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T his article presents methodologies for constructing and examining equity factor portfolios, which are illustrated using the monthly returns and factor exposures on 1,000 large U.S. stocks for the 50 years ending 2016. Specifically, we construct primary and pure portfolios for five well-known factors: value, momentum, small size, low beta, and profitability. We add a sixthbond beta factor to examine the dynamic nature of interest rate risk on the equity market and on the various factor portfolios. The intent of this case study is not to argue for another factor in equity market analysis, but rather to illustrate how interest rate exposure can be compared to the better-known factor exposures. Similarly, we employ the value factor, as measured by the inverse price/earnings (P/E), to examine the "cheapness" of the various factor portfolios over time and compared to each other, but we emphasize that value is only one of several possible equity market factors.
The methodological contribution of this article begins with primary factor portfolios constructed using a security-weighting formula that incorporates both market capitalization and standardized factor exposure. The security-weighting formula is consistent with the role of the capitalization-weighted portfolio as the benchmark and the use of Fama and MacBeth [1973] cross-sectional regressions as an empirical investigation tool. When the regressions are multivariate (i.e., security returns are regressed on several exposures simultaneously), the slope coefficients equate to implementable analytic formulas for the security weights of factor portfolios that have market-relative exposures of zero to the other factors. Tying factor portfolio return calculations to analytically derived security weights avoids the black-box nature of backtests based on single and double sorts with quintile cutoffs and other ad hoc portfolio construction criteria. The concept of equating regression slope coefficients with investable portfolios is discussed in Clarke, de Silva, and Thorley [2014], with further extensions in the online Appendix A of this article at www.iijpm.com .
Numerous studies in both academic and practitioner literature document the performance of one or more equity market factors but include uncontrolled and often substantial exposures to secondary factors. Fama and French [1996] established a process for controlling the exposure of a factor portfolio with a second factor: The small size factor portfolio SMB is created by a secondary sort on value exposures,...