Is the Ex-Ante Equity Risk Premium Always Positive? Evidence from a Statistical Learning Method

Abstract

In this paper, we propose a new two-stage method, including Principal Component Analysis and Boosted Regression Tree, to model conditional expected returns. With this technique, we address two potential criticisms on how to capture the true identity of the investors’ information set, and how investors use the information in forming expected returns. Applying this risk premium proxy, we test whether risk premium is always positive. A number of asset pricing studies have focused on testing linear restrictions imposed by asset pricing models and largely ignore this important restriction. We find evidence that the positivity condition of the risk premium is violated for the US (CRSP index) in some states of the economy; these states are associated with periods of low corporate returns, low long term government bond returns, lagged negative risk premium, and downward sloping term structure.

Keywords: Ex-ante risk premium, conditional asset pricing, boosted regression tree, principal component analysis, multiple conditional inequality constraints

JEL Classification: G12; C22