Nonlinear Factor Effects on Returns

In this chapter, we use the US public equity market to discuss nonlinearity at the factor level, the most basic element of an investment process. We show how the adjustment for nonlinearity adds value based on a quantamental approach. We focus on the four most common factors used by both fundamental and quantitative portfolio managers: beta, dividends, value, and momentum. We start with beta, demonstrating the conditions and validity of beta in a nonlinear context. Turning to dividend, we illustrate the strong nonlinear relationship between dividends and stock returns. We then show how to apply a quantamental approach to identify and model nonlinear relationships between value factors and stock returns and understand the causes underlying such relationships. Next, we apply the same approach to momentum to distinguish true persistent winners from mere tide riders. Finally, we summarize commonly used methods for constructing nonlinear models at the factor level as well as the most common forms these nonlinear relationships take. These methods and forms can then be applied as parts of a general approach to investigating nonlinear pricing relationships.