CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
A stock trades at $50 and pays no dividends. The annual risk-free rate is 4% (discrete compounding). The no-arbitrage price of a 9-month forward contract on the stock, using a 0.75-year term, is closest to:
The forward price is about $51.50. It equals the spot price of $50 compounded at 4% for 0.75 years, 50 × 1.04^0.75 ≈ 51.49. Charging a full year of interest would give $52.00, which overstates the cost of carry.
- A$50.00
- B$51.50Correct
- C$52.00
Explanation
F0 = S0(1+r)^T = 50 × 1.04^0.75. ln1.04 = 0.039221; ×0.75 = 0.029416; exp = 1.02985. So F0 = 51.49, about $51.50. Using simple interest (50 × 1.04 = 52.00) wrongly applies a full year of interest.
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