本研究主要建構一個跨產業多因子選股模型，結合貝氏定理的概念做跨產業間模型的產出調整，同時維持產業內的分數排序，且合理地結合跨產業間的分數排序，使得跨產業的選股模型更為完善與合理。在此架構下，使用台股市場為樣本做模型的測試與建構，選取各產業內有效的因子，並分別建構不同產業的選股模型，分別得出各產業模型所計算出的阿爾法值，並以電子指數、金融指數與非金非電指數為基礎，建構三檔股票型增值指數基金；最後也使用貝氏定理的概念，依照理論基礎，將三個產業的阿爾法值做調整並統整為全市場的阿爾法值，以台灣加權指數為標竿指數，建立一檔全市場股票型增值指數基金。
在投資組合建構方法的研究中，使用基準指數原始權重的保留率，可有效降低本研究中建構之增值指數基金的追蹤誤差，也可降低該基金的週轉率，經過在樣本外期間（2008/01/01~2010/12/31）的回測結果顯示，本文所建構之增值指數基金，可以提供高達0.98的資訊比率，且累積投資報酬率明顯高於台灣加權指數。

This study constructs a quantitative stock selection model across multiple sectors with the application of the Bayesian method. It employees factors from the Taiwan stock market which could explain stock returns. Under this structure, each sector that has different significant factors is allowed to be imported into sub models. The factors are calculated into alpha scores and used to do stock selection. Therefore, the demonstration of both intra and inter-sector alpha scores into sector-specific integration alpha scores is an important concept in this study.
Furthermore, an enhanced index fund is built based on the model and related to the benchmark to illustrate the power of this model. Once the contents of a portfolio are decided, this model could provide stock selection criterion based on the predictive power of stock return. Finally, the results demonstrate that this model is practical and flexible for local stock portfolio analysis.

Contents
I. Introduction ........................................................................................................... 1
II. Literature Review.................................................................................................. 5
2.1 Multi-Factor Models ............................................................................................. 5
2.1.1 BARRA ............................................................................................. 5
2.1.2 Information Coefficient Analysis ...................................................... 5
2.1.3 Information Ratio Analysis ............................................................... 7
2.2 Evidence from Taiwan Stock Market .................................................................... 9
2.2.1 A System Platform of Multi-Factor Risk Model............................... 9
2.2.2 Multi-Factor Alpha Model ................................................................ 9
2.3 Bayesian Theory ................................................................................................. 10
2.3.1 Bayesian Estimation of Security Betas ........................................... 10
III. Methodology ....................................................................................................... 13
3.1 Model Framework ............................................................................................... 13
3.2 Factor Construction ............................................................................................. 15
3.2.1 Computation and Determination of the Factors .............................. 15
3.2.2 Outlier Adjustment .......................................................................... 18
3.2.3 Standardization of the Factors ........................................................ 19
3.2.4 Effectiveness Tests of Factors ......................................................... 20
3.3 Information Coefficients (IC) ............................................................................. 20
3.3.1 Characteristics of ICs ...................................................................... 21
3.3.2 Quintile Analysis ............................................................................. 21
3.4 Computation of the Alpha Score ......................................................................... 22
3.4.1 Combination of the Multiple Alpha Factor by Two Stage Model ... 22
3.5 Bayesian Theory to Integrate the Alpha Scores .................................................. 23
3.6 Application of the Sector-Specific MFM............................................................ 28
3.6.1 Stock Pool Screening ...................................................................... 28
3.6.2 Portfolio Construction ..................................................................... 29
3.6.3 Turnover Rate Calculation .............................................................. 30
3.7 Benchmark .......................................................................................................... 31
IV. Empirical Results ................................................................................................ 32
4.1 Data Description ................................................................................................. 32
4.2 Core Factor Selection .......................................................................................... 33
4.2.1 Monthly and Weekly Core Factors ................................................. 33
4.2.2 Summary of Core Factors ............................................................... 36
4.3 Quintile Return Analysis ..................................................................................... 38
4.4 Portfolio Performance ......................................................................................... 39
4.4.1 Sub-Sector Portfolio........................................................................ 40
4.4.2 Sector-Specific Integrated Portfolio ............................................... 42
4.4.3 General Alpha Portfolio .................................................................. 43
V. Conclusions ......................................................................................................... 45
VI. References ........................................................................................................... 50
List of Figures
Figure 1. Alpha Model Framework .............................................................. 13
Figure 2. Sector-Specific Alpha Model Framework .................................... 14
Figure 3. Core Factor Selection and Back-testing Period ............................ 32
Figure4. Example of Factor Quintile Analysis ............................................ 38
List of Tables
Table1. Weekly Factors and Descriptors ...................................................... 16
Table2. Monthly Factors and Descriptors .................................................... 17
Table3. Monthly core factors ....................................................................... 33
Table4. Weekly core factors ......................................................................... 35
Table5. Summary of monthly core factor performance ............................... 37
Table6. Quintile portfolio returns in each model ......................................... 39
Table7. The Performance of sub-portfolios ................................................. 41
Table8 . The Performance of Sector-Specific Integrated Portfolio .............. 42
Table9 . The Performance of General Portfolio ........................................... 43

