Futures curve

What Is a Futures Curve?

A futures curve is a graphical representation depicting the prices of futures contracts for a specific commodity or financial instrument across different maturity dates. It falls under the broader category of derivatives and financial markets, providing a visual snapshot of market expectations for future prices. Each point on the futures curve corresponds to a different delivery month, with the horizontal axis representing time to maturity and the vertical axis representing the futures price. Understanding the shape and movement of the futures curve is crucial for participants engaged in hedging, speculation, and arbitrage.

History and Origin

The concept of agreeing on a price for future delivery dates has ancient roots in commerce. However, the formalization of standardized "exchange traded" contracts, known as futures contracts, originated in the mid-19th century. The Chicago Board of Trade (CBOT), established on April 3, 1848, initially served as a cash market for grain, with forward contracts trading almost immediately.¹⁰ By 1864, the CBOT listed the first standardized futures contracts, primarily for agricultural commodities like wheat and corn. This standardization was a significant development, as it allowed for greater market participation and liquidity by defining uniform contract sizes, quality specifications, and delivery procedures.

As the futures markets grew in complexity and scope, extending beyond just agricultural products to include financial instruments such as U.S. Treasury bonds by 1977⁹, the need for regulatory oversight became apparent. This led to the establishment of the Commodity Futures Trading Commission (CFTC) in 1974.⁸ The CFTC is an independent U.S. government agency tasked with regulating the U.S. derivatives markets, including futures, to promote integrity, resilience, and vibrancy, and to protect market participants from manipulation and fraud.⁶, ⁷

Key Takeaways

• A futures curve plots the prices of futures contracts for a given asset across various expiration dates.
• It provides insights into market expectations regarding the future spot price of an asset.
• The two primary shapes of a futures curve are contango (upward sloping) and backwardation (downward sloping).
• The shape of the curve is influenced by factors such as storage costs, interest rates, convenience yield, and supply and demand dynamics.
• The futures curve is a vital tool for risk management, price discovery, and trading strategies in commodity and financial markets.

Formula and Calculation

The theoretical price of a futures contract can be estimated using the cost of carry model, especially for storable commodities and financial assets that generate income or incur costs. The formula generally accounts for the spot price of the underlying asset, the risk-free interest rate, and any associated storage costs or convenience yield.

The formula for the theoretical futures price (F) is:

$F = S \times e^{(r + c - y)T}$

Where:

• (F) = Futures price
• (S) = Current spot price of the underlying asset
• (e) = The base of the natural logarithm (approximately 2.71828)
• (r) = Risk-free interest rate (annualized)
• (c) = Storage costs (as a percentage of the asset's value, annualized)
• (y) = Convenience yield (the benefit of holding the physical asset, as a percentage of the asset's value, annualized)
• (T) = Time to maturity of the futures contract (in years)

For financial instruments like currencies or equities that pay dividends, the "cost of carry" might incorporate the interest rate differential or the dividend yield, respectively, instead of storage costs and convenience yield.

Interpreting the Futures Curve

The shape of the futures curve offers significant insights into market sentiment and the underlying dynamics of supply and demand for the asset. There are two primary shapes:

• Contango: A futures curve is in contango when the futures price is higher than the spot price, and futures prices for more distant maturities are progressively higher than those for nearer maturities. This results in an upward-sloping curve. Contango often reflects the cost of carrying the commodity over time, including storage, insurance, and financing costs. It can also indicate an expectation that the spot price will rise in the future.
• Backwardation: Conversely, a futures curve is in backwardation when the futures price is lower than the spot price, and futures prices for more distant maturities are progressively lower than those for nearer maturities. This creates a downward-sloping curve. Backwardation typically occurs when there is high current demand or a perceived shortage of the underlying asset, leading to a higher spot price relative to future prices. It may also imply a significant convenience yield, meaning there is a benefit to possessing the physical commodity now.

These shapes can change rapidly in response to new information, geopolitical events, or shifts in fundamental market conditions.

Hypothetical Example

Consider a hypothetical crude oil futures curve. Suppose the current spot price for West Texas Intermediate (WTI) crude oil is $80 per barrel.

A market participant observes the following futures prices:

• 1-month futures: $81.50
• 3-month futures: $82.75
• 6-month futures: $83.50
• 12-month futures: $84.00

Plotting these prices against their respective maturities would show an upward-sloping futures curve. This indicates a state of contango. In this scenario, the market anticipates that crude oil prices will gradually increase over the next year. This could be due to expected increases in demand, known future supply constraints, or simply the cost of storing crude oil for delivery in later months.

