Extracting Factors with Maximum Explanatory Power∗

Security returns are heteroscedastic both cross-sectionally and over time, which affects the accuracy of standard factor extraction methods. In order to reduce the impact of such heterogeneity and to preserve the true factor structure, this paper studies the performance of a factor extracting method based on maximizing the explanatory power of the extracted factors. The implementation of the methodology is largely based on the principal components analysis on a correlation structure of asset returns. However, such a simple extension allows us to improve the finite sample performance over other popular approaches when returns are heteroscedastic both across individual assets and over time. Moreover, the out-of-sample study suggests that the extracted factors are not only stable across different sample groups, but also more pervasive in explaining the out-of-sample individual stock returns than other methods. These factors even have better out-of-sample explanatory power than the Fama and French factors. In addition, we shed light on the issue of choosing the correct number of factors. ∗I am grateful to Stephen J. Brown, Lewis Chan, Nai-fu Chen, Ted Day, Yacine Hammami, Chris Jones, Raymond Kan, Bob Korajczyk, Craig MacKinlay, Jianping Mei, Larry Merville, John Wei, Steven Wei, Chu Zhang, Guofu Zhou, and seminar participants at SMU, Hong Kong University of Science and Technology, Hong Kong Polytech University, 2002 Western Finance Association Conference, and 2002 European Financial Management Association Conference for helpful comments. Address correspondence to: Yexiao Xu, School of Management, The University of Texas at Dallas, PO Box 688, Richardson, Texas 75080, USA; Email: [email protected] Extracting Factors with Maximum Explanatory Power