FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures
A commodity has a spot price of 80. Storage costs are 2% of the spot price per year, and they are treated as a continuously compounded proportional cost. The risk-free rate is 4% per year, continuously compounded. What is the fair one-year forward price? Assume there is no convenience yield.
The fair forward price is 84.95. Storage costs are a proportional cost of carry, so they add to the risk-free rate in the exponent: 80 times e to the power 0.06. Omitting storage or subtracting it gives incorrect values.
- A84.95Correct
- B83.27
- C81.62
- D86.66
Explanation
With proportional storage costs, F = S·e^((r+u)T) = 80·e^0.06 = 80 × 1.061837 = 84.95. Using only r gives 83.27 and omits storage. Subtracting u gives 81.62, which is the wrong sign. 86.66 uses a 8% rate by doubling the storage cost.
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