High-Frequency Returns, Jumps and the Mixture of Normals Hypothesis

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Abstract
Previous empirical studies find both evidence of jumps in asset prices and that returns standardized by `realized volatility' are approximately standard normal. These findings appear to be contradictory. Using a sample of high-frequency returns for 20 heavily-traded US stocks, we show that microstructure noise may artificially reduce the variance and increase the kurtosis of returns standardized using realized variance. When we apply a bias-corrected realized variance estimator, standardized returns are platykurtotic and the standard normal distribution is easily rejected. Moreover, when daily returns are standardized using realized bipower variation, an estimator for integrated volatility that is robust to the presence of jumps, the resulting series appear more consistent with the standard normal distribution. These results suggest that there is no empirical contradiction: jumps should be included in stock price models.

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