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Marginal VaR

The incremental VaR contributed by adding one more unit of a position.

Marginal VaR measures how much portfolio VaR changes when you add $1 (or 1 unit) of a specific position. It answers: 'If I increase my Apple position by $1M, how much does my portfolio VaR increase?' Use: Risk budgeting — allocate risk to positions with the best return-per-unit-of-marginal-risk. Diversification insight: Marginal VaR can be negative—adding a position that's negatively correlated with the portfolio reduces total VaR. For example, adding bonds to a stock portfolio might have negative marginal VaR due to diversification. Component VaR: Marginal VaR × Position Size = Component VaR (each position's contribution to total VaR). Sum of all component VaRs = Total Portfolio VaR.

Formula
Marginal VaR=∂VaR∂wi\text{Marginal VaR} = \frac{\partial \text{VaR}}{\partial w_i}