Free (Almost) Variance Insurance

45 Pages Posted: 15 Jul 2013 Last revised: 23 Feb 2014

See all articles by Yan Xu

Yan Xu

HKU, Faculty of Business and Economics

Yuzhao Zhang

Rutgers, The State University of New Jersey - Department of Finance

Date Written: January 31, 2014


The expected returns of short maturity options are large and negative, implying a negative variance risk premium. We find that the magnitude of this negative risk premium decreases monotonically with option maturity. Specifically, the risk premium becomes insignificant for maturities beyond 6 months, and the cost to insure the variance risk using long maturity options is 2 bps per month. In the context of a classical asset pricing model, this pattern suggests that variance betas should also decline with maturity because the risk premium is proportional to the factor loading. However, variance betas increase with option maturity, challenging a one-factor model of the variance risk. In particular, a one-factor model of the short-term variance risk (level) fails to explain the cross-section of option returns and is forcefully rejected by asset pricing tests. We identify a slope factor in the term structure of risk-neutral variances and find this slope crucial for explaining the cross section of option returns. When combined, the slope and level factors explain majority of the option return variations.

Keywords: variance risk premium, option returns

JEL Classification: G12

Suggested Citation

Xu, Yan and Zhang, Yuzhao, Free (Almost) Variance Insurance (January 31, 2014). Available at SSRN: or

Yan Xu

HKU, Faculty of Business and Economics ( email )

Pok Fu Lam Road
Hong Kong
Hong Kong

Yuzhao Zhang (Contact Author)

Rutgers, The State University of New Jersey - Department of Finance ( email )

94 Rockafeller Road
Piscataway, NJ 08854
United States

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