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Skewness in the conditional distribution of daily equity returns

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  • Richard Harris
  • C. Coskun Kucukozmen
  • Fatih Yilmaz

Abstract

The conditional distribution of asset returns is important for a number of applications in finance, including financial risk management, asset pricing and option valuation. In the GARCH framework, it is typically assumed that returns are drawn from a symmetric conditional distribution such as the normal, Student-t or power exponential. However, the use of a symmetric distribution is inappropriate if the true conditional distribution of returns is skewed. This study models the conditional distribution of daily returns in five international equity market indices and a world equity index using the skewed generalised-t (SGT) distribution, a distribution that allows for a very wide range of skewness and kurtosis, and which nests the three most commonly used distributions as special cases. It is shown that the use of a conditional SGT distribution offers a substantial improvement in the fit of both GARCH and EGARCH models. Moreover, for both models, the study strongly rejects the restrictions on the SGT that are implied by the normal, Student-t and power exponential distributions. With the GARCH specification, the conditional distribution is negatively skewed for all six series. However, for three of these series - namely the US, Japan and the World index - this skewness can be explained by leverage effects, which are captured by the EGARCH model. For the remaining three series - the UK, Canada and Germany - the skewness in the conditional distribution of returns remains even after allowing for leverage effects.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Financial Economics.

Volume (Year): 14 (2004)
Issue (Month): 3 ()
Pages: 195-202

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Handle: RePEc:taf:apfiec:v:14:y:2004:i:3:p:195-202

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References

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  1. Jenny N. Lye, 1998. "Parametric Distributional Flexibility and Conditional Variance Models with An Application to Hourly Exchange Rates," IMF Working Papers 98/29, International Monetary Fund.
  2. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
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  5. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
  6. 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.
  7. Lau, Amy Hing-Ling & Lau, Hon-Shiang & Wingender, John R, 1990. "The Distribution of Stock Returns: New Evidence against the Stable Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 217-23, April.
  8. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
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Cited by:
  1. C. J. Adcock, 2005. "Exploiting skewness to build an optimal hedge fund with a currency overlay," The European Journal of Finance, Taylor & Francis Journals, vol. 11(5), pages 445-462.
  2. Adcock, C.J. & Shutes, K., 2005. "An analysis of skewness and skewness persistence in three emerging markets," Emerging Markets Review, Elsevier, vol. 6(4), pages 396-418, December.
  3. Changli He & Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Parameterizing Unconditional Skewness in Models for Financial Time Series," Research Paper Series 169, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Thomas R. Allen Corns & Stephen E. Satchell, 2010. "Modelling conditional heteroskedasticity and skewness using the skew-normal distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 251-263.
  5. 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.
  6. José L. B. Fernandes & Augusto Hasman & Juan Ignacio Peña, 2006. "Risk Premium: Insights Over The Threshold," Working Papers Series 126, Central Bank of Brazil, Research Department.
  7. C. James Hueng, 2006. "Short-sales constraints and stock return asymmetry: evidence from the Chinese stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 707-716.

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