Cost of Carry

Decoding the Cost of Carry: A Key Concept in Financial Markets

The "cost of carry" is a crucial concept in financial markets, representing the total cost of holding an asset over a specific period. It essentially measures the difference between the benefits of owning an asset (like dividends or interest) and the costs associated with holding it (like storage, insurance, and financing). Understanding cost of carry is vital for making informed investment decisions across various asset classes, from commodities and bonds to equities and derivatives.

Dissecting the Cost of Carry:

At its core, cost of carry bridges the gap between the returns an asset generates and the expenses incurred while owning it. Let's break down the components:

Benefits: This typically involves the income generated by the asset. For a bond, it's the interest payments received. For stocks, it's the dividends paid out. For commodities, it might be the convenience yield (the benefit of having physical access to the commodity).
Costs: These are the expenses related to holding the asset. The most significant is usually the financing cost, which is the interest paid on borrowed funds used to purchase the asset. Other costs might include:
- Storage costs: Applicable to physical commodities like gold or oil.
- Insurance costs: Protecting the asset against damage or loss.
- Taxes: Depending on the jurisdiction and asset type.
- Depreciation: For assets that lose value over time.

The Calculation:

While the exact calculation varies based on the asset, a simplified formula is:

Cost of Carry = Financing Costs - Income from the Asset

Positive Carry vs. Negative Carry:

The relationship between benefits and costs determines whether an asset has positive or negative carry:

Positive Carry: When the income generated from the asset exceeds the costs of holding it (Income > Costs). This indicates that holding the asset is profitable, even before considering price appreciation. Investors are effectively compensated for holding the asset. Examples include high-yielding bonds or dividend-paying stocks with low financing costs.
Negative Carry: When the costs of holding the asset outweigh the income generated (Income < Costs). This means holding the asset is costly, even if its price appreciates. Investors effectively pay a premium to hold the asset. This is common with assets requiring high financing costs and generating little or no income, such as certain futures contracts or assets held on margin with high interest rates.

Cost of Carry and Futures Pricing:

Cost of carry plays a particularly significant role in futures markets. The theoretical price of a futures contract is often linked to the spot price of the underlying asset, adjusted for the cost of carry. This relationship forms the basis of many arbitrage strategies. A simple model suggests that the futures price should be approximately equal to the spot price plus the cost of carry. Deviations from this relationship can create arbitrage opportunities for traders.

Examples:

Treasury Bonds: A long position in Treasury bonds generally carries a positive carry due to the interest earned. However, the carry can become negative if interest rates rise significantly, increasing the opportunity cost of holding the bonds.
Gold: The cost of carry for gold includes storage and insurance costs, offset by any potential increase in the gold price. If storage costs and financing charges exceed the price appreciation of gold, the position has negative carry.
Futures Contracts: For commodities futures, the cost of carry includes storage and financing, potentially offset by the convenience yield. Futures contracts can exhibit either positive or negative carry depending on the market dynamics.

Conclusion:

The cost of carry is a fundamental concept influencing investment decisions and market pricing across various asset classes. By understanding the components of cost of carry, investors can better evaluate the profitability of holding different assets and identify potential arbitrage opportunities. Careful consideration of positive and negative carry is essential for effective portfolio management and risk assessment.

Test Your Knowledge

Quiz: Cost of Carry

Instructions: Choose the best answer for each multiple-choice question.

1. Which of the following BEST defines the cost of carry? (a) The profit earned from selling an asset. (b) The total cost of holding an asset over a period, considering both benefits and costs. (c) The difference between the buying and selling price of an asset. (d) The risk associated with holding an asset.

Answer

(b) The total cost of holding an asset over a period, considering both benefits and costs.

2. What is a key component of the "costs" side of the cost of carry calculation? (a) Dividends received from stocks. (b) Interest earned on bonds. (c) Financing costs of borrowing to purchase the asset. (d) Convenience yield from commodities.

Answer

3. An asset with positive carry means: (a) The costs of holding the asset exceed the income generated. (b) The income generated from the asset exceeds the costs of holding it. (c) The asset's price is decreasing. (d) The asset's price is volatile.

Answer

(b) The income generated from the asset exceeds the costs of holding it.

