The Variance Risk Premium in Equilibrium Models

Abstract

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 only moderate persistence. High variance risk premiums coincide with the left tail of the consumption growth distribution shifting down. These facts, together with risk neutral skewness being substantially more negative than physical return skewness, 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.

Keywords: variance risk premium, risk-neutral skewness, non-Gaussian dynamics, bad volatility, VIX, habit

JEL Classification: E44, G12, G13