What is incremental VaR and how is it used for position sizing decisions?

Incremental VaR (IVaR) measures the change in portfolio VaR when an entire position is added to or removed from the portfolio. It's the most useful metric for position-level decision making — should I add this trade?

Definition:

IVaR = VaR(portfolio WITH position) - VaR(portfolio WITHOUT position)

Key properties:

1. IVaR can be positive (position increases risk) or negative (position hedges)
2. IVaR depends on the existing portfolio — the same trade has different IVaR depending on what else you hold
3. IVaR accounts for correlations with all other positions
4. IVaR does NOT sum to portfolio VaR (that's component VaR's property)

Example:

Silverstone Capital has a $200M equity-heavy portfolio with VaR = $12M (99%, 1-day).

Scenario 1: Add a $20M US Treasury position

• New portfolio VaR = $11.2M
• IVaR = $11.2M - $12M = -$0.8M (reduces risk — acts as diversifier)

Scenario 2: Add a $20M EM equity position

• New portfolio VaR = $13.5M
• IVaR = $13.5M - $12M = +$1.5M (increases risk — adds to existing equity concentration)

Scenario 3: Add a $20M short equity index futures position

• New portfolio VaR = $9.8M
• IVaR = $9.8M - $12M = -$2.2M (hedges existing equity exposure)

Incremental VaR vs. the other VaR measures:

Approximation shortcut:

For small position changes, IVaR can be approximated using marginal VaR:

IVaR ≈ (Marginal VaR) × (Position size change)

This avoids recalculating the entire portfolio VaR for each candidate trade.

Practical use in risk management:

1. Pre-trade risk assessment: Before executing a trade, calculate IVaR to see its portfolio impact
2. Risk limits: Set IVaR limits — no single trade can increase VaR by more than X%
3. Hedge effectiveness: Measure how much a proposed hedge reduces VaR (negative IVaR)
4. Position right-sizing: If IVaR is too large, scale down the position until it's within limits

Exam tip: FRM Part II often asks you to distinguish between the four VaR measures and identify which is appropriate for a given scenario. Remember: component VaR for reporting, incremental VaR for decision-making.

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