本研究以平均變異數模型(Markowitz Mean-Varience model)以
及人工智慧之基因演算法(Genetic Algorithm)為主要基礎及架構，
建構基金組合配置權重最佳化模型。基於平均變異數模型(Markowitz Mean-Varience model)以及基因演算法(Genetic
Algorithm)之權重配置模型下，探討與S&P 500以及平均權重配置組
合相互間之績效比較。本研究以十七筆基金作為建構投資組合之投資
標的，此十七筆基金含括了美元及歐元兩種貨幣計價，並含括了以下
八大市場:歐洲市場、歐洲聯合市場、新興市場、太平洋市場、星馬
泰市場、亞太市場、美國市場及全球市場。基金之研究區間介於一九
九八年二月一日至二○○六年十二月一日之歷史資料。
平均變異數模型(Markowitz Mean-Varience model)為直至目前
仍然為許多研究中研究的重點，但平均變異數模型(Markowitz Mean-
Varience model)必須符合其基本假設，而此基本假設也成為了平均
變異數模型(MarkowitzMean-Varience model)的限制。相對的，基因
演算法(Genetic Algorithm)無此限制。本研究另一項重點即在於探
討此兩種模型之績效比較。
本研究發現: (1) 基因演算法(Genetic Algorithm)之投資組合
績效擊敗平均變異數模型(Markowitz Mean-Varience model)之投資
組合績效。 (2) 基因演算法(Genetic Algorithm)及平均變異數模型
(Markowitz Mean-Variencemodel)之投資組合績效皆擊敗平均權重配
置組合之績效。 (3) 基因演算法(Genetic Algorithm)及平均變異數
模型(Markowitz Mean-Varience model)之投資組合績效皆無法顯著
擊敗S&P 500。

This study investigates the performance of the weight
optimization by comparing the performance of the portfolios
of fund of funds (FoF) constructed by the Markowitz Mean-
Variance (MV) model or Genetic Algorithm (GA) to that of
S&P 500 and that of equal weight portfolio of Mutual funds.
The chosen targetfunds are denominated in U.S. dollar or
euros, and are chosen from the European market, United
European market, Emerging market, Pacific market, South
Asia market, Asia Pacific Zone market, American market, and
Global market. The study period started on February 1, 1998
and ended on December 1, 2006.
The Markowitz Mean-Variance model is a famous
investment theory in portfolio selection problems. But
Markowitz Mean-Variance model requires theassumption that
the securities must follow the normal distribution. On the
contrary, Genetic Algorithm is a methodology with artificial
intelligence that is free of theassumption of normal
distribution, and it can also be applied to the portfolio
selection and optimization problems. In this thesis, we test
whether the Genetic Algorithm can beat the traditional
Markowitz Mean-Variance model or not.
At last, we get some results from empirical evidence.
First, the GeneticAlgorithm model performs better than the
Markowitz Mean-Variance in performance measures of Sharpe,
Treynor and Jensen’s alpha. Second, both the Markowitz
Mean-Variance model and Genetic Algorithm can beat the
equal weight portfolios. Finally, the Markowitz Mean-
Variance model and the Genetic Algorithm are not better
than market index significantly.

Allen, F., and R. Karjalainen. 1999. “Using Genetic Algorithms to Find Technical Trading Rules”, Journal of Financial Economics, Vol. 51, 245~271.
Bers, M. K., and J. Madura. 2000. “The performance persistence of close-end funds”, The Financial Review 35, 33-52.
Bers, M. K., and J. Madura. 2001. “The performance persistence of foreign close-end funds”, Review of Finacial Economics 11, 263-285.
Bian, J. 1995. “An Genetic-Algorithm Model for Taiwan Stock Index” M.A. thesis, Graduate Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan), in Chinese.
Brightman, J. S. 1980. Journal of Portfolio Management. New York: Winter. Vol. 6, Iss. 2; p. 43.
Brown, S. J., and W. N. Goetzmann. 1995. “Performance persistence”, Journal of Finance 50, 679-698.
Carhart, M. M. 1997. “On persistence in mutual fund performance”, Journal of Finance 52,57–82.
Carlson, R. S. 1970. “Aggregate performance of mutual funds”, Journal of Financial and Quantitative Analysis 5, 1-31.
Chang, C. C. 2003. “Construction of Stock Index Simulation Portfolio Using Genetic Algorithm” M.A. thesis, Graduate Institute of Accounting, National Taipei University, Taipei, Taiwan), in Chinese.
Chang, T. J. 1998. “Heuristics for cardinality constrained portfolio optimisation” The Management School, Imperial College, London SW7 2AZ, UK.
