Pure Factor Portfolios and Multivariate Regression Analysis

Abstract

Linking factor portfolio construction to cross-sectional regressions of security returns on standardized factor exposures leads to a transparent and investable perspective on factor performance. Under capitalization-weighting, multivariate regression coefficients translate to portfolio returns that are benchmark relative and cleared of secondary factor exposures. The methodological contributions in this paper are illustrated using a 50-year data set of one-thousand large U.S. stocks and five factor exposures: Value, Momentum, Small Size, Low Beta, and Profitability. Each of the five pure factor portfolios have exposures to the other four factors that match the benchmark portfolio. As two case studies in factor portfolio analysis, we focus on cheapness as measured by Earnings Yield, and interest rate risk as measured by sensitivity to the 10-year Treasury Bond return.