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FRM Part I · FRM Exam Part I · Trading Strategies

A bank designs a 100-notional principal-protected note on an index starting at 100. The zero-coupon bond needed to guarantee principal costs 90. The bank uses the remaining funds to buy a bull call spread: long a call with strike 100 (price 12) and short a call with strike 130 (price 5), per unit of index. What is the maximum redemption per 100 of notional, assuming the bank invests exactly the remaining funds?

The maximum redemption is about 142.9. The remaining 10 buys 10/7 ≈ 1.43 bull spreads costing 7 each. Each spread pays at most 30, adding about 42.9 to the guaranteed principal of 100, so the cap is 142.9 per 100 of notional.

  1. A142.9Correct
  2. B130.0
  3. C125.0
  4. D160.0

Explanation

Funds for options = 100 − 90 = 10. Spread cost = 12 − 5 = 7, so the number of spreads = 10/7 = 1.4286. Maximum spread payoff = 30 each, giving 42.86. Maximum redemption = 100 + 42.86 = 142.9. Using the long call alone (10/12 × 30 = 25) gives 125, ignoring the premium from the short call.

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