FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A portfolio of options on one stock has delta of 0, gamma of -2,000 per USD and theta of +USD 1,500 per day. Using the delta-gamma-theta approximation, the stock moves by USD 1.00 in one day (either direction). What is the approximate one-day change in portfolio value?
The approximate change is +USD 500. Theta adds USD 1,500 for the passing day, while negative gamma costs 0.5 × 2,000 × 1² = USD 1,000 from the USD 1 move, and delta contributes nothing, leaving a net gain of USD 500.
- A+USD 500Correct
- B-USD 2,500
- C+USD 2,500
- D+USD 1,500
Explanation
Change = theta*dt + 0.5*gamma*(dS)^2 = 1,500 + 0.5*(-2,000)*(1)^2 = 1,500 - 1,000 = +500. Ignoring the gamma term gives +1,500, and wrongly flipping the gamma sign gives +2,500.
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