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

A portfolio manager combines three option positions on the same underlying. Position A has delta 1,500 and gamma 300; position B has delta -2,200 and gamma -100; position C has delta 900 and gamma 50. What are the portfolio's delta and gamma?

The portfolio has delta of 200 and gamma of 250. Greeks on the same underlying add across positions, so delta is 1,500 minus 2,200 plus 900, and gamma is 300 minus 100 plus 50.

  1. ADelta 200, gamma 250Correct
  2. BDelta 200, gamma 450
  3. CDelta 4,600, gamma 250
  4. DDelta -200, gamma 250

Explanation

Portfolio Greeks on the same underlying are additive. Delta = 1,500 - 2,200 + 900 = 200. Gamma = 300 - 100 + 50 = 250. The gamma of 450 option ignores the sign of position B.

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