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

Gold (an investment asset) trades at a spot price of USD 1,900 per ounce. The continuously compounded risk-free rate is 4% per year, and storage costs are 1% of the spot value per year, also continuously compounded. What is the no-arbitrage one-year forward price?

The forward price is USD 1,997.41. Storage costs add to the cost of carry, so the forward equals spot times e raised to (risk-free rate plus storage rate) times time: 1,900 × e^0.05. Ignoring storage or subtracting it gives wrong values.

  1. AUSD 1,977.54
  2. BUSD 1,957.86
  3. CUSD 1,997.41Correct
  4. DUSD 1,995.00

Explanation

With proportional storage costs, F = S·e^((r+u)T) = 1,900 × e^0.05 = 1,900 × 1.051271 = USD 1,997.41. Ignoring storage gives 1,977.54, and subtracting storage as if it were an income yield gives 1,957.86. Using simple interest of 5% gives 1,995.00, which is not consistent with continuous compounding.

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