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

A commodity has spot price $80, continuously compounded risk-free rate 5% per year, storage costs of 2% of spot per year (continuous proportional), and a one-year futures price of $81.00. Using F = S·exp((r + u − y)T), what is the implied convenience yield, closest to?

The implied convenience yield is about 5.76%. The futures-to-spot log ratio ln(81/80) is 1.24%, and since r plus storage cost equals 7%, the convenience yield must be 7% minus 1.24%, which is 5.76% per year.

  1. A5.76%Correct
  2. B-5.76%
  3. C8.24%
  4. D1.24%

Explanation

ln(81/80) = ln(1.0125) = 0.01242. So r + u − y = 0.01242, with r + u = 0.07, giving y = 0.07 − 0.01242 = 0.0576, or 5.76%. Option 3 mistakenly adds the log return to r+u instead of subtracting it.

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