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Parametric Value at Risk


A value at risk (VaR) measure/ method that only uses two main variables or parameters as inputs: the mean and standard deviation of a portfolio. Additionally, the principal assumption that underlies calculation is that the portfolio’s returns are normally distributed (that is, follow normal distribution). The calculated standard deviation is used to derive a standard normal z score to size up the position with a confidence degree/ confidence level (according to a pre-determined table).

The normal distribution is used as a proxy for expected returns (return normality). Furthermore, the returns are premised to be serially independent: no prior return influences the return that is generated thereafter.

For example, if the two parameters for a portfolio were determined to be:

  • Standard deviation (in monetary terms): CU 100,000
  • Mean (in monetary terms): CU 40,000
  • Z Score for 95% confidence: 1.5

Assuming confidence was set at 95%, parametric VaR for the period is calculated as follows:

40,000 – 100,000 (1.5) = CU -110,000

This measure of VaR is also known as a variance/ covariance value at risk (variance/ covariance VaR).



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Comments


  • Adam Ozcan
    June 21, 2023 at 2:35 pm

    Hello, would you please explain where 40,000 come from in the equation above?

    • Fincyclopedia
      June 21, 2023 at 8:18 pm

      Hello, Adam. It represents the mean as given in the above example.

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