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研究生：	詹凱翔 Chan, Kai-Hsiang
論文名稱：	運用平均變異數及基因演算法來建構最佳基金投資組合權重之研究 Applying Mean-Variance Model and Genetic Algorithms to Construct Optimal Weights of Portfolio of Funds
指導教授：	李宏志 Li, Hung-chih 賴秀卿 Lai, Hsiu-ching
學位類別：	碩士 Master
系所名稱：	管理學院 - 財務金融研究所 Graduate Institute of Finance
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	79
中文關鍵詞：	平均數變異數模型、基因演算法、基金投資組合
外文關鍵詞：	Markowitz Mean-Variance Model, Genetic Algorithm, funds portfolio
相關次數：	點閱：109 下載：5
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本研究利用Markowitz所提出的平均數變異數模型 (Mean-Variance Model) 以及人工智慧裡的基因演算法 (Genetic Algorithm)，來建構最佳化權重的基金投資組合，並且利用MSCI全球指數、S＆P 500以及平均權重基金投資組合來比較其績效的優劣。本研究採用十七檔富蘭克林基金做為基金投資組合的標的，並且依照富蘭克林基金公司將市場分為以下五個區域：全球型、歐洲、新興市場、美國以及單一國家。研究期間為一九九九年一月至二００七年十二月。
Markowitz的投資組合理論至今仍為許多投資理論的研究重心，但是其中常態分配的基本假設使得平均數變異數模型(Mean-Variance Model)在過去實務上的績效表現較差，而基因演算法(Genetic Algorithm)則無此項基本假設的限制。但本研究中取自富蘭克林的標的基金大部分均服從常態分配，因此探討基因演算法(Genetic Algorithm)所建構的基金投資組合是否還能夠優於平均數變異數模型(Mean-Variance Model)也為本研究中的探討重點。
本研究發現：(一) 在報酬最大操作下的績效表現優於風險最小下的績效表現。 (二) 平均數變異數模型(Mean-Variance Model)及基因演算法(Genetic Algorithm)在Jensen及Sharpe下可以顯著擊敗MSCI全球指數、S＆P 500以及平均權重基金投資組合。(三) 基因演算法(Genetic Algorithm)只能在風險最小下的Jensen及Treynor擊敗平均數變異數模型(Mean-Variance Model)。(四) 平均數變異數模型(Mean-Variance Model)在風險最小及報酬最大下的績效均具有持續性，基因演算法(Genetic Algorithm)則只能在風險最小下的績效具有持續性。

This study applies Mean-Variance Model proposed by Markowitz and Genetic Algorithm developed from artificial intelligence to construct optimal weighted simulated fund portfolios. We also compare the performance of simulated fund portfolios with MSCI All Country World Index, S&P 500, and equally weighted fund portfolios. We adopt Franklin Investments as our target funds which are categorized into five regions: Global market, European market, Emerging market, American market and Single country market. The period of this study starts from January 1999 to December 2007.
Markowitz’s Mean-Variance Model is still a famous investment theory for asset allocation until now. Normal distribution is the main assumption of Mean-Variance Model and if the distribution is not normal, then, the optimal solution can not be achieved by using Mean-Variance Model. Genetic Algorithm does not require the assumption of normal distribution. But most of our chosen funds follow normal distribution. The main purpose of this thesis is to investigate whether Genetic Algorithm can perform better than Mean-Variance Model or not in this thesis.
Our results are as follows. First, the performance of Mean-Variance Model and Genetic Algorithms based on maximizing return for a given risk is better than that based on minimizing risk for a given return. Second, Mean-Variance Model and Genetic Algorithms can outperform MSCI All Country World Index, S&P 500, and equally weighted fund portfolios based on Jensen’s measure and Sharpe’s measure under return-maximizing procedure. Third, Genetic Algorithms can only outperform Mean-Variance Model based on Jensen’s measure and Treynor’s measure under risk-minimizing procedure. Finally, the performance of Mean-Variance Model has better persistence than that of Genetic Algorithms in the future period.

ABSTRACT	IV
Contents	V
List of Tables	VII
List of Figures	X
CHAPTER 1 INTRODUCTION	1
1.1 Motivation and Background	1
1.2 Objective	2
1.3 Contribution	3
CHAPTER 2 LITERATURE REVIEW	  4
2.1 Fund of Funds (FoF)	4
2.2 Models for Portfolio Construction	4
2.2.1 Markowitz Mean-Variance Portfolio Selection Model  4
2.2.2 The Genetic Algorithm	  9
CHAPTER 3 MODEL SPECIFICATIONS AND METHODOLOGY	13
3.1 Data	13
3.1.1 Source of Data	13
3.1.2 Detail List of Sample Data	13
3.2 Research Hypothesis	15
3.3 Research Designs and Procedures	16
3.4 Definition of Parameters	17
3.4.1 Estimation of Monthly Volatility of MSCI All Country 
      World Index	 17
3.4.2 Estimation of the Systematic Risk	17
3.4.3 Sharpe’s Measure	18
3.4.4 Treynor’s Measure	19
3.4.5 Jensen’s Measure	19
3.5 Methodology	20
3.5.1 Markowitz Mean-Variance Model	20
3.5.2 Genetic Algorithms	25
3.6 Normal Distribution Test: One-Sample Kolmogorov-
    Smirnov Test	 31
3.7 Performance Persistence Test: Spearman Rank
    Correlation Coefficient Test	32
CHAPTER 4 EMPIRICAL RESULTS	  35
4.1 Normality Test	  35
4.2 Performance Comparison	 37
4.2.1 Paired T-test based on Jensen’s Alpha under Risk-  
      Minimizing Scenario	  38
4.2.2 Paired T-test based on Sharpe’s Measure among Mean-
      Variance Model, Genetic Algorithms, MSCI, S&P500 and 
      Equal Weight Method under Risk-Minimizing Scenario 41
4.2.3 Paired T-test based on Treynor’s Measure among Mean-
      Variance Model, Genetic Algorithms, MSCI, S&P500 and 
      Equal Weight Method under Risk-Minimizing Scenario 45
4.2.4 Paired T-test based on Jensen’s Alpha under Return-
      Maximizing Scenario	 49
4.2.5 Paired T-test based on Sharpe’s Measure among Mean-
      Variance Model, Genetic Algorithms, MSCI, S&P500 and 
      Equal Weight Method under Return-Maximizing
      Scenario    51
4.2.6 Paired T-test based on Treynor’s Measure among Mean-
      Variance Model, Genetic Algorithms, MSCI, S&P500 and
      Equal Weight Method under Return-Maximizing Scenario
                                                         55
4.2.7 Summary of Paired T-test based on Jensen’s Alpha, 
      Sharpe’s and Treynor’s Measure	    59
4.3 Performance Persistence	 62
4.3.1 Spearman Rank Correlation Coefficient under Risk-
      Minimizing Scenario	 62
4.3.2 Spearman Rank Correlation Coefficient under Return-
      Maximizing Scenario	 64
CHAPTER 5 CONCLUSIONS AND SUGGESTIONS	67
5.1 Conclusions	67
5.2 Suggestions	69
REFERENCES	70
APPENDIX	 75
                                    

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校內：2011-06-26公開
校外：2011-06-26公開

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