Time-Varying Exposure to Long-Run Consumption Risk

Abstract

This paper develops a model of time-varying expected returns and shows that, when investors care about the long-run consumption risk, they also care about the persistence of an asset's exposure to this risk, and demand substantially higher compensation for more persistent exposure. The model also implies a negative sensitivity of price-dividend ratios to expected excess returns, and the magnitude of the sensitivity is substantially larger for more persistent exposure. In an application of the model, I specify individual stocks' dividend growth as containing two time-varying components of exposure to the long-run consumption risk - a fast mean-reverting component whose shocks are positively correlated with the independent dividend growth shocks, and a slow mean-reverting component whose shocks are negatively correlated with the independent dividend growth shocks. Firm level simulations from this model produce short-run momentum and long-run reversal quantitatively comparable to empirically documented patterns in the cross section as well as along the time dimension. The simulations also show that the value premium across price-dividend ratio sorted portfolios is driven by a spread in the slow mean-reverting risk exposure. Together, these results propose potential interpretations of the value and momentum factors as representing time-varying loadings of different persistence on the long-run consumption risk factor.