Real-Time Learning, Macroeconomic Uncertainty, and the Variance Risk Premium

Abstract

The variance risk premium represents the compensation paid to index option sellers for the risk of losses following upward movements in realized market return volatility. Common wisdom connects these spikes with elevated uncertainty on economic fundamentals. I incorporate this link within a single-agent general equilibrium model, embedding real-time learning on state variables and parameters. I show that infrequent, large and relatively transitory macroeconomic uncertainty shocks produce a sizable and volatile variance risk premium. These shocks coincide with major events such as the LTCM/Russian crisis, the onset of the second Gulf War, and the great financial crisis of 2008-2009. I compute macroeconomic uncertainty as the dispersion of the agent’s belief about the expected growth rate of consumption. Its time-varying nature reflects in the variance risk premium, generating short-term predictability for market excess returns, consistent with the data. In addition, the model matches the higher order moments of the realized equity premium, with a reasonably low level of relative risk aversion equal to five. I finally provide evidence that parameter uncertainty may represent an extra-source of risk which is priced in equilibrium. In fact, a model with parameter learning and standard CRRA preferences, matches around half of the historical variance risk premium.