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題名 以模擬退火法建構資本資產模型的獲利風險最佳化研究－以 0050 指數型 50 檔股票為例
Research into Optimization of Profit with Hedging for Stock Investment by Constructing Capital Asset Model with Simulated Annealing Method- with Example of 50 Stocks of 0050作者 林宜萱
Lin, Yi-Hsuan貢獻者 姜國輝
Chiang, Kuo-Huie
林宜萱
Lin, Yi-Hsuan關鍵詞 模擬退火法
波茲曼機器
夏普比率
風險最佳化
股票
Simulated Annealing
Boltzmann Machine
Sharpe Ratio
Optimization of Profit
Stocks日期 2021 上傳時間 2-九月-2021 15:53:52 (UTC+8) 摘要 Markowitz 所提出之投資組合選擇問題須面臨計算工作繁重且高度複雜的最佳化組合問題，如何在所選擇投資之資產分配最佳資金權重，使所建構之投資組合符合效用前緣線。本研究以股票市場為例，期望在股票市場中尋找風險最小且報酬率最大之資產投資組合並給予較高的資金權重。基於此理由，選擇夏普比率 (Sharpe Ratio) 當作投資組合的選擇策略，夏普比率是利用報酬率除以標準差去衡量承受風險的單位報酬率之大小。其次，本研究再利用霍普菲爾類神經網路 (Hopfield-Tank Neural Network) 結合波茲曼機器 (Boltzmann Machine) 優良的權重學習能力求解最佳投資組合問題。在退火程序中，溫度很高時，系統往高能量方向移動和往低能量方向移動的機率就愈來愈大；當溫度降低時，波茲曼機器則應用神經元狀態改變所造成的能量差 ΔΕ 概念，根據 ΔΕ 和溫度值給定的機率，當溫度高時不管 ΔΕ > 0 或 ΔΕ < 0，即不管能量是往上升或往下降，狀態改變的接受率大約相同，當溫度愈來愈低時，會使得 ΔΕ < 0 狀態被接受的機率愈來愈大。因此，波茲曼機器擁有跳脫局部最佳解 (Local Optimum) ，往全域最佳解 (Global Optimum) 方向移動的能力。本研究期望以模擬退火法建構夏普比率最大化並符合效益前緣的股票投資組合。
The investment portfolio selection problem proposed by Markowitz has to face the intensive and highly complex optimal portfolio problem. How to allocate the best capital weight to the selected investment assets in order to make the constructed investment portfolio meets the efficient frontier is the problem. This thesis takes the stock market as an example, hoping to find the asset portfolio with the lowest risk and the highest return rate in the stock market and give it a higher capital weight. For this reason, Sharpe Ratio is chosen as the investment portfolio selection strategy which uses the rate of return divided by the standard deviation to measure the rate of return per unit of risk.Secondly, this research reuses Hopfield-Tank Neural Network and excellent weight learning ability of Boltzmann Machine to solve the optimal portfolio problem. During the process, if the temperature is high, the probability of the system moving to high energy or low energy becomes greater; if the temperature decreases, Boltzmann Machine applies the concept of energy difference ΔΕ caused by the change of neuron state. According to the probability given by ΔΕ and temperature, when the temperature is high, regardless of ΔΕ > 0 or ΔΕ < 0, that is, regardless of whether the energy is rising or falling, the accepted probability of the changing state is about the same. When the temperature is getting lower, the accepted probability of ΔΕ<0 is getting higher. Therefore, Boltzmann Machine has the ability to escape the local optimum and move towards the global optimum.This research expects to construct a stock portfolio that maximizes Sharpe Ratio and meets the efficient frontier with Simulated Annealing Method.參考文獻 1. 林向愷、楊適予（2008）。財務管理：理論與實務（初版）。台灣：新陸書局。2. 張德丰（2012）。MATLAB神經網絡應用設計（第2版）。中國：機械工業出版社。3. 鄒忠毅、李世炳（2002）。簡介導引模擬退火法及其應用。物理雙月刊。24（2），307-319。4. 鄒忠毅、李定國（2003）。最佳化運用在計算生物學。中央研究院學術諮詢總會通訊。13（1），72-76。5. 葉怡成（2009）。類神經網路模式應用與實作（初版）。台灣：儒林出版社。6. 陳慶瀚（2006）。