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

Spot copper is USD 9,000 per tonne. The continuously compounded risk-free rate is 4% per year, storage costs are 2% per year of spot price (continuous), and the convenience yield is 8% per year. Using the cost-of-carry model, the 6-month futures price is closest to:

The cost-of-carry price is spot times exp of (risk-free plus storage minus convenience yield) times maturity. Net carry is minus 2% per year, so over six months the futures price is 9,000 times exp(-0.01), about USD 8,910, indicating backwardation.

  1. AUSD 8,822Correct
  2. BUSD 9,000
  3. CUSD 9,273
  4. DUSD 8,640

Explanation

F = S*exp((r+u-y)T) = 9,000*exp((0.04+0.02-0.08)*0.5) = 9,000*exp(-0.01) = 9,000*0.99005 = 8,910.5. Recomputing: exp(-0.01)=0.990050, giving 8,910. So the correct value is about USD 8,910, which is none of the listed figures; check: the intended net carry is -2%, giving 8,910.

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