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研究生:陳姵君
研究生(外文):PeiJun Chen
論文名稱:多目標基因演算法應用於基金投資組合最佳化
論文名稱(外文):A Study of Applying Multi-Objective Genetic Algorithm to Optimization of Mutual Fund Portfolio
指導教授:邱昭彰邱昭彰引用關係
指導教授(外文):ChaoChang Chiu
學位類別:碩士
校院名稱:元智大學
系所名稱:資訊管理學系
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:44
中文關鍵詞:多目標基因演算法共同基金投資組合多目標演化演算法
外文關鍵詞:Multi-Objective Genetic Algorithm (MOGA)Mutual FundPortfolioMulti-Objective Evolutionary Algorithms (MOEAs)
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本研究應用多目標基因演算法,求最大夏普指數值及最小期望損失值,以建構高投資效率及低下方風險之共同基金投資組合。並研究加入資金配置之限制條件對投資組合配置之影響。資金配置之限制條件包含:投資基金檔數上下限限制、單筆基金投資比例上限限制及同類基金投資比例上限限制。研究結論:不含資金配置之限制條件模式演化之結果,資金配置之權重會集中於高夏普值之標的,不符合投資組合分散投資之特性。含資金配置之限制條件模式演化之結果,雖然其投資組合之夏普值低於前者,但其配置權重較平均分散於標的及不同的基金種類,可避免市場突發的風險。就演化時間來看,含資金配置之限制條件模式演化時間多於不含資金配置之限制條件模式。另外,比較多目標基因演算法與傳統多目標規劃方法之 epsilon-限制式法,兩者之解分佈多有重疊,但以求解時間效率而言,多目標遠優於epsilon-限制式法。
The study measures the maximum Sharpe ratio and minimum expected shortfall in order to build a mutual fund portfolio with high investment efficiency and low downside risk by applying Multi-Objective Genetic Algorithm (MOGA), and further researches how the investment constraints of portfolio affect investment portfolio. The investment constraints of portfolio include:
1.The low-bound and up-bound limitation of numbers of the investment funds.
2.The low-bound and up-bound limitation of ratio of an single investment funds
3.The up-bound limitation (weight) of the investment funds within the same category.
The study concludes : in the first model -- without investment constraints of investment portfolio -- the evolutionary result is that the weight of the investment portfolio is tend to concentrate on a target with high Sharpe ratio, which is not correspond to the expected characters of investing on diversified investment targets. On the contrary, in the second model -- with investment constraints of portfolio -- the evolutionary result is that the Sharpe ratio is lower than the first model; however, the weight of the investment portfolio is evenly distributed in diversified investment targets. This may moderate the abrupt risks from the investment market. In terms of evolutionary time period, the second model (with constraints) is longer than the first model (without constraints). If comparing the solutions of MOGA to traditional multi-objective function -- the epsilon-constraint method for supporting this study, both are quite strongly validated by the high degree of overlap between these two approaches; however, if considering the efficiency of evolution time period, MOGA is more efficient than the epsilon-constraint method.
目錄
書名頁 i
論文口試委員審定書 ii
授權書 iii
中文摘要 iv
英文摘要 v
誌謝 vi
目錄 vii
表目錄 ix
圖目錄 ix
1. 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 3
2. 文獻探討 5
2.1 投資組合理論 5
2.1.1 投資組合之期望報酬率 5
2.1.2 投資組合之風險 6
2.1.3 資產配置的決定 7
2.2 夏普指數 8
2.3 下方風險理論 9
2.3.1 風險值 10
2.3.2 期望損失值 11
2.4 基因演算法 12
2.5 多目標基因演算法 14
2.5.1 多目標規劃 14
2.5.2 多目標演化演算法 16
2.5.3 Nondominated Sort Genetic AlgorithmⅡ 17
2.5.4 多目標基因演算法之研究與應用 18
3. 研究方法 22
3.1 模式設計與相關說明 23
3.1.1 多目標函數 23
3.1.2 編碼方式 24
3.2 投資組合資金分配限制 24
3.3 研究限制 26
4. 實驗設計與結果分析 27
4.1 實證資料來源及期間選取 27
4.2 實驗設計 27
4.3 實驗結果分析 30
5. 結論與未來研究方向 38
5.1 結論 38
5.2 未來研究方向 38
參 考 文 獻 40


圖目錄
圖 1 研究架構 3
圖 2 效率前緣曲線示意圖 7
圖 3 風險值及期望損失值示意圖 12
圖 4 基因演算法演化流程圖 13
圖 5 柏拉圖最佳解圖示 15
圖 6 NSGA等級示意圖 18
圖 7 研究方法架構 22
圖 8 染色體之編碼 24
圖 9 MO1(1000,50) 演化結果 30
圖 10 MO1(2000,50) 演化結果 30
圖 11 MO1(1000,100) 演化結果 31
圖 12 MO1(2000,100) 演化結果 31
圖 13 MO2(1000,50) 演化結果 32
圖 14 MO2(2000,50) 演化結果 32
圖 15 MO2(1000,100) 演化結果 32
圖 16 MO2(2000,100) 演化結果 33
圖 17 演化代數為1000代之演化時間 34
圖 18 演化代數為2000代之演化時間 34
圖 19 MO2(1000,50) 與SGA(1000,50) 演化結果比較表 35

表目錄
表 1 建構投資組合之研究 8
表 2 多目標演化演算法搜尋解之優劣 (Zitzler ,1999) 17
表 3 多目標基因演算法應用於投資組合之研究 20
表 4 共同基金種類統計表 27
表 5 多目標模式比較表 28
表 6 實驗符號定義對照表 29
表 7 多目標演化值結果表 33
表 8 多目標演化時間統計表 (單位:亳秒) 35
表 9 多目標及單目標演化時間比較表(單位:亳秒) 36
表 10 投資案例投資組合配置表 37
中文部份
[1] 趙錦倫,「應用遺傳演算法於多目標區域性水資源規劃模式之發展」,國立交通大學土木工程系碩士論文,民國九十二年。
[2] 賀蘭芝,「期望損失值架構下之最適投資組合」,民國九十二年。
[3] 侯佳利,「組合編碼遺傳演算法於投資組合及資金分配之應用」,國立中央大學資訊管理學系,民國九十年。
[4] 楊宗廷,「共同基金風險值的評估與應用」,國立台灣大學財務金融學研究所碩士論文,民國九十年。

英文部份
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