The value at risk (VaR) that is attributed to a given component of a portfolio. For a portfolio where VaR that is derived under the assumption of normality, the portfolio risk can be decomposed into the risks associated with each component of the portfolio. More specifically, VaR can be decomposed in a financially meaningful manner into the risk contributions made by the portfolio holdings, each considered separately, and all as part of the entire portfolio.

Portfolio decomposition may involve multiple bases including sectors, trades, instrument type, sub-portfolios as long as component weights can be properly attributed. Decomposition of the estimated portfolio VaR is not only beneficial for risk analysis, but it can also be applied in areas such as portfolio construction, where a number of analytical measures may be used to construct portfolios subject to specific constraints on such measures.