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Performance & Risk Metrics

Marginal VaR

The incremental change in portfolio Value-at-Risk resulting from adding one unit of a given position or asset, measuring the marginal contribution of that holding to total portfolio risk.

Marginal VaR is the partial derivative of portfolio VaR with respect to a position's size: the rate at which total risk changes as you nudge that position up or down. Where Component VaR attributes risk that already exists, Marginal VaR is forward-looking, telling you the risk cost of the next dollar you put into a holding.

It can be computed parametrically (assuming joint normality) or non-parametrically (historical simulation, Monte Carlo). A high Marginal VaR warns that adding to a position would amplify tail risk out of proportion to its size, usually because it is correlated with what you already hold or because it is illiquid. That makes it the practical input for sizing the next trade.

Formula

wi
Weight or notional size of position i in the portfolio
\textVaR(\mathbfw)
Portfolio Value-at-Risk at confidence level (e.g., 95 percent, 99 percent) and time horizon
Sources: Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed. McGraw-Hill. · Dowd, K. (2007). Measuring Market Risk, 2nd ed. John Wiley & Sons. · Basel Committee on Banking Supervision. (2019). Minimum capital requirements for market risk. BCBS 457.