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研究生： 黃秋凌
Huang, Chiu-Ling
論文名稱： 股票型基金之投資最佳組合考慮當未來報酬率與風險為模糊數
Portfolio Optimization of Equity Mutual Funds with Fuzzy Return Rates and Risks
指導教授： 陳梁軒
Chen, Liang-Hsuan
學位類別： 碩士
Master
系所名稱： 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年： 2005
畢業學年度： 93
語文別： 英文
論文頁數： 88
外文關鍵詞： fuzzy numbers, equity mutual funds, performance indices, cluster analysis
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    In this low-interest rate era, people start to pay attention to diverse financial products. Mutual funds are one of the most popular outlets of investment, since mutual funds have the characteristics of accumulation risk and return. The objective of mutual funds is to disperse investment risk to the smallest degree.
    This research attempts to perform empirical study to Taiwan Listed Equity Mutual Fund, and analyzes the performance of equity mutual funds based on their rates of return, volatility, Treynor Index, and Turnover rate. According to those indices, we apply cluster analysis to cluster Equity mutual funds due to their performance, thus providing investors information of investment. Since the future expected return rates and future risk cannot be predicted accurately, thus we adopt the concept of fuzzy numbers to denote expected return rates and risk. The portfolio optimization problem is developed in two manners: to maximize the future expected return subject to given greatest future risk, and to minimize the future risk subject to a given lowest future expected return. The aim is to determine asset allocation to each cluster so that total expected return is greater than or equal to some lowest fuzzy return.

    TABLE OF CONTENTS ABSTRACT ............................................................ I ACKNOWLEDGEMENT...................................................... II TABLE OF CONTENTS.................................................... III LIST OF TABLES....................................................... IV LIST OF FIGURES...................................................... V CHAPTER I. INTRODUCTION.................................................. 1 1.1 Motivation and Background.................................. 1 1.2 Objectives................................................. 3 1.3 Thesis Organization........................................ 3 II. LITERATURE REVIEW.............................................. 5 2.1 Introduction to Mutual Funds............................... 5 2.1.1 Definition........................................... 6 2.1.2 Types of Mutual Funds................................ 6 2.1.3 Advantages and disadvantages of mutual funds......... 8 2.2 Introduction to Portfolio Theory........................... 9 2.2.1 Markowitz Mean-Variance Model........................ 9 2.2.2 Market (Single Index) Model.......................... 12 2.2.3 Capital Asset Pricing Model (CAPM)................... 14 2.3 Performance Evaluation Techniques for Mutual Funds......... 16 2.4 Introduction to Fuzzy Theory............................... 24 2.4.1 Fuzzy set............................................ 24 2.4.2 α-cut................................................ 25 2.4.3 Fuzzy number......................................... 25 2.4.4 The operators of triangular fuzzy number............. 26 2.5 Fuzzy Approaches to Portfolio Selection.................... 27 2.5.1 Goal Programming..................................... 27 2.5.2 Fuzzy Goal Programming............................... 29 III. RESEARCH METHODOLOGY........................................... 31 3.1 Research Structure.......................................... 31 3.2 Data........................................................ 32 3.3 Evaluation Indices.......................................... 33 3.4 Clustering of Funds......................................... 36 3.4.1 Distance Measure...................................... 37 3.4.2 Amalgamation Rule..................................... 38 3.4.3 Clustering Method..................................... 39 3.5 The Asset Allocation Model.................................. 40 3.5.1 Notations and Assumptions............................. 40 3.5.2 Optimization based on Fuzzy Models.................... 42 IV. NUMERICAL RESULTS.............................................. 49 4.1 Empirical Data............................................. 49 4.1.1 Research Subject and Period of Data................... 49 4.1.2 Source of Data........................................ 50 4.2 Clustering of Funds Performance by Statistical Analysis.... 50 4.2.1 Normalization......................................... 50 4.2.2 Cluster Analysis...................................... 52 4.3 Asset Allocation........................................... 56 4.3.1 Fuzzified Return Rates and Risks...................... 56 4.3.2 The Result of Optimization Problem.................... 60 4.4 Conclusions................................................ 69 V. CONCLUSIONS AND FUTURE DIRECTIONS.............................. 71 5.1 Conclusions................................................ 71 5.2 Future Directions.......................................... 73 REFERENCES............................................................ 74 Appendix A............................................................ 78 Appendix B............................................................ 85

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    Database:
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