For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and severe excess kurtosis. This stylized fact has been supported by a vast collection of empirical studies. Given that the conventional measures of skewness and kurtosis are computed as an average and that averages are not robust, we ask: "How useful are the measures of skewness and kurtosis used in previous empirical studies?" To answer this question, we provide a survey of robust measures of skewness and kurtosis from the statistics literature and carry out extensive Monte Carlo simulations that compare the conventional measures with the robust measures of our survey. An application of the robust measures to daily S&P500 index data indicates that the stylized facts might have been accepted too readily. We suggest that looking beyond the standard skewness and kurtosis measures can provide deeper and more accurate insight into market returns behavior.
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