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FRM Part I · FRM Exam Part I · Trading Strategies

A long call butterfly uses strikes 50, 55 and 60 (long one 50 call, short two 55 calls, long one 60 call) on the same expiry. The net premium paid is 1.80. What is the maximum profit and the range of terminal stock prices at which the position makes a profit?

Maximum profit is 3.20 and the position is profitable for stock prices between 51.80 and 58.20. The maximum payoff of 5 occurs at 55, less the 1.80 premium. Breakevens are the lower strike plus the premium and the upper strike minus the premium.

  1. AMaximum profit 3.20; profitable between 51.80 and 58.20Correct
  2. BMaximum profit 5.00; profitable between 51.80 and 58.20
  3. CMaximum profit 3.20; profitable between 50 and 60
  4. DMaximum profit 3.20; profitable between 53.20 and 56.80

Explanation

Maximum payoff is 5 at S=55, so maximum profit = 5 - 1.80 = 3.20. Between 50 and 55 payoff = S-50, which must exceed 1.80, so S>51.80. Between 55 and 60 payoff = 60-S > 1.80 gives S<58.20. Option with 5.00 ignores the premium.

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