CFA Level I · CFA Level I Exam · Pricing and Valuation of Futures Contracts
An index trades at 2,000. The index dividend yield is 2.0% per year continuously compounded, and the risk-free rate is 5.0% per year continuously compounded. The no-arbitrage price of a nine-month futures contract on the index is closest to:
The futures price is closest to 2,045. Because the risk-free rate exceeds the dividend yield, net carry is positive at 3%, so the futures price is spot times e^(0.03×0.75), which is about 2,045.5. A lower figure would reflect a sign error.
- A1,955
- B2,000
- C2,045Correct
Explanation
F = S0 × e^((r − δ)T) = 2,000 × e^(0.03×0.75) = 2,000 × e^0.0225 = 2,000 × 1.022755 = 2,045.5, about 2,045. Subtracting the carry instead of adding it gives about 1,955 (wrong sign). 2,000 ignores net cost of carry.
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