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

A copper producer observes spot copper at USD 9,000 per tonne and a 1-year forward at USD 9,450. The continuously compounded risk-free rate is 3% per year, and storage costs are a continuous proportional cost of 1.5% per year. Which value is closest to the implied annual convenience yield?

The implied convenience yield is about -0.4%, closest to -0.5%. The forward implies a carry of ln(1.05), about 4.88%, while interest plus storage is 4.5%. Convenience yield equals 4.5% minus 4.88%, which is slightly negative.

  1. A0.0%
  2. B-0.5%Correct
  3. C1.5%
  4. D3.0%

Explanation

Since F = S e^((r+u-y)T), ln(9,450/9,000) = ln(1.05) = 4.879%. Then r+u-y = 4.879%, and with r+u = 4.5%, y = 4.5% - 4.879% = -0.38%, which is closest to -0.5%. The 0.0% option ignores the 0.38 percentage point gap and the 1.5% option treats storage as the yield.

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