FRM Part II · FRM Exam Part II · VaR Mapping
A portfolio consists of options on 1,000 shares of a stock priced at $100. Per share, the position has a delta of 0.50 and a gamma of 0.04. Using a delta-gamma approximation, what is the change in portfolio value if the stock price falls by $5?
The portfolio falls by about $2,000. The delta term gives -$2.50 per share, and the gamma term adds back +$0.50 per share (0.5 × 0.04 × 25). The net change is -$2.00 per share, or -$2,000 across 1,000 shares.
- A-$2,000Correct
- B-$2,500
- C-$3,000
- D-$1,500
Explanation
Per share, the change in value = delta × dS + 0.5 × gamma × dS² = 0.5 × (-5) + 0.5 × 0.04 × 25 = -2.5 + 0.5 = -2.0. Over 1,000 shares the change is -$2,000. The delta-only answer is -$2,500. Subtracting the gamma term gives -$3,000. Omitting the one-half factor gives -$1,500.
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