4. Which of the following is NOT typically a component of the cost of carrying a physical commodity? (a) Storage costs (b) Insurance costs (c) Brokerage commissions on purchase (d) Depreciation

Answer

(c) Brokerage commissions on purchase (While brokerage commissions are a cost of acquiring the asset, they are not part of the ongoing cost of carry.)

5. In futures markets, the theoretical futures price is often related to the spot price adjusted for: (a) Market sentiment. (b) The cost of carry. (c) Speculative demand. (d) Government regulations.

Answer

(b) The cost of carry.

Exercise: Calculating Cost of Carry

Scenario: You are considering investing in a gold futures contract. The spot price of gold is $1,800 per ounce. The futures contract matures in three months. The relevant data is:

Financing cost: 5% annual interest rate (simple interest) on the value of the gold.
Storage cost: $2 per ounce per year.
Insurance cost: $1 per ounce per year.

Task: Calculate the approximate three-month cost of carry per ounce of gold. Assume that income from the asset (convenience yield) is negligible.

Exercice Correction

Here's how to calculate the three-month cost of carry:

1. Calculate annual costs:

Financing cost: $1800 * 0.05 = $90 per ounce per year
Storage cost: $2 per ounce per year
Insurance cost: $1 per ounce per year
Total annual cost: $90 + $2 + $1 = $93 per ounce per year

2. Calculate three-month costs:

Total three-month cost: $93/year * (3 months / 12 months) = $23.25 per ounce

Therefore, the approximate three-month cost of carry per ounce of gold is $23.25. Note that this is a simplified calculation; real-world cost of carry calculations can be more complex.

Books

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Options, Futures, and Other Derivatives by John C. Hull: A comprehensive textbook covering derivatives pricing, including detailed explanations of cost of carry and its application in futures pricing.
Investment Science by David G. Luenberger: A rigorous mathematical treatment of investment theory, incorporating the cost of carry within broader portfolio optimization frameworks.
The Handbook of Commodity Investing (various editions): Provides insights into the cost of carry for different commodities, including storage, insurance, and transportation expenses.
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Articles

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(Searching for these keywords in academic databases like JSTOR, ScienceDirect, and Google Scholar will yield relevant articles):*
"Cost of Carry and Futures Prices"
"Convenience Yield and Cost of Carry in Commodity Markets"
"The Impact of Cost of Carry on Investment Strategies"
"Arbitrage Opportunities and Cost of Carry Deviations"
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Online Resources

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Investopedia: Search for "cost of carry" on Investopedia for a beginner-friendly explanation and examples.
Corporate Finance Institute (CFI): CFI offers detailed explanations of financial concepts, including cost of carry, often with interactive elements.
*Google

Search Tips

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Use specific keywords: Instead of just "cost of carry," try more precise searches like "cost of carry gold," "cost of carry futures contracts," or "cost of carry arbitrage."
Combine keywords with asset classes: For example, "cost of carry treasury bonds," "cost of carry oil futures."
Include terms related to your specific interest: For example, if interested in the mathematical model, add "cost of carry formula," "cost of carry model," or "cost of carry calculation."
Explore advanced search operators: Use quotation marks (" ") to search for exact phrases. Use the minus sign (-) to exclude unwanted terms. Use the asterisk (*) as a wildcard. This expanded response provides a more complete and structured set of references to help you delve deeper into the concept of cost of carry. Remember to critically evaluate the information you find from various sources.

Techniques

Decoding the Cost of Carry: A Comprehensive Guide

Chapter 1: Techniques for Calculating Cost of Carry

The calculation of cost of carry varies depending on the asset class. While the fundamental principle remains consistent—the difference between income generated and holding costs—the specifics of each component differ significantly.

1.1. Commodities:

For physical commodities like gold or oil, the cost of carry includes:

Storage Costs: Warehouse rental, security, insurance related to storage. These costs are often dependent on storage location, quantity, and time.
Insurance Costs: Premiums paid to insure against theft, damage, or spoilage.
Transportation Costs: Expenses associated with moving the commodity.
Financing Costs: Interest paid on loans taken to purchase and hold the commodity.
Convenience Yield: A benefit for holding the physical commodity, reflecting the value of having immediate access to the asset for use or sale. This partially offsets other costs.

