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Delta-Hedged Gains and Risk-Neutral Moments

We investigate the well-documented underperformance of delta-hedged option portfolios in relation to ex ante moments of the stock market's return distribution. Using a sample of Standard and Poor's 500 index options, we find that delta-hedged option gains decrease with ex ante volatility, in support of a negative volatility risk premium. Moreover, the delta-hedged gains are negatively associated with skewness and kurtosis of call options, but positively associated with the higher moments of put options. These results suggest that investors pay a premium for call options in anticipation of a positive jump, while they pay a premium for put options in anticipation of a negative jump.