BARRA (1998), United States Equity Version 3, Risk Model Hand Book.

Connor, G. (1995). The Three Types of Factor Models: A Comparison of Their Explanatory Power. Financial Analysis Journal, May/June.

Fama, E.F. and French, K.R. (1992), “The Cross-Section of Expected Stock Returns,” Journal of Finance, Vol. 47, No. 2, June, pp. 427-465.

Fama, E.F. and French, K.R. (1993), “Common Risk Factors in The Returns to Stocks and Bonds,” Journal of Financial Economics, Vol. 33 No.1, February, pp. 3-56.

Frost, P.A. and Savarino, J.E. (1986), “An Empirical Bayes Approach to Efficient Portfolio Selection,” Journal of Financial and Quantitative Analysis, Vol. 21, No. 3, September, pp. 293-305.

Grinold, R.C. and Kahn, R.N. (2000), “Active Portfolio Management,” McGrew-Hill, New York.

Hui, T.K., Kwan, E.K. and Lee, C.B. (1993), “Optimal Portfolio Diversification: Empirical Bayes Versus Classical Approach,” Journal of the Operational Research Society, Vol. 44, No. 11, December, pp. 1155-1159.

Jeng, Y., Tzang, S.W., Lee, Y.H. and Hsu, Y.H. (2011) . “Enhanced Index Fund Performance Analysis by Multi-Factor Alpha Model: Evidence From Taiwan , 2011 International Conference of Taiwan Finance Association.

Jorion, P. (2003), ”Portfolio Optimization with Tracking-Error Constraints,” Financial Analysts Journal, 59 (5), pp.70-82.

Jorion, P. (1986), “Bayes-Stein Estimation for Portfolio Analysis,” Journal of Financial and Quantitative Analysis, Vol.21, No.3, September, pp. 279-292.

Jorion, P. (1991), “Bayesian and CAPM estimators of the means: Implications for Portfolio Selection,” Journal of Banking and Finance, pp. 717-727, North-Holland.

Qian, E.E., Hua, R. and Sorensen E.H., (2007), “Quantitative Equity Portfolio Management: modern techniques and application,” Chapman & Hall.

Rachev, S.T., Hsu, J.S.J., Bagasheva, B.S. and Fabozzi, F.J. (2008) “Bayesian Methods in Finance,” John Willey & Sons.

Sorensen, E.H., Qian, E., Hua, R., and Schoen, R. (2004), “Multiple alpha sources and active management,” Journal of Portfolio management, Vol. 31, No. 2, pp. 39-45, winter.

Tsai, Z.X. (2009). “A System Platform of Multi-Factor Risk Model “(Master’s thesis, National Sun Yat-Sen University).

Vasicek, O.A. (1973), “A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Betas ,” Journal of Finance, Vol. 28, No. 5, December, pp. 1233-1239.