How do storage costs and convenience yield affect commodity futures pricing?

Commodity futures pricing extends the cost-of-carry model by adding two physical-market-specific factors: storage costs and convenience yield.

The Commodity Cost-of-Carry Model:

F(0,T) = S(0) x e^((r + u - y) x T)

Where:

• F(0,T) = Futures price for delivery at time T
• S(0) = Current spot price
• r = Risk-free rate
• u = Storage cost (as continuous rate)
• y = Convenience yield (as continuous rate)

Storage Costs (u):

Physical commodities require warehousing, insurance, and handling. These costs increase the futures price because holding physical commodity is more expensive than holding a financial asset.

Convenience Yield (y):

The convenience yield reflects the benefit of physically holding the commodity. This benefit accrues to industrial users who need guaranteed supply:

• A refinery holding crude oil avoids production shutdowns
• A grain processor holding wheat avoids supply disruptions during harvest shortfalls
• The convenience yield is higher when inventories are tight (low supply)

Example — Westbrook Refining Co.:

Crude oil spot: $75/barrel, risk-free rate: 5%, storage: 3%/year, convenience yield: 7%/year.

6-month futures: F = $75 x e^((0.05 + 0.03 - 0.07) x 0.5) = $75 x e^(0.005) = $75.38

Now if inventories tighten and convenience yield rises to 12%:

F = $75 x e^((0.05 + 0.03 - 0.12) x 0.5) = $75 x e^(-0.02) = $73.51

Contango vs. Backwardation:

• Contango (futures > spot): When storage costs + financing exceed convenience yield. Common when inventories are plentiful.
• Backwardation (futures < spot): When convenience yield dominates. Common during supply shortages — holders value physical inventory highly.

Key FRM Points:

• Convenience yield is NOT directly observable — it's implied from the futures-spot relationship
• Backwardation is more common for energy commodities due to supply disruption risk
• The 'theory of normal backwardation' (Keynes) is different — it says futures trade below expected future spot prices as a risk premium to hedgers
• Roll return is positive in backwardation (buy cheap futures, sell at higher spot) and negative in contango

Master commodity derivatives in our FRM Part I course.