Inference and Prediction of Stock Returns using Multilevel Models

Abstract

Multilevel models are a generalized form of traditional linear regression models and have several benefits relative to traditional OLS regression including the regularization of parameter estimates, the ability to incorporate prior information, better out-of-sample forecasts, desirable inferential properties, and the ability to directly model the time-series/cross-sectional nature of financial security returns. We demonstrate that multilevel models generalize well-known asset pricing regression techniques like Fama-Macbeth and Fama-French regressions. They also have stronger explanatory power than traditional regression techniques, with a substantially lower out of sample mean squared error and a 5% to 10% higher out of sample R² vs. the comparable model fit with OLS.

Keywords: Bayesian Statistics, Multilevel Models, Stock Returns, Factor Model

JEL Classification: G12, C11, C58