If, however, the prices were:

• 1-month futures: $79.00
• 3-month futures: $78.00
• 6-month futures: $77.00
• 12-month futures: $76.50

With a current spot price of $80, the curve would be downward-sloping, indicating backwardation. This might happen if there's an immediate, unexpected disruption to oil supply, causing the current spot price to surge, while market participants expect the supply issue to resolve or demand to temper in the future. The Energy Information Administration (EIA) provides weekly reports on U.S. crude inventories, which can significantly influence spot and futures prices.⁴, ⁵

Practical Applications

The futures curve has numerous practical applications across finance and commodity markets:

• Risk Management and Hedging: Businesses and investors use futures contracts to manage price risk. For example, an airline can use jet fuel futures to lock in a future purchase price, protecting itself from unexpected increases. The futures curve helps them identify appropriate maturity dates for their hedging needs.
• Price Discovery: Futures markets serve as a robust mechanism for price discovery, as market participants collectively bid and offer, reflecting a consensus view on future prices. This information is distilled into the futures curve, providing valuable benchmarks for producers, consumers, and policymakers.
• Investment and Speculation: Traders analyze the futures curve to identify potential trading opportunities based on their expectations of future price movements or changes in the curve's shape. They might take long positions in contango markets if they expect spot prices to rise more than implied, or short positions in backwardated markets if they foresee price declines.
• Arbitrage: If the futures curve deviates significantly from the theoretical cost of carry, arbitrageurs may exploit these mispricings to generate risk-free profits. This activity helps ensure that the futures curve remains aligned with economic fundamentals, contributing to overall market efficiency.
• Inventory Management: For producers and consumers of physical commodities, the shape of the futures curve can influence decisions about inventory levels. A strong contango might encourage storing commodities, while backwardation could incentivize immediate sale.

Limitations and Criticisms

Despite its utility, the futures curve is not without limitations and criticisms.

• Market Efficiency Debates: A common debate revolves around whether futures prices are unbiased predictors of future spot prices. While theoretically, in an efficient market, futures prices should reflect all available information and be unbiased forecasts, empirical research has yielded mixed results.², ³ Some studies suggest that expected excess returns to futures speculation can be non-zero, indicating that futures prices may not always be perfectly unbiased predictors.¹ Factors such as risk premiums demanded by hedgers, or market inefficiencies, can cause deviations.
• Liquidity and Far-Out Contracts: Futures contracts with distant maturities often have lower liquidity compared to near-term contracts. This can lead to less reliable pricing for the far end of the futures curve, as fewer participants are actively trading those maturities. Wider bid-ask spreads and less transparent pricing can make it challenging to interpret the curve accurately for long-term outlooks.
• Unforeseen Events: The futures curve reflects current market expectations. However, it cannot perfectly account for sudden, unforeseen events such as natural disasters, geopolitical crises, or unexpected regulatory changes, which can drastically alter future supply and demand dynamics and, consequently, the shape of the curve.
• Cost of Carry Assumptions: The theoretical cost of carry model relies on certain assumptions, such as a constant risk-free rate, which may not hold true in real-world markets. Additionally, accurately quantifying storage costs and convenience yields can be complex and may vary between market participants, leading to different interpretations of the "fair value" futures price.

Futures Curve vs. Forward Curve

While often used interchangeably in casual conversation, a crucial distinction exists between a futures curve and a forward curve. Both illustrate prices for future delivery, but their underlying contracts and market structures differ significantly:

The futures curve is constructed from prices set on organized exchanges, ensuring standardization and transparency. The forward curve, on the other hand, is derived from privately negotiated forward contracts, which are flexible and tailored to specific needs but lack the standardization and public price transparency of futures. This difference in structure and trading environment means that while the shapes of the two curves may often align, they are not identical.

FAQs

What does an upward-sloping futures curve mean?

An upward-sloping futures curve, known as contango, indicates that futures prices for later delivery dates are higher than those for earlier dates. This typically reflects the cost of carrying the commodity over time (storage, insurance, financing) and can also suggest that the market expects the spot price of the asset to increase in the future.

What does a downward-sloping futures curve indicate?

A downward-sloping futures curve, known as backwardation, means that futures prices for later delivery dates are lower than those for earlier dates. This often occurs when there is a current shortage or strong demand for the physical asset, making the immediate (spot) price higher than future prices. It can also be driven by a significant "convenience yield," which is the benefit of having the physical commodity available for immediate use.

How do supply and demand affect the futures curve?

Supply and demand are fundamental drivers of the futures curve. High current demand relative to supply can push the spot price up, potentially leading to backwardation. Conversely, an oversupply or expectation of future oversupply, combined with storage costs, can lead to contango. Anticipated changes in future supply or demand can shift the entire futures curve.

Can the futures curve predict future prices?

While the futures curve reflects the market's collective expectation of future prices, it is not a perfect predictor. Futures prices incorporate various factors, including the cost of carry, risk premiums, and market sentiment, which can cause them to deviate from the eventual spot price at maturity. Academic research on market efficiency in futures markets continues to explore the extent to which futures prices serve as unbiased forecasts.