Carry_cost: Meaning, Criticisms & Real-World Uses

What Is Carry Cost?

Carry cost, also known as cost of carry or carrying charge, represents the expenses incurred to hold an investment or asset over a period of time. These costs are a crucial component within Financial Management, particularly when dealing with physical commodities or financial instruments like futures contracts and certain types of derivatives. Understanding carry cost is essential for investors and traders, as it directly impacts the profitability and pricing of assets. For physical assets, carry cost can include storage costs, insurance, and financing expenses (such as interest rates paid on borrowed funds). In the context of financial securities, it often refers to the net cost of holding a position, taking into account interest paid on margin loans versus any income received from the asset, such as dividends. Ultimately, carry cost can significantly detract from an investment's total return.⁷

History and Origin

The concept of carry cost emerged naturally with the development of organized markets for deferred delivery of goods, predating modern financial instruments. Early forms of futures contracts, known as "to-arrive" contracts, began trading in the mid-19th century at places like the Chicago Board of Trade (CBOT) for grains.⁶ As these markets evolved from simple private agreements to standardized exchange-traded contracts, the need to account for the costs associated with holding a physical commodity until a future delivery date became formalized. Farmers or merchants holding inventory would incur expenses for storage, insurance, and the interest on capital tied up in the physical goods. These tangible costs directly influenced the price at which they were willing to sell for future delivery compared to the immediate spot price. This fundamental relationship laid the groundwork for the modern understanding of carry cost in derivative pricing.

Key Takeaways

Carry cost refers to the expenses associated with holding an asset or investment over time.
These costs can include interest expenses on borrowed funds, storage costs for physical assets, and insurance premiums.
For income-generating assets, any income received, such as dividends, reduces the effective carry cost.
Carry cost is a critical factor in the pricing of futures contracts and other derivatives, influencing whether a market is in contango or backwardation.
Understanding and accounting for carry cost is vital for investors and traders engaged in hedging, arbitrage, and speculation.

Formula and Calculation

The calculation of carry cost, particularly in the context of futures contracts, aims to establish the theoretical fair value of a future price relative to its current spot price. The simplified formula for the theoretical futures price (F) based on the spot price (S) and carry cost is often expressed as:

F = S \times e^{(r + s - c) \times t}

Where:

( F ) = Futures price
( S ) = Spot price of the underlying asset
( e ) = The base of the natural logarithm (approximately 2.718)
( r ) = The risk-free rate of interest (e.g., the rate at which one could borrow or lend without risk)
( s ) = Storage costs (expressed as a percentage of the spot price, applicable for physical commodities)
( c ) = Convenience yield (the benefit of holding the physical asset, such as the ability to use it immediately or profit from temporary shortages)
( t ) = Time to delivery of the contract, expressed as a fraction of one year

In this formula, ( r + s - c ) collectively represents the annual carry cost as a percentage. For financial assets that do not incur storage costs or offer a convenience yield (like a stock), the formula simplifies to ( F = S \times e^{(r - d) \times t} ), where ( d ) is the dividend yield, as dividends reduce the cost of holding the asset.

Interpreting the Carry Cost

Interpreting carry cost is crucial for understanding the pricing dynamics in financial markets, especially for commodities and derivatives. A positive carry cost indicates that it is more expensive to hold an asset over time than to acquire it immediately. This typically results in a futures price being higher than the current spot price, a market condition known as contango. In contango, investors holding the physical asset incur expenses like storage costs and interest rates on financing, which are then priced into the future delivery cost.

Conversely, a negative carry cost implies that holding the asset provides a benefit that outweighs its costs, or that the present supply is unusually tight. This scenario often leads to the futures price being lower than the spot price, a situation called backwardation. This can occur in commodity markets when there's a strong demand for immediate delivery, creating a high "convenience yield" that makes the spot commodity more valuable than its future equivalent. Understanding the direction and magnitude of carry cost helps traders assess potential profit opportunities and risks in various market structures.

Hypothetical Example

Consider a hypothetical scenario for a barrel of crude oil. Suppose the current spot price of crude oil is $80 per barrel. An investor wants to purchase a futures contract for delivery in six months.

The relevant components of the carry cost are:

Interest rates: Assume a risk-free rate of 5% per annum.
Storage costs: Assume storage and insurance costs amount to $0.50 per barrel per month. Over six months, this is $3.00.
Convenience Yield: For crude oil, there might be a small convenience yield due to the utility of having physical supply for immediate processing, let's say $0.20 per barrel over six months.

Let's calculate the theoretical futures price for one barrel:

Interest Cost: Six months is 0.5 years. Interest cost on $80 at 5% for 0.5 years = $80 * 0.05 * 0.5 = $2.00.
Storage Costs: $3.00 for six months.
Convenience Yield (reduces carry cost): -$0.20 for six months.

