The Variance Risk Premium in Equilibrium Models

The equity variance risk premium is the expected compensation earned for selling variance risk in equity markets. The variance risk premium is positive and shows moderate persistence. High variance risk premiums coincide with the left tail of the consumption growth distribution shifting down. These facts, together with a positive, yet moderate, difference between the risk-neutral entropy and variance of the aggregate market return, refute the bulk of the extant consumption-based asset pricing models. We introduce a tractable habit model that does fit the data. In the model, the variance risk premium depends positively (negatively) on "bad" ("good") consumption growth uncertainty.