It is well know that VaR is not subaddtive measure which means that condition
$$ \text{VaR}(X+Y) \leq \text{VaR}(X) + \text{VaR}(Y), $$
where $X$ and $Y$ are portfolios, is not satisfied. As a result, in some cases a simple division of portfolio to its subportfolios can lead to lower risk. Especially for this feature, VaR was criticised and subadditive measures like CVaR were introduced.
My question are:
- If VaR has so conterintuitive and unrealistic feature like not being subadditive, why is it still used?
- In which cases can we neglect that VaR is not subadditive?