Cheney, J. M., S. Atkinson, and B. A. Bailey, 1992., “International Mutual Fund Performance U.S. vs. U.K.”,Managerial Finance. Patrington,Vol. 18, Iss. 2.
Chiu, C. R. 1998. “An Application of Genetic Algorithms on Portfolio Strategies” M.A. thesis, Graduate Institute of Economics, National Sun Yat-sen University, Kaohsiung, Taiwan), in Chinese.
Chopra, N., J. Lakonishok, and J. R. Ritter. 1992. “Measuring abnormal performance: Do stocks overreact?” Journal of Financial Economics 31, 235–268.
Daniel, K, and S. Titman. 1997. “Evidence on the characteristics of cross-sectional variation in stock returns”, Journal of Finance 52, 1–33.
Daniel, K., M. Grinblatt, S. Titman, and R. Wermers. 1997. ” Measuring mutual fund performance with characteristic-based benchmarks”, Journal of Finance 52, 1035–1058.
Daniel, W. W. 1994. ”Applied Nonparametric Statistics”, Pws-Kent Publishing Company, 358-364.
Darrell, W., T. Starkweather, and D. Shaner. 1990. “The Traveling Salesman and Sequence Scheduling Quality Solutions Using Genetic Edge Recombination”.
Detzler, M. L. 2002. “The value of mutual fund rankings to the individual investor”, Journal of Business & Economic Studies 8, 48-72.
Droms, W. G., and D. A. Walker. 2001. “Performance persistence of international mutual funds”, Global Finance Journal 12, 237-248.
Dunn, P. C., and R. D. Theisen. 1983. “How consistently do active managers win”, Journal of Portfolio Management 9, 47-51.
Elton, E., and M. Gruber. 1981. “Modern Portfolio Theory and Investment Analysis”. New York:　John Wiley & Sons.
Enrique, B., and C. Romero. 1996. “Portfolio Selection: A Compromise Programming Solution”, Journal of the Operational Research Society, Vol. 47, No. 11, 1377-1386.
Fama, E. F., and K. R. French. 1993. “Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics 33, 3–56.
Fama, E. F., and K. R. French. 1996. “Multifactor explanations of asset pricing anomalies”, Journal of Finance 51, 55–84.
Fang, C. J. 2006. “Comparing Personal Portfolio Strategies by Genetic Algorithm Mixed with Association Rules”.
Geert, B., C. B. Erb, C. R. Harvey, and T. E. Viskanta. 1998. “Distributional characteristics of emerging market returns and asset allocation.” Journal of Portfolio Management, Winter, pp. 102-116.
Goetzmann, W. N., and R. G. Ibbotson. 1994. “Do winners repeat?” Journal of Portfolio Management, 9-18.
Goldberg, D. E. 1989., “Genetic Algorithms in Search, Optimization and Machine Learning.” Addison-Wesley Publishing Co.
Grinblatt, M., and S. Titman. 1992., ” The persistence of mutual fund performance”, Journal of Finance 47, 1977-1984.
Grinblatt, M., and S. Titman. 1992., “Mutual fund performance: An analysis of quarterly portfolio holdings”. Journal of Business 62:393-416.
Hendricks, D., J. Patel, and R. Zeckhauser. 1974-88. “Hot hands in mutual funds: short-run persistence of relative performance”, Journal of Finance 48, 93-130.
Holland, J. 1975. “Adaptation in Natural and Artificial System” .
Huang, Y., and S. K. Quan. 1996. “Genetic Algorithms in the Identification of Fuzzy Compensation System,” IEEE Int. Conf. on Systems Man and Cybernetics, vol. 2, pp. 1090-1095.
Hull, J., and A. White. 1987. “The Pricing of Options on Assets with Stochastic Volatilities”The Journal of Finance. Cambridge: Jun. Vol. 42, Iss. 2; p. 281.
Ippolito, R. A. 1992. ” Consumer reaction to measures of poor quality: evidence from the mutual fund industry”, Journal of Law and Economics 35, 45-70.
Jensen, M. C. 1969. “The performance of mutual funds in the period 1945-1964”, Journal of Finance 23, 389-416.
Kaly, E. 2001. “Using Neural Networks and Genetic Algorithms to Predict Stock Market Returns : University of Manchester, U.K”.
Karjalainen, R. 1995. “Using Genetic Algorithms To Find Technical Trading Rules”.
Konno, H., Piecewise linear risk function and portfolio optimization. Journal of the Operational Research Society of Japan 33 2 (1990), pp. 139–156.
