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# Incremental Value at Risk

## What Is Incremental Value at Risk?

Incremental value at risk (incremental VaR) is the amount of uncertainty added to or subtracted from a portfolio by purchasing or selling an investment. Investors use incremental value at risk to determine whether a particular investment should be undertaken, given its likely impact on potential portfolio losses.

The idea of incremental value at risk was developed by Kevin Dowd in his 1999 book, Beyond Value at Risk: The New Science of Risk Management. Incremental VaR is closely related to marginal VaR but differs from it.

### Key Takeaways

• Incremental value at risk is a measure of how much risk a particular position is adding to a portfolio.
• It's a risk assessment used by investors who are thinking of making a change to their holdings, by either adding or removing a particular position.
• Incremental value at risk is a variation in the value at risk measurement (VaR), which looks at the worst-case scenario for a portfolio as a whole in a specific period of time.

## Understanding Incremental Value At Risk

Incremental value at risk is based on the value at risk measurement (VaR), which attempts to calculate the likely worst-case scenario for a portfolio as a whole in a given time frame. The entire value at risk measurement tells the analyst the amount by which the entire portfolio might drop if the bear case plays out. Value at risk takes into account a time frame, a confidence level, and a loss amount or percentage.

Value at risk is calculated by either using the historical method, which looks at historical returns to predict future behavior, the variance-covariance method, which looks at the average or expected return on investment and the standard deviation, or the Monte Carlo simulation, in which a model is developed for future stock price returns and hypothetical trials are repeatedly run through the model.

## Calculating Incremental Value at Risk

Incremental value at risk just looks at an investment individually and analyzes how much the addition of that single investment to the total portfolio might cause the portfolio to rise or fall in value. It is a precise measurement, as opposed to marginal value at risk, which is an estimation of 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 particular asset in question's rate of return and portfolio share.

## Applying the Incremental Value at Risk

For example, if you calculate that the incremental value at risk of Security ABC is positive, then either adding ABC to your portfolio or if you already hold it, increasing how many shares you hold of ABC within your portfolio will increase the portfolio's overall VaR. Similarly, if you calculate the VaR of Security XYZ and it is negative, then adding it to your portfolio or increasing your holdings will lower the overall portfolio's VaR. The same idea applies and the same calculation can be put to use if you are considering removing one particular security from your portfolio.

## 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 the 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.

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