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

A portfolio has delta +5,000 and gamma -800. A trader wants to be both delta-neutral and gamma-neutral using a traded option with delta 0.50 and gamma 0.04 and the underlying stock. How many options and how many shares are needed?

Buy 20,000 options and sell 15,000 shares. Gamma of -800 needs 800/0.04 = 20,000 options. These add delta of 10,000, lifting total delta to 15,000, which is offset by selling 15,000 shares, since the stock has zero gamma.

  1. ABuy 20,000 options and sell 15,000 sharesCorrect
  2. BBuy 20,000 options and sell 10,000 shares
  3. CSell 20,000 options and buy 5,000 shares
  4. DBuy 32,000 options and sell 11,000 shares

Explanation

Gamma: need +800 from options, so 800/0.04 = 20,000 options bought. Their delta is 20,000 x 0.50 = +10,000, so portfolio delta becomes 15,000. Sell 15,000 shares (delta 1 each) to neutralize. Selling only 10,000 shares ignores the added option delta... actually it ignores the original 5,000.

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