Monotonic Effects of Characteristics on Returns
38 Pages Posted: 1 Aug 2018
Date Written: July 12, 2018
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 many of these effects should also be monotonic. To this end, we present a time-dynamic, additive quadratic spline model that can constrain individual splines to be monotonic. The model shrinks irrelevant spline coefficients toward zero and selects the appropriate number of knots through carefully designed shrinkage priors. The additive nature of the model allows it to handle many characteristics from many firms. Selection among characteristics and model complexity are established through utility-based posterior summarization. This model design admits parsimony and economically meaningful interpretation. As the model maintains interpretability, these relationships can be evaluated for linearity, stationarity, and monotonicity.
Keywords: Bayesian Econometrics, Monotonic Splines, Cross Section of Returns
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