## What Is Marginal VaR?

Marginal VaR refers to the additional amount of risk that a new investment position adds to a firm or portfolio. Marginal VaR allows risk managers to study the effects of adding or subtracting positions from an investment portfolio.

Since value at risk (VaR) is affected by the correlation of investment positions, it is not enough to consider an individual investment's VaR level in isolation. Rather, it must be compared with the total portfolio to determine what contribution it makes to the portfolio's VaR amount.

### Key Takeaways

• Marginal VaR computes the incremental change in aggregate risk to a firm or portfolio due to adding one more investment.
• Value at risk (VaR) models the probability of a loss for a firm or portfolio based on statistical techniques.
• Marginal VaR allows risk managers or investors to understand how new investments will alter their VaR picture.

## Understanding Marginal VaR

Value at risk (VaR) is a statistical technique that measures and quantifies the level of financial risk within a firm, portfolio, or position over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios. Risk managers use VaR to measure and control the level of risk exposure. One can apply VaR calculations to specific positions or whole portfolios or to measure firm-wide risk exposure.

An individual investment may have a high VaR individually, but if it is negatively correlated to the portfolio, it may contribute a much lower amount of VaR to the portfolio than its individual VaR.

When measuring the effects of changing positions on portfolio risk, individual VARs are not adequate, because volatility measures the uncertainty in the return of an asset in isolation. As part of a portfolio, what matters is the asset's contribution to portfolio risk. Marginal VaR helps isolate added security-specific risk from adding an additional dollar of exposure.

## Example of Marginal VaR

For example, consider a portfolio with only two investments. Investment X has a value at risk of \$500, and investment Y has a value at risk of \$500. Depending on the correlation of investments X and Y, putting both investments together as a portfolio might result in a portfolio value at risk of only \$750. This means that the marginal value at risk of adding either investment to the portfolio was \$250.

## Marginal VaR vs. Incremental VaR

The incremental VaR is sometimes confused with the marginal VaR. Incremental VaR tells you the precise amount of risk a position is adding or subtracting from the whole portfolio, while marginal VaR is just an estimation of the change in total amount of risk. Incremental VaR is thus a more precise measurement, as opposed to marginal value at risk, which is an estimation using mostly the same information. To calculate the incremental value at risk, an investor needs to know the portfolio's standard deviation, the portfolio's rate of return, and the asset in question's rate of return and portfolio share.