Forward curves

What Are Forward Curves?

Forward curves are graphical representations that plot the forward prices of a given asset or financial instrument for different delivery or settlement dates in the future. They provide a visual depiction of the market's expectations for future prices, extending beyond the current spot price. These curves are a fundamental concept within derivatives markets and are widely used for pricing, hedging, and speculative purposes across various asset classes, including commodities, currencies, and fixed income products. A forward curve effectively summarizes a series of forward contracts.

History and Origin

The concept underlying forward curves has ancient roots, predating formalized financial markets. Early forms of "to-arrive" contracts, which specified future delivery at a pre-agreed price, can be traced back to Sumerian merchants in Mesopotamia around 3000 BCE, who recorded agreements for future delivery of agricultural goods on clay tablets. These early forward contracts helped manage price uncertainty for farmers and merchants⁵.

In more recent history, the formalization of such agreements led to the development of futures exchanges. For instance, the Chicago Board of Trade (CBOT) was founded in 1848, and "to-arrive" contracts for grains began trading almost immediately, marking a significant step towards standardized trading in the United States⁴. The evolution of these markets and the agreements traded within them laid the groundwork for the modern analysis of future price expectations, leading to the development and widespread use of forward curves in contemporary finance. Regulatory bodies like the Commodity Futures Trading Commission (CFTC), established in 1974, play a role in overseeing these markets to ensure integrity and prevent manipulation³.

Key Takeaways

• Forward curves illustrate expected future prices for an asset over various future dates.
• They are derived from the prices of forward contracts, which are customized agreements between two parties.
• The shape of a forward curve can indicate market sentiment, showing whether prices are expected to rise (contango) or fall (backwardation).
• Investors and businesses use forward curves for risk management, pricing, and identifying potential arbitrage opportunities.
• Forward curves are distinct from historical price charts as they represent future expectations rather than past performance.

Formula and Calculation

The pricing of a single forward contract, from which a forward curve is constructed, often relies on the "cost of carry" model. This model suggests that the forward price should reflect the spot price plus the costs associated with holding the asset until the delivery date, minus any benefits received.

For a non-dividend-paying asset or commodity, the theoretical forward price (F) can be calculated as:

Where:

• (F) = Forward Price
• (S) = Current Spot Price of the underlying asset
• (e) = The base of the natural logarithm (approximately 2.71828)
• (r) = The risk-free interest rates (annualized, continuously compounded)
• (q) = Annualized storage costs or convenience yield (for commodities) or dividend yield (for equities), if applicable
• (T) = Time to maturity in years

To construct a full forward curve, this calculation (or a more complex model incorporating market supply and demand dynamics) is performed for multiple future delivery dates, with each resulting forward price plotted against its respective maturity.

Interpreting the Forward Curve

Interpreting a forward curve involves understanding its shape, which provides insights into market expectations for future prices.

• Contango (Normal Market): A forward curve is in contango when the forward price is higher than the spot price, and longer-dated forward prices are progressively higher than shorter-dated ones. This upward-sloping curve often indicates that market participants expect the price of the underlying asset to increase over time, potentially due to storage costs, interest rates, or anticipated scarcity. For commodities, this is common as it reflects the cost of carrying inventory.
• Backwardation (Inverted Market): A forward curve is in backwardation when the forward price is lower than the spot price, and longer-dated forward prices are progressively lower than shorter-dated ones. This downward-sloping curve suggests that the market expects the price to decrease in the future. This can occur in commodity markets due to immediate high demand or supply shortages, leading to a "convenience yield" for holding the physical asset.

The steepness and direction of the curve are crucial. A steep upward slope in contango might suggest strong future demand or rising carrying costs, while a steep downward slope in backwardation might indicate current supply constraints or anticipated future oversupply. Changes in factors like supply and demand expectations, interest rates, and geopolitical events can cause the forward curve to shift and change shape.

Hypothetical Example

Consider a hypothetical scenario for a commodity like crude oil. An energy trading firm wants to understand the market's expectation for oil prices over the next year. They look at the current spot price and available forward contract prices for various delivery months:

• Current Spot Price: $80.00/barrel
• 1-month Forward: $80.50/barrel
• 3-month Forward: $81.20/barrel
• 6-month Forward: $82.50/barrel
• 12-month Forward: $84.00/barrel

When these prices are plotted on a graph with time to maturity on the x-axis and price on the y-axis, the result is a forward curve. In this example, the curve is upward sloping (in contango), indicating that the market expects crude oil prices to gradually increase over the next year.

