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

A market maker is short options with a portfolio gamma of -4,000 and delta-neutral. The stock price is $50. Which action would make the portfolio both delta-neutral and gamma-neutral, using a traded option with delta 0.5 and gamma 0.8 per option and the stock?

Buy 5,000 options to add gamma of 4,000 (4,000 divided by 0.8), which offsets the -4,000. Those options add delta of 2,500, so sell 2,500 shares of stock to return to delta neutrality, since stock has no gamma.

  1. ABuy 5,000 options and sell 2,500 shares of stockCorrect
  2. BBuy 5,000 options and buy 2,500 shares of stock
  3. CSell 5,000 options and buy 2,500 shares of stock
  4. DBuy 3,200 options and sell 1,600 shares of stock

Explanation

To offset gamma of -4,000 need +4,000/0.8 = 5,000 long options. These add delta of 5,000×0.5 = 2,500, so sell 2,500 shares to restore delta neutrality (stock has zero gamma). Buying shares would double the delta exposure; selling options would worsen the negative gamma.

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