Bayesian Reconciliation of Return Predictability

TL;DR

This paper develops a Bayesian method with a new shrinkage prior to assess return predictability in a VAR model, comparing it to traditional estimators and applying it to historical stock return data.

Contribution

It introduces a novel Bayesian shrinkage prior for return predictability parameters and demonstrates its superiority over existing estimators through simulations and empirical analysis.

Findings

Bayesian approach outperforms reduced-bias estimator in simulations.

Supports no return predictability in 1926-2004 data.

Weak evidence of predictability in 1953-2021 data.

Abstract

This article considers a stable vector autoregressive (VAR) model and investigates return predictability in a Bayesian context. The VAR system comprises asset returns and the dividend-price ratio as proposed in Cochrane (2008), and allows pinning down the question of return predictability to the value of one particular model parameter. We develop a new shrinkage type prior for this parameter and compare our Bayesian approach to ordinary least squares estimation and to the reduced-bias estimator proposed in Amihud and Hurvich (2004). A simulation study shows that the Bayesian approach dominates the reduced-bias estimator in terms of observed size (false positive) and power (false negative). We apply our methodology to annual CRSP value-weighted returns running, respectively, from 1926 to 2004 and from 1953 to 2021. For the first sample, the Bayesian approach supports the hypothesis of no return predictability, while for the second data set weak evidence for predictability is observed.