FRM Part I · FRM Exam Part I · Commodity Forwards and Futures
A commodity has a spot price of USD 50. Storage costs with a present value of USD 3 are paid up front, and the continuously compounded risk-free rate is 4% per year. The six-month forward price quoted in the market is USD 56. There is no convenience yield. What is the riskless profit at expiry per unit from a cash-and-carry arbitrage?
The arbitrage profit is USD 1.93 per unit. The fair forward is (50 + 3) × e^0.02 = 54.07, so a market forward of 56 is too high. Buying spot, financing it, and selling the forward locks in 56 − 54.07.
- AUSD 1.93Correct
- BUSD 1.99
- CUSD 4.99
- DUSD 3.00
Explanation
Fair forward = (50 + 3)·e^(0.04×0.5) = 53 × 1.020201 = USD 54.07. The forward is overpriced at 56, so buy the commodity, pay storage, and sell the forward, locking in 56 − 54.07 = USD 1.93. Omitting storage gives 4.99, and not compounding the storage cost gives 1.99.
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