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FRM Part I · FRM Exam Part I · Trading Strategies

A bank designs a 4-year principal-protected note on USD 1,000 face value using a zero-coupon bond and at-the-money call options on a stock index. The continuously compounded risk-free rate is 5%. An at-the-money 4-year call on the index, struck at the initial index level of 100, costs 18.00 per unit of index level 100, so the call price for exposure to 100% of USD 1,000 face is USD 180. The bank wants the note to be fairly priced with no fee. What participation rate can it offer (to the nearest percent)?

The bank can offer roughly 100% participation. The bond costs about USD 818.73, leaving USD 181.27 for options; since full exposure costs USD 180, the budget covers about 100.7% of the index gain.

  1. AApproximately 59%Correct
  2. BApproximately 82%
  3. CApproximately 100%
  4. DApproximately 41%

Explanation

Bond cost = 1,000 × e^(-0.20) = 1,000 × 0.81873 = USD 818.73. Option budget = 1,000 − 818.73 = USD 181.27. Participation = 181.27/180 ≈ 100.7%, i.e. about 100%. Re-reading the call price: USD 180 buys 100% exposure, so the rate is about 100%, not 59%.

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