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FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures

A commodity trades at a spot price of 100. Storage costs of 2 per unit are paid at six months and another 2 at one year. The risk-free rate is 5% per year, continuously compounded. There is no convenience yield. What is the fair one-year forward price?

The fair forward price is 109.18. Discrete storage costs are added to spot at their present value, about 3.85, and the total is compounded at the risk-free rate for one year. Using undiscounted storage costs overstates the price, and ignoring them understates it.

  1. A109.18Correct
  2. B109.33
  3. C105.13
  4. D101.08

Explanation

PV of storage = 2e^-0.025 + 2e^-0.05 = 1.9506 + 1.9025 = 3.8531. F = (100 + 3.8531)e^0.05 = 103.8531 × 1.051271 = 109.18. Adding the undiscounted 4 of storage before compounding gives 109.33, which is wrong. Ignoring storage gives 105.13, and subtracting its PV gives 101.08.

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