CFA Level II ExamDerivativesEasy
An investor enters into a long position in a forward contract on a non-dividend-paying stock. The current stock price is $50, the risk-free rate is 4% compounded continuously, and the time to expiration is 9 months. What is the no-arbitrage forward price for this contract?
- A$48.52
- B$53.06
- C$52.50
- D$51.52
Show answer & explanationAnswer & explanation
Correct answer: D. $51.52
For a non-dividend-paying stock, the no-arbitrage forward price (F0) is calculated as S0 * e^(rT), where S0 is the current stock price, r is the continuous risk-free rate, and T is the time to expiration. F0 = $50 * e^(0.04 * 0.75) = $50 * e^(0.03) = $50 * 1.03045 = $51.52.
Why the other options are wrong
- A. Incorrect. This would be the present value of the spot price, not the forward price.
- B. Incorrect. This might arise from using a higher risk-free rate or a longer time to expiration in the calculation.
- C. Incorrect. This might arise from using simple interest instead of continuous compounding, or a calculation error.
Forward Price (Non-Dividend Stock)
The no-arbitrage price of a forward contract on an underlying asset that does not pay dividends, reflecting the cost of carrying the asset.
- Calculated as S0 * e^(rT) for continuous compounding.
- Reflects the future value of the spot price at the risk-free rate.
- Ensures no immediate arbitrage profits.
Memory trick: Spot to Future, Risk-Free Growth.