最近幾年，中國和台灣之間的經濟交流變得越來越頻繁，未來的金融活動也會更加熱絡，因此我們需要更積極的去研究和參與中國的金融市場。
本研究首先參考美商BARRA的多因子模型建構流程，以此為基礎架設中國的多因子模型。然後應用中國多因子模型建立上證50增值指數基金。
本研究的第一個目標是找到能解釋股票超額報酬的顯著因子，建立中國大陸因子資料庫。第二個目標則是利用顯著因子預測股票報酬，並藉由本研究提出的直覺式權重配置模型呈現alpha效果。
結果發現共有八個顯著的風險因子，分別是盈餘品質、效率、成長、動能、規模、交易活動、價值和波動度。而增值指數基金的績效也優於標竿指數，資訊比率為0.86。周轉率則是213%，在可接受的範圍之內。

In recent years, the economic exchanges between China and Taiwan have become more frequent, hence the Chinese financial market is the main target that we should research and participate in actively.
This study refers to Barra Multi-Factor Modeling process to construct a China Multi-Factor Model. We then apply MFM to establish a Shanghai Stock Exchange 50 enhanced index fund.
The first objective of this study is to discover significant factors which can explain excess return of securities. The second is to identify significant factors to forecast stock returns and show the alpha effect in an Enhanced Index Fund via a new weight allocating model developed by this study.
The result shows that the eight significant factors are Earning Quality, Efficiency, Growth, Momentum, Size, Trading Activity, Value, and Volatility. The performance of Enhanced Index Fund is better than that of the benchmark. Information ratio is 0.86, and turnover rate is 213%, which is acceptable.

Contents
I. INTRODUCTION 1
I.1 Background Information 1
I.1.1 Quantitative asset management 1
I.1.2 Quantitative investment in China 2
I.1.3 Enhanced index fund 3
I.2 Purpose of Research 4
I.3 Research framework 4
II. LITERATURE REVIEW 6
II.1 Modern Portfolio Theory 6
II.2 Multi-Factor Model 6
II.3 Enhanced index fund 8
II.4 Performance analysis of fund 9
III. METHODOLOGY 11
III.1 Multi-Factor Model construction 11
III.1.1Developing significant descriptor 13
III.1.2Forming composite risk factors 16
III.1.3 MFM－Return 18
III.1.4 MFM－Risk 21
III.2 Application of Multi-Factor Model—Enhanced Index Fund 24
III.2.1 Computation of benchmark index 24
III.2.2 Construction of Enhanced Index Fund 24
III.2.3 Calculation of turnover rate 27
III.2.4 Performance analysis—Information Ratio 28
IV. EMPIRICAL RESULTS 29
IV.1 Data 29
IV.2 Sample 29
IV.3 Empirical result－Multi-Factor-Model 31
IV.3.1 Result of significant descriptors selection 31
IV.3.2 The PCA results 31
IV.3.3 Result of testing composite factors 32
IV.3.4 Multicollinearity and Heteroscedasticity tests 33
IV.3.5 Model explanation 35
IV.3.6 Empirical result of MFM 35
IV.4 Empirical result－Enhanced Index Fund 41
IV.4.1 Result of significant factor selection 41
IV.4.2 Cumulative active return 41
IV.4.3 Sensitivity analysis 42
IV.4.4 Back-testing performance 43
V. CONCLUSION 45
REFERENCES 47
APPENDIX: Descriptor Definitions 50

Barra (1998). United States Equity Version 3 (E3): Risk Model Handbook.
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 Analysis Journal, May/June.
Carhart, M.M. (1997). On Persistence in Mutual Fund Performance. Journal of Finance, 52 (1), 57-82.
DiBartolomeo, D. (2000). The Enhanced Index Fund as an Alternative to Indexed Equity Management. Working paper, Northfield Information Services, Boston, MA.
Fama, E.F. and French, K.R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, 47 ( 2), 427-465.
Grinold, R.C. and Kahn, R.N. (2000). Active Portfolio Management. McGraw-Hill.
Gujarati, D.N. (2003). Basic Econometrics (4th Edition).
Jensen, M.C. (1968). The Performance of Mutual Funds in the Period 1945-1964. Journal of Finance, 23 (2), 89-416.
Jorion, P. (2002). Enhanced Index Funds and Tracking Error Optimization. Working paper, University of California at Irvine.
Jorion, P. (2003). Portfolio Optimization with Tracking-Error Constraints. Financial Analysts Journal, 59 (5), 70-82.

Knez, P.J. and Ready, M.J. (1997). On the Robustness of Size and Book-to-market in Cross-sectional Regressions. Journal of Finance, 52 (4), 1355−1382.
MacQueen, J. (2003). The Structure of Multifactor Equity Risk Models. Journal of Asset Management, 3 (4), 313-322.
Northfield Information Services. U.S. Fundamental Equity Risk Model.
Neal, G.S. (1999). Inside an Enhanced Index Fund. Journal of Financial Planning, 12 (4), 64-68.
Ross, Stephen A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Finance, 13, 341-360.
Riepe, M.W. and Werner M.D. (1998). Are Enhanced Index Mutual Funds Worthy of Their Name?. Journal of Investing, 18 (3), 6-15.
Treynor, J. L. and F. Black (1973). How to Use Security Analysis to Improve Portfolio Selection. Journal of Business, 46 (1), 66-86.
Wu, L.C., Chou, S.C., Yang, C.C. and Ong, C.S. (2007). Enhanced Index Investing Based on Goal Programming. The Journal of Portfolio Management, 33 (3), 49-55.
Syu, M.S. (2007). Stock Selection Performance Analysis Using Multi-Factor Model
in Taiwan (Master’s thesis, National Sun Yat-Sen University). Retrieved from http://www.oia.nsysu.edu.tw/english/index.html
Tsai, T.H. (2009). A System Platform of Multi-Factor Model (Master’s thesis, National Sun Yat-Sen University). Retrieved from http://www.oia.nsysu.edu.tw/english/index.html
Chen, W.C. (2009). The Enhanced Index Fund Performance and Risk Analysis under MFM Model (Master’s thesis, National Sun Yat-Sen University). Retrieved from http://www.oia.nsysu.edu.tw/english/index.html
Chang, S.Y. (2009). The Performance of Enhanced Index Fund in Taiwan (Master’s thesis, National Central University). Retrieved from http://www.ncu.edu.tw/?hl=en
Wang, W.C. (2008). Performance Analysis of Enhanced Index Funds –The Innovative “Multi-section Adjustment” Building Model (Master’s thesis, National Sun Yat-Sen University). Retrieved from http://www.oia.nsysu.edu.tw/english/index.html