Although Value at Risk (VaR) has become one of the most widely used measures of financial risk, it is not without important limitations.
First, VaR estimates can vary significantly depending on the methodology used. Results derived from historical data and those obtained via simulation approaches are not always directly comparable and may differ materially, as demonstrated in numerous empirical studies. As a result, practical use of VaR requires careful assessment of the precision and reliability of the estimate. However, existing techniques for evaluating VaR accuracy are often complex and can be difficult to implement in real-world settings.
Second, VaR exhibits certain undesirable theoretical properties, most notably a lack of subadditivity (i.e., risk aggregation). As shown by Artzner and Delbaen (1998), the VaR of a portfolio can exceed the sum of the VaRs of its individual components. This counterintuitive outcome implies that diversification may not always reduce measured risk within the traditional VaR framework. To address this issue, Uryasev (2000) introduced Conditional Value at Risk (CVaR) as a more coherent alternative.
Third, standard VaR provides no information about the magnitude of losses beyond the VaR threshold. In other words, it does not capture the severity of extreme tail losses and cannot answer the question: how large can losses be once VaR is breached?
Finally, under typical assumptions (e.g., normality), VaR leads to a non-convex, multi-extremal optimization problem. Consequently, unlike mean-variance frameworks, portfolio optimization based on VaR often requires more advanced global optimization techniques to identify optimal asset allocations.