Total Carry Cost for six months = Interest Cost + Storage Costs - Convenience Yield
Total Carry Cost = $2.00 + $3.00 - $0.20 = $4.80.

Theoretical Futures Price = Spot Price + Total Carry Cost
Theoretical Futures Price = $80 + $4.80 = $84.80.

Therefore, the theoretical fair price for the crude oil futures contract for delivery in six months would be $84.80, reflecting the carry cost associated with holding the physical asset.

Practical Applications

Carry cost plays a vital role in several areas of financial markets and investment analysis. For example, in the commodity markets, understanding carry cost is fundamental to analyzing the relationship between spot prices and futures contracts. Traders and analysts frequently examine the "curve" of futures prices (e.g., for oil or agricultural commodities) to determine if the market is in contango (futures prices higher than spot, indicating positive carry) or backwardation (futures prices lower than spot, indicating negative carry or a high convenience yield). This analysis helps in making informed decisions regarding inventory management, hedging strategies, and speculation. The Federal Reserve Bank of St. Louis, through its FRED database, provides extensive data on commodity prices, which allows for empirical analysis of these market conditions and the underlying carry costs.⁵

Beyond commodities, carry cost applies to other financial instruments. In currency markets, the "carry trade" strategy explicitly exploits the carry cost differential between two currencies. Investors borrow in a currency with a low interest rate and invest in a currency with a higher interest rate, aiming to profit from the interest rate differential, assuming exchange rates remain stable or move favorably. Similarly, in the bond market, the carry cost can refer to the net return from holding a bond versus the cost of funding that position.

Limitations and Criticisms

While carry cost is a powerful concept for pricing and understanding financial instruments, it has limitations. The theoretical models for calculating carry cost, particularly for futures contracts, assume efficient markets with no arbitrage opportunities. In reality, factors like transaction costs, liquidity constraints, and varying credit risks among market participants can lead to deviations from theoretical carry cost pricing.

Furthermore, the "convenience yield" component for physical commodities can be challenging to quantify accurately, as it reflects the subjective value of having immediate access to a physical asset. This makes the precise calculation and interpretation of carry cost for certain real assets less straightforward than for purely financial instruments. Academic research, such as that by the National Bureau of Economic Research, explores the complexities of carry trades and their relationship with commodity prices, highlighting that while the concept explains a substantial portion of carry trade risk premia, it also interacts with broader economic factors like trade costs and market segmentation.⁴ Unexpected market events or disruptions to supply chains can also drastically alter storage costs and convenience yields, leading to unexpected shifts in futures pricing that are not easily predicted by standard carry cost models.

Carry Cost vs. Opportunity Cost

While closely related within financial management, carry cost and opportunity cost represent distinct financial concepts. Carry cost is the direct expense of holding an asset over time. These are explicit out-of-pocket costs such as storage costs, insurance, and the interest rates paid on funds borrowed to finance the asset. For example, if you buy physical gold, the cost of storing it in a vault and insuring it are direct carry costs.

Opportunity cost, on the other hand, is the value of the next best alternative that was foregone when a particular decision was made. It's an implicit cost, not a direct expense. If you invest $10,000 in a stock, the opportunity cost is the return you could have earned if you had invested that $10,000 in a different asset, such as a bond or a savings account. While the interest paid on a margin account used to buy the stock is a carry cost, the foregone return from not investing in an alternative is an opportunity cost. Both are crucial for assessing the true economic profitability of an investment, but carry cost is tangible and directly impacts cash flow, whereas opportunity cost reflects a missed potential benefit.

FAQs

What drives carry cost in commodity markets?

In commodity markets, carry cost is primarily driven by three factors: the prevailing interest rates (cost of financing the asset), storage costs (for holding the physical commodity), and convenience yield (the benefit of having the physical commodity available for immediate use or to meet demand). When these costs are high and convenience yield is low, futures prices tend to be higher than spot prices, indicating positive carry.

How does carry cost affect futures prices?

Carry cost has a direct impact on futures contract pricing. In an efficient market, the futures price of an asset should reflect its spot price plus the net carry cost incurred until the contract's expiration. A positive carry cost leads to futures prices being higher than the spot price (contango), while a negative carry cost can lead to futures prices being lower than the spot price (backwardation).², ³

Is carry cost always positive?

No, carry cost is not always positive. While typically positive for physical commodities due to storage costs and financing, it can be negative. A negative carry cost often occurs when the convenience yield (the benefit of holding the physical asset) outweighs the financing and storage expenses. This situation, known as backwardation, can arise from temporary supply shortages or high immediate demand for the underlying asset.¹