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A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution

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  • Su Xu

    (Anhui University of Science and Technology)

Abstract

In estimating VaR using the variance–covariance approach, the returns of a portfolio are commonly assumed to follow a Student t distribution rather than a normal distribution, given the Student distribution’s ability to capture more tail events. However, it is not clear to what measurable extent the Student t distribution is superior to the normal distribution in this exercise. This paper shows that the two assumptions do not produce significantly different VaR values when the degrees of freedom are greater than 4. This paper also determines a sigma threshold for the Student t distribution, which generally lies between 3 and 4 sigma’s when the degrees of freedom are greater than 4.

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  • Su Xu, 2017. "A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution," Risk Management, Palgrave Macmillan, vol. 19(3), pages 189-201, August.
    • Handle: RePEc:pal:risman:v:19:y:2017:i:3:d:10.1057_s41283-017-0017-9
    DOI: 10.1057/s41283-017-0017-9
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    1. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 203-214, June.
    2. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    3. Arnold Polanski & Evarist Stoja, 2011. "Dynamic density forecasts for multivariate asset returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(6), pages 523-540, September.
    4. Angelidis, Timotheos & Benos, Alexandros & Degiannakis, Stavros, 2004. "The Use of GARCH Models in VaR Estimation," MPRA Paper 96332, University Library of Munich, Germany.
    5. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    6. 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.
    7. Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December.
    8. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    10. Anonymous, 2009. "Abstract of the discussion," British Actuarial Journal, Cambridge University Press, vol. 15(1), pages 202-217, March.
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    Cited by:

    1. Nupur Moni Das & Bhabani Sankar Rout, 2024. "Equity Price Risk of Commercial Banks in India," Arthaniti: Journal of Economic Theory and Practice, , vol. 23(2), pages 179-201, December.

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