本篇論文以台灣、中國大陸、新加坡三個股票市場，建構各自的股票多因子風險模型(Local Multi-Factor Model) ；再藉由各市場之因子報酬與三市場共同之世界因子、國家因子、風險因子與產業因子與貨幣因子為基礎，開發而成跨市場股票多因子風險模型(Cross-Market Multi-Factor Model)。
在數量化投資組合日益精進的今日，傳統之單一市場多因子模型已相當成熟；然而，對於國際投資者與基金經理人而言，所持有之投資組合往往為跨國、跨市場之組合。如何將各市場獨有之因子，轉化為各市場可共通使用，並可解釋、拆解投資組合之風險與報酬之模型，為本論文之研究動機與目的。
本篇模型參考Barra (2005)與劉襄儀 (2010)的跨國多因子模型流程，並建構一跨三市場之投資組合，進行風險與報酬拆解之實證。將跨國多因子模型應用在各市場之風險與報酬拆解、歸因，以及整體投資組合之風險與報酬歸因。最後，將模型導入貨幣因子，可讓使用不同幣別的投資人，適時發現貨幣轉換時所產生之風險與報酬。
本篇模型包含了1個世界因子、3個國家因子、14個風險複合因子、24個產業因子、4個跨國風險因子以及2個貨幣因子。此模型不但能提供各市場之投資組合分析，更能應用至國際投資組合拆解，兼具廣度與深度。

This study constructs a cross-market risk model based upon local multi-factor risk models of Taiwan, China and Singapore equity markets. This model allows each local market to adopt different local factors rather than force all local markets to use one parsimonious set of factors. We employ the world, country, industry, and global risk factors to build a structural model which could explain the relationship between local factors across market by further decomposing local factor returns. Therefore, this model could provide both in-depth and broad coverage analysis of international equity portfolios.

Furthermore, we build a simple portfolio and its corresponding benchmark to illustrate the usage of our model. Once the contents of a portfolio are decided, this model could provide not only the risk estimation and decomposition in advance but also the performance attribution compared with the benchmark after the portfolio is realized. The analytical viewpoint could also easily change with different numeraire perspectives. The result demonstrates that this model is practical and flexible for international equity portfolio analysis.

Contents
論文審定書 II
摘 要 III
Abstract IV
I. Introduction 1
1.1 Quantitative Asset Management 1
1.2 Purpose of Research 3
1.3 Research Framework 5
II. Literature Review 6
2.1 Modern Portfolio Theory 6
2.2 Multi-Factor Model 7
2.3 Cross-market Equity Model 12
2.3.1 Global Equity Model 12
2.3.2 The Barra Integrated Model 15
III. Data and Methodology 18
3.1 Data 18
3.2 Methodology 19
3.2.1 The Construction of a Local Risk Model 23
3.2.2 Structural Model – Integrating Local Models into a Global Model 26
3.2.3 Estimating Returns to a Global Equity Factors 29
3.2.4 Consistency Adjustment between Local and Global Model 32
3.2.5 The Currency Model 33
3.2.6 Summary of the Model 35
IV. Empirical Results 38
4.1 Local Risk Models 38
4.2 The Structural Model and Global Factor Returns 41
4.3 Application: Portfolio Analysis 44
4.3.1 Return and Risk Analysis 48
4.3.1.1 Return Analysis 48
4.3.1.2 Risk Analysis 54
4.3.2 Return and Risk Decomposition 59
4.3.2.1 Return Decomposition 59
4.3.2.2 Risk Decomposition 61
4.3.3 The change of numeraire 63
V. Conclusions 67
Reference 71
Appendix A 73
Appendix B 77

Barra (1998). ”Global Equity Risk Model Handbook.”

Barra (1998). “United States Equity Version 3 (E3): Risk Model Handbook. “

Campbell, J., and Shiller, R. (1988). ”The Dividend Price Ratio and Expectations of Future Dividends and Discount Factors. ” Review of Financial Studies, 1 (1), March, 195−228.

Chincarini, Ludwig 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, May/June.

Edin, P. A., and Zetterberg, J. (1992). ”Inter-industry Wage Differentials: Evidence from Sweden and a Comparison with the United States. ” American Economic Review, 82 (5), 1341-1349.

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.

Gilfedder, N. (2005). ”The Barra Integrated Model, Version 203: Implications for Risk Forecasts”. Horizon-The Barra Newsletter, autumn, 11-19.

Greene, W. H., and Seaks, T. G. (1991) ”The Restricted Least Squares Estimator: A Pedagogical Note. ” Review of Economics and Statistics, 73 (3), 563-567.

Grinold and Kahn (2000). ”Active Portfolio Management. ”

Haisken-DeNew, J. P., and Christoph M. Schmidt(1997). ”Inter-industry and Inter-region Differentials: Mechanics and Interpretation. ” Review of Economics and Statistics, 79 (3), 516-521.

Hemmati, F., Hsieh, A., Puchkov, A. V., and Stefek, D. (2005). ”The Barra Integrated Model Version 204. ”

Jun, S., Marathe, A., and Shawky, H. A. (2003). ”Liquidity and Stock Returns in Emerging Equity Markets. ” Emerging Market Review, 4 (1), 1-24.

Kennedy, P. (1986). ”Interpreting Dummy Variable. ” Review of Economics and Statistics, 68(1), 174-175.

Krueger, A. B., and Summers, L. H. (1998). ” Efficiency Wages and the Inter-Industry Wage Structure. ” Econometrica, 56 (2), 259-293.

Lakonishok, J., Shleifer, A., and Vishny, R. W. (1994). ”Contrarian Investment, Extrapolation and Risk. ” Journal of Finance, 49 (5), December, 1541−1578.

Lee, C. J. (2010). ”Multi-Factor Model and Enhanced Index Fund Performance Analysis in China(Master’s thesis, National Sun Yat-Sen University). ”
Liu, S.Y. (2010). ”The Construction of Cross Market Stock Risk Model - With Application in Taiwan and China (Master’s thesis, National Sun Yat-Sen University).”

Northfield (2004). ”Global equity risk model. ”

Senecha, E, and Somerville, S. (2004). ”The Barra Integrated Model: The Next Generation of Global Risk Models. ” Horizon-The Barra Newsletter, spring, 23-29.
Shyu, S., Jeng, Y., Ton, W.H., Lee, K.J., and Chuang, H.M. (2006). ”Taiwan Multi-factor Model Construction: Equity Market Neutral Strategies Application. ” Managerial Finance, 32 (11), 915-947.
Siuts, D. B. (1984). ”Dummy Variables: Mechanics V. Interpretation. The Review of Economics and Statistics, ” 66 (1), 177-180.

Tsai, T. H. (2009). ”A System Platform of Multi-Factor Model (Master’s thesis, National Sun Yat-Sen University). ”