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

A commodity has spot price $50, r = 4% continuously compounded, no storage costs, and a convenience yield of 6% per year. Using F = S·exp((r − y)T), what is the theoretical six-month futures price, closest to?

The six-month futures price is about $49.50. The net cost of carry is the 4% interest rate minus the 6% convenience yield, or −2% per year, so F equals 50 times exp(−0.01), which gives roughly $49.50, below spot, indicating backwardation.

  1. A$49.50Correct
  2. B$50.50
  3. C$48.51
  4. D$51.01

Explanation

F = 50·exp((0.04 − 0.06)·0.5) = 50·exp(−0.01) = 50·0.99005 = 49.50. Option 2 ignores the convenience yield and uses 4%·0.5 growth (50·e^0.02 = 51.01), so that figure is wrong.

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