數量化分析是投資組合管理的一支。及時而且客觀是數量化分析主要的優點。最近由於電腦科技的發展快速，使得數量化分析更受到重視。這篇論文以多因子模型( multi-factor model, MFM) 為架構，進行新加坡股票市場的數量化分析。
新加坡有目前東南亞最繁榮的金融市場。而新加坡交易所(Singapore Stock Exchange, SGX ) 與英國的富時公司(Financial Times and the London Stock Exchange, FTSE) 合作，更為新加坡市場增添了活力。新加坡市場對全球金融市場重要的影響性，是我們選擇新加坡的股票市場做為我們模型的研究目標的原因。
本篇模型參考Jeng and Tsai (2011) 的多因子模型流程，並以增值指數策略進行樣本外回測。將多因子模型給予我們有關未來股價的訊息，反應在我們的增值策略上，以此建構增值的投資組合。
本篇模型包含了68個顯著要素、14個複合因子以及7個產業因子。在樣本期間內，模型的平均解釋能力為43%。而最後我們建議的投資組合，它的訊息比率為76.80%，追蹤誤差為4.02%，平均(月) 周轉率為1.53%。

Quantitative analysis is one branch of portfolio management. The advantages of quantitative analysis are fast and objective. It has developed significantly in recent years because of the improvements in computer technology. This thesis applies the structure of a multi-factor model (MFM) to undertake quantitative analysis.

Singapore has one of the most prosperous financial markets in Southeast Asia. The Singapore Stock Exchange (SGX) and Financial Times and the London Stock Exchange (FTSE) are now in cooperation, which has added vitality to this market. It has great influence in global financial markets, and this is why we select its security market to be our target in MFM.

The model refers the multi-factor processes of Jeng and Tsai (2011) . For backtesting, we adopt an enhanced strategy as testimony. We transmit information from the MFM to the enhanced strategy. Then we create the stock weightings to constitute the enhanced portfolio.

This model includes 68 significant descriptors, 14 composite factors and 7 industry factors. The Singapore MFM shows 43% adjusted R-Square in the sample period. The enhanced portfolio we suggested has an information ratio of 76.80% with a tracking error of 4.02% and 1.53% for monthly turnover rate.

論文審定書 i
誌 謝 ii
摘 要 iii
Abstract iv
I. Introduction 1
1.1 Background 1
1.2 Research Motivation and Purpose 4
1.3 Research Framework and Flow 8
II. Literature Review 10
2.1 Modern Portfolio Theory 10
2.2 MFM 11
2.3 Enhanced Index Fund 15
III. Methodology 18
3.1 Development of Significant Descriptors 19
3.1.1 Adjust the Outliers 19
3.1.2 Standardize the values 20
3.1.3 Significance Test of Descriptors 21
3.1.4 Significant Ratio 23
3.1.5 Positive Ratio 23
3.2 Development of Significant Factor 25
3.2.1 Principal Component Analysis (PCA) 25
3.2.2 Allocate the Industry Factor 26
3.2.3 Significance Test of Factors 27
3.3 The Return of MFM 27
3.3.1 Cross-sectional Regression to Estimate the Factor Return 27
3.3.2 Revise the Regression Model 29
3.4 The Risk of MFM 29
3.4.1 Estimation of the Factor Covariance-Matrix 30
3.4.2 Estimation of Specific Risk 31
3.4.3 Estimation of Portfolio Risk 31
3.5 Application in Enhanced Strategy 33
3.5.1 Enhanced Strategy 34
3.5.2 Performance Evaluation 38
IV. Empirical Results 40
4.1 Description of the data 40
4.1.1 Sources and Database 40
4.1.2 Sample Time Period 40
4.1.3 Frequency 41
4.1.4 Industry Classification 44
4.2 The Selection of Effective Factors 46
4.2.1 Select the Significant Descriptors 46
4.2.2 PCA Results 48
4.2.3 Select the Factors 49
4.3 Testing for Multicollinearity and Heteroscedasticity 50
4.3.1 Multicollinearity 50
4.3.2 Heteroscedasticity 52
4.4 Empirical Evidence: Singapore MFM 54
4.4.1 MFM: Explanatory Power 54
4.4.2 MFM: Fundamental Factor Return and Industry Return 55
4.4.3 MFM: Industry Factor Return 57
4.5 Application in Enhanced Strategy 59
4.5.1 Returns and Cumulative Returns 60
4.5.2 Comparison between Enhanced Portfolios and Benchmark 63
4.5.3 Summary of Enhanced Portfolio and Benchmark 65
V. Conclusions and Suggestions for Further Research 67
5.1 Conclusions 67
5.2 Suggestions for Further Research 68
5.2.1 The regression model 68
5.2.2 Combine with other factor model 69
5.2.3 Combine with other markets 69
References 70
Appendix: Descriptor Definitions 72

