Cost of Carry

The cost of carry is a fundamental concept in finance that refers to the total cost associated with holding a financial position or physical asset over a period of time until its delivery or sale. It represents the net expense incurred from maintaining an investment, including financing costs, storage costs, insurance, and any foregone income or benefits.
The cost of carry plays a crucial role in the pricing of derivative instruments—particularly futures and forwards—since it determines the relationship between spot prices and future prices of assets such as commodities, equities, and currencies.

Definition and Concept

The cost of carry can be defined as the difference between the futures price and the spot price of an asset, which arises from the costs and benefits of holding (carrying) that asset until the contract’s maturity date.
Mathematically, the cost of carry can be expressed as:
F=S×e(r+c−y)tF = S \times e^{(r + c – y)t}F=S×e(r+c−y)t
where:

• FFF = Futures price
• SSS = Spot price of the underlying asset
• rrr = Risk-free interest rate (cost of financing)
• ccc = Storage or other carrying costs
• yyy = Income yield or convenience yield
• ttt = Time to maturity (in years)

This formula shows that the futures price rises relative to the spot price when carrying costs exceed income yields, and falls when the opposite is true.

Components of the Cost of Carry

The cost of carry comprises several components that vary depending on the nature of the underlying asset:

1. Financing Cost (Interest Cost): The cost of borrowing funds to purchase the asset. For investors using leverage, this is often the risk-free rate or the margin interest rate charged by a broker.
2. Storage Cost: Applicable to physical commodities such as oil, metals, or agricultural goods, reflecting warehousing, preservation, and insurance expenses.
3. Insurance and Handling Costs: Additional expenses to protect and manage physical assets during storage.
4. Income Yield: Any income earned from holding the asset, such as dividends (for equities), coupons (for bonds), or convenience yield (for commodities). These reduce the overall cost of carry.
5. Convenience Yield: A non-monetary benefit of physically holding a commodity, such as ensuring production continuity or hedging operational risk. It effectively acts as a negative carrying cost, reducing the net cost of carry.

Theoretical Relationship between Spot and Futures Prices

The cost of carry model establishes a link between the spot price (S) and the futures price (F):

• When F>SF > SF>S, the market is said to be in contango—futures prices are higher than spot prices due to positive carrying costs.
• When F<SF < SF<S, the market is in backwardation, usually because the convenience yield or expected future scarcity outweighs carrying costs.

This relationship ensures that arbitrage opportunities are eliminated in efficient markets, as traders can buy the cheaper asset and sell the more expensive one until prices align with theoretical values.

Cost of Carry in Financial Derivatives

In derivatives markets, the cost of carry model is used to determine fair futures prices across asset classes:
1. Equity Futures: For stocks, the cost of carry includes financing costs and foregone dividends:
F=S×e(r−d)tF = S \times e^{(r – d)t}F=S×e(r−d)t
where ddd represents the dividend yield.If dividends exceed financing costs, futures prices may trade below spot prices, leading to backwardation.
2. Commodity Futures: For commodities, carrying costs (storage and insurance) tend to be substantial, while convenience yields may offset some of these costs. The futures price formula becomes:
F=S×e(r+s−y)tF = S \times e^{(r + s – y)t}F=S×e(r+s−y)t
where sss = storage cost and yyy = convenience yield.
3. Currency Futures (Interest Rate Parity): In foreign exchange markets, the cost of carry reflects the difference between domestic and foreign interest rates:
F=S×e(rd−rf)tF = S \times e^{(r_d – r_f)t}F=S×e(rd​−rf​)t
where rdr_drd​ is the domestic interest rate and rfr_frf​ is the foreign interest rate.
This formulation is the foundation of covered interest rate parity (CIRP), ensuring that currency futures align with interest rate differentials between two economies.

Example: Cost of Carry in Equity Futures

Suppose the spot price of a share is £100, the annual risk-free rate is 5%, and the dividend yield is 2%. For a 6-month (0.5-year) futures contract:
F=100×e(0.05−0.02)×0.5=100×e0.015=101.51F = 100 \times e^{(0.05 – 0.02) \times 0.5} = 100 \times e^{0.015} = 101.51F=100×e(0.05−0.02)×0.5=100×e0.015=101.51
Thus, the theoretical futures price is £101.51.If the actual market futures price is higher, say £103, arbitrageurs can short the futures and buy the stock to earn a risk-free profit until prices converge.

Role of Cost of Carry in Arbitrage

The cost of carry concept underpins cash-and-carry and reverse cash-and-carry arbitrage strategies:

• Cash-and-Carry Arbitrage: Executed when the futures price is overpriced. The trader buys the asset in the spot market and sells futures, earning a profit as prices converge.
• Reverse Cash-and-Carry Arbitrage: Used when futures are underpriced. The trader sells the asset short and buys the futures, profiting when the price gap closes.

These arbitrage mechanisms help maintain equilibrium between spot and futures prices.

Cost of Carry and Market Conditions

Different market situations influence the level and sign of the cost of carry:

Factors such as interest rate changes, storage limitations, and seasonal demand shifts affect whether a market is in contango or backwardation.

Importance in Financial and Commodity Markets

The cost of carry has significant applications in various areas of finance:

• Derivative Pricing: Establishes fair value of futures and forward contracts.
• Hedging Strategies: Guides producers, exporters, and investors in managing price risk efficiently.
• Arbitrage and Trading Decisions: Identifies mispricing opportunities in futures markets.
• Investment Analysis: Assists in evaluating the economic viability of holding physical assets versus financial substitutes.

Limitations of the Cost of Carry Model

Although widely used, the cost of carry model has certain limitations:

1. Assumption of Perfect Markets: Ignores transaction costs, taxes, and liquidity constraints.
2. Constant Interest Rates: Real-world interest rates fluctuate, affecting accuracy.
3. Uncertainty of Income or Yields: Dividends or convenience yields may not be precisely predictable.
4. Storage and Risk Factors: Especially in commodities, practical difficulties such as perishability or transportation risks complicate the estimation of carrying costs.
5. Market Imperfections: Regulations, short-selling restrictions, and credit risk can distort theoretical pricing.

Real-World Applications

• Commodity Traders: Use cost of carry to determine whether to store or sell goods immediately.
• Equity Derivative Traders: Apply it to price stock index futures and arbitrage mispriced contracts.
• Foreign Exchange Dealers: Rely on it for pricing forward exchange rates under interest rate parity.
• Corporate Treasurers: Use it to assess hedging costs in managing inventory and foreign exposure.