Compute cost of carry and theoretical futures price from spot, rates, storage, convenience yield, and dividends.
Pricing Parameters
Input spot prices, rates, and yields to determine the fair futures value
Formula Used
F = S × e^((r + u - y - d) × t)
Where F is the Theoretical Futures Price, S is the Spot Price, r is the risk-free rate, u is storage cost, y is convenience yield, d is dividend yield, and t is time to maturity in years.
Usage of this Calculator
Who needs theoretical futures pricing?
Arbitrage Traders
Compare the calculated Theoretical Price against the actual market price. If they diverge significantly, an arbitrage window (Cash-and-Carry) exists.
Portfolio Managers
Estimate the "roll yield" cost or benefit when holding long-term commodity positions via futures contracts.
Corporate Hedgers
Determine if the futures curve is offering "fair value" for hedging future production or consumption needs.
Students & Academics
Visualize how interest rates, storage costs, and dividends interact to shape the futures forward curve.
Summary
The Cost of Carry Futures Calculator is the engine behind accurate derivatives pricing.
It proves that futures prices are not just "predictions" of the future, but mathematically linked to spot prices via holding costs.
It identifies whether a market Contango is justified by storage/interest costs, or excessive sentiment.
It serves as the baseline for identifying Arbitrage risks and opportunities.
Mastering Cost of Carry: The Mathematical Foundation of Futures Pricing
The Cost of Carry model is the cornerstone of fair value analysis in derivatives markets, explaining the price gap between today's spot market and tomorrow's futures contract.
The Cost of Carry refers to the total costs involved in holding a physical asset or financial instrument over a specific period. In futures markets, the price of a futures contract is essentially the Spot Price + Cost of Carry.
If the futures price deviates significantly from this theoretical value, arbitrageurs step in to restore equilibrium.
The 4 Key Components
Depending on the asset class (Commodities, Equities, Currencies), the cost of carry consists of different variables:
1. Financing Cost (Interest Rate)
Buying an asset requires capital. The interest paid on borrowed money (or lost interest on own capital) is the financing cost. This is relevant for ALL assets.
2. Storage & Insurance Costs
Relevant for Commodities (Oil, Wheat, Gold). It costs money to store and insure physical goods. High storage costs increase the futures price (Steeper Contango).
3. Income / Dividend Yield
Relevant for Equities and Bonds. Holding the asset pays dividends or coupons. This income reduces the net cost of carry.
4. Convenience Yield
Relevant for Physical Commodities. The intangible benefit of holding the physical inventory (e.g., to keep a refinery running during a shortage). It acts like a "negative cost" or a "dividend" for commodities.
The Cost of Carry Formula
Using continuous compounding (standard for professional derivatives pricing):
F = S × e(r + u - y - d)t
r = Risk-free interest rate
u = Storage cost (percentage)
y = Convenience yield (percentage)
d = Dividend yield (percentage)
t = Time to maturity (years)
Arbitrage: Cash-and-Carry
The model empowers traders to identify risk-free profit opportunities known as Cash-and-Carry Arbitrage.
Scenario: Futures Price > Theoretical Price
The Future is "overvalued."
Borrow money at rate r.
Buy the Spot asset at S.
Sell the Futures contract at F.
Store the asset until expiry.
Deliver asset against the Futures contract.
The profit is the difference between the Actual F and Theoretical F*.
Implications for Market Structure
The sign of the net Cost of Carry determines the market structure:
Positive Carry (r + u > y + d): The theoretical futures price is higher than spot. Market is in Contango.
Negative Carry (r + u < y + d): The theoretical futures price is lower than spot. Market is in Backwardation.
Frequently Asked Questions
Common questions about the Cost of Carry model
Why are gold futures always in Contango?
Gold has significant storage costs and insurance costs, but it has zero industrial "convenience yield" (it mostly sits in vaults) and pays no dividends. Thus, `r + u` is always positive, making Futures > Spot (Contango).
How does the convenience yield affect the price?
Convenience yield lowers the theoretical futures price. If the convenience yield helps offset storage and interest costs, the market flips into Backwardation (Futures < Spot). This happens during supply shortages.
What risk-free rate should I use?
Professionals typically use the rate on government treasury bills or SOFR (Secured Overnight Financing Rate) that matches the duration of the futures contract.
Can storage costs be negative?
No, storage costs are real expenses. However, for financial assets like Bitcoin or digital tokens, storage costs might be negligible, meaning the cost of carry is driven almost entirely by interest rates.
What happens if I ignore dividends?
For Equity Index Futures (like S&P 500), ignoring dividends will make your theoretical price way too high. Dividends effectively reduce the cost of holding the stock, pushing the futures price down relative to spot.
Does this model apply to Cryptocurrencies?
Yes. For Bitcoin futures, the cost of carry is dominated by the USD interest rate (financing cost) since storage is cheap. This is why Bitcoin futures usually trade at a premium (Contango) in bull markets.
Why is the outcome different from the market price?
The "Theoretical Pice" assumes perfect markets. Real markets have transaction costs, borrowing constraints, and differing expectations of convenience yield. The difference is the "Arbitrage Gap" or "Basis Risk."
Is Reverse Cash-and-Carry easy to execute?
It's harder than Cash-and-Carry because it requires short-selling the spot asset. Many commodities (like Oil or Wheat) are very difficult or impossible to short-sell in the spot market.
How does time to maturity affect the calculation?
The longer the time to maturity (`t`), the larger the effect of the cost of carry. This is why the spread between spot and futures is widest for distant contracts and converges to zero as time expires.
What is "Full Carry"?
"Full Carry" is a situation in grain markets where the price difference between delivery months covers the full cost of storage and interest. If the spread is less than full carry, it discourages storage.
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Compute cost of carry and theoretical futures price from spot, rates, storage, convenience yield, and dividends.
How to use Cost of Carry (Futures) Calculator
Step-by-step guide to using the Cost of Carry (Futures) Calculator:
Enter your values. Input the required values in the calculator form
Calculate. The calculator will automatically compute and display your results
Review results. Review the calculated results and any additional information provided
Frequently asked questions
How do I use the Cost of Carry (Futures) Calculator?
Simply enter your values in the input fields and the calculator will automatically compute the results. The Cost of Carry (Futures) Calculator is designed to be user-friendly and provide instant calculations.
Is the Cost of Carry (Futures) Calculator free to use?
Yes, the Cost of Carry (Futures) Calculator is completely free to use. No registration or payment is required.
Can I use this calculator on mobile devices?
Yes, the Cost of Carry (Futures) Calculator is fully responsive and works perfectly on mobile phones, tablets, and desktop computers.
Are the results from Cost of Carry (Futures) Calculator accurate?
Yes, our calculators use standard formulas and are regularly tested for accuracy. However, results should be used for informational purposes and not as a substitute for professional advice.