What is the Cost of Carry? Calculation & Example

If you want to understand futures pricing, you need to know what the cost of carry means.

In simple terms, the cost of carry refers to the total cost involved in holding an asset until the expiry of a futures contract. It includes expenses like financing costs (interest you would pay to hold the asset), storage costs (for physical commodities), and deducts any income earned (like dividends for stocks).

This concept explains why the futures price of an asset is often higher (or lower) than its spot price (the current market price). Keep reading to know more.

Cost of Carry Formula

The general formula for calculating the cost of carry futures contract is:

Futures Price = Spot Price × e ^ ((r + s – c) × t)

Where:

• Futures Price (F): Price of the asset in the futures market

• Spot Price (S): Current market price of the asset

• e: Mathematical constant (approx. 2.718)

• r: Risk-free interest rate (such as government bond yield)

• s: Storage cost (as a percentage of the asset value, often zero for financial assets)

• c: Convenience yield (any non-monetary benefit of holding the asset, mainly in commodities)

• t: Time remaining until contract expiry (as a fraction of a year)

For financial assets like stocks or indices, storage costs and convenience yield are usually zero, making the formula simpler.

Another simplified version commonly used:

Cost of Carry = Financing Cost + Storage Cost – Income Earned

Where:

• Financing Cost: Opportunity cost or interest on borrowed funds

• Storage Cost: Physical storage, if applicable

• Income Earned: Dividends or interest earned during the holding period

How to Calculate Cost of Carry?

If you want to calculate the cost of carry futures, follow these steps:

1. Determine the Spot Price: Find the current market price of the underlying asset.

2. Estimate the Risk-Free Interest Rate (r): Use the prevailing government bond yield for the relevant holding period.

3. Calculate Storage Cost (if any): For physical commodities, add storage, insurance, and transportation costs. For financial assets, this is often zero.

4. Account for Income Earned (q): Estimate dividends or other income expected from holding the asset during the period.

5. Determine Time to Expiry (t): Calculate the time left until the futures contract expires, expressed as a fraction of a year.

6. Apply the Formula: For short durations and simple cases, you can use this quick version:

Cost of Carry for the period = Spot Price × (r + s – q) × t

For example, if the spot price of an index is ₹23,000, the risk-free rate is 7% per year, the expected dividend yield is 1.5%, and the time to expiry is 3 months:

Cost of Carry = 23,000 × (0.07 – 0.015) × (3/12) = ₹316.25 per unit

This calculation helps you estimate the fair value of the futures contract compared to the spot price.

What Is the Cost of Carry in Derivatives?

In derivatives trading, the cost of carry plays a crucial role in pricing futures contracts.

The cost of carry futures contract pricing model ensures that the futures price reflects both the current spot price and the total cost of holding the asset until expiry. This is based on the no-arbitrage principle, meaning there should be no guaranteed profit opportunities between spot and futures markets.

For you as a trader, tracking the cost of carry helps in:

• Understanding why a futures contract trades at a premium or discount to the spot price.

• Spotting potential arbitrage opportunities if futures prices deviate significantly.

• Analysing trader sentiment (For example, rising cost of carry may suggest bullish market expectations as traders are willing to pay more to hold long positions).

Futures Cost of Carry Model

The futures cost of carry model explains how the futures price of an asset relates to its spot price (current market price). In simple terms, the difference between the futures and spot price reflects the cost of carry—the total cost (or benefit) of holding the asset until the futures contract expires.

The model assumes two main things:

• You hold the futures contract until expiry (without exiting early).

• The market is efficient, meaning any mispricing between spot and futures gets corrected quickly through arbitrage.

The basic formula for the observed cost of carry is:

Cost of Carry = Futures Price – Spot Price

A positive cost of carry means the futures price is higher than the spot price (known as contango). Whereas, a negative cost of carry means the futures price is below the spot price (known as backwardation).

