Cost of carry

Cost of Carry

The **cost of carry** is a fundamental concept in finance, particularly relevant to futures contracts, options, and fixed income securities. It represents the net cost of holding an asset over a period of time. Understanding the cost of carry is crucial for traders, investors, and anyone involved in pricing derivatives or managing portfolios. This article provides a comprehensive explanation of the cost of carry, its components, calculation, and implications for various financial instruments.

What is Cost of Carry?

At its core, the cost of carry is the total expense associated with maintaining a position in an asset. This isn't simply the purchase price. It encompasses all costs incurred while ‘carrying’ the asset until it's sold or the contract expires. These costs can be explicit, like storage and insurance, or implicit, like the opportunity cost of capital. Conversely, there can also be benefits to carrying an asset, such as dividends or interest earned. The net of these costs and benefits is the cost of carry.

The concept is most readily applied to commodities, but extends to financial assets as well. Consider holding a barrel of oil. You need to pay for storage, insurance, and potentially transportation. These are direct costs. However, you also forgo the opportunity to invest that capital elsewhere – this is the opportunity cost. If the oil generates no income (like dividends), the cost of carry is positive. If you *receive* income from the oil (uncommon, but conceptually possible through a lease agreement), then the cost of carry could be negative.

Components of Cost of Carry

The cost of carry is a composite of several elements. These elements vary depending on the asset class, but the core principles remain consistent.

Storage Costs:* This is the most straightforward component, particularly for commodities. It includes the physical cost of storing the asset – warehouse rent, security, and potentially climate control. For example, storing grains, metals, or crude oil all have significant storage costs.

Insurance Costs:* Protecting the asset against damage, theft, or other risks incurs insurance premiums. The level of insurance depends on the asset’s value and the risks involved.

Financing Costs:* If the asset is purchased with borrowed funds, the interest paid on the loan is a financing cost. Even if purchased with equity, there's an *opportunity cost* of capital – the return that could have been earned by investing the capital elsewhere. This is often calculated using a risk-free rate, such as the yield on a government bond.

Transportation Costs:* Moving the asset to and from storage or to the point of sale adds to the cost of carry. This is less relevant for financial assets but significant for physical commodities.

Spoilage/Deterioration Costs:* Perishable goods, like agricultural products, are subject to spoilage. The potential loss in value due to deterioration must be factored into the cost of carry.

Income Earned (Convenience Yield):* This is the offsetting benefit. Some assets generate income while held. This could be dividends from stocks, interest from bonds, or a 'convenience yield' for commodities – the benefit of having the physical commodity readily available for use, avoiding potential supply disruptions. The convenience yield is particularly important in commodities markets, especially during times of scarcity. This can be seen as an implicit benefit.

Calculating Cost of Carry

The basic formula for cost of carry is:

Cost of Carry = Storage Costs + Insurance Costs + Financing Costs - Income Earned (Convenience Yield)

However, in practice, calculating the cost of carry can be more complex. For example, determining the appropriate financing cost (opportunity cost of capital) requires careful consideration of risk and investment alternatives. The convenience yield is often difficult to quantify directly and is often inferred from market prices.

Let's consider a simplified example:

Suppose you want to hold 100 barrels of crude oil for one year.

Storage cost: $5 per barrel per year = $500
Insurance cost: $1 per barrel per year = $100
Financing cost (opportunity cost of capital): 5% per year on the purchase price of $80 per barrel = $400 (0.05 * $80 * 100)
Convenience yield: $2 per barrel per year = $200

Cost of Carry = $500 + $100 + $400 - $200 = $800

In this example, the net cost of carry is $800 per year for holding 100 barrels of crude oil.

Cost of Carry and Futures Contracts

The cost of carry is particularly important when understanding the relationship between spot prices (the current market price) and futures prices. The theoretical futures price is often calculated based on the cost of carry. The formula is:

Futures Price = Spot Price + Cost of Carry

This formula implies that futures prices should be higher than spot prices if the cost of carry is positive, and lower if the cost of carry is negative. This is known as **contango** (futures price > spot price) and **backwardation** (futures price < spot price), respectively.

