43
     
     表目錄
     表1　切面法解MILP模型的效率-----31
     表2　啟發式演算法的效率-----34
     表3　指數基金追蹤標的指數的效能（資料集合：D1）-----36
     表4　指數基金追蹤標的指數的效能（資料集合：D2）-----37
     表5　指數基金追蹤標的指數的效能（資料集合：D3）-----37
     附表1　D1所建構的投資組合-----44
     附表2　D2所建構的投資組合-----45
     附表3　D3所建構的投資組合-----46
     
     圖目錄
     圖1　研究架構流程圖-----5
     圖2　Z-N0圖（時間資料長度：6個月）-----32
     圖3　Z-N0圖（時間資料長度：12個月）-----32
     圖4　Z-N0圖（時間資料長度：18個月）-----33
參考文獻 [1] Andrews, C., D. Ford, and K. Mallinson (1986), "The design of index funds and alternative methods of replication," The Investment Analyst 82 (October), 16-23.
     [2] Brooke, A., D. Kendrick, and A. Meeraus (1988), GAMS-A User"s Guide, The Scientific Press, Redwood City, CA.
     [3] Cooper, W. W., V. Lelas, and T. Sueyoshi (1997), "Goal programming models and their duality relations for use in evaluating security portfolio and regression relations," European Journal of Operational Research 98, 431-443.
     [4] Feinstein, C. D. and M. N. Thapa (1993), "Notes: A reformulation of a mean-absolute deviation portfolio optimization model,"Management Science 39, 1552-1553.
     [5] Konno, H. and H. Yamazaki (1991), ``Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market," Management Science 37, 519-531.
     [6] Lodge, S. (1993),"Tracking the market," Investors Chronicle 104, 12-13.
     [7] Mansini, R. and M. G. Speranza (1999), "Heuristic algorithms for the portfolio selection problem with minimum transaction lots,"European Journal of Operational Research 114, 219-233.
     [8] Markowitz, H. M. (1952),"Portfolio selection,"Journal of Finance (March), 77-91.
     [9] Meade, N. and G. R. Salkin (1989),"Index funds-construction and performance measurement,"Journal of Operational Research Society 40, 871-879.
     [10] Nemhauser, G. L. and L. A. Wolsey (1988), Integer and Combinatorial Optimization, New York, Wiley.
     [11] Rudd, A. (1980),"Optimal selection of passive portfolios,"Financial Management (Spring), 57-66.
     [12] Sharpe, W. F. (1971),"Mean-absolute-deviation characteristic lines for securities and portfolios,"Management Science 18, B-1-B-13.
     [13] Stone, B. K. (1973),"A linear programming formulation of the general portfolio selection problem,"Journal of Financial and Quantitative Analysis (September), 621-636.
     [14] Tabata, Y. and E. Takeda (1995),"Bicriteria optimization problem of designing an index fund,"Journal of Operational Research Society 46, 1023-1032.
     [15] Toy, W. W. and M. A. Zurack (1989),"Tracking the Euro-Pac Index,"Journal of Portfolio Management (Winter), 55-58.
     [16] Van Roy, T. J. and L. A. Wolsey (1986),"Valid inequalities for mixed 0-1 programs ,"Discrete Applied Mathematics 14, 199-213.
     [17] Willis, C. (1996),"Why every investor should own an index fund," Working Woman 21, 34.
     [18] 卞志祥 （民85），台灣加權股價指數投資組合之基因演算法建構模型，國立交通大學資訊管理研究所碩士論文。
     [19] 莊智祥 （民87），Index Fund Construction via Goal Programming，國立政治大學應用數學研究所碩士論文。
描述 碩士
國立政治大學
應用數學系
88751011
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2010000244
資料類型 thesis
dc.contributor.advisor 劉明郎zh_TW
dc.contributor.author (Authors) 白惠琦zh_TW
dc.creator (作者) 白惠琦zh_TW
dc.date (日期) 2002en_US
dc.date.accessioned 9-May-2016 16:39:19 (UTC+8)-
dc.date.available 9-May-2016 16:39:19 (UTC+8)-
dc.date.issued (上傳時間) 9-May-2016 16:39:19 (UTC+8)-
dc.identifier (Other Identifiers) A2010000244en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95620-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 88751011zh_TW
dc.description.abstract (摘要) 　　指數基金係提供投資者追隨市場指數成長的投資工具，且投資者僅需考量市場風險即可，其建構方式有完全複製法、分層法、抽樣法、及最佳化法。本論文使用目標規劃模型建構指數基金，此法可歸類為最佳化法。由於模型中每種股票的投資數量設為整數變數，加上控制股票種類數量的0-1變數，因此所建構的目標規劃模型為混合型整數線性規劃問題。此問題在大尺度模型時往往無法求得其最佳解，我們研究此模型的結構提出一組縮小解集合空間的合理不等式，應用切面法加入必需的不等式後再根據本模型的對偶性質發展出有效率的啟發式演算法，最後將此模型及演算法應用在模擬台灣發行量加權股價指數。zh_TW
dc.description.abstract (摘要) 　　Index fund is an investment tool which tracks a stock-market index and thus is associated with market risk only. Its attraction to investors is low investment risk and low administrative expenses. Four different approaches to index fund construction can be classified as full replication, stratification, sampling, and optimizing respectively. In this thesis, we construct an index fund via the goal programming model with the optimizing approach. The model can be formulated as a mixed integer linear programming. The exact optimal solution can not be obtained when the model becomes large. We then develop a valid inequality and use this valid inequality to develop a cutting plane method. We also propose an efficient heuristic by adopting the dual property. Finally, an empirical study applying to the Taiwan Stock Exchange Capitalization Weighted Stock Index is given to show the efficiency of the algorithm.en_US
dc.description.abstract (摘要) 謝辭
     摘要-----i
     Abstract-----ii
     目錄-----iii
     表目錄-----iv
     圖目錄-----V
     1 緒論-----1
     　　1.1 前言-----1
     　　1.2 研究目的與架構-----3
     2 文獻回顧-----6
     3 選擇投資組合的數學模型-----9
     4 指數基金的數學模型與演算法-----16
     　　4.1 追蹤誤差-----16
     　　4.2 指數基金的目標規劃模型及其對偶模型-----18
     　　4.3 演算法-----22
     　　　　4.3.1 切面法-----22
     　　　　4.3.2 啟發式演算法-----28
     　　　　4.3.3 結合切面法的啟發式演算法-----29
     5 實證研究-----30
     6 結論與建議-----39
     參考文獻-----41
     附錄 附表-----43
     
