多目標基因演算法應用於基金投資組合最佳化

A Study of Applying Multi-Objective Genetic Algorithm to Optimization of Mutual Fund Portfolio

陳姵君(PeiJun Chen)

指導教授 ： 邱昭彰

元智大學/資訊學院/資訊管理學系/碩士(2006年)

摘要

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。

關鍵字

多目標基因演算法 ； 共同基金 ； 投資組合 ； 多目標演化演算法

並列摘要

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.

並列關鍵字

Multi-Objective Genetic Algorithm (MOGA) ； Mutual Fund ； Portfolio ； Multi-Objective Evolutionary Algorithms (MOEAs)

參考文獻

[5] Abraham, A., Grosan, C., S. Y. Han and A. Gelbukh, "Evolutionary Multiobjective Optimization Approach for Evolving Ensemble of Intelligent Paradigms for Stock Market Modeling," IEEE Congress on Evolutionary Computation, Edinburgh, UK, September 2nd-5th, pp. 673-681, 2005.

[6] Alexandre, H. F. D., Joao, A. V., “Multiobjective Genetic Algorithms Applied to Solve Optimization Problems,” IEEE Transactions on Magnetics, Vol. 38, No. 2, pp.1133-1136, 2002.

[9] Ballestero, E., Pla-Santamaria, D., "Selecting portfolios for mutual funds," Omega Vol. 32, Iss. 5, pp. 385-394, 2004.

[10] Campbell, R., Huisman, R., Koedijk, K., “Optimal portfolio selection in a value-at-risk framework,” Journal of Banking and Finance, 25, pp. 1789-1804, 2001.

[11] Cvetkovic, D., Parmee, I. C., "Preferences and their application in evolutionary multiobjective optimization," IEEE Transactions on Evolutionary Computation, Vol. 6, Iss. 1, pp.42-57, 2002.