Korczak, J. J. 2001. “Portfolio Design and Simulation Using Evolution Based Strategy : University of Worclaw, Poland”.
Lee, S., and K. P. Chang. 1995. “Mean-variance-instability portfolio analysis: A case of Taiwan's stock market”, Management Science. Linthicum: Jul. Vol. 41, Iss. 7; p. 1151 (7 pages) .
Leinweber, D. J., and R. D. Arnott. 1995. “Quantiative and Computational Innovation in Investment Management” Journal of Portfolio Management, pp. 8-15.
Leinweber, D. J. 2003. “The perils and the promise of evolutionary computation on the Wall Street, Journal of Investing”.
Li, J., and P. K. Tsang. 1999. “Improving Technical Analysis Prediction - An Application of Genetic Programming : University of Essex” .
Lin, P. C. 1997. “An Application of Genetic Algorithms on User-Oriented Portfolio Selection” M.A. thesis, Graduate Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan), in Chinese.
Lyon, J.D., B.M. Barber, and C. L. Tsai. 1999. “Improved methods for tests of longrun abnormal stock returns”, Journal of Finance 54, 165–201.
Malkiel, B. 1995. “Returns form investing in equity mutual funds”, Journal of Finance 50, 549-572.
Markowitz, H., M. 1952. “Portfolio Selection, Yale University Press”
Markowitz, H. 1995. “Portfolio selection”. Journal of Finance 1952; pp.77-91
Moses, E. A., J. M. Cheyney, and E. T. Viet, .1987., “A new and more complete performance measure”, Journal of Portfolio Management 13, 24-33.
Nawrocki, D. 1991. “Optimal algorithms and lower partial moment”, Applied Economics 23, 465 – 470.
Pouge, G. A. 1970. “An extension of the Markowitz portfolio selection model to include variable transaction costs, shorts sales, leverage policies and taxes”, Journal of Finance 45, 1005-1027.
Praetz, P. D., “The distribution of share price changes.” Journal of Business 45,pp. 45-55.
Raymer, M. L., W. F. Punch, E. d. Goodman, L. A. Kuhn, and A. K. Jain. 2000. “Dimensionality Reduction Using Genetic Algorithms,” IEEE Trans. on Evolutionary Computation, vol. 4, pp. 164-171.
Schaerf, A. 2002. “Local search techniques for constrained portfolio selection problems”, Computational Economics, 177–190.
Schandl, K. 2001. “Norm-based approximation in bicriteria programming”.
Schyns, M., Y. Crama, and G. Hübner, .2003., “Grafting Information in Scenario Trees Application to Option Prices”.
Sharpe, W. F. 1972. “Mutual fund performance”, Journal of Business 39,119-138.
Shapcott, J. 1992. “Index Tracking: Genetic Algorithms for Investment Portfolio Selection”.
Shih, H. C., H. Hsu, and T. Y. Hsieh. 2003. “Determinants of the Volatility of Stock Prices”, Journal of Risk Management Vol.5 No.2, 167-193
Smith, K. V., and D. A. Tito. 1969. “Risk-return measures of ex-post portfolio performance”, Journal of Financial and Quantitative Analysis 4,449-471.
Song, Y. H., and C. S. Chou. 1997. “Advanced Engineered-Conditioning Genetic Approach to Power Economic Dispatch,” IEEE Proc.-Gener. Transm. Distrib., vol. 144, pp. 285-292.
Sumanth K., P. Rao, and H. Shankar. 2003. “Portfolio Selection Using Genetic Algorithms” : Sri Sathya Sai Institute of Higher Learning, Working Paper.
Treynor, J. L. 1965. “How to rate management of investment funds”, Harvard Business Review 43, 63-75.
Venugopal, M.,and S. Subramanian. 2004. “Journal of Financial Management & Analysis” , Vol. 17, Iss. 1; p. 45 (9 pages)
Vigna, E., and H. Steven. 2001. "Optimal investment strategy for defined contribution pension schemes", Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 233-262, April.
Warshawsky, M., M. DiCarlantonio, and L. Mullan. 2000. “The persistence of morningstrar ratings”, Journal of Financial Planning, 110-128.
Williamson, P. J. 1972. “Measurement and forecasting of mutual fund performance: choosing an investment strategy”, Financial Analysts Journal 28, 78-84.
Xiaoulou, Y. 2006. “Improving Portfolio Efficiency”: A Genetic Algorithm Approach.
Yu, L., S. Y. Wang, and K. K. Lai. 2006. “An Integrated Data Preparation Scheme for Neural Network Data Analysis”, IEEE Transactions on Knowledge and Data Engineering, 217-230.