Marginal VaR

Marginal VaR, or Marginal Value at Risk, measures how a component's or asset’s addition or deletion affects a portfolio's value. This metric measures the amount of financial risk associated with a company, portfolio, or position over a given time frame (horizon). It isolates marginal risk.

It is a tool that assists investors in maximizing risk-adjusted returns by highlighting investments with the greatest growth potential. This risk-adjusted return helps investors maximize their returns by enabling them to make well-informed decisions and guaranteeing asset diversification. Essentially, it facilitates the comparison of returns across several assets with varied degrees of risk.

• The Marginal VaR (Value at Risk) shows how the risk of a portfolio will fluctuate depending on how much money is put into a particular financial instrument.
• It also aids in risk management by identifying significant shifts in the portfolio's risk profile, enabling investors to make risk-aware decisions. However, the primary goal of marginal VaR calculation is to manage risk effectively, not just calculate it.
• Marginal VaR formula = Total VaR (TvaR) – Initial VaR (IvaR)
• Marginal, Component, and Incremental Value at Risk (VaR) are crucial tools for market risk managers to understand the root cause of market risk.

Marginal VaR (Value at Risk) calculates the impact of eliminating or adding a single position from the portfolio on the overall VaR. It records the shift in a portfolio's value that is exposed to risk whenever a dollar is added to or removed from the portfolio. This measure shows the amount of risk added to or deducted from the overall portfolio by the given amount of change for each alteration in the dollar composition. It helps measure the risk when new or additional exposures are introduced to a portfolio.

It assists in figuring out the best way to distribute risk among investments by evaluating the relative risk impact of various assets or strategies. To determine the best way to distribute risk among investments, it is helpful to evaluate the relative risk impact of various assets or strategies. It measures the extent of change seen in VaR when the position size of a specific asset in the portfolio changes.

Additionally, it helps with risk management by pointing out crucial moments when the risk profile of the portfolio drastically shifts. This allows investors to make risk-aware choices that are in line with their risk tolerance and investment goals.

The Value at Risk (VaR) model is useful, but its main objective is not to calculate risk; rather, it is to manage risk effectively. For example, an organization may need to sell off a portion of its portfolio to lower overall risk if the VaR model produces an unsatisfactory result. Hence, the risk characteristics of sub-portfolios inside the portfolio must be measured to decide which portion should be divested, guaranteeing the optimal choice for the firm.

Marginal VaR captures and reflects the change seen in the value of a portfolio when exposed to risks introduced due to adding or deleting assets from a portfolio. Let us study a few examples to understand this better.

Example #1

Suppose Debbie is an investor who uses Marginal VaR to determine stock selection. She has a portfolio with a VaR of $200,000. Debbie considers adding a unit of risk to the portfolio, and the VaR of the portfolio after the addition becomes $500,000.

Based on the provided information, the Marginal VaR can be calculated as follows:

Total VaR (TvaR) = $500,000

Initial VaR (IvaR) = $200,000

Marginal VaR formula = TvaR - IvaR

= $500,000 - $200,000

= $300,000

Therefore, in this case, the Marginal VaR would be $300,000. With this, Debbie has more data to make informed decisions.

Example #2

A research-based study suggested evaluating an asset's suitability for inclusion in a managed portfolio by applying the marginal VaR method. This was a proposed metric, which was applied to a larger index with more assets included in it than the benchmark index. Also, the larger index covered all the assets that the benchmark index held.

Empirical testing was initiated on the S&P Bombay Stock Exchange (S&P BSE) 100 as the benchmark and the S&P BSE 200 for the MVaR index across five optimization problems involving specific decision variables. This test demonstrated that using the MVaR analysis to ascertain asset selection improves the performance of the managed portfolio and proves better than employing the original benchmark index assets.

Example #3

In a Moody’s Analytics paper, various methods and metrics for asset portfolio performance analysis were discussed. It highlighted the importance of using both credit and market risk parameters to assess the performance of a portfolio over a given period. 

One of the aspects the paper explored was how combining credit and market Value-at-Risk (VaR) factors to form an Aggregate VaR requires a correlation parameter, which can help understand how credit and market VaRs move. This is likely to enable investors, portfolio managers, and traders to better understand the interactions between credit and market risks before deriving any specific conclusions.

Both marginal and incremental VaR help investors, portfolio managers, and traders assess the effects of portfolio changes. Incremental VaR may offer a more accurate assessment compared to marginal VaR, which relies on similar information for estimation. However, for optimum results, analyzing changes using both approaches is recommended. The differences between these concepts have been tabulated below.

Marginal and component VaR throw light on how individual assets affect portfolio risk. The differences between these concepts are listed below.

This article has been a guide to what is Marginal VaR. Here, we compare it with incremental and component VaRs, and explain its examples. You may also find some useful articles here -

• Risk-Neutral Probability
• Risk Reduction
• Risk Categories