IDEAS home Printed from https://ideas.repec.org/p/cdl/ucsdec/qt7b52v07p.html
   My bibliography  Save this paper

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

Author

Listed:
  • Kim, Tae-Hwan
  • White, Halbert

Abstract

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
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/7b52v07p.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Samuel Kotz & Edith Seier, 2009. "An analysis of quantile measures of kurtosis: center and tails," Statistical Papers, Springer, vol. 50(3), pages 553-568, June.
    2. Christopher G. Lamoureux & Huacheng Zhang, 2021. "An Empirical Assessment of Characteristics and Optimal Portfolios," Papers 2104.12975, arXiv.org, revised Feb 2024.
    3. Ayman Alzaatreh & Hana Sulieman, 2021. "On fitting cryptocurrency log-return exchange rates," Empirical Economics, Springer, vol. 60(3), pages 1157-1174, March.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    2. Bonato, Matteo, 2011. "Robust estimation of skewness and kurtosis in distributions with infinite higher moments," Finance Research Letters, Elsevier, vol. 8(2), pages 77-87, June.
    3. Dunbar, Kwamie & Owusu-Amoako, Johnson, 2022. "Hedging the extreme risk of cryptocurrency," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    4. Alexander Eastman & Brian Lucey, 2008. "Skewness and asymmetry in futures returns and volumes," Applied Financial Economics, Taylor & Francis Journals, vol. 18(10), pages 777-800.
    5. Chang, Bo Young & Christoffersen, Peter & Jacobs, Kris, 2013. "Market skewness risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 107(1), pages 46-68.
    6. Maheu, John M. & McCurdy, Thomas H. & Zhao, Xiaofei, 2013. "Do jumps contribute to the dynamics of the equity premium?," Journal of Financial Economics, Elsevier, vol. 110(2), pages 457-477.
    7. Chiao, Chaoshin & Hung, Ken & Srivastava, Suresh C., 2003. "Taiwan stock market and four-moment asset pricing model," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 13(4), pages 355-381, October.
    8. Zhiyuan Pan & Yudong Wang & Li Liu, 2021. "Realized bipower variation, jump components, and option valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1933-1958, December.
    9. ROCKINGER, Michael & JONDEAU, Eric, 2000. "Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence," HEC Research Papers Series 710, HEC Paris.
    10. Dark Jonathan Graeme, 2010. "Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-50, March.
    11. Akbar, Muhammad & Nguyen, Thuy Thu, 2016. "The explanatory power of higher moment capital asset pricing model in the Karachi stock exchange," Research in International Business and Finance, Elsevier, vol. 36(C), pages 241-253.
    12. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    13. Attiya Y. Javid & Eatzaz Ahmad, 2008. "Test of Multi-moment Capital Asset Pricing Model: Evidence from Karachi Stock Exchange," PIDE-Working Papers 2008:49, Pakistan Institute of Development Economics.
    14. Eric Jondeau & Michael Rockinger, 2005. "Conditional Asset Allocation under Non-Normality: How Costly is the Mean-Variance Criterion?," FAME Research Paper Series rp132, International Center for Financial Asset Management and Engineering.
    15. Lin, Yuehao & Lehnert, Thorsten & Wolff, Christian, 2019. "Skewness risk premium: Theory and empirical evidence," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 174-185.
    16. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers 2009s-34, CIRANO.
    17. Abed Masrorkhah, Sara & Lehnert, Thorsten, 2017. "Press freedom and jumps in stock prices," Economic Systems, Elsevier, vol. 41(1), pages 151-162.
    18. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    19. Giuseppe Arbia & Riccardo Bramante & Silvia Facchinetti, 2020. "Least Quartic Regression Criterion to Evaluate Systematic Risk in the Presence of Co-Skewness and Co-Kurtosis," Risks, MDPI, vol. 8(3), pages 1-14, September.
    20. Giuseppe arbia, 2014. "Least quartic Regression Criterion with Application to Finance," Papers 1403.4171, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cdl:ucsdec:qt7b52v07p. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/deucsus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.