Characteristics of Factor Portfolios, March 2010

A key to deeper understanding of factor models lies in the concept of factor-mimicking portfolios, whose returns exactly replicate the payoffs to the factors. Simple factor portfolios are obtained by considering each factor in isolation, whereas pure factor portfolios are constructed by treating all factors jointly. In this paper, we derive the holdings of simple factors portfolios for the World factor, as well as for countries, industries, and styles. We also discuss the characteristics of pure factor portfolios, and how differences between simple and pure factor portfolios arise due to collinearity between factors. We introduce several intuitive measures of collinearity in factor models, and present their empirical distributions in the context of a global equity model. Finally, we describe how collinearity can be reduced through factor rotation, and discuss the interpretation of such factors.