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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A trader holds a portfolio of options on a single stock with a net delta of +4,000 shares and a net gamma of -500 per $1 move in the stock. Which statement best describes the portfolio's exposure to a large move in the stock price?

The portfolio loses from large moves in either direction. Negative gamma means the position is short convexity, so the second-order term in the Taylor approximation is always negative, and delta moves adversely as the price changes.

  1. AIt gains from a large move in either direction because gamma is negative
  2. BIt loses from a large move in either direction, because negative gamma makes delta shift against the positionCorrect
  3. CIt is unaffected by large moves because delta is positive
  4. DIt gains from a large upward move and loses from a large downward move by exactly the same amount

Explanation

Negative gamma means the position is short convexity. As the stock rises, delta falls, and as the stock falls, delta rises, so the delta hedge works against the trader. Large moves in either direction therefore hurt, beyond the linear delta effect. The gamma term in the Taylor expansion is -0.5 x 500 x (change in S)^2, which is always negative.

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