Contango:* When the cost of carry is positive (storage, insurance, financing costs outweigh income earned), futures prices are typically higher than spot prices. This is because those holding the physical commodity would prefer to sell a futures contract, deferring delivery and avoiding the costs of storage and financing. Arbitrage opportunities can arise if the futures price deviates significantly from the theoretical price based on the cost of carry.

Backwardation:* When the convenience yield is high enough to outweigh the costs of storage, insurance, and financing, futures prices can be lower than spot prices. This often occurs when there is a perceived shortage of the commodity, and having the physical commodity immediately available is highly valued. Again, arbitrage opportunities can emerge if the prices diverge considerably.

Cost of Carry and Options

While less direct than with futures, the cost of carry also impacts options pricing. The cost of carry influences the underlying asset's expected future price, which in turn affects the value of an option on that asset.

For example, in a stock index option, the dividend yield (a negative cost of carry component) affects the option's price. Higher dividend yields generally reduce call option prices and increase put option prices.

Cost of Carry and Fixed Income Securities

In the context of bonds, the cost of carry includes the financing cost (interest paid on funds used to purchase the bond) less any coupon payments received. The **repo rate** (the rate at which a bond can be borrowed and lent in the repurchase agreement market) often serves as a proxy for the financing cost.

Positive Carry:* When the coupon rate on a bond exceeds the repo rate, the carry is positive. This means investors are earning more from the bond's income than they are paying to finance its purchase.

Negative Carry:* When the repo rate exceeds the coupon rate, the carry is negative. Investors are paying more to finance the bond than they are receiving in income.

Implications for Trading and Investment

Understanding the cost of carry has several important implications for trading and investment decisions:

Arbitrage Opportunities:* Deviations between theoretical futures prices (based on cost of carry) and actual market prices create arbitrage opportunities for traders. Arbitrageurs can profit by simultaneously buying and selling the asset in different markets to exploit these price discrepancies.

Roll Yield:* For investors holding futures contracts, the roll yield (the profit or loss from rolling a futures contract to the next expiration date) is directly influenced by the shape of the futures curve (contango or backwardation). In contango, rolling a contract typically results in a negative roll yield (a loss), while in backwardation, it results in a positive roll yield (a profit).

Portfolio Management:* Cost of carry considerations are crucial for managing portfolios of commodities, futures, and fixed income securities. Understanding the carry implications of different positions can help investors optimize their risk-adjusted returns.

Hedging Strategies:* The cost of carry impacts the effectiveness of hedging strategies. For example, using futures contracts to hedge a physical commodity position requires careful consideration of the cost of carry to ensure the hedge is economically viable.

Factors Affecting Cost of Carry

Several factors can influence the cost of carry:

Interest Rates:* Higher interest rates generally increase financing costs, leading to a higher cost of carry.

Storage Capacity:* Limited storage capacity can drive up storage costs, especially during periods of oversupply.

Supply and Demand:* Tight supply and strong demand can increase the convenience yield, reducing the cost of carry.

Geopolitical Events:* Political instability or disruptions to supply chains can impact both storage costs and convenience yields.

Seasonality:* Commodities with seasonal production patterns often exhibit varying costs of carry throughout the year.

Advanced Considerations

Dynamic Cost of Carry:* The cost of carry is not static. It changes over time in response to changing market conditions.

Implied Convenience Yield:* Traders can infer the convenience yield from futures prices using the cost of carry formula.

Carry Trade:* A carry trade involves borrowing in a currency with a low interest rate and investing in a currency with a high interest rate, profiting from the difference in rates. This is essentially exploiting a positive carry.

Relationship to Volatility:* Volatility can impact storage costs (due to increased insurance premiums) and convenience yields (due to increased uncertainty about future supply).

Impact of Inflation:* Inflation affects all components of the cost of carry, increasing storage, insurance, and financing costs.

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