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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

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.

Suggested Citation

  • Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-472, October.
  • Handle: RePEc:ucp:jnlbus:v:61:y:1988:i:4:p:451-72
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    References listed on IDEAS

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    1. Simon Benninga & Marshall Blume, "undated". "On the Optimality of Portfolio Insurance," Rodney L. White Center for Financial Research Working Papers 5-85, Wharton School Rodney L. White Center for Financial Research.
    2. Sanford J. Grossman, 1977. "The Existence of Futures Markets, Noisy Rational Expectations and Informational Externalities," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 431-449.
    3. Benninga, Simon & Blume, Marshall E, 1985. " On the Optimality of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 40(5), pages 1341-1352, December.
    4. Simon Benninga & Marshall Blume, "undated". "On the Optimality of Portfolio Insurance," Rodney L. White Center for Financial Research Working Papers 05-85, Wharton School Rodney L. White Center for Financial Research.
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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. Christie-David, Rohan & Chaudhry, Mukesh, 2001. "Coskewness and cokurtosis in futures markets," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 55-81, March.
    3. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 875-886, November.
    4. Georges Hübner & Thomas Lejeune, 2015. "Portfolio choice and investor preferences : A semi-parametric approach based on risk horizon," Working Paper Research 289, National Bank of Belgium.
    5. Lars Forsberg & Anders Eriksson, 2004. "The Mean Variance Mixing GARCH (1,1) model," Econometric Society 2004 Australasian Meetings 323, Econometric Society.
    6. Lakshman A. Alles & John L. Kling, 1994. "Regularities In The Variation Of Skewness In Asset Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(3), pages 427-438, September.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. repec:sbe:breart:v:19:y:1999:i:1:a:2795 is not listed on IDEAS
    16. Chen Yi-Ting & Lin Chang-Ching, 2008. "On the Robustness of Symmetry Tests for Stock Returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-40, May.
    17. 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.
    18. 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.
    19. 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.

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