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FRM Part I · FRM Exam Part I · Trading Strategies

A bank issues a 3-year principal-protected note with a notional of USD 1,000,000, sold at par. The continuously compounded 3-year risk-free rate is 4% (e^-0.12 = 0.88692). An at-the-money 3-year call on the index costs 12.5% of the initial index value per unit of notional. Assuming the bank spends all funds not needed for the zero-coupon bond on calls, what participation rate can it offer?

The participation rate is about 90.5%. The zero-coupon bond costs USD 886,920, leaving USD 113,080 to buy calls. Dividing by the cost of a full-notional at-the-money call, USD 125,000, gives roughly 90.5% participation in index gains.

  1. A90.5%Correct
  2. B85.7%
  3. C31.4%
  4. D11.3%

Explanation

Bond cost = 1,000,000 × 0.88692 = 886,920. Remaining for options = 113,080. Call cost per unit of notional = 125,000, so participation = 113,080 / 125,000 = 90.5%. Using simple annual discounting (1/1.12) would give 85.7%, an error from the wrong discount method.

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