The Pricing of Variance of Variance Risk in Cross-Sectional Equity Premium and Variance Premium

Abstract

Based on an extended general equilibrium long-run risks (LRR) model, this paper examines the pricing of market variance of variance risk in the cross-sectional stock returns and variance premium. We calibrate the economic dynamics with a market-based three-factor model, in which the equilibrium market return, market variance, and market variance of variance are exactly identified to substitute out the consumption information. Using the high-frequency S&P 500 index option data, we estimate the market variance of variance by calculating the model-free realized bipower variance from a series of five-minute-based model-free implied variance. Consistent with the model, we find that stocks with high return sensitivities to market variance of variance have lower stock returns than stocks with low return sensitivities by 10.5 percent annually. Furthermore, stock with high square of return sensitivities to market variance of variance have higher 30-day variance risk premium, which is the difference between risk-neutral variance and realized variance, than stocks with low sensitivities by 27 percent square per month. Our results support the rational pricing of market variance of variance risk, which provides a sufficient condition for the return predictability through market variance risk premium.

Keywords: Variance of Variance Risk, Return Predictability, Cross-Sectional Stock Returns, Cross-Sectional Variance Risk Premium

JEL Classification: G12, G13, E44