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Heavy-tailed Distributions and Risk Management of Equity Market Tail Events

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  • Zi-Yi Guo

Abstract

Traditional econometric modelling typically follows the idea that market returns follow a normal distribution. However, the concept of tail risk indicates that the distribution of returns is not normal, but skewed and has heavy tails. Thus, a heavy-tailed distribution, which accurately estimates the tail risk, would significantly improve quantitative risk management practice. In this paper, we compare four widely used heavy-tailed distributions using the S&P 500 daily returns. Our results indicate that the Skewed t distribution in Hansen (1994) has the superior empirical performance compared with the Student’s t distribution, the normal reciprocal inverse Gaussian distribution and the generalized hyperbolic distribution. We further showed the Skewed t distribution could generate the VaR estimates closest to the nonparametric historical VaR estimates compared with other heavy-tailed distributions.

Suggested Citation

  • Zi-Yi Guo, 2017. "Heavy-tailed Distributions and Risk Management of Equity Market Tail Events," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 31-41.
  • Handle: RePEc:rmk:rmkjrc:v:4:y:2017:i:1:p:31-41
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    References listed on IDEAS

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    1. Anders Wilhelmsson, 2009. "Value at Risk with time varying variance, skewness and kurtosis--the NIG-ACD model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 82-104, March.
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    5. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    7. Lesedi Mabitsela & Eben Maré & Rodwell Kufakunesu, 2015. "Quantification of VaR: A Note on VaR Valuation in the South African Equity Market," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 8(1), pages 1-24, February.
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    Cited by:

    1. Naeem, Muhammad & Shahbaz, Muhammad & Saleem, Kashif & Mustafa, Faisal, 2019. "Risk analysis of high frequency precious metals returns by using long memory model," Resources Policy, Elsevier, vol. 61(C), pages 399-409.
    2. Jianhua Ding & Turen Guo & Bin Guo, 2018. "Fat Tails, Value at Risk, and the Palladium Returns," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 7(2), pages 95-103, May.

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    More about this item

    Keywords

    Tail risk; Value at Risk; Goodness of fit.;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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