Commodity Markets and Futures › Futures Pricing: Contango and Backwardation

Having developed the theoretical framework for understanding spot-futures relationships, we can now examine how these relationships manifest in actual market conditions. The term structure of futures prices, which shows how futures prices vary across different delivery months, reveals important information about market conditions and expectations. By observing whether futures prices rise or fall as we look further into the future, we can infer information about storage costs, convenience yields, and market participants' views on future supply and demand.

When markets are well-supplied and convenience yield is low, the cost of carry dominates the pricing relationship. Futures prices exceed spot prices because someone buying for future delivery must compensate the counterparty for the costs of storing and financing the commodity until the delivery date. This market condition has a specific name.

In contango, the futures curve slopes upward, meaning prices increase as we look at contracts with later delivery dates. Mathematically, this relationship can be expressed as an ordering of prices across maturities:

$$F_{T_2} > F_{T_1} > S_0 \quad \text{where } T_2 > T_1$$

where:

• $F_{T_1}, F_{T_2}$: futures prices for maturities $T_1, T_2$
• $S_0$: spot price

Contango is the "normal" condition predicted by the simple cost of carry model when convenience yield is low. The upward slope compensates holders of physical inventory for their storage costs. Without this compensation, no rational actor would store commodities for future sale. A market in contango provides incentives for storage: traders can buy spot, sell futures, and earn the spread minus storage costs. This cash-and-carry trade is one of the fundamental arbitrage strategies in commodity markets.

When supply conditions tighten and convenience yield rises, a different market structure emerges. If the value of holding physical inventory exceeds the costs of storage and financing, the theoretical futures price falls below the spot price. This creates an inverted term structure.

In backwardation, the futures curve slopes downward, with prices declining as delivery dates extend further into the future:

$$F_{T_2} < F_{T_1} < S_0 \quad \text{where } T_2 > T_1$$

where:

• $F_{T_1}, F_{T_2}$: futures prices for maturities $T_1, T_2$
• $S_0$: spot price

Backwardation signals tight supply conditions. When inventories are low and immediate demand is strong, spot prices rise relative to futures. The market is "paying" for immediate delivery because the commodity is needed now, not later. This premium for immediacy reflects the high convenience yield that holders of physical inventory enjoy. Producers can lock in attractive prices by selling futures, while consumers face a premium for immediate supply.

To quantify the relationship between spot and futures prices, traders and analysts use several standard measures. These metrics provide a common language for discussing market conditions and comparing opportunities across different commodities and time periods.

The basis measures the relationship between spot and futures prices:

$$\text{Basis} = S_0 - F_0$$

where:

• $S_0$: spot price
• $F_0$: futures price

A positive basis indicates backwardation (spot above futures), while a negative basis indicates contango (futures above spot). The basis matters to hedgers because it directly affects the cost or benefit of maintaining hedged positions. Changes in the basis represent a source of risk that even perfectly hedged positions must bear.

The calendar spread measures the price difference between two futures contracts with different delivery months:

$$\text{Calendar Spread} = F_{T_1} - F_{T_2}$$

where:

• $F_{T_1}$: price of near-term contract
• $F_{T_2}$: price of far-term contract

Calendar spreads are particularly useful if you want to take views on changes in market structure without exposure to outright price direction. If you believe that supply conditions will tighten, you can buy the spread, profiting if backwardation deepens, without betting on whether overall prices will rise or fall.

The roll yield captures the return from maintaining a futures position as contracts approach expiration and must be rolled into longer-dated contracts. In backwardation, roll yield is positive because investors sell expensive near-term contracts and buy cheaper far-term contracts. In contango, roll yield is negative. This concept is essential for understanding the performance of commodity index investments, which must continuously roll their futures positions.