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題名 追蹤穩定成長目標線的投資組合隨機最佳化模型
Stochastic portfolio optimization models for the stable growth benchmark tracking作者 林澤佑
Lin, Tse Yu貢獻者 劉明郎
Liu, Ming Long
林澤佑
Lin, Tse Yu關鍵詞 目標線追蹤問題
期貨避險
投資組合調整
混合整數非線性規劃
二階段隨機規劃
情境樹
benchmark tracking problem
futures hedging
portfolio rebalance
mixed-integer nonlinear programming
two-stage stochastic programming
scenario tree日期 2011 上傳時間 30-Oct-2012 11:28:00 (UTC+8) 摘要 本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。
To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect thevalue of the tracking portfolio.參考文獻 Andrews, C., D. Ford, and K. Mallinson, The design of index funds and alternative methods of replication, The Investment Analyst 82 (October), 16-23 (1986).Benders, J. F., Partitioning procedures for solving mixed-variable programming problems, Numerische Mathematic 4, 238-252 (1962).Brooke, A., D. Kendrick, and A. Meeraus, GAMS-A User’s Guide, The Scientific Press, Redwood City, CA, (1988).Canakgoz N. A., and J. E. Beasley, Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research196, 384-399 (2008).Feinstein, C. D., and M. N. Thapa, A reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39 (12), 1552-1553 (1993).Frauendorfer, K., The stochastic programming extension of the Markowitz approach Journal on Neural and Mass-Parallel Computing and Information Systems 5, 449-460 (1995).Gülpınar, N., B. Rustem, and R. Settergren, Multistage stochastic mean-variance portfolio analysis with transaction costs, Innovations in Financial and Economics Networks 3 , 46-63 (2003).Kalvelagen, E., Two stage stochastic linear programming with GAMS, http://amsterdamoptimization.com/pdf/twostage.pdf, 2003Konno, H., and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37 (5), 519-531 (1991).Markowitz, H., Portfolio selection, Journal of Finance 7 (1), 77-91 (1952).Markowitz, H., Portfolio selection: Efficient diversification of investmenst, John Wiley & Sons, New York (1959).Meade, N., and G. R. Salkin, Index funds-construction and performance measurement, Journal of the Operational Research Society 40 (10), 871-879 (1989).Speranza, M. G., Linear programming models for portfolio optimization, Finance 14(1), 107-123 (1993).Steinbach, M., Recursive direct optimization and successive renement in multistage stochastic programs, Preprint SC 98-27, Konrad-Zuse Centrum für Informationstechnik Berlin, 1998.Yao, D. D., S. Zhang, and X. Y. Zhou, Tracking a financial benchmark using a few assets, Operations Research 54 (2), 232-246 (2006).Young, M. R., A minimax portfolio selection rule with linear programming solution, Management Science 44 (5), 673-683 (1998).莊智祥，使用目標規劃建立指數基金，國立政治大學應用數學系碩士論文（民87）。楊靜宜，選擇權交易策略的整數線性規劃模型，國立政治大學應用數學系碩士論文（民93）。陳明瑩，考慮交易成本的選擇權交易策略，國立政治大學應用數學系碩士論文（民96）。謝承哲，追蹤穩定成長目標線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99）。 描述 碩士
國立政治大學
應用數學研究所
99751016
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0997510162 資料類型 thesis dc.contributor.advisor 劉明郎 zh_TW dc.contributor.advisor Liu, Ming Long en_US dc.contributor.author (Authors) 林澤佑 zh_TW dc.contributor.author (Authors) Lin, Tse Yu en_US dc.creator (作者) 林澤佑 zh_TW dc.creator (作者) Lin, Tse Yu en_US dc.date (日期) 2011 en_US dc.date.accessioned 30-Oct-2012 11:28:00 (UTC+8) - dc.date.available 30-Oct-2012 11:28:00 (UTC+8) - dc.date.issued (上傳時間) 30-Oct-2012 11:28:00 (UTC+8) - dc.identifier (Other Identifiers) G0997510162 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54647 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學研究所 zh_TW dc.description (描述) 99751016 