5.3 Commodities Markets, Contango & Backwardation

Commodity investing differs fundamentally from investing in traditional financial assets such as stocks and bonds. Equities represent claims on expected future corporate earnings, and bonds represent contractual rights to interest and principal payments. Commodities, by contrast, are physical assets that generate no ongoing cash flows, pay no dividends or interest, and incur ongoing storage, insurance, and transportation costs. Consequently, exposure to commodities is primarily achieved through exchange-traded derivative contracts—most notably commodity futures contracts.

Spot Prices vs. Futures Prices and the Cost of Carry Model

Understanding commodity derivatives requires distinguishing between the spot price ($S_0$)—the price for immediate physical delivery of a commodity—and the futures price ($F_t$)—the price agreed upon today for physical delivery at a specified future date $t$.

The theoretical relationship between spot and futures prices is governed by the Cost of Carry Model. Under full arbitrage conditions, the futures price equals the spot price plus net carrying costs:

$F_t = S_0 \times (1 + r)^t + U_t - C_t$

In continuous-time notation, the relationship is expressed as:

$F_t = S_0 \cdot e^{(r + u - y)t}$

where:

• $r$ = Risk-free financing interest rate (the cost of capital to finance the physical purchase)
• $u$ (or $U_t$) = Physical storage, insurance, and transportation cost rate
• $y$ (or $C_t$) = Convenience yield rate

The Convenience Yield & Theory of Storage

The convenience yield ($y$) represents the non-monetary benefit or option value derived from physically holding the actual commodity in inventory rather than holding a futures contract. According to the Theory of Storage developed by Kaldor, Working, and Telser:

• High Inventory / Abundant Supply: When physical inventories are high, the convenience yield is low ($y \approx 0$). Industrial processors face little risk of supply disruption, so physical inventory offers minimal extra benefit over a futures contract.
• Low Inventory / Severe Shortage: When physical inventories are depleted, the convenience yield rises dramatically ($y > r + u$). Manufacturers are willing to pay a premium for immediate physical delivery to prevent factory shutdowns or customer default, driving the spot price significantly above the futures price.

Term Structure of Futures: Contango vs. Backwardation

The relationship between commodity futures prices across different expiration dates forms the futures term structure curve. The shape of this curve determines whether a commodity market is in Contango or Backwardation.

Contango Markets

In a contango market, futures prices trade at a premium to spot prices ($F_t > S_0$), and longer-dated futures trade at higher prices than shorter-dated futures.

• Underlying Drivers: Contango occurs when physical supply is abundant, storage space is available, and the convenience yield is low ($y < r + u$). Futures prices must exceed spot prices to compensate market participants for financing and physical storage costs over time.
• Convergence: As a futures contract approaches its expiration date ($t \rightarrow 0$), the futures price must converge downward to meet the spot price, eliminating arbitrage opportunities at maturity.

Backwardation Markets

In a backwardation market, futures prices trade at a discount to spot prices ($S_0 > F_t$), and longer-dated futures trade at lower prices than near-term futures.

• Underlying Drivers: Backwardation occurs when immediate physical demand is high, inventories are tight, and the convenience yield exceeds carrying costs ($y > r + u$).
• Keynes' Theory of Normal Backwardation: Economist John Maynard Keynes proposed that commodity producers (hedgers) naturally seek to eliminate price risk by selling futures contracts forward. To entice speculators to assume this price risk, producers sell futures at a discount below the expected future spot price. Speculators are rewarded for absorbing price risk as the futures contract converges upward toward the spot price at maturity.

Components of Commodity Futures Total Return

Investors who gain commodity exposure through passive long futures positions do not simply earn the change in spot prices. The total return of a fully collateralized long commodity futures position consists of three distinct structural components:

$\text{Total Return} = \text{Spot Return} + \text{Roll Yield} + \text{Collateral Yield}$

1. Spot Return (Price Return)

The percentage change in the underlying physical commodity's spot price over the holding period:

$\text{Spot Return} = \frac{S_t - S_0}{S_0}$

2. Roll Yield (Roll Return)

Because futures contracts expire on specific dates, a long-term investor who wishes to maintain continuous commodity exposure must repeatedly close out expiring near-term contracts ($F_{\text{near}}$) and purchase longer-dated contracts ($F_{\text{far}}$). This process is called rolling the futures position. The roll yield is defined as:

$\text{Roll Yield} = \frac{F_{\text{near}} - F_{\text{far}}}{F_{\text{near}}}$

• Negative Roll Yield in Contango: In contango ($F_{\text{far}} > F_{\text{near}}$), the investor sells the expiring cheaper near-month contract and buys the higher-priced far-month contract. Over time, as each newly purchased contract converges downward toward the spot price, the investor experiences a structural loss. Long positions in persistent contango suffer severe return drag.
• Positive Roll Yield in Backwardation: In backwardation ($F_{\text{near}} > F_{\text{far}}$), the investor sells the expiring higher-priced near-month contract and buys the cheaper far-month contract. As the newly bought cheaper contract converges upward toward the spot price, the investor earns a structural gain.

3. Collateral Yield (Cash Return)

Futures contracts are leveraged instruments that require investors to deposit margin collateral. When an investor takes an unleveraged long commodity futures position, 100% of the contract value is deposited in safe, short-term interest-bearing securities such as U.S. Treasury bills. The interest earned on this cash collateral forms the collateral yield.