     表目錄
     表1　切面法解MILP模型的效率-----31
     表2　啟發式演算法的效率-----34
     表3　指數基金追蹤標的指數的效能（資料集合：D1）-----36
     表4　指數基金追蹤標的指數的效能（資料集合：D2）-----37
     表5　指數基金追蹤標的指數的效能（資料集合：D3）-----37
     附表1　D1所建構的投資組合-----44
     附表2　D2所建構的投資組合-----45
     附表3　D3所建構的投資組合-----46
     
     圖目錄
     圖1　研究架構流程圖-----5
     圖2　Z-N0圖（時間資料長度：6個月）-----32
     圖3　Z-N0圖（時間資料長度：12個月）-----32
     圖4　Z-N0圖（時間資料長度：18個月）-----33		-
dc.description.tableofcontents 謝辭
     摘要-----i
     Abstract-----ii
     目錄-----iii
     表目錄-----iv
     圖目錄-----V
     1 緒論-----1
     　　1.1 前言-----1
     　　1.2 研究目的與架構-----3
     2 文獻回顧-----6
     3 選擇投資組合的數學模型-----9
     4 指數基金的數學模型與演算法-----16
     　　4.1 追蹤誤差-----16
     　　4.2 指數基金的目標規劃模型及其對偶模型-----18
     　　4.3 演算法-----22
     　　　　4.3.1 切面法-----22
     　　　　4.3.2 啟發式演算法-----28
     　　　　4.3.3 結合切面法的啟發式演算法-----29
     5 實證研究-----30
     6 結論與建議-----39
     參考文獻-----41
     附錄 附表-----43
     
