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On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index

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  • Badrinath, S G
  • Chatterjee, Sangit
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    Abstract

    This article is an exploratory investigation of the distributional properties of market index returns using J. W. Tukey's g and h distributions. Specifically, it is shown that over sufficiently long periods of time, the distribution of the market index is adequately explained as a skewed, elongated (g x h) distribution. Estimates of skewness and elongation are developed that are easy to calculate and are robust with respect to outliers. Functional forms for the appropr iate distributions are provided. The findings reported here have implications for understanding skewness and elongation, developing appropriate portfolio strategies, and devising pricing models incorporating higher moments. Copyright 1988 by the University of Chicago.

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    Bibliographic Info

    Article provided by University of Chicago Press in its journal Journal of Business.

    Volume (Year): 61 (1988)
    Issue (Month): 4 (October)
    Pages: 451-72

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    Handle: RePEc:ucp:jnlbus:v:61:y:1988:i:4:p:451-72

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    Web page: http://www.journals.uchicago.edu/JB/

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    Cited by:
    1. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    2. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    3. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
    4. Fischer, Matthias J., 2006. "Generalized Tukey-type distributions with application to financial and teletraffic data," Discussion Papers 72/2006, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    5. X. Henry Wang & Carmen F. Menezes, 2004. "Increasing Outer Risk," Working Papers 0413, Department of Economics, University of Missouri, revised 23 Dec 2004.
    6. Lars Forsberg & Anders Eriksson, 2004. "The Mean Variance Mixing GARCH (1,1) model," Econometric Society 2004 Australasian Meetings 323, Econometric Society.
    7. Tian, Yisong Sam, 1998. "A Trinomial Option Pricing Model Dependent on Skewness and Kurtosis," International Review of Economics & Finance, Elsevier, vol. 7(3), pages 315-330.
    8. Christie-David, Rohan & Chaudhry, Mukesh, 2001. "Coskewness and cokurtosis in futures markets," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 55-81, March.
    9. Werner Hürlimann, 2003. "General affine transform families: why is the Pareto an exponential transform?," Statistical Papers, Springer, vol. 44(4), pages 499-518, October.
    10. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    11. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
    12. Fischer, Matthias J. & Horn, Armin & Klein, Ingo, 2003. "Tukey-type distributions in the context of financial data," Discussion Papers 52/2003, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    13. Andreas Behr & Ulrich Pötter, 2009. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models," Annals of Finance, Springer, vol. 5(1), pages 49-68, January.
    14. Xu, Yihuan & Iglewicz, Boris & Chervoneva, Inna, 2014. "Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 66-80.
    15. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.

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