On Tree-Structured Linear and Quantile Regression Based Asset Pricing

Abstract

A tree-structured linear and quantile regression framework is proposed for the analysis and modeling of equity market returns. The approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The modeling framework is applied on numerous asset pricing models related to the whole U.S. equity market, using alternative mimicking factor portfolios, frequency of data and widely followed market indices. The findings reveal strong evidence that asset returns exhibit asymmetric effects and nonlinear patterns to different common factors.

Keywords: Asset pricing; Bayesian inference; Markov chain Monte Carlo; Nonlinear dynamics; Tree-structured (linear and quantile) regression models

JEL Classification: G11, G12, C1, C11