What it means
Value at risk, or VaR, estimates a loss threshold over a stated period at a stated confidence level. A portfolio manager might report a one-day 95% VaR of $2 million, meaning the model estimates losses exceed $2 million on roughly 5% of comparable days.
That statement does not describe how large losses beyond the threshold might be. Marginal VaR asks what happens to that portfolio number when a holding changes a little: add a small position, rerun the risk model and compare the total with the earlier result.
The difference, scaled to the position change, is a local estimate of its risk contribution. It is not the same as the holding's stand-alone VaR.
Correlation explains why, since two assets may each swing widely but move in opposite directions, so combining them can reduce portfolio risk. Conversely several apparently different assets can all fall together in stress.
Academic portfolio-risk work treats marginal contributions as properties of the complete portfolio and its estimated dependence structure. The measure supports limits and pricing: a treasury can ask how much an added currency hedge changes its total risk, or a fund can compare which holding consumes more of a VaR budget.
A trading desk may seek higher expected return for positions that add more risk at the margin. This helps allocate scarce risk capacity rather than treating every line item separately.
Marginal does not mean permanent, because a derivative position can have a very different effect after the market moves, and correlations estimated in calm periods can fail in a panic. VaR also says little about the severity of losses past its chosen threshold.
Test scenarios and liquidity needs alongside the number, and never present it as a worst-case loss. For a non-finance owner, the practical question is simple: will this next investment make our total position more fragile or more balanced?
An adviser should show both the portfolio before and after, state the horizon and confidence level, and explain the scenarios in which the estimate breaks down.
In practice
Real-world examples.
Example
A fund holds many exporters vulnerable to a stronger domestic currency. A small position that gains when the currency strengthens may have positive stand-alone risk yet lower the fund's total VaR.
Example
A bank adds another loan to the same industry as its existing book. The new loan looks modest alone, but concentrated exposure makes its marginal portfolio risk substantial.
Example
A treasurer compares two hedges that cost the same. One cuts modelled VaR more, but the other protects a severe cash-flow scenario the model misses, so she reports both views to the board.
Formula
Calculation
Approximate marginal VaR for holding i = change in portfolio VaR / small change in holding i's size. For a finite proposed trade, incremental VaR = portfolio VaR after trade minus portfolio VaR before trade. The two are related but not identical when risk changes nonlinearly.
Worked example. An invented portfolio has a one-day 95% VaR of $2,000,000. Adding a $1,000,000 position in a new asset, whose stand-alone VaR would be $80,000, lifts the modelled portfolio VaR to $2,050,000.
- Incremental VaR = $2,050,000 - $2,000,000 = $50,000, lower than the stand-alone $80,000 because part of the new asset's movement offsets existing holdings.
- A $500,000 hedge instead lowers the modelled portfolio VaR to $1,970,000, an incremental VaR of $1,970,000 - $2,000,000 = -$30,000, so it reduces total risk even though the hedge has a stand-alone VaR of its own.Case study
Seen in the real world.
Fictional example: Oriole Imports, a fictional electronics wholesaler, held cash in three currencies and had supplier payments due in a fourth. Its adviser suggested adding a currency fund for diversification, quoting the fund's own low VaR. Oriole's finance manager modelled the total cash and payment exposures before and after the purchase. The fund moved with two currencies the firm already held and raised total VaR rather than reducing it.
A smaller forward contract against the supplier payment lowered the modelled risk and protected a specific cash deadline. Management also tested an extreme exchange-rate jump, since past correlations might not hold. The board chose the forward for the payment and declined the fund, recording both the marginal VaR and the stress scenario. The useful insight was portfolio context, not a claim that one statistical number had captured every danger.
Watch out
Common mistakes.
- Treating an asset's stand-alone VaR as its contribution to a diversified portfolio.
- Describing VaR as the maximum possible loss instead of a modelled threshold at a defined horizon and confidence level.
- Trusting correlations estimated in calm markets without stress tests for concentration, liquidity and tail events.
Questions
People also ask.
Can marginal VaR be negative?
Yes. A small position that offsets other holdings can reduce the portfolio's modelled VaR, even though the position has its own risk.
How is it different from incremental VaR?
Marginal VaR describes a local change per small unit of position. Incremental VaR compares the portfolio before and after a particular proposed trade, which may be large enough for nonlinear effects.
What information should I request with the number?
Ask for the model's time horizon, confidence level, holdings and correlation assumptions, plus a stress test of losses beyond the VaR threshold.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related