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On More Robust Estimation of Skewness and Kurtosis: Simulation and Application to the S&P500 Index


  • Kim, Tae-Hwan
  • White, Halbert


For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and 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 insight into market returns behaviour.

Suggested Citation

  • Kim, Tae-Hwan & White, Halbert, 2003. "On More Robust Estimation of Skewness and Kurtosis: Simulation and Application to the S&P500 Index," University of California at San Diego, Economics Working Paper Series qt7b52v07p, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt7b52v07p

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    References listed on IDEAS

    1. Hwang, Soosung & Satchell, Stephen E, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 4(4), pages 271-296, October.
    2. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    5. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
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    Cited by:

    1. Sinclair-Maragh, Gaunette & Gursoy, Dogan, 2015. "Imperialism and tourism: The case of developing island countries," Annals of Tourism Research, Elsevier, vol. 50(C), pages 143-158.
    2. IORGULESCU Filip, 2012. "The Stylized Facts Of Asset Returns And Their Impact On Value-At-Risk Models," Revista Economica, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 0(4), pages 360-368.

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    skewness; kurtosis; quantile; robustness;


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