Delta-Hedged Gains and the Negative Market Volatility Risk Premium

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Abstract
We investigate whether the volatility risk premium is negative by examining the statistical properties of delta‐hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta‐hedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the delta‐hedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility. Fourth, the volatility risk premium significantly affects delta‐hedged gains, even after accounting for jump fears. Our evidence is supportive of a negative market volatility risk premium.