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We propose a new decomposition of the variance risk premium (VRP) in terms of upside and downside VRPs. These components reflect market compensation for changes in good and bad uncertainties. Empirically, we establish that the downside VRP is the main component of the VRP. We find a positive and significant link between the downside VRP and the equity premium, and a negative but statistically insignificant link between the upside VRP and the equity premium. The opposite relationships between these two components and the equity premium explains the stronger link found between the downside VRP and the equity premium compared with the well-established relationship between VRP and the equity premium. A simple equilibrium consumption-based asset pricing model, fitted to the U.S. data, supports our decomposition.
Feunou et al. (Tue,) studied this question.