退火式神經網路，2021 年 7 月 27 日，取自：http://ccy.dd.ncu.edu.tw/~chen/course/Neural/index.htm。7. 謝劍平（2014）。現代投資銀行 Investment Banking: In Greater China（第4版）。台灣：智勝出版社。8. Ajay Raina, & C. Mukhopadhyay. (2004). Optimizing a Portfolio of Equities, Equity Futures and Equity European Options by Minimizing Value-at-Risk - a Simulated Annealing Framework. The ICFAI Journal of APPLIED FINANCE, 10(5), 19-39.9. Andre F. Perold, & Kenneth A. Froot. (2008). Measuring Investment Performance. Retrieved July 27, 2021, from https://hbsp.harvard.edu/product/208110-PDF-ENG.10. Armananzas, R., & Lozano, J.A. (2005). A multiobjective approach to the portfolio optimization problem. The Congress on Evolutionary Computation, 2(5), 1388-1395.11. Chou, C. I., Han, R. S., Li, S. P., & Lee, T. K. (2003). Guided simulated annealing method for optimization problems. Phys. Rev., 67(066704).12. Chung-Chain Lai. (2010). Simulated annealing in multifactor equity portfolio management. International MultiConference of Engineers and Computer Scientists (IMECS), 3, 2092-2097.13. Curtis Faith. (2007). Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders (1st Ed.). United States: McGraw-Hill.14. D. E. Van den Bout, & T. K. Miller. (1989). Improving the performance of the Hopfield-Tank neural network through normalization and annealing. Biological Cybernetics, 62(2), 129-139.15. David H. Ackley, Geoffrey E. Hinton, & Terrence J. Sejnowski. (1985). A learning algorithm for Boltzmann Machines. Cognitive Science, 9(1), 147-169.16. J.J. Hopfield, & D.W. Tank. (1985). Neural Computation of Decisions in Optimization Problems. Biological Cybernetics, 52(3), 141-152.17. Jingjing Lu, & Merrill Liechty. (2007). An empirical comparison between nonlinear programming optimization and simulated annealing (SA) algorithm under a higher moments Bayesian portfolio selection framework. 2007 Winter conference simulation, 1021-1027.18. John C. Hull. (2002). Options, Futures and Other Derivatives (4th Ed.). United States: Prentice Hall.19. Markowitz, H. M. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91.20. Nate Schmidt. (2010). Simulated Annealing. Retrieved July 27, 2021, from http://personal.denison.edu/~havill/272S04/papers/simulated_annealing.pdf.21. Reto Gallati. (2003). 15.433 Investments Lecture 6: The CAPM and APT Part 1: Theory. Retrieved July 27, 2021, from http://core.csu.edu.cn/NR/rdonlyres/Sloan-School-of-Management/15-433InvestmentsSpring2003/090E1B17-E442-41DB-8355-98A065059021/0/154336capm1.pdf.22. Reto Gallati. (2003). 15.433 Investments Lecture 7: Applications and Tests. Retrieved July 27, 2021, from http://core.csu.edu.cn/NR/rdonlyres/Sloan-School-of-Management/15-433InvestmentsSpring2003/ADA3E7B7-C053-4300-936E-3D6ACF342ECE/0/154337capm2.pdf.23. S. Kirkpatrick, C. D. Gelatt, & M. P. Vecchi. (1983). Optimization by Simulated Annealing. Science Volume, 220(4598), 671-680.24. S. Kirkpatrick. (1984). Optimization by Simulated Annealing: Quantitative Studies. Journal of Statistical Physics, 34, 975-986.25. Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442.26. Simon C. Lin, & James H.C. Hsueh. (1994). A new methodology of simulated annealing for the optimisation problems. Physical A: Statistical Mechanics and its Applications, 205(1-3), 367-374.27. Simon Haykin. (1994). Neural networks: A comprehensive foundation. United States: Prentice Hall.28. Y. Crama, & M. Schyns. (2003). Simulated annealing for complex portfolio selection problems. European Journal of Operational Research, 150(3), 546-571.29. Zhao Xinchao. (2010). Simulated annealing algorithm adaptive neighborhood. Applied Soft Computing, 11(2), 1827-1836. 描述 碩士
國立政治大學
資訊管理學系
108356019資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108356019 資料類型 thesis dc.contributor.advisor 姜國輝 zh_TW dc.contributor.advisor Chiang, Kuo-Huie en_US dc.contributor.author (作者) 林宜萱 zh_TW dc.contributor.author (作者) Lin, Yi-Hsuan en_US dc.creator (作者) 林宜萱 zh_TW dc.creator (作者) Lin, Yi-Hsuan en_US dc.date (日期) 2021 en_US dc.date.accessioned 2-九月-2021 15:53:52 (UTC+8) - dc.date.available 2-九月-2021 15:53:52 (UTC+8) - dc.date.issued (上傳時間) 2-九月-2021 15:53:52 (UTC+8) - dc.identifier (其他 識別碼) G0108356019 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/136844 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 資訊管理學系 zh_TW dc.description (描述) 108356019 zh_TW dc.description.abstract (摘要) Markowitz 所提出之投資組合選擇問題須面臨計算工作繁重且高度複雜的最佳化組合問題，如何在所選擇投資之資產分配最佳資金權重，使所建構之投資組合符合效用前緣線。本研究以股票市場為例，期望在股票市場中尋找風險最小且報酬率最大之資產投資組合並給予較高的資金權重。基於此理由，選擇夏普比率 (Sharpe Ratio) 當作投資組合的選擇策略，夏普比率是利用報酬率除以標準差去衡量承受風險的單位報酬率之大小。其次，本研究再利用霍普菲爾類神經網路 (Hopfield-Tank Neural Network) 結合波茲曼機器 (Boltzmann Machine) 優良的權重學習能力求解最佳投資組合問題。在退火程序中，溫度很高時，系統往高能量方向移動和往低能量方向移動的機率就愈來愈大；當溫度降低時，波茲曼機器則應用神經元狀態改變所造成的能量差 ΔΕ 概念，根據 ΔΕ 和溫度值給定的機率，當溫度高時不管 ΔΕ > 0 或 ΔΕ < 0，即不管能量是往上升或往下降，狀態改變的接受率大約相同，當溫度愈來愈低時，會使得 ΔΕ < 0 狀態被接受的機率愈來愈大。因此，波茲曼機器擁有跳脫局部最佳解 (Local Optimum) ，往全域最佳解 (Global Optimum) 方向移動的能力。本研究期望以模擬退火法建構夏普比率最大化並符合效益前緣的股票投資組合。 zh_TW dc.description.abstract (摘要) The investment portfolio selection problem proposed by Markowitz has to face the intensive and highly complex optimal portfolio problem. How to allocate the best capital weight to the selected investment assets in order to make the constructed investment portfolio meets the efficient frontier is the problem. This thesis takes the stock market as an example, hoping to find the asset portfolio with the lowest risk and the highest return rate in the stock market and give it a higher capital weight. For this reason, Sharpe Ratio is chosen as the investment portfolio selection strategy which uses the rate of return divided by the standard deviation to measure the rate of return per unit of risk.Secondly, this research reuses Hopfield-Tank Neural Network and excellent weight learning ability of Boltzmann Machine to solve the optimal portfolio problem. During the process, if the temperature is high, the probability of the system moving to high energy or low energy becomes greater; if the temperature decreases, Boltzmann Machine applies the concept of energy difference ΔΕ caused by the change