Marginal VaR

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21 Aug, 2024

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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.

What Is Marginal VaR?

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 Explained

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.

Examples

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.

Marginal VaR vs Incremental VaR

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.

Points	Marginal VaR	Incremental VaR
Concept	It measures the increase in risk resulting from a new investment position within a firm or portfolio.	Incremental VaR quantifies and measures the change in VaR when an additional stock is added to the portfolio.
Purpose	This offers an evaluation of the total risk change.	Incremental VaR provides an exact measure of how much risk a position contributes to or reduces from the overall portfolio.
Calculation	To compute the value, subtract the original VaR from the VaR after incorporating the incremental risk unit.	To calculate incremental VaR, investors require information on the portfolio's rate of return, standard deviation, and the respective asset's rate of return and portfolio allocation.

Marginal VaR vs Component VaR

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

Points	Marginal VaR	Component VaR
Points	Marginal VaR	Component VaR
Concept	It evaluates the change in portfolio VaR when a new unit of risk is incorporated.	Component VaR estimates the change due to the contribution of each of the assets or components to the total portfolio VaR. The concept of component VaR is connected to marginal VaR. Component VaR can be understood as VaR expressed in monetary terms.
Purpose	It assists investors in evaluating the impact of overall changes in risk on portfolio performance.	Component Value at Risk (CoVaR) is valuable for setting position limits, making investment decisions, and determining capital requirements. It highlights which positions represent significant risks and which positions are hedges.
Calculation	Marginal VaR calculation is calculated by comparing the portfolio VaR before and after, including an additional unit of risk.	Component VaR is calculated by determining the weight of the position being removed from the portfolio.

Frequently Asked Questions (FAQs)

1. What is the difference between conditional VaR and marginal VaR?

Conditional Value at Risk (CVaR) quantifies the expected losses that can be seen beyond the VaR breakpoint. On the other hand, marginal value at risk quantifies the change in value at risk when an additional unit of risk is added to or deducted from a portfolio.

2. How does marginal VaR affect portfolio performance?

Through insights into the effects of adding or reducing risk from the portfolio, it influences portfolio performance. It supports investors in determining how much overall risk may rise and in making well-informed choices on portfolio construction, risk allocation, and risk management techniques.

3. What is the marginal VaR calculation?

It is a measure of risk that is calculated by subtracting the initial value at risk (Ivar) from the total VaR (Tvar). To calculate the marginal value at risk, first determine the total VaR, then the initial value at risk. Then, use the formula MVaR = Tvar – Ivar.