FRM Part I · FRM Exam Part I · Trading Strategies
An investor puts $1,000,000 into a 3-year note with 100% principal protection. The issuer buys a zero-coupon bond using a continuously compounded risk-free rate of 4% and spends the remainder on at-the-money 3-year calls on an index. The calls cost 15% of the index notional. Using e^(-0.12) = 0.88692, what participation rate can be offered, to the nearest 0.1%?
The participation rate is 75.4%. The zero-coupon bond costs $886,920 at 4% continuous compounding, leaving $113,080. At a call price of 15% of notional, this buys options on about $753,867 of index exposure, or 75.4% of the invested amount.
- A75.4%Correct
- B74.0%
- C80.0%
- D88.7%
Explanation
Bond cost = 1,000,000 × 0.88692 = $886,920, leaving $113,080 for options. Call notional = 113,080 / 0.15 = $753,867, which is 75.4% of the investment. Discrete discounting at 4% would give 74.0%, which is the wrong compounding convention.
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