Decomposing the VIX: Implications for the Predictability of Stock Returns

Abstract

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.

Keywords: Polynomial Variation, Quadratic Variation, Variance Risk Premium, Tail Risk Premium, Predictability

JEL Classification: C22, C51, C52, G1, G12, G13