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

For a commodity held mainly for consumption (not purely as an investment), which statement about the cost-of-carry relationship is correct?

For consumption commodities the forward satisfies F ≤ S·e^((r+u)T). Cash-and-carry arbitrage sets the upper bound, but reverse arbitrage is not reliable because holders value physical inventory. The convenience yield captures that benefit and lowers the forward price relative to full carry.

  1. AThe forward price must equal S·e^((r+u)T) exactly, because arbitrageurs can always short the physical commodity.
  2. BThe forward price satisfies F ≤ S·e^((r+u)T), and the convenience yield measures the gap that reflects the benefit of holding the physical commodity.Correct
  3. CThe forward price must always exceed S·e^((r+u)T) because of the benefit of holding the physical commodity.
  4. DThe convenience yield accrues to the holder of a long forward contract, so it raises the forward price.

Explanation

Cash-and-carry arbitrage caps the forward at S·e^((r+u)T), but holders of the physical commodity who value inventory will not sell it to exploit the reverse arbitrage, so the forward can be lower. The convenience yield reduces the forward price, not raises it, and accrues to holders of the physical commodity, not to forward holders.

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