This forward curve provides valuable information. For instance, an airline looking to hedge its fuel costs might use the 6-month forward price as a reference point for a future purchase. A producer might interpret the rising curve as an incentive to increase future production.

Practical Applications

Forward curves have diverse practical applications across financial markets and industries:

• Risk Management and Hedging: Companies use forward curves to hedge against adverse price movements for raw materials, finished goods, or currency exposures. An airline, for example, might use a jet fuel forward curve to lock in a future price, mitigating the risk of rising fuel costs.
• Pricing of Derivatives: Forward curves are critical inputs for pricing other derivatives, such as options, where future price expectations directly influence premium calculations.
• Investment and Trading Decisions: Traders and investors analyze forward curves to formulate views on future price movements. Identifying shapes like contango or backwardation can inform trading strategies.
• Valuation: In sectors like energy or agriculture, forward curves provide a basis for valuing inventory, long-term supply contracts, and capital projects whose profitability depends on future commodity prices.
• Monetary Policy and Economic Analysis: For central banks and economists, forward curves for interest rates (like a yield curve derived from forward rates) can signal market expectations for future policy rates and economic growth. The transition away from benchmarks like LIBOR to alternative reference rates significantly impacts how interest rate forward curves are constructed and used.
• Market Oversight: Regulators, such as the Commodity Futures Trading Commission (CFTC), monitor forward curves and related derivatives markets to ensure fair and transparent pricing, prevent market manipulation, and maintain overall market integrity². The Federal Reserve also publishes resources to help market participants understand the structure and functioning of derivatives markets and their role in risk management¹.

Limitations and Criticisms

While powerful tools, forward curves have several limitations and criticisms:

• Theoretical vs. Actual Prices: Forward curves represent theoretical or market-implied future prices, not guarantees. Actual future prices can, and often do, deviate significantly from what the forward curve indicates. Unforeseen events, changes in supply and demand dynamics, or shifts in market participants' sentiment can lead to discrepancies.
• Liquidity Issues: For longer maturities or less actively traded assets, the liquidity of forward contracts can be thin. This means that the prices used to construct the far end of the forward curve may not be truly representative or easily executable, leading to less reliable insights.
• Model Dependence: The construction of sophisticated forward curves, especially for complex instruments, relies on various pricing models and assumptions (e.g., risk-free rates, volatility). Errors or inaccuracies in these models can lead to misleading curve shapes or price predictions.
• Arbitrage Limitations: While arbitrage opportunities are theoretically arbitraged away, in practice, transaction costs, capital constraints, and market frictions can prevent perfect alignment between spot and forward prices.

Forward Curves vs. Futures Curves

While often used interchangeably in casual conversation, especially for commodities, "forward curves" and "futures curves" refer to distinct concepts based on the underlying contractual agreements.

A key source of confusion arises because for highly liquid commodities and financial instruments, the prices of comparable forward and futures contracts tend to converge due to arbitrage. However, their structural differences, particularly concerning standardization, clearing, and counterparty risk, remain important distinctions for market participants.

FAQs

What does the shape of a forward curve tell you?

The shape of a forward curve indicates the market's collective expectation for how the price of an asset will change over time. An upward-sloping curve (contango) suggests expectations of rising prices, while a downward-sloping curve (backwardation) suggests expectations of falling prices.

How are forward curves used in investing?

Investors use forward curves to gain insights into market sentiment and potential future price movements. They can inform decisions about entry and exit points for trades, help in valuing assets sensitive to future prices, and guide hedging strategies to protect portfolios from adverse price swings.

Are forward curves always accurate predictors of future prices?

No, forward curves are not always accurate predictors. They reflect market expectations at a given point in time based on available information, but unforeseen events, changes in supply and demand, or shifts in economic conditions can cause actual future prices to diverge significantly from what the curve implied.

What is the difference between a forward curve and a spot price?

A spot price is the current price of an asset for immediate delivery. A forward curve, on the other hand, is a series of prices for future delivery dates, providing a snapshot of the market's expectations for that asset's price at various points in the future.