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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A portfolio has a delta-equivalent exposure of +2,000 units of an underlying asset and a gamma of -300 per $ (change in delta per $1 move). Management assumes the worst one-day move at the chosen confidence level is $4 in either direction. Using the delta-gamma approximation, which is the worst-case one-day loss?

The worst-case loss is $10,400. A $4 fall costs 2,000 x 4 = $8,000 from delta, and negative gamma adds a further 0.5 x 300 x 16 = $2,400 loss. The $4 rise yields a net gain of $5,600, so the downward scenario governs.

  1. A$10,400Correct
  2. B$8,000
  3. C$5,600
  4. D$12,800

Explanation

P&L = 2,000 x dS + 0.5 x (-300) x dS^2. For dS = -4: -8,000 - 2,400 = -10,400. For dS = +4: 8,000 - 2,400 = +5,600, a gain. The worst loss is $10,400. Delta alone gives $8,000. Dropping the 0.5 factor gives $12,800.

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