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

Commodity forwards are different from financial forwards because physical commodities have storage costs and convenience yield — two factors absent from equity or bond forwards.

The Full Cost-of-Carry Model:

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

Where:

• S(0) = spot price
• r = risk-free rate
• u = storage cost rate (annualized, as % of spot)
• y = convenience yield (annualized)
• T = time to maturity

Storage Costs (u): Physical commodities must be warehoused, insured, and maintained. Crude oil needs tank farms. Wheat needs grain elevators. These costs push the forward price above spot — the buyer is paying the seller to store until delivery.

Convenience Yield (y): Holding the physical commodity provides an intangible benefit — you can meet unexpected demand, keep a refinery running, or exploit spot shortages. This yield is highest when inventories are tight. It pulls the forward price below what pure cost-of-carry would suggest.

Worked Example — Meridian Petroleum:

Meridian Petroleum is pricing a 6-month crude oil forward:

• Spot price: $78/barrel
• Risk-free rate: 5.0%
• Storage cost: 3.0% annually
• Convenience yield: 7.0% annually

F(0, 0.5) = $78 x e^{(0.05 + 0.03 - 0.07) x 0.5}

= $78 x e^{0.005}

= $78 x 1.005013

= $78.39/barrel

Despite 8% in carry costs (rate + storage), the 7% convenience yield nearly offsets everything, keeping the forward barely above spot.

Now suppose inventories drop and convenience yield rises to 12%:

F(0, 0.5) = $78 x e^{(0.05 + 0.03 - 0.12) x 0.5}

= $78 x e^{-0.02}

= $78 x 0.9802

= $76.46/barrel

The forward is now below spot — this is backwardation.

Key Exam Insight: When convenience yield exceeds the cost of carry (r + u), the market is in backwardation. This is common in energy markets during supply disruptions. The convenience yield is not directly observable — it's backed out from the forward curve.

Check out our FRM Part I course for more on commodity derivatives.