Banz, R. W. (1981). “The Relationship Between Return and Market Value of Common Stocks,” Journal of Financial Economics, 9(1), 3-18.
Barra. (1998). United States Equity Version 3 (E3): Risk Model Handbook. Morgan Stanley Capital International.
Chan, L. K. C., Hamao, Y. and Lakonishok, J. (1991). “Fundamentals and Stock Returns in Japan,” Journal of Finance, 46(5), 1739-1764.
Chen, W. C. (2009). “The Enhanced Index Fund Performance and Risk Analysis under MFM Model,” Master Thesis, National Sun Yat-Sen University. Retrieved from http://www.oia.nsysu.edu.tw/english/index.html.
Chincarini, L. B. and Kim, D. (2006). Quantitative Equity Portfolio Management: An Active Approach to Portfolio Construction and Management. McGraw-Hill.
Connor, G. (1995). “The Three Types of Factor Models: A Comparison of Their Explanatory Power,” Financial Analysts Journal, 51(3), 42.
Elton, E. J., Gruber, M. J. and Busse, J. A. (2004). “Are Investors Rational? Choices among Index Funds,” Journal of Finance, 59(1), 261-288.
Fama, E. F. and French, K. R. (1992). “The Cross-Section of Expected Stock Returns,” Journal of Finance, 47(2), 427-465.
Fama, E. F. and MacBeth, J. D. (1973). “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, 81(3), 607.
Gruber, M. J. (1996). “Another Puzzle: The Growth in Actively Managed Mutual Funds,” Journal of Finance, 51(3), 783-810.
Hill, J. M. and Naviwala, H. (1999). “Synthetic and Enhanced Index Strategies Using Futures on U.S. Indexes,” Journal of Portfolio Management, 25(3), 61-74.
Jeng, Y. and Tsai, T. H. (2011). “A Multi-Factor Risk Model: Evidence from Taiwan,” Working Paper.
Lee, C. J. (2010). “Multi-Factor Model and Enhanced Index Fund Performance Analysis in China,” Master Thesis, National Sun Yat-Sen University. Retrieved from http://www.oia.nsysu.edu.tw/english/index.html.
Malkiel, B. G. (1995). “Returns from Investing in Equity Mutual Funds 1971 to 1991,” Journal of Finance, 50(2), 549-572.
Markowitz, H. (1952). “Portfolio Selection,” Journal of Finance, 7(1), 77-91.
Miller, T. and Meckel, T. S. (1999). “Beating Index Funds With Derivatives,” Journal of Portfolio Management, 25(3), 75-87.
Rosenberg, B., Reid, K. and Lanstein, R. (1985). “Persuasive evidence of market inefficiency,” Journal of Portfolio Management, 11(3), 9-16.
Ross, S. A. (1976). “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, 13(3), 341-360.
Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 19(3), 425-442.
Treynor, J. L. and Black, F. (1973). “How to Use Security Analysis to Improve Portfolio Selection,” Journal of Business, 46(1), 66-86.