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

Gold spot is USD 1,900 per ounce. The one-year continuously compounded risk-free rate is 5% and the one-year gold lease rate is 2%. The one-year forward price is quoted at USD 1,990. A trader executes the appropriate arbitrage: borrow cash to buy gold, lend the gold at the lease rate, and sell gold forward. What is the arbitrage profit per ounce at the end of one year? Assume lease payments are made in gold and the lent gold is returned at maturity.

The profit is about USD 32.14 per ounce. The fair forward price is 1,900 × e^{0.03}, about 1,957.86, because lease income offsets part of the financing cost. Selling forward at 1,990 locks in the difference of roughly 32.14.

  1. AUSD 32.14Correct
  2. BUSD 90.00
  3. C-USD 7.42
  4. D-USD 47.77

Explanation

The no-arbitrage forward is 1900 × e^{0.03} = 1900 × 1.030455 = USD 1,957.86. The trader receives 1,990 from the forward sale and owes only the net carry cost, which is the loan repayment less the lease income, equivalent to 1,957.86. Profit is 1,990 - 1,957.86 = 32.14. Using e^{0.05} ignores the lease income, and using e^{0.07} adds the lease rate to r, which is wrong.

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