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We explore the cross-section of realized variance, skewness, and kurtosis for stock returns obtained from intraday data. We investigate the properties of the realized higher moments, and more importantly, examine relations between the realized moments and subsequent stock returns. We find evidence of a negative relation between realized skewness and next week’s returns. A strategy buying stocks in the lowest realized skewness quintile and selling stocks in the highest realized skewness quintile earns 0.79 percent per week a risk-adjusted basis. Our results on the realized skewness are robust to controls for various firm characteristics such as size and book-to-market. Little evidence exists that either the realized volatility or the realized kurtosis is significantly related to next week’s returns.

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