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

A commodity has a spot price of 80, a risk-free rate of 5% per year (continuously compounded), and storage costs of 3% per year of spot price (continuously compounded). The one-year futures price is 82.0. Using the cost-of-carry relationship F = S·exp((r + u − y)T), what is the implied convenience yield (continuously compounded, approx.)?

The implied convenience yield is about 5.6%. The log of F/S is 2.47%, while the cost of carry (interest plus storage) is 8%. The convenience yield is the amount by which carry costs exceed the observed futures premium, so 8% minus 2.47% gives roughly 5.5–5.6%.

  1. A5.6%Correct
  2. B10.5%
  3. C0.0%
  4. D2.4%

Explanation

Solve F/S = exp((r+u−y)T): ln(82/80)=0.02469. So r+u−y=0.02469, with r+u=0.08, y=0.08−0.02469=0.0553, about 5.6%. Using 0.02469 as y directly (2.5%) or ignoring storage costs would give wrong answers.

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