medium · FRM Part 1 Valuation and Risk Models
An analyst uses a 99% daily Value-at-Risk (VaR) model based solely on Delta. A portfolio has Δ = $1,000,000 and Γ = -$500,000 (both expressed as dollar-sensitivities for a 1% move).
If the 1-day 99% change in the underlying is 2.33%, how does the inclusion of Gamma affect the estimated VaR?
- The VaR remains unchanged because VaR is a first-order measure that traditionally ignores non-linear effects.
- The VaR increases because negative Gamma accelerates losses as the underlying price moves unfavorably.
- The VaR increases because the squared term (2.33%)^2 is added directly to the Delta-based loss.
- The VaR decreases because Gamma provides a 'cushion' against large directional moves through its squared term.
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