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) 本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 zh_TW dc.description.abstract (摘要) To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect thevalue of the tracking portfolio. en_US dc.description.tableofcontents 第一章 緒論 ...11.1 研究動機 ...11.2 研究目的與架構...3 第二章 文獻回顧 ...42.1 資產配置 ...42.2 指數追蹤 ...62.3 隨機規劃 ...9第三章 數學模型探討 ...113.1 資產配置的數學模型 ...113.2 指數追蹤的數學模型 ...22第四章 建立追蹤目標線投資組合的數學模型與實證研究 ...304.1 建立投資組合的數學模型 ...304.2 調整投資組合的數學模型 ...384.3 實證研究 ...44第五章 模型的修正與實證研究 ...605.1 修正建立投資組合的數學模型 ...605.2 實證研究 ...62第六章 結論與建議 ...66參考文獻 ...68附錄 附表 ...70 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0997510162 en_US dc.subject (關鍵詞) 目標線追蹤問題 zh_TW dc.subject (關鍵詞) 期貨避險 zh_TW dc.subject (關鍵詞) 投資組合調整 zh_TW dc.subject (關鍵詞) 混合整數非線性規劃 zh_TW dc.subject (關鍵詞) 二階段隨機規劃 zh_TW dc.subject (關鍵詞) 情境樹 zh_TW dc.subject (關鍵詞) benchmark tracking problem en_US dc.subject (關鍵詞) futures hedging en_US dc.subject (關鍵詞) portfolio rebalance en_US dc.subject (關鍵詞) mixed-integer nonlinear programming en_US dc.subject (關鍵詞) two-stage stochastic programming en_US dc.subject (關鍵詞) scenario tree en_US dc.title (題名) 追蹤穩定成長目標線的投資組合隨機最佳化模型 zh_TW dc.title (題名) Stochastic portfolio optimization models for the stable growth benchmark tracking en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Andrews, C., D. Ford, and K. Mallinson, The design of index funds and alternative methods of replication, The Investment Analyst 82 (October), 16-23 (1986).Benders, J. F., Partitioning procedures for solving mixed-variable programming problems, Numerische Mathematic 4, 238-252 (1962).Brooke, A., D. Kendrick, and A. Meeraus, GAMS-A User’s Guide, The Scientific Press, Redwood City, CA, (1988).Canakgoz N. A., and J. E. Beasley, Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research196, 384-399 (2008).Feinstein, C. D., and M. N. Thapa, A reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39 (12), 1552-1553 (1993).Frauendorfer, K., The stochastic programming extension of the Markowitz approach Journal on Neural and Mass-Parallel Computing and Information Systems 5, 449-460 (1995).Gülpınar, N., B. Rustem, and R. Settergren, Multistage stochastic mean-variance portfolio analysis with transaction costs, Innovations in Financial and Economics Networks 3 , 46-63 (2003).Kalvelagen, E., Two stage stochastic linear programming with GAMS, http://amsterdamoptimization.com/pdf/twostage.pdf, 2003Konno, H., and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37 (5), 519-531 (1991).Markowitz, H., Portfolio selection, Journal of Finance 7 (1), 77-91 (1952).Markowitz, H., Portfolio selection: Efficient diversification of investmenst, John Wiley & Sons, New York (1959).Meade, N., and G. R. Salkin, Index funds-construction and performance measurement, Journal of the Operational Research Society 40 (10), 871-879 (1989).Speranza, M. G., Linear programming models for portfolio optimization, Finance 14(1), 107-123 (1993).Steinbach, M., Recursive direct optimization and successive renement in multistage stochastic programs, Preprint SC 98-27, Konrad-Zuse Centrum für Informationstechnik Berlin, 1998.Yao, D. D., S. Zhang, and X. Y. Zhou, Tracking a financial benchmark using a few assets, Operations Research 54 (2), 232-246 (2006).Young, M. R., A minimax portfolio selection rule with linear programming solution, Management Science 44 (5), 673-683 (1998).莊智祥，使用目標規劃建立指數基金，國立政治大學應用數學系碩士論文（民87）。楊靜宜，選擇權交易策略的整數線性規劃模型，國立政治大學應用數學系碩士論文（民93）。陳明瑩，考慮交易成本的選擇權交易策略，國立政治大學應用數學系碩士論文（民96）。謝承哲，追蹤穩定成長目標線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99）。 zh_TW