     表目錄
     表1　切面法解MILP模型的效率-----31
     表2　啟發式演算法的效率-----34
     表3　指數基金追蹤標的指數的效能（資料集合：D1）-----36
     表4　指數基金追蹤標的指數的效能（資料集合：D2）-----37
     表5　指數基金追蹤標的指數的效能（資料集合：D3）-----37
     附表1　D1所建構的投資組合-----44
     附表2　D2所建構的投資組合-----45
     附表3　D3所建構的投資組合-----46
     
     圖目錄
     圖1　研究架構流程圖-----5
     圖2　Z-N0圖（時間資料長度：6個月）-----32
     圖3　Z-N0圖（時間資料長度：12個月）-----32
     圖4　Z-N0圖（時間資料長度：18個月）-----33		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2010000244en_US
dc.subject (關鍵詞) 指數基金zh_TW
dc.subject (關鍵詞) 目標規劃zh_TW
dc.subject (關鍵詞) 切面法zh_TW
dc.subject (關鍵詞) index funden_US
dc.subject (關鍵詞) goal programming modelen_US
dc.subject (關鍵詞) cutting plane methoden_US
dc.title (題名) 指數基金追蹤模型的最佳化zh_TW
dc.title (題名) A Tracking Model for Index Fund Portfolio Optimizationen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Andrews, C., D. Ford, and K. Mallinson (1986), "The design of index funds and alternative methods of replication," The Investment Analyst 82 (October), 16-23.
     [2] Brooke, A., D. Kendrick, and A. Meeraus (1988), GAMS-A User"s Guide, The Scientific Press, Redwood City, CA.
     [3] Cooper, W. W., V. Lelas, and T. Sueyoshi (1997), "Goal programming models and their duality relations for use in evaluating security portfolio and regression relations," European Journal of Operational Research 98, 431-443.
     [4] Feinstein, C. D. and M. N. Thapa (1993), "Notes: A reformulation of a mean-absolute deviation portfolio optimization model,"Management Science 39, 1552-1553.
     [5] Konno, H. and H. Yamazaki (1991), ``Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market," Management Science 37, 519-531.
     [6] Lodge, S. (1993),"Tracking the market," Investors Chronicle 104, 12-13.
     [7] Mansini, R. and M. G. Speranza (1999), "Heuristic algorithms for the portfolio selection problem with minimum transaction lots,"European Journal of Operational Research 114, 219-233.
     [8] Markowitz, H. M. (1952),"Portfolio selection,"Journal of Finance (March), 77-91.
     [9] Meade, N. and G. R. Salkin (1989),"Index funds-construction and performance measurement,"Journal of Operational Research Society 40, 871-879.
     [10] Nemhauser, G. L. and L. A. Wolsey (1988), Integer and Combinatorial Optimization, New York, Wiley.
     [11] Rudd, A. (1980),"Optimal selection of passive portfolios,"Financial Management (Spring), 57-66.
     [12] Sharpe, W. F. (1971),"Mean-absolute-deviation characteristic lines for securities and portfolios,"Management Science 18, B-1-B-13.
     [13] Stone, B. K. (1973),"A linear programming formulation of the general portfolio selection problem,"Journal of Financial and Quantitative Analysis (September), 621-636.
     [14] Tabata, Y. and E. Takeda (1995),"Bicriteria optimization problem of designing an index fund,"Journal of Operational Research Society 46, 1023-1032.
     [15] Toy, W. W. and M. A. Zurack (1989),"Tracking the Euro-Pac Index,"Journal of Portfolio Management (Winter), 55-58.
     [16] Van Roy, T. J. and L. A. Wolsey (1986),"Valid inequalities for mixed 0-1 programs ,"Discrete Applied Mathematics 14, 199-213.
     [17] Willis, C. (1996),"Why every investor should own an index fund," Working Woman 21, 34.
     [18] 卞志祥 （民85），台灣加權股價指數投資組合之基因演算法建構模型，國立交通大學資訊管理研究所碩士論文。
     [19] 莊智祥 （民87），Index Fund Construction via Goal Programming，國立政治大學應用數學研究所碩士論文。		zh_TW