Formula (simplified): Cost of Carry = Storage + Insurance + Transportation + Financing Costs – Convenience Yield

1.2. Bonds:

For bonds, the calculation is relatively straightforward:

Income: Coupon payments received during the holding period.
Financing Costs: Interest paid on borrowed funds used to purchase the bonds.

Formula (simplified): Cost of Carry = Financing Costs – Coupon Payments

1.3. Equities:

For equities, the cost of carry involves:

Income: Dividends received during the holding period.
Financing Costs: Interest paid on margin loans or other financing used to buy the stocks. (For outright purchases without leverage, financing costs are typically zero).

Formula (simplified): Cost of Carry = Financing Costs – Dividends

1.4. Futures Contracts:

Futures contracts present a more complex scenario:

Income: None directly from the contract itself.
Financing Costs: Interest accrued on margin deposits.
Rollover Costs: Costs associated with rolling over positions from one contract expiration to the next. This is a significant component and can introduce substantial negative carry.

Formula (simplified): Cost of Carry = Financing Costs + Rollover Costs

Chapter 2: Models for Cost of Carry Analysis

Several models help analyze and predict cost of carry.

2.1. Simple Cost of Carry Model (for Futures): This model posits that the futures price (F) is approximately equal to the spot price (S) plus the cost of carry (C): F ≈ S + C. This model is a simplified representation and ignores factors like volatility and market sentiment.

2.2. More Sophisticated Models: These incorporate additional factors, such as:

Volatility: Models like the Black-Scholes model incorporate volatility to account for price fluctuations.
Market Sentiment: Speculative demand can significantly impact futures prices and deviate them from the cost-of-carry prediction.
Dividends/Interest Rates: Stochastic models account for the uncertainty in future dividend payments or interest rates.

Chapter 3: Software and Tools for Cost of Carry Calculation

Numerous software packages and tools facilitate the calculation and analysis of cost of carry:

Spreadsheets (Excel, Google Sheets): These can be used for basic calculations, particularly for simpler asset classes.
Financial Modeling Software (Bloomberg Terminal, Refinitiv Eikon): These provide sophisticated tools for calculating and analyzing cost of carry, incorporating various market data and modeling capabilities.
Programming Languages (Python, R): These allow for the creation of custom scripts and models for complex cost of carry calculations.
Dedicated Trading Platforms: Many brokerage platforms include built-in tools for calculating cost of carry for specific instruments.

The choice of software depends on the user's needs, technical skills, and the complexity of the asset class being analyzed.

Chapter 4: Best Practices in Cost of Carry Analysis

Accurate cost of carry analysis requires meticulous attention to detail and a comprehensive understanding of the relevant market dynamics:

Data Accuracy: Using reliable and up-to-date data sources is crucial for obtaining accurate results.
Appropriate Model Selection: Choose a model that appropriately reflects the characteristics of the asset and market conditions.
Consideration of All Costs: Ensure all relevant costs, including those that might be easily overlooked (e.g., transaction fees, taxes), are included in the calculation.
Sensitivity Analysis: Conducting sensitivity analysis to assess the impact of changes in input variables on the cost of carry is essential.
Regular Monitoring: Market conditions are constantly changing, so regular monitoring and adjustments to the cost of carry calculation are necessary.

Chapter 5: Case Studies of Cost of Carry in Action

5.1. Gold Futures: Analyzing the cost of carry for gold futures requires considering storage costs, insurance, financing costs, and the convenience yield (related to industrial demand for gold). Periods of high interest rates can increase financing costs, potentially resulting in negative carry.

5.2. Treasury Bond Carry: The cost of carry for Treasury bonds depends on the coupon rate and prevailing interest rates. If interest rates rise sharply, the opportunity cost of holding bonds can exceed the coupon income, leading to negative carry.

5.3. Oil Futures: Analyzing oil futures involves considering storage costs (tanker rentals, pipeline fees), insurance, and financing costs. The convenience yield can be particularly significant for oil futures, reflecting the industrial demand for immediate access to oil.

These case studies highlight the importance of considering various factors and selecting an appropriate model to accurately assess cost of carry for different asset classes under changing market conditions. Understanding cost of carry provides valuable insights for effective investment and trading decisions.

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