of neuron state. According to the probability given by ΔΕ and temperature, when the temperature is high, regardless of ΔΕ > 0 or ΔΕ < 0, that is, regardless of whether the energy is rising or falling, the accepted probability of the changing state is about the same. When the temperature is getting lower, the accepted probability of ΔΕ<0 is getting higher. Therefore, Boltzmann Machine has the ability to escape the local optimum and move towards the global optimum.This research expects to construct a stock portfolio that maximizes Sharpe Ratio and meets the efficient frontier with Simulated Annealing Method. en_US dc.description.tableofcontents 致謝 i摘要 iiAbstract iii目錄 iv表目錄 vi圖目錄 vii第一章 緒論 1第一節 研究動機與背景 1第二節 研究目的 1第三節 研究架構 2第二章 文獻探討 3第一節 Markowitz 投資組合選擇理論和效率前緣公式 3第二節 CAPM 資本資產定價模式 4第三節 風險調整報酬（Risk-Adjusted Return） 7壹、多因子標竿報酬（Multi-Factor Benchmark Return） 7貳、夏普比率（Sharpe Ratio） 7第四節 模擬退火演算法 8壹、李亞普諾夫函數（Liapunov Function）與 Hopfield 神經網路 8貳、Hopfield 神經網路與 TSP 最短路經問題簡介 14參、Boltzmann 機率原理 17肆、模擬退火法熱平衡原理 21伍、模擬退火演算法流程與權重學習調整原理 27陸、模擬退火法應用於解決 TSP 問題和模擬退火法的優化探討 31第五節 做多與做空 34第六節 風險值（Value-at-Risk）與計算模型 34第七節 影子價格（Shadow Price） 35第三章 研究設計 37第一節 模型設計 37壹、台股投資組合目標函數模型 37第二節 研究流程 38壹、夏普比率最大化模擬退火法流程 38第三節 預期成果 39第四章 研究結果 41第一節 Boltzmann Machine 結果 41第二節 模擬退火演算法結果 42第三節 研究模型與 ETF50 比較 44壹、使用研究模型的結果 44貳、目標函數比較 46參、資金比較 47第五章 結論與建議 49第一節 研究結論 49第二節 未來展望 49第三節 研究貢獻與結語 50參考文獻 51 zh_TW dc.format.extent 1814036 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108356019 en_US dc.subject (關鍵詞) 模擬退火法 zh_TW dc.subject (關鍵詞) 波茲曼機器 zh_TW dc.subject (關鍵詞) 夏普比率 zh_TW dc.subject (關鍵詞) 風險最佳化 zh_TW dc.subject (關鍵詞) 股票 zh_TW dc.subject (關鍵詞) Simulated Annealing en_US dc.subject (關鍵詞) Boltzmann Machine en_US dc.subject (關鍵詞) Sharpe Ratio en_US dc.subject (關鍵詞) Optimization of Profit en_US dc.subject (關鍵詞) Stocks en_US dc.title (題名) 以模擬退火法建構資本資產模型的獲利風險最佳化研究－以 0050 指數型 50 檔股票為例 zh_TW dc.title (題名) Research into Optimization of Profit with Hedging for Stock Investment by Constructing Capital Asset Model with Simulated Annealing Method- with Example of 50 Stocks of 0050 en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1. 林向愷、楊適予（2008）。財務管理：理論與實務（初版）。台灣：新陸書局。2. 張德丰（2012）。MATLAB神經網絡應用設計（第2版）。中國：機械工業出版社。3. 鄒忠毅、李世炳（2002）。簡介導引模擬退火法及其應用。物理雙月刊。24（2），307-319。4. 鄒忠毅、李定國（2003）。最佳化運用在計算生物學。中央研究院學術諮詢總會通訊。13（1），72-76。5. 葉怡成（2009）。類神經網路模式應用與實作（初版）。台灣：儒林出版社。6. 陳慶瀚（2006）。退火式神經網路，2021 年 7 月 27 日，取自：http://ccy.dd.ncu.edu.tw/~chen/course/Neural/index.htm。7. 謝劍平（2014）。現代投資銀行 Investment Banking: In Greater China（第4版）。台灣：智勝出版社。8. Ajay Raina, & C. Mukhopadhyay. (2004). Optimizing a Portfolio of Equities, Equity Futures and Equity European Options by Minimizing Value-at-Risk - a Simulated Annealing Framework. The ICFAI Journal of APPLIED FINANCE, 10(5), 19-39.9. Andre F. Perold, & Kenneth A. Froot. (2008). Measuring Investment Performance. Retrieved July 27, 2021, from https://hbsp.harvard.edu/product/208110-PDF-ENG.10. Armananzas, R., & Lozano, J.A. (2005). A multiobjective approach to the portfolio optimization problem. The Congress on Evolutionary Computation, 2(5), 1388-1395.11. Chou, C. I., Han, R. S., Li, S. P., & Lee, T. K. (2003). Guided simulated annealing method for optimization problems. Phys. Rev., 67(066704).12. Chung-Chain Lai. (2010). Simulated annealing in multifactor equity portfolio management. International MultiConference of Engineers and Computer Scientists (IMECS), 3, 2092-2097.13. Curtis Faith. (2007). Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders (1st Ed.). United States: McGraw-Hill.14. D. E. Van den Bout, & T. K. Miller. (1989). Improving the performance of the Hopfield-Tank neural network through normalization and annealing. Biological Cybernetics, 62(2), 129-139.15. David H. Ackley, Geoffrey E. Hinton, & Terrence J. Sejnowski. (1985). A learning algorithm for Boltzmann Machines. Cognitive Science, 9(1), 147-169.16. J.J. Hopfield, & D.W. Tank. (1985). Neural Computation of Decisions in Optimization Problems. Biological Cybernetics, 52(3), 141-152.17. Jingjing Lu, & Merrill Liechty. (2007). An empirical comparison between nonlinear programming optimization and simulated annealing (SA) algorithm under a higher moments Bayesian portfolio selection framework. 2007 Winter conference simulation, 1021-1027.18. John C. Hull. (2002). Options, Futures and Other Derivatives (4th Ed.). United States: Prentice Hall.19. Markowitz, H. M. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91.20. Nate Schmidt. (2010). Simulated Annealing. Retrieved July 27, 2021, from http://personal.denison.edu/~havill/272S04/papers/simulated_annealing.pdf.21. Reto Gallati. (2003). 15.433 Investments Lecture 6: The CAPM and APT Part 1: Theory. Retrieved July 27, 2021, from http://core.csu.edu.cn/NR/rdonlyres/Sloan-School-of-Management/15-433InvestmentsSpring2003/090E1B17-E442-41DB-8355-98A065059021/0/154336capm1.pdf.22. Reto Gallati. (2003). 15.433 Investments Lecture 7: Applications and Tests. Retrieved July 27, 2021, from http://core.csu.edu.cn/NR/rdonlyres/Sloan-School-of-Management/15-433InvestmentsSpring2003/ADA3E7B7-C053-4300-936E-3D6ACF342ECE/0/154337capm2.pdf.23. S. Kirkpatrick, C. D. Gelatt, & M. P. Vecchi. (1983). Optimization by Simulated Annealing. Science Volume, 220(4598), 671-680.24. S. Kirkpatrick. (1984). Optimization by Simulated Annealing: Quantitative Studies. Journal of Statistical Physics, 34, 975-986.25. Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442.26. Simon C. Lin, & James H.C. Hsueh. (1994). A new methodology of simulated annealing for the optimisation problems. Physical A: Statistical Mechanics and its Applications, 205(1-3), 367-374.27. Simon Haykin. (1994). Neural networks: A comprehensive foundation. United States: Prentice Hall.28. Y. Crama, & M. Schyns. (2003). Simulated annealing for complex portfolio selection problems. European Journal of Operational Research, 150(3), 546-571.29. Zhao Xinchao. (2010). Simulated annealing algorithm adaptive neighborhood. Applied Soft Computing, 11(2), 1827-1836. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202101169 en_US
