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FRM Part I · FRM Exam Part I · Trading Strategies

A bank offers a 2-year capped principal-protected note on $1,000,000. The risk-free rate is 5% with annual compounding, and the principal is fully protected. The leftover funds buy a bull call spread on an index: long an at-the-money call costing 12% of index notional and short a call struck at 125% of the initial index level costing 5% of notional. The spread is bought on as large a notional as the leftover funds allow. What is the maximum total payoff at maturity, to the nearest dollar?

The maximum payoff is $1,332,038. The bond costs $907,029, leaving $92,971. The spread costs a net 7% of notional, so it covers about $1,328,150 of notional. The 25% cap yields about $332,038, which is added to the $1,000,000 principal.

  1. A$1,332,038Correct
  2. B$1,193,689
  3. C$1,250,000
  4. D$1,092,971

Explanation

Bond cost = 1,000,000/1.1025 = $907,029, leaving $92,971. Net spread cost = 12% - 5% = 7%, so notional = 92,971/0.07 = $1,328,150. The maximum spread payoff is 25% of that notional, about $332,038. Adding principal gives $1,332,038. Using only the long call's 12% cost gives $1,193,689, which ignores the premium received from the short call.

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