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

A gold spot price is USD 2,000 per ounce. The continuously compounded risk-free rate is 4% per year, and storage costs and the convenience yield are negligible. Using the cost-of-carry model, what is the no-arbitrage price of a 6-month gold forward (approximately)?

The no-arbitrage forward price is about USD 2,040.40. With no storage cost or convenience yield, the forward equals spot compounded at the risk-free rate for the term: 2,000 × e^(0.04×0.5). Discounting or using a full year of interest gives wrong values.

  1. AUSD 2,040.40Correct
  2. BUSD 2,000.00
  3. CUSD 2,080.00
  4. DUSD 1,960.80

Explanation

F = S e^(rT) = 2,000 × e^(0.04×0.5) = 2,000 × e^0.02 = 2,000 × 1.020201 = 2,040.40. USD 2,080 wrongly uses a full year of interest (simple 4% on one year). USD 1,960.80 discounts instead of compounding.

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