Direct Answer
Marginal VaR is the rate of change of portfolio Value at Risk with respect to a small increase in one position's size. Under a normal model it is proportional to the position's covariance with the portfolio. A larger marginal VaR means a bit more of that position raises tail risk faster.
Marginal VaR: Formula, Meaning, Signals, Examples and How to Use It
How Is Marginal VaR Calculated?
Marginal VaR is the rate of change of portfolio Value at Risk with respect to a small increase in one position's size. Under a normal model it is proportional to the position's covariance with the portfolio.
Formula: MVaR_i = dVaR/dw_i = z x cov(r_i, r_p) / sigma_p (parametric normal, zero mean)
Inputs:
- Z-score for the confidence level (about 1.65 for 95% one-tailed)
- Covariance of the position with the portfolio
- Portfolio volatility
- Horizon
Worked example. With z = 1.65, a position covariance with the portfolio of 0.018 and portfolio volatility of 12%, the marginal VaR is 24.75% of value per unit of weight. The inputs are illustrative numbers, not market data.
Reading it. A larger marginal VaR means a bit more of that position raises tail risk faster. Weight times marginal VaR gives component VaR. It differs from incremental VaR, which measures a finite change, not an infinitesimal one.
Limits. The formula shown assumes normal returns and a stable covariance matrix, which understates fat tails. It is a local approximation and loses accuracy for large position changes.
What is Marginal VaR?
Marginal VaR is the rate of change of portfolio Value at Risk with respect to a small increase in one position's size. Under a normal model it is proportional to the position's covariance with the portfolio.
How to use Marginal VaR
A larger marginal VaR means a bit more of that position raises tail risk faster. Weight times marginal VaR gives component VaR. It differs from incremental VaR, which measures a finite change, not an infinitesimal one. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- The z-score times covariance over portfolio volatility makes the marginal figure additive in the normal model, which supports a clean decomposition.
- It translates a position's covariance with the portfolio into a loss threshold, so each holding can be ranked by its effect on VaR.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- It tells how VaR would change for a tiny increase, but its size shifts whenever the portfolio's composition changes.
- The confidence level scales every marginal figure by the same z-score, so rankings do not change across confidence levels while magnitudes do.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Marginal VaR a buy or sell signal?
No. A larger marginal VaR means a bit more of that position raises tail risk faster. The formula shown assumes normal returns and a stable covariance matrix, which understates fat tails. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Marginal VaR?
Marginal VaR is computed from z-score for the confidence level (about 1.65 for 95% one-tailed); covariance of the position with the portfolio; portfolio volatility, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner.
Can Marginal VaR be used by itself?
The formula shown assumes normal returns and a stable covariance matrix, which understates fat tails. It is a local approximation and loses accuracy for large position changes. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Marginal VaR work on every timeframe?
The calculation (MVaR_i = dVaR/dw_i = z x cov(r_i, r_p) / sigma_p (parametric normal, zero mean)) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Marginal VaR give false signals?
It tells how VaR would change for a tiny increase, but its size shifts whenever the portfolio's composition changes. The confidence level scales every marginal figure by the same z-score, so rankings do not change across confidence levels while magnitudes do. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Marginal VaR be backtested?
Rebuild Marginal VaR from z-score for the confidence level (about 1.65 for 95% one-tailed) using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.