本論文依據基礎橫斷面法建構台灣股市多因子模型，主要建構原理是根據BARRA’E3 的原則進行。在本多因子模型中，最後決定選用34個解釋因子(包括7個風險因子和27個產業因子)。根據研究發現，產業因子在台灣股市為重要的風險來源。本多因子模型平均解釋能力為43.18%，此結果令人滿意。
此外，本研究以多因子模型為基礎，建構一追蹤台灣加權股價指數的增值型指數基金。在研究過程中，採用最適化法並最小化追蹤誤差來決定投資組合的權重。增值型指數基金的建構策略為同時運用被動式管理與主動式管理策略，建構出與標竿指數特性相仿且同時又能提供優於標竿指數報酬之投資組合。本研究以2000年1月到2005年12月的月資料，來建構追蹤台灣加權股價指數的增值型基金，回測期間為2006年1月到2007年12月。研究結果顯示，所建構出的台灣加權股價指數增值型基金績效優於標竿指數，且追蹤誤差為1.36%，追蹤誤差仍在可接受的範圍內。

We construct the multi-factor model using fundamental cross-sectional approach in the thesis. We adopt the principal of BARRA’E3 for constructing our multi-factor model. In our study period, we finally obtain 34 significant explanatory factors including 7 risk indices and 27 industry factors. In particular, the industry factors are an important risk source of the stock returns. The explanatory power of the multi-factor model is 43.18% on average and it ranges from 12.89% to 82.35%. The study results can be considered satisfactory.
Moreover, based on the multi-factor model, we construct the Taiwan Weighted Stock Index enhanced index fund by the tracking error minimization method in our study. Enhanced Index Fund was built to make use of both passive management and active management to construct a portfolio which has the similar characteristics but higher returns compared to benchmark index. Hence, we want to track the Taiwan Weighted Stock Index while producing at least 2% outperformance over the Taiwan Weighted Stock Index. Our empirical period is from January 2000 to December 2005 and the simulated period is from January 2006 to December 2007. The performance of our constructed Taiwan Weighted Stock Index enhanced index fund in the simulated period is better than the benchmark and the tracking error is 1.36%. We are satisfied with the study results.

1. Introduction 1
2. Literature review 3
2.1 The multi-factor model 3
2.2 Enhanced index fund 4
3. Data and methodology 6
3.1 Data description 6
3.2 The methodologies of modeling multi-factor risk model 8
3.2.1 Factor selection and calculation 9
3.2.2 Risk index formulation 12
3.2.3 Factor return and covariance matrix estimation 15
3.2.4 Estimate specific returns and specific risks 18
3.3 Portfolio construction 19
3.3.1 Stock screening and ranking 19
3.3.2 Determine portfolio weights 19
4. Empirical results 20
4.1 Factor Analysis results 20
4.2 Factor return estimation 21
4.3 Covariance matrix calculation 24
4.4 Specific risk matrix estimation 26
4.5 Analysis of empirical result for multi-factor risk model 27
4.6 Portfolio performance 29
4.6.1 Stock selection 29
4.6.2 Results of constructing Taiwan Weighted Stock Index enhanced fund 30
5. Summary 35
6. Reference 37

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