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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.

Suggested Citation

  • 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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