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Abstract:
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Using standard linear regression to describe the cross-section of expected returns implies that the relationships between firm characteristics and returns are both linear and stationary. While this is historically a common practice, finance literature now suggests that these relationships are nonlinear and/or nonstationary. We submit that these effects should also be monotonic. To this end, we present a Bayesian time-dynamic, additive quadratic spline model that can constrain individual splines to be monotonic. This model allows us to see the relationships that characteristics have with returns while controlling for many other covariates. Thus, these relationships can be evaluated for linearity, stationarity, and monotonicity. We present several of these relationships for examination.
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