As a risk metric, value at risk (VaR) does lack subadditivity, i.e., it is not subadditive (does not support the subadditivity condition). Differently put, this risk measure does not support the condition that risks can be reduced by diversification (of a portfolio/ holdings/ etc.). No matter the level of diversification, risk will not get reduced even if this looks counterintuitive. Excluding subadditivity, VaR satisfies a host of key conditions such as homogeneity, monotonicity, and risk free condition.

Lack of subadditivity can drive financial institutions into application difficulties, particularly when using VaR to rank investment choices or set limits on traders, etc. An institution is likely to take on excess risk, or ignore much-needed hedging.

From a regulatory perspective, lack of subadditivity might result in a situation where institutions hold less capital than practically required.