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FRM Part I · FRM Exam Part I · Commodity Forwards and Futures

A gold dealer observes a spot price of USD 2,000 per ounce. The risk-free rate is 5% per year (continuously compounded), and storage costs are negligible. There are no convenience benefits. Using the cost-of-carry model, what is the theoretical one-year forward price (to the nearest dollar)?

The theoretical forward price is about USD 2,103, because with no storage costs or convenience yield the forward equals spot compounded at the risk-free rate: 2,000 times e to the 0.05, which is roughly 2,102.5.

  1. AUSD 2,000
  2. BUSD 2,100
  3. CUSD 2,103Correct
  4. DUSD 1,903

Explanation

F = S x e^(rT) = 2,000 x e^0.05 = 2,000 x 1.05127 = 2,102.5, about USD 2,103. USD 2,100 uses simple interest rather than continuous compounding. USD 1,903 wrongly discounts the spot price instead of compounding it forward.

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