This paper studies variance risk premiums in the Treasury market. We first develop a theory to price variance swaps and show that the realized variance can be perfectly replicated by a static position in Treasury futures options and a dynamic position in the underlying. Pricing and hedging is robust even in the underlying jumps. Using a large options panel data set on Treasury futures with different tenors, we report the following findings: First, the term structure of implied variances is downward sloping across maturities and increases in tenors. Moreover, the slope of the term structure is strongly linked to economic activity. Second, returns to the Treasury variance swap are negative and economically large. Shorting a variance swap produces an annualized Sharpe ratio of almost two and the associated returns cannot be explained by standard risk factors. Finally, the returns remain highly statistically significant even when accounting for transaction costs and margin requirements.

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