What it means
A stand-alone risk number for a new trade can be misleading, because the trade does not sit in isolation. If it moves in the opposite direction to existing holdings, it can actually reduce total risk.
If it moves in line with them, the combined risk can be close to the sum of the parts. IVaR captures that interaction by comparing two numbers: the portfolio VaR with the position and the portfolio VaR without it.
The difference is the incremental contribution, and it can be positive, zero or negative. The key driver is correlation, which measures how closely two investments move together on a scale from -1 to 1.
A low or negative correlation means diversification, so the incremental risk is smaller than the stand-alone risk. A high correlation means the new position adds nearly its full risk on top of what is already there.
Banks, asset managers and trading desks use IVaR before approving a trade, when setting position limits, and when deciding which holding to sell to reduce risk most efficiently. It is particularly useful for choosing between two attractive trades when only one can fit within the limit.
Like all VaR measures, IVaR depends on the model, the confidence level and the time horizon chosen, and it says nothing about losses beyond the VaR threshold. It also changes as markets and correlations move, so it must be recalculated regularly rather than set once.
In practice
Real-world examples.
Example
An equity fund manager wants to add a $20,000,000 position in a technology company. The risk team calculates that, because the fund already holds many similar stocks, the incremental VaR is almost the same as the stand-alone VaR, and the manager chooses a smaller position.
Example
A bank's trading desk holds a large amount of fuel price exposure and is offered an airline hedge. The hedge moves in the opposite direction to the fuel positions, so IVaR is negative and the desk adds the trade because it reduces total risk.
Example
A pension fund's chief risk officer must cut risk by 10%. She ranks every holding by IVaR and sells the ones with the highest incremental contribution, rather than simply selling the largest positions.
Formula
Calculation
IVaR = VaR of portfolio with the position - VaR of portfolio without the position
For a parametric approach, portfolio VaR = z x portfolio volatility, where z is a statistical multiplier for the confidence level (about 1.65 for 95%).
An existing portfolio has daily dollar volatility of $1,000,000, so its VaR is 1.65 x 1,000,000 = $1,650,000. A new position has daily dollar volatility of $400,000 and a correlation of 0.25 with the portfolio. Combined variance = 1,000,000^2 + 400,000^2 + 2 x 0.25 x 1,000,000 x 400,000 = 1,360,000,000,000, so combined volatility is about $1,166,190 and combined VaR is 1.65 x 1,166,190 = about $1,924,000. IVaR is therefore about 1,924,000 - 1,650,000 = $274,000, compared with a stand-alone VaR of 1.65 x 400,000 = $660,000.Case study
Seen in the real world.
Clearwater Capital is an illustrative, fictional investment firm with a daily VaR limit of $2,000,000 and a current VaR of $1,650,000. Two traders each ask to add a position, and each has the same stand-alone VaR of $660,000.
The risk team ran IVaR for both. The first trade, in sectors the firm already held, had an IVaR of $550,000 and would have breached the limit. The second, in an unrelated market, had an IVaR of only $120,000.
The fictional firm approved the second trade and asked the first trader to halve the size. The illustrative lesson is that two trades with identical stand-alone risk can have very different effects on a portfolio.
Watch out
Common mistakes.
- Using the stand-alone VaR of a new trade to judge its impact, which ignores how it interacts with everything already held.
- Assuming IVaR is always positive, when a hedging position can have a negative IVaR and reduce overall risk.
- Treating the IVaR of several trades as additive, when each trade changes the portfolio and the correlations, so the effects must be recalculated together.
Questions
People also ask.
How is IVaR different from marginal VaR?
Marginal VaR measures the effect of a very small change in a position, while IVaR measures the effect of a full, discrete addition or removal of that position.
Can IVaR be calculated without a statistical model?
Yes, it can also be found using historical simulation or Monte Carlo methods, by running the portfolio with and without the position and comparing the results.
Why do risk managers care about IVaR when they already have total VaR?
Total VaR shows how much risk exists, while IVaR shows which positions are responsible for it and what a proposed change would do.
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