FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A portfolio on a stock has delta 2,000 and gamma 500 (per $1 change in the stock price, share-equivalent units). The stock rises from $50 to $52. Using the delta-gamma Taylor approximation, what is the estimated change in portfolio value?
The estimated change is $5,000. The delta term gives 2,000 x $2 = $4,000, and the gamma term gives 0.5 x 500 x 2^2 = $1,000. Adding the convexity correction to the linear delta estimate yields $5,000.
- A$5,000
- B$4,000
- C$4,500Correct
- D$3,000
Explanation
dV = delta x dS + 0.5 x gamma x dS^2 = 2,000 x 2 + 0.5 x 500 x 4 = 4,000 + 1,000 = $5,000. Using delta only gives $4,000, and omitting the one-half factor gives $5,000... so check: the correct value is $5,000.
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