For a more accurate calculation of fair futures price, traders use the formal cost of carry formula:

Futures Price (F) = Spot Price (S) × e ^ [(rf + s – c) × t]

Where:

• rf: Risk-free interest rate

• s: Storage cost (if any)

• c: Convenience yield (benefit of holding the asset)

• t: Time to expiry (in years)

Scenario Data

Let’s look at an example using the Nifty 50 Index Futures traded on the NSE:

• Underlying Asset: Nifty 50 Index

• Spot Price (S): ₹22,500

• Futures Price (F): ₹22,615 (April 2025 futures)

• Days to Expiry: 14 days (from April 10 to April 24, 2025)

• Time to Expiry (t): 14 ÷ 365 ≈ 0.0384 years

• Risk-Free Rate (rf): 7% per annum (0.07)

• Storage Cost (s): 0 (financial index)

• Convenience Yield (c): 0 (no holding benefit for an index)

Calculations

Let’s calculate the observed and theoretical values for this futures contract.

Observed Cost of Carry

Observed Cost of Carry (CoC) = Futures Price – Spot Price

CoC = ₹22,615 – ₹22,500 = 115 points

This shows that traders are paying a 115-point premium to hold the Nifty futures contract over the next 14 days.

Theoretical Futures Price (using the formula)

Using the simplified cost of carry futures contract formula (since s = 0 and c = 0):

F = S × e ^ (rf × t)

Where:

• F = Theoretical futures price

• S = Spot price (₹22,500)

• e = Mathematical constant (approx. 2.718)

• rf = Risk-free rate (0.07)

• t = Time to expiry (0.0384 years)

Calculation:

F = 22,500 × e^(0.07 × 0.0384)

F = 22,500 × e^(0.002688)

F = 22,500 × 1.002691

F = ₹22,560.55

So, the theoretical futures price should be around ₹22,560.55.

Net Return Calculations

Now, let’s compare the observed market price with the theoretical value:

• Observed Futures Price: ₹22,615

• Theoretical Futures Price: ₹22,560.55

Difference = ₹54.45

This means the actual market futures price is trading higher than the model’s fair value estimate.

The extra premium above the theoretical level could reflect additional market demand, short-term supply issues, or expectations of stronger price moves before expiry.

By tracking this gap, you can assess whether the market is overpricing or underpricing the contract compared to standard cost of carry assumptions.

Conclusion

The cost of carry plays an important role in futures pricing and market decision-making. By knowing how to calculate it and by reviewing real examples, you gain a clearer view of why futures prices differ from spot prices. Whether you are trading in financial indices, stocks, or commodities, understanding the cost of carry helps you make more informed choices.

FAQs

What is the impact of the cost of carry on financial markets?

The cost of carry affects how futures prices are set in relation to spot prices. It helps maintain price consistency between the spot and futures markets by reflecting financing costs, storage costs, and expected income from holding the asset. For example, a high cost of carry often leads to futures trading at a premium (contango), while a low or negative cost of carry can result in futures trading below spot prices (backwardation).

Where does the cost of carry fit in future derivative pricing?

The cost of carry is a core component in the pricing of futures contracts. It explains the gap between the spot price and the futures price. In futures derivative pricing, the standard formula is:

Futures Price = Spot Price × e ^ ((risk-free rate + storage cost – income yield) × time to expiry)

This calculation helps traders determine whether a futures contract is priced fairly compared to the underlying asset.

What cost of carry factors should an investor account for?

When calculating the cost of carry futures contracts, you should consider:

• Financing Cost: Interest or opportunity cost of the capital used to hold the asset.

• Storage Cost: Relevant for physical commodities, covers warehousing and insurance.

• Income Yield: Any income earned from holding the asset, such as dividends or bond interest.

• Time to Expiry: Duration remaining until the futures contract settles.

For financial indices and stocks, storage costs are typically zero, but dividend yields and interest rates still matter.

Can the cost of carry be negative?

Yes, the cost of carry can be negative. This usually happens when the income earned from holding the asset (like dividends) is higher than the financing and storage costs combined. In some cases, it may also reflect strong short-term demand for the underlying asset or specific market conditions driving prices lower in the futures market.