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The cross-section of stock returns has substantial exposure to risk captured by higher moments in market returns. The authors estimate these moments from daily S&P 500 index option data. The resulting time series of factors are thus genuinely conditional and forward-looking. Stocks with high sensitivities to innovations in implied market volatility and skewness exhibit low returns on average, whereas those with high sensitivities to innovations in implied market kurtosis exhibit somewhat higher returns on average. The results on market skewness risk are robust to various permutations of the empirical setup. The estimated premium for bearing market skewness risk is between −3.72% and −5.76% annually.
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