Uncertainty and leveraged Lucas Trees: the cross section of equilibrium volatility risk premia

Volatility risk premia compensate agents for holding assets whose payoffs correlate with times of high return variation. This paper takes a structural approach to explain the cross-section of volatility risk premia of stocks using a Lucas orchard with heterogeneous beliefs, stochastic macro-economic uncertainty, and default risk. I study two manifestations of uncertainty, namely (i) agents’ disagreement and (ii) time-varying volatility of fundamental growth rates. The paper shows that while the former source of risk accounts for the level of the risk premia, the latter mainly affects the higher order moments of the risk premium distribution. Together with uncertainty, default risk associated with levered trees implies a non-monotonic equilibrium link between stock returns and volatility which allows for positive or negative risk premia. Calibrating the economy, I show that the model accounts for predictability of excess stock returns and corporate credit spreads. I construct volatility risk premia from option and stock prices and document that in the time-series, volatility risk premia of individual stocks can be positive or negative, and switch sign rather often. In the cross-section, they are only weakly related to traditional risk factors. I then test the model predictions and find that empirical proxies for investors’ uncertainty about expected growth rates and macro-economic uncertainty are priced risk factors that convey information over and above those contained in other standard factors to explain these risk premia. In line with the model predictions, I present predictability evidence of individual volatility risk premia for stock excess returns and corporate credit spreads.