How do storage costs and convenience yield affect forward pricing for commodities?

Forward pricing for commodities is more complex than for financial assets because physical commodities cost money to store and can provide benefits from physical possession. These additional factors modify the basic cost-of-carry formula.

Basic Forward Pricing (Financial Assets):

F = S x (1 + r + storage - convenience yield)^T

Or more precisely: F = (S + PV of storage costs - PV of convenience yield) x (1 + r)^T

Storage Costs: Why They Increase the Forward Price

If you buy a commodity today and hold it for delivery in 6 months, you must pay for warehousing, insurance, and spoilage prevention. This carrying cost is added to the forward price because the forward buyer avoids these costs by waiting.

Convenience Yield: Why It Decreases the Forward Price

Convenience yield is the non-monetary benefit of holding the physical commodity rather than a futures contract. It represents:

• Ability to keep a factory running if supply chains disrupt
• Ability to meet unexpected customer demand immediately
• Protection against supply shortages

This benefit accrues to the spot holder, so it reduces the forward price (the forward buyer doesn't get this benefit, so they pay less).

Example — Creston Refining Crude Oil Forward

Creston Refining is pricing a 6-month crude oil forward:

• Spot price: $78/barrel
• Risk-free rate: 5% annually
• Storage costs: $2.50/barrel for 6 months
• Convenience yield: $1.80/barrel for 6 months

Calculation:

F = ($78 + $2.50 - $1.80) x (1.05)^0.5

F = $78.70 x 1.0247

F = $80.64/barrel

Compare to a financial asset (no storage, no convenience):

F = $78 x (1.05)^0.5 = $79.93

The storage cost added $2.56 and the convenience yield subtracted $1.85, netting +$0.71 on top of the financial forward price.

Why Stocks and Bonds Don't Have These Factors:

For stocks: F = S x (1 + r)^T - PV(Dividends) x (1 + r)^T (income reduces forward price, similar to convenience yield)

Backwardation vs Contango:

• If convenience yield > storage costs + financing: F < S (backwardation — forward is cheaper than spot)
• If storage costs + financing > convenience yield: F > S (contango — forward is more expensive)

During supply crunches, convenience yield spikes and the market goes into sharp backwardation — physical oil today is worth far more than a promise of oil in 6 months.

Exam Tip: CFA Level I may give you spot price, rate, storage, and convenience yield and ask you to calculate the forward price. Keep the signs straight: storage adds, convenience yield subtracts.

Explore commodity derivatives in our CFA Level I course.