COST-OF-CARRY MODEL EXPLAINED

What is the Cost-of-Carry Model?

The cost-of-carry model is a fundamental principle in finance used to determine the fair value of derivative instruments, particularly futures contracts. It is based on the premise that the price of a futures contract should depend on the spot price of the underlying asset, plus the costs incurred in holding that asset until the contract's expiration. These costs include storage costs, financing costs, and the convenience yield.

In its simplest form, the cost-of-carry model is represented as:

F = S × e(r + s - c)t

Where:

• F = Futures price
• S = Spot price of the asset
• r = Risk-free rate (financing cost)
• s = Storage cost
• c = Convenience yield
• t = Time to maturity (in years)

The model assumes a frictionless market, meaning no transaction costs or taxes and the ability to borrow and lend at the risk-free rate. Despite its theoretical simplicity, it is widely used in practice and adjusted as needed for asset class-specific nuances.

This model plays a crucial role in arbitrage strategies, commodity pricing, and understanding market behaviours. It provides a benchmark price for futures traders and allows them to assess whether a particular futures contract is overvalued or undervalued relative to the spot market and associated carrying costs.

The cost-of-carry model is particularly influential in commodities, where the physical attributes of the underlying asset—such as perishability and storage requirements—affect the total carrying cost. It also applies to financial instruments like stock index futures, interest rate futures, and currency futures, albeit with some differences depending on dividend yields or forward rate structures.

Overall, the cost-of-carry model serves as an essential financial framework, ensuring coherent pricing between spot and derivative markets and supporting traders, investors, and analysts in making informed pricing decisions based on the rational cost of holding an asset over time.

Understanding Storage and Financing Costs

Storage and financing costs are key elements of the cost-of-carry model. They represent the direct and indirect expenses associated with holding a physical or financial asset until the maturity of a futures contract. These costs differ depending on the nature of the asset and market conditions but are integral to understanding futures pricing.

Storage Costs

Storage costs are particularly significant in commodities markets, where the physical nature of goods like oil, grain, precious metals, or natural gas entails tangible holding expenses. These include:

• Warehouse fees
• Insurance premiums
• Deterioration or spoilage (in the case of perishables)
• Security measures
• Temperature control and maintenance

These costs are typically expressed as a percentage of the asset’s value or in fixed monetary terms over a specific period. When storage costs are high, futures prices tend to rise relative to spot prices to reflect the additional burden carried by the holder.

Financing Costs

Financing, or interest cost, is the theoretical cost of capital required to purchase and hold the asset instead of allocating that capital elsewhere. In the cost-of-carry model, this is typically represented by the risk-free rate, such as the yield on a government bond over the same maturity period.

For investors who borrow funds to finance the asset purchase, the financing cost is the interest paid on that loan. For cash investors, it represents the opportunity cost of tying up capital in the underlying position. In practice, financing costs can be impacted by:

• Prevailing interest rates
• Leverage and margin requirements
• Credit spreads or borrowing terms

For example, if an investor buys gold and funds the purchase with borrowed money, the cost of borrowing directly affects the overall carrying cost. The higher the interest rates, the greater the cost of carry, and thus the higher the forward price will rise above the spot price, assuming other factors remain equal.

In commodity futures, both financing and storage costs contribute to the phenomenon known as “contango,” where futures prices exceed spot prices. A deep understanding of these costs is vital for risk management and effective futures trading.

Examining Convenience Yield in Futures Pricing

The convenience yield is a more nuanced concept in the cost-of-carry model, representing the non-monetary benefits of holding the physical commodity rather than a futures contract. It is especially relevant in markets where physical possession offers strategic or operational advantages.

Defining Convenience Yield

Convenience yield is essentially the implied return on holding the actual asset. It can be thought of as the yield or utility derived from immediate possession, even though this return doesn’t reflect any cash inflows.

For example, an oil refiner may value having immediate access to crude oil more than a futures contract for delivery in three months due to potential supply disruptions or operational flexibility. This preference for possession creates a yield that offsets some or all of the financing and storage costs, reducing the overall cost of carry.

Factors Influencing Convenience Yield

• Inventory Levels: When inventories are low, the convenience yield tends to rise as the value of guaranteed access increases.
• Market Volatility: In uncertain markets, possession mitigates risks from delays or shortages, enhancing the convenience yield.
• Seasonality: In agricultural commodities, planting and harvesting cycles may increase the need for physical stocks at certain times.
• Logistical Considerations: Transportation delays, bottlenecks, or political risks increase the value of accessible stock.

The convenience yield is often difficult to measure directly. However, it is inferred from observed futures prices and known storage and financing costs. In backwardation—where futures prices are below spot prices—the convenience yield exceeds the cost of carry, indicating a strong incentive to hold the asset.

Financial theory views convenience yield as a form of implied income that justifies why futures may trade at a discount. It affects trading decisions by indicating the value participants place on flexibility, supply security, and inventory management in their business models.

In practice, convenience yield can fluctuate significantly even over short periods, influencing forward curves, hedging strategies, and investor positioning. Comprehending this component not only aids in accurate pricing but also aligns trading approaches to real-world supply dynamics and operational needs.