Variance Risk Premia on Stocks and Bonds

Investors in fixed income markets are willing to pay a very large premium to be hedged against shocks in expected volatility and the size of this premium can be studied through variance swaps. Using thirty years of option and high-frequency data, we document the following novel stylized facts: First, exposure to bond market volatility is strongly priced with a Sharpe ratio of -1.8, 20% higher than what is observed in the equity market. Second, while there is strong co-movement between equity and bond market variance risk, there are distinct periods when the bond variance risk premium is different from the equity variance risk premium. Third, the conditional correlation between stock and bond market variance risk premium switches sign often and ranges between -60% and +90%. We then show that these stylized facts pose a challenge to standard consumption-based asset pricing models.