Although the VaR became a very popular assessment of risk, it is not a problem-free solution also. First, it is not always possible to compare the VaR measured by historical and simulation approaches. They may often be fairly different, as demonstrated by numerous studies.

Therefore, using the VaR in practice requires valuation of the precision of the estimated VaR. Unfortunately, the existing methods of gauging VaR accuracy make their application in practice rather complex.

Second, the VaR exhibits some undesirable properties such as lack of risk aggregation. Artzner and Delbaen (1998) show that the VaR of a portfolio may be greater than the sum of individual components’ VaR; therefore, in some cases, the original VaR framework prevents diversification. This problem was addressed by Uryasev (2000), who suggested the Conditional VaR (CVaR) as an alternative solution.

Third, the original or normal VaR interpretation is uninformative about the extreme tail losses beyond VaR. In other words, it cannot answer the question of the potential loss exceeding VaR.

Fourth, the Normal VaR presents a non-convex multiextreme function; therefore, in contrast to the mean-variance risk measures, it requires complex global optimization techniques, when finding the optimal weights of portfolio’s elements.