Cost of carry

What Is Cost of Carry?

Cost of carry refers to the expenses associated with holding a financial asset or physical commodity over a period. It is a fundamental concept within Derivatives Pricing and plays a crucial role in determining the theoretical price of futures and forward contracts. The cost of carry encompasses various charges, including financing costs, such as the interest rates incurred on borrowed funds to acquire the asset, and any storage costs for physical goods. It also accounts for income generated by the asset, such as dividends or convenience yield, which effectively reduce the overall cost of carry. Understanding the cost of carry is essential for traders and investors to evaluate the profitability and feasibility of holding a position.

History and Origin

The concept of cost of carry has long been implicit in financial markets, particularly in commodity markets, where the physical burden of holding inventory was always evident. However, its formalization as a pricing model for futures contracts gained prominence with the development of modern financial theory. Early academics, including Fischer Black and Myron Scholes in the 1970s, contributed to the framework for pricing options and futures, which inherently relied on the cost of carry principle. For instance, the academic examination of commodity futures prices has consistently shown the relevance of the cost of carry model, often focusing on how it explains the difference between spot and futures prices, particularly for assets like gold where storage costs are relatively minor.⁵ The evolution of the modern financial system, with its complex array of financial instruments and sophisticated trading strategies, necessitated a clear and quantifiable understanding of these holding costs.

Key Takeaways

Cost of carry represents the total expenses (or benefits) incurred from holding an asset over time.
It is a critical component in the pricing of futures and forward contracts, influencing the relationship between spot price and forward price.
Key elements typically include financing costs (interest), storage expenses (for physical assets), and income generated (dividends, convenience yield).
A positive cost of carry implies the futures price is higher than the spot price (contango), while a negative cost (often termed a net benefit) implies the futures price is lower (backwardation).
Changes in underlying factors like interest rates significantly impact the cost of carry and, consequently, derivative prices.

Formula and Calculation

The cost of carry model for a non-dividend-paying asset or a commodity without a convenience yield can be expressed in terms of the relationship between its spot price and its theoretical futures price.

For a non-dividend-paying asset or a commodity without a convenience yield, the theoretical futures price (F) is given by:

F = S \times e^{(r \times T)}

Where:

(F) = Futures price
(S) = Spot price of the underlying asset
(e) = The base of the natural logarithm (approximately 2.71828)
(r) = The risk-free rate of interest (annualized, continuously compounded)
(T) = Time to expiration of the contract (in years)

When considering assets with income or physical commodities with storage costs and convenience yield, the formula is adjusted:

F = S \times e^{(r + SC - CY) \times T}

Where:

(SC) = Storage Cost (as a percentage of the spot price)
(CY) = Convenience yield (as a percentage of the spot price, representing the benefit of holding the physical asset)

The "cost of carry" itself in this context is ( (r + SC - CY) ).

Interpreting the Cost of Carry

Interpreting the cost of carry involves understanding its implications for asset valuation, particularly in futures and forward markets. A positive cost of carry indicates that it is more expensive to hold an asset for future delivery than to buy it at the current spot price and carry it forward. This scenario, known as contango, is common in commodity markets where storage and financing costs are significant. Conversely, a negative cost of carry, or a net benefit of holding the asset, implies that the future price is lower than the spot price. This situation, known as backwardation, often occurs when there is high current demand for the physical asset, leading to a high convenience yield. Traders and investors use the cost of carry to identify potential arbitrage opportunities if the actual futures price deviates significantly from the theoretical price implied by the cost of carry model.

Hypothetical Example

Consider an investor evaluating a one-year futures contract for a non-dividend-paying stock.

Current spot price (S) = $100
Annual risk-free rate (r) = 5% (or 0.05)
Time to expiration (T) = 1 year

In this simplified scenario, the only cost of carry is the financing cost.
Using the formula ( F = S \times e^{(r \times T)} ):
( F = $100 \times e^{(0.05 \times 1)} )
( F = $100 \times e^{0.05} )
( F \approx $100 \times 1.05127 )
( F \approx $105.13 )

The theoretical futures price is $105.13. The cost of carry, in this case, is approximately $5.13, representing the interest that would be forgone or paid to hold the asset for one year. If the actual futures contract is trading at, say, $106, an investor might consider short selling the futures contract and buying the underlying stock, effectively earning the difference less transaction costs, a classic arbitrage strategy.

