Non-Linear Factor Returns in the U.S. Equity Market

Abstract

We examine non-linear return-to-characteristic relationships for five equity market factors: Value, Momentum, Small Size, Low Beta, and Profitability. Our study employs monthly returns and characteristics for the largest one thousand U.S. stocks from 1964 to 2023 with a focus on average active returns over the last twenty years. Beyond simplicity in modeling the return generating process we find no reason to assume a linear relationship between characteristics and security returns. Allowance for non-linearity leads to increases in Information Ratios for some factor portfolios neutralized with respect to non-linear exposure to the other factors. The return to the pure Profitability characteristic across stocks is highly non-linear, as is the alpha return within the Low Beta portfolio. Non-linearity of the Small Size return across the largest one thousand stocks is complex and changed around the turn of the century. In contrast, over the last twenty years, the return to earnings yield has been linear and flat across the entire Value spectrum.

Keywords: Equity Market Factors, Non-Linear Return, Pure Factor Portfolios, Value Factor, Price Momentum, Small Size Effect, Low Beta/Risk Anomaly, Profitability/Quality Factor

JEL Classification: C1, C3, C5, D5, D8, G1, G4