Is the ex-ante equity risk premium always positive? Evidence from a new conditional expectations model

We model the conditional risk premium by combining principal component analysis and a statistical learning technique, known as boosted regression trees. The method is validated through various out-of-sample tests. We apply the estimates to test the positivity restriction on the risk premium and find evidence that the risk premium is negative in periods of low corporate and government bond returns, high inflation and downward-sloping term structure. These periods are linked with changes in business cycles; the states when theories predict the existence of negative risk premium. Based on the evidence, we reject the conditional capital asset pricing model and raise a question over the practice of imposing the positive risk premium constraint in predictive models.