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

The spot price of a commodity is $120. The one-year futures price is $126 and the two-year futures price is $127.5. The continuously compounded risk-free rate is 4%, and storage costs are zero. Assuming a constant convenience yield between the two years, what is the forward convenience yield for year 2 (the period from year 1 to year 2), closest to?

The year-2 forward convenience yield is about 2.81%. The ratio of the two-year to one-year futures price is 127.5/126, with log of about 1.18%. Since this equals r minus y, the convenience yield is 4% minus 1.18%, roughly 2.8%.

  1. A2.81%Correct
  2. B1.19%
  3. C4.00%
  4. D5.81%

Explanation

The forward ratio is 127.5/126 = 1.011905, and ln = 0.011834. Then r − y = 0.011834, so y = 0.04 − 0.011834 = 0.0282, about 2.8%. Checking: 126·exp(0.04−0.0282)=126·1.01187≈127.5. Option 2 gives the net carry rather than y.

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