Lesson 4 of 6 · 14 min

Commodity pricing: carry, convenience yield and curve shape

No-arbitrage ties the forward price to the spot price: carry costs push the forward up and convenience yield pulls it down, so the curve is in contango when costs dominate and in backwardation when the benefit of holding the physical commodity dominates.

In short

  • Commodities trade in physical (spot) and derivative markets; no-arbitrage links the two prices.
  • Cost of carry: financing at the risk-free rate rr plus storage, transport and insurance cc. It raises the forward price.
  • Convenience yield ii: the non-cash benefit of holding the physical good, highest when inventories are low. It lowers the forward price.
  • F0(T)=S0e(r+c−i)TF_0(T) = S_0 e^{(r + c - i)T}. Forward > spot only when r+c>ir + c > i.
  • Contango: forward above spot, upward-sloping curve (costs > benefits). Backwardation: forward below spot, inverted curve (benefits > costs).
  • Rule of thumb: contango tends to lower and backwardation tends to raise the return of a long-only investor.

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Commodity pricing: carry, convenience yield and curve shape · Natural Resources