Practical Applications

The cost of carry is a fundamental concept with widespread applications across various financial sectors. In capital markets, it is extensively used in the pricing of futures contracts and forward contracts on commodities, currencies, and financial instruments. It helps market participants determine the fair value of these derivatives relative to their underlying assets. For instance, in commodity markets, the cost of carry directly incorporates storage costs and any yield from holding the physical asset, influencing trading decisions and inventory management.⁴

Furthermore, the cost of carry is crucial for hedging strategies, allowing businesses and investors to quantify the expense of maintaining a hedged position over time. It also informs arbitrage opportunities, where discrepancies between theoretical and actual prices can be exploited. Macroeconomic factors, particularly interest rates, have a significant impact on the cost of carry. When the Federal Reserve adjusts interest rates, it directly affects the financing component of the cost of carry, influencing borrowing costs across the economy and impacting the pricing of financial assets and derivatives.³,²

Limitations and Criticisms

While the cost of carry model is a powerful tool in derivatives pricing, it operates under certain simplifying assumptions that can limit its real-world applicability and predictive accuracy. One primary criticism is its assumption of efficient markets where arbitrage opportunities are quickly eliminated. In reality, market frictions, transaction costs, and liquidity constraints can prevent perfect arbitrage, leading to persistent deviations from theoretical prices.

Another limitation arises from the difficulty in accurately estimating certain components, such as the convenience yield for commodities, which is often an implied value rather than a directly observable cost. For options contracts, while the cost of carry influences the underlying asset's futures price, option pricing models like Black-Scholes also rely on factors like volatility, which are not directly captured by the cost of carry itself. Academic studies on the cost of carry model's application, such as in gold futures pricing, often highlight how actual market prices can deviate from the model's predictions due to factors beyond simple financing and storage costs.¹ Furthermore, unforeseen events, supply chain disruptions, or sudden shifts in market sentiment can introduce complexities that the static cost of carry model may not fully account for.

Cost of Carry vs. Carrying Value

While both terms relate to holding assets, "cost of carry" and "carrying value" refer to distinct concepts in finance. Cost of carry specifically identifies the expenses (or net costs/benefits) associated with maintaining an investment position over a period. These are typically recurring costs like interest on borrowed funds, storage fees for physical commodities, and the opportunity cost of capital. Its primary application is in the pricing of derivative instruments like futures contracts, where it helps explain the relationship between the spot and future price of an asset.

In contrast, carrying value refers to the value of an asset as recorded on a company's balance sheet. It is an accounting term, representing the asset's original cost minus any accumulated depreciation, amortization, or impairment charges. Carrying value reflects the book value of an asset at a given point in time and is not directly concerned with the ongoing expenses of holding that asset in the same way cost of carry is. The confusion often arises because both terms are related to "holding" an asset, but cost of carry focuses on the flow of costs over time, while carrying value focuses on the stock value at a specific moment.

FAQs

Q1: What is a "negative" cost of carry?
A: A "negative" cost of carry, often referred to as a net benefit or yield, occurs when the income generated from holding an asset (such as dividends from stocks or the convenience yield from a physical commodity) exceeds the financing and storage costs. In such cases, the futures price tends to be lower than the current spot price, a situation known as backwardation.

Q2: How do interest rate changes affect the cost of carry?
A: Interest rates are a significant component of the cost of carry. An increase in interest rates raises the financing cost of holding an asset, thereby increasing the overall cost of carry. Conversely, a decrease in interest rates reduces the financing cost, lowering the cost of carry and making it cheaper to hold positions, particularly those financed by borrowing.

Q3: Is cost of carry only relevant for commodities?
A: No, while often discussed in the context of commodity markets due to obvious storage costs, cost of carry is also highly relevant for financial assets like stocks, bonds, and currencies. For these assets, the primary components are typically financing costs (interest rates) and any income generated, such as dividends for stocks or interest payments for bonds.