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Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the portolio returns.

The volatility of the portfolio is retrieved by building a variance-covariance matrix. However how do you get the volatility of each asset? Do you need to get historical returns for each asset? If that is the case then how is it easier to implement than historical VaR where full history is needed to reprice the portfolio?

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  • $\begingroup$ where did you get the easier part from? in what context is it easier? $\endgroup$
    – AK88
    Oct 31, 2018 at 23:06

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Yes, you would need historical returns for each asset to calculate a variance-covariance matrix.

I am not sure that people think using the variance-covariance matrix is "easier". As you point out, using historical returns makes it very simple to simulate the portfolio returns. On the other hand, there are various practical considerations that might make using a variance-covariance matrix more efficient. For example, the calculation of VaR is likely to be much quicker for equity portfolios since it just involves using simple matrix multiplication to calculate the variance ($=x'Vx$).

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  • $\begingroup$ Variance covariance VaR is also a coherent risk measure, which is often mathematically useful $\endgroup$
    – Attack68 ♦
    Dec 28, 2018 at 18:50
  • $\begingroup$ Attack68 I thought that VaR in general was not a coherent risk measure because it is not subadditive? $\endgroup$
    – tweedi
    Feb 5, 2019 at 11:36

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