Incremental VaR

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21 Aug, 2024

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Incremental Value At Risk (iVaR) refers to the extent of positive or negative risk change added to an investment portfolio whenever one trades a security. Investors can use it to examine the potential outcomes of changing the composition of an asset in their portfolio.

It allows one to assess how various assets impact the overall risk profile. It aids in evaluating whether the newly added risk outweighs potential gains. Investors use it in estimating accurate portfolio additional risk and precise calculation, making informed decisions regarding risk mitigation planning and portfolio allocation.

Incremental VaR Meaning

Incremental Value at Risk (iVaR) gauges the risk impact of adding or removing an investment from an investment portfolio.
It helps investors assess if a potential investment aligns with their risk tolerance by measuring its influence on potential portfolio losses.
It is essential because it offers portfolio optimization, risk diversification, and capital allocation.
Incremental VaR acts like a scale, precisely measuring the risk change caused by a slight tweak in your portfolio; in contrast, marginal VaR paints a broader picture, revealing the total risk shift if you altogether remove a particular investment.

Incremental VaR Explained

Incremental VaR definition refers to a metric of risk attribution telling investors the extent of risk in a sub-portfolio or a position to bring into a portfolio, which can be either negative or positive. If a position has a positive iVaR value, then increasing the magnitude of the position will enhance the VaR of the portfolio. Similarly, if a position has a negative value, then any slight increase in the magnitude of the position would lower the portfolio risk.

Incremental Value at Risk (VaR) is an important risk management tool that quantifies potential losses for organizations when adding or removing assets from a portfolio.

There are several reasons why incremental VaR is necessary:

1. Portfolio Optimization: It aids in portfolio optimization by assessing the impact of asset addition or removal, enabling informed investment strategy decisions.

2. Risk Diversification: Organizations can find opportunities to lower overall risk through diversification by evaluating the benefits of adding new assets to their portfolios with the aid of incremental VaR.

3. Capital Allocation: Organizations can optimize capital allocation by identifying assets with the highest risk impact, allowing for modification of capital and resource allocations to reduce risk exposure.

Understanding how individual assets contribute to overall portfolio risk allows firms to optimize portfolios, make more informed decisions, and allocate capital more effectively. Incremental value at risk (VaR) is a critical tool in risk management.

Examples

Let us assume a few examples to understand the topic.

Example #1

Let us assume Alex has a portfolio with stocks A, B, & C with a total VaR of $1,000. Alex wants to add new stock D to his portfolio but is still determining if it will be good or bad. As a result, he calculates the VaR of the new portfolio. After calculation, he gets the new VaR of his portfolio as $1,200.

As a result, the incremental VaR for the portfolio would be 1,200-1,000 = $200. It means that if Alex adds D to his portfolio, then it will increase his risk by $200. Therefore, Alex decided to leave it off of his portfolio. Hence, investors use this method to keep their portfolios in the lowest risk zone.

Example #2

A research paper published on March 24, 2020 has highlighted the use of iVaR in predicting operational risk capital in the future. IVaR has a basis for the differences in data among the consecutive or continuous capital calculations. Hence, it can be easily used in predicting the short-term VaR or in the validation of pre-calculated capital values.

The methodology involved creating artificial data using Bayesian analysis just after the capital calculation. As a result, it gets used like a container for accurate data. After that, the capital gets estimated and coordinated based on the quantile distribution. Moreover, the iVaR method has the assumption of data homogeneity and can reach up to a 5% accuracy level for a single month ahead prediction of operational risk.

Incremental VaR vs Marginal VaR

Both of them measure the degree of a position or sub-portfolio contribution to overall VaR, but they have inherent differences, as listed below in the table:

Incremental Var	Marginal Var
It indicates precisely the net impact on the overall VaR of a portfolio by a slight change in position.	Marginal VaR explains the level of change in the overall VaR of the portfolio if the entire position is removed.
It accurately measures the change in the overall degree of risk.	It just gives an estimate of the change in the complete value risk of a portfolio.
Optimizes risk management and portfolio structure	Manages risk efficiently and identifies optimal portfolio allocations.

Frequently Asked Questions (FAQs)

How to calculate the incremental VaR?

To calculate incremental VaR (IVaR), one has to subtract the VaR of the portfolio before adding any new position from the VaR of the portfolio after the summation. As a result, the difference so obtained represents the change of risk owing to new positions.

Is incremental VaR additive?

No, the incremental VaR is not basically additive. Actually, the addition of VaRs for every position does not necessarily equal the overall VaR change. It is because of portfolio diversification and correlation effects, even if it quantifies the risk variation for a specific position.

What is the difference between conditional VaR and incremental VaR?

Conditional VaR quantifies the average loss severity one would suffer if the loss exceeded the predetermined risk level or VaR. On the other hand, incremental risk (VaR) determines the effect of addition, removal, or adjustment of investment position.