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The Empirical Distribution of UK and US Stock Returns


  • Richard D. F. Harris

    (University of Exeter)

  • C. Coskun Küçüközmen

    (University of Exeter)


There is now substantial evidence that daily equity returns are not normally distributed but instead display significant leptokurtosis and, in many cases, skewness. Considerable effort has been made in order to capture these empirical characteristics using a range of "ad hoc" statistical distributions. In this paper, we investigate the distribution of daily, weekly and monthly equity returns in the UK and US using two very flexible families of distributions that have been recently introduced: the exponential generalised beta (EGB) and the skewed generalised-"t" (SGT). These distributions permit very diverse levels of skewness and kurtosis and, between them, nest many of the distributions previously considered in the literature. Both the EGB and the SGT provide a very substantial improvement over the normal distribution in both markets. Moreover, for daily returns, we strongly reject the restrictions on the EGB and SGT implied by most of the distributions that are commonly used for modelling equity returns, including the student-"t", the power exponential and the logistic distributions. Instead, our preferred distributions for daily returns are the generalised-"t" for the US and the skewed-"t" for the UK, both of which are members of the SGT family. For weekly returns, our preferred distributions are the student-"t" for the UK and the skewed-"t" for the US, while for monthly returns, our preferred distributions are the EBR12 for the UK and the logistic for the US. We consider the implications of our findings for the implementation of value-at-risk, a risk management methodology that rests heavily on the distributional characteristics of returns. Copyright Blackwell Publishers Ltd 2001.

Suggested Citation

  • Richard D. F. Harris & C. Coskun Küçüközmen, 2001. "The Empirical Distribution of UK and US Stock Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(5-6), pages 715-740.
  • Handle: RePEc:bla:jbfnac:v:28:y:2001-06:i:5-6:p:715-740

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    Cited by:

    1. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    2. Fabio Pizzutilo, 2012. "Use of the Pearson System of Frequency Curves for the Analysis of Stock Return Distributions: Evidence and Implications for the Italian Market," Economics Bulletin, AccessEcon, vol. 32(1), pages 272-281.
    3. Konstantinos Tolikas, 2011. "The rare event risk in African emerging stock markets," Managerial Finance, Emerald Group Publishing, vol. 37(3), pages 275-294, February.
    4. Cheng, Wan-Hsiu & Hung, Jui-Cheng, 2011. "Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 160-173, January.
    5. Richard Harris & C. Coskun Kucukozmen & Fatih Yilmaz, 2004. "Skewness in the conditional distribution of daily equity returns," Applied Financial Economics, Taylor & Francis Journals, vol. 14(3), pages 195-202.
    6. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    7. repec:eee:empfin:v:43:y:2017:i:c:p:1-32 is not listed on IDEAS
    8. Jan Bulla, 2010. "Hidden Markov models with t components. Increased persistence and other aspects," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 459-475.
    9. BenSaïda, Ahmed, 2015. "The frequency of regime switching in financial market volatility," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 63-79.
    10. Arnold Polanski & Evarist Stoja, 2010. "Incorporating higher moments into value-at-risk forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(6), pages 523-535.

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