Calculator
Cost of Carry Calculator
Cost of Carry Calculator
Fair Futures Price
$2,435.53
Carry Analysis
Carrying the underlying asset costs a net 7.15% per year (financing at 5.25%, plus 3.5% storage and 0.4% insurance, minus a 2% convenience yield). Compounded continuously over 6 months, the no-arbitrage futures price is $2,435.53 — $85.53 above spot. The market contract at $2,410.00 trades 1.05% below fair value. For commodities this discount usually signals tight physical supply — a convenience yield higher than the number assumed here — and the model underestimates the benefit of holding the asset right now.
*Uses continuous compounding for the fair-value estimate. Real futures prices also embed expected supply/demand and convenience yields that the model cannot forecast. Educational only, not investment advice.
Why Futures Don't Trade at Spot
A futures contract promises to deliver an asset at a future date, and its price almost never equals the spot price of the asset today. The difference is the cost of carry — the net expense, or benefit, of owning the underlying until delivery. Owning physical gold means financing the purchase, paying to store and insure it, but also enjoying the convenience of holding the real metal. Owning a stock index means financing the position but collecting dividends along the way. The futures price is what remains after all those carrying costs and benefits are compounded across the remaining months to maturity, and no-arbitrage pricing forces the two markets to agree. This concept matters far beyond the futures pit. Commodity producers hedge by selling forwards priced off carry; index funds roll their contracts at prices set by carry; and anyone deciding whether to buy an asset today or lock in a future delivery price is implicitly comparing the same financing, storage, and yield components. When the quoted futures price drifts away from the fair carry value, it signals either an exploitable gap or — more often — that the market expects supply tightness, a shortage premium, or a shift in rates. Reading the cost of carry is how professionals explain the futures curve, and how they know when the curve is telling them something about the physical market itself.
Financing Plus Storage, Minus Any Yield
The fair futures price is the spot price grown at the net cost of carry, compounded continuously over the time to maturity: Futures = Spot × e^((r + u − y) × t). Here r is the annualized risk-free financing rate, u is the sum of storage and insurance costs for physical commodities, and y is the convenience yield for commodities or the income yield for financial assets. The exponent t is the time to maturity measured in years. For a financial asset such as a stock index, there is no storage or insurance, so the carry reduces to the financing rate minus the dividend yield. Two derived numbers give the figure its meaning. The carry cost is simply the fair futures price minus spot — the dollar premium paid for delivery later rather than now. Comparing a quoted market futures price against the fair value produces a basis: a quote above fair suggests a cash-and-carry opportunity or tight expected supply, while a quote below fair (backwardation for commodities) typically indicates that holding the physical asset right now is worth more than the carry model assumes. Running the calculation in reverse — taking the log of the price ratio — extracts the market's implied net carry rate, which is often the most useful diagnostic of all.
Expert Insights
The Convenience Yield Is the Market's Supply Signal
The convenience yield — the benefit of physically holding a commodity — is not a fixed number; it is the market's gauge of scarcity. In a well-supplied market it sits near zero and futures trade at a healthy premium to spot (contango). When inventories run low, the benefit of holding physical barrels, bushels, or ingots right now surges, and futures can drop below spot (backwardation). That flip is a powerful signal: it says the market fears shortage. Traders who learn to read the implied convenience yield from the futures curve can detect physical tightness weeks before it appears in headline inventory reports.
Index Futures Are a Pure Rates-vs-Dividends Trade
Stock index futures strip out storage entirely, leaving a clean two-sided carry: you forgo the risk-free rate on the cash you would have spent, but you also skip the dividends the holder collects. When interest rates sit above dividend yields, index futures naturally trade above spot, and the spread widens as rates rise. This is why the 2022-24 rate surge visibly inflated index futures bases. Conversely, when dividends exceed short rates, the fair futures price dips below spot. Anyone pricing ETF hedges, roll costs, or synthetic long positions should anchor every calculation to this simple financing-minus-yield relationship.
Arbitrage Gaps Are Usually Illusions for Retail Traders
Textbooks say a futures price above fair carry invites you to buy spot and sell futures, locking a risk-free profit. In reality, the apparent gap usually evaporates once you apply real borrowing rates (which exceed the risk-free rate), transaction costs, and storage fees. What looks like a 1% edge often turns out to be a 0.2% loss after implementation. Genuine cash-and-carry opportunities get closed by professional arbitrageurs within minutes. For retail investors the more valuable use is diagnostic: the size and sign of the market-versus-fair gap tells you whether the curve is pricing stress, not a free lunch.
Actionable Tips
- 1
Extract the Implied Carry Before Trusting the Quote
Rather than assuming your own rate and storage inputs, reverse the formula: take the natural log of the quoted futures price divided by spot, divided by time, to back out the market's implied net carry. Compare that implied number against current financing rates and typical storage costs. A wide divergence means the market is pricing in convenience or shortage that your inputs miss. Running this reverse calculation turns the tool from a price-checker into a market-intelligence instrument, revealing what the futures curve believes about physical supply and rates.
- 2
Match the Time Basis Before Comparing Rates
All inputs must speak the same language: annualized rates, and time to maturity expressed in years. A common error is feeding a three-month maturity as zero point three (months) instead of zero point two five (years), which inflates the fair price. Likewise, express storage and insurance as annualized percentages of value, not one-time fees. Before trusting any output, verify the time fraction equals months divided by twelve. This single discipline prevents most of the discrepancies people see when comparing this model against broker-quoted futures prices.
- 3
Use the Model to Judge Hedge and Roll Costs
If you hedge a commodity exposure with futures, the carry embedded in the curve is your roll cost or benefit each month. When futures trade above spot (contango), rolling a long hedge forward means buying high and selling low — a recurring drag. When they trade below spot, the opposite is true. Compute the fair carry for your horizon, compare it to the actual curve, and decide whether the hedge's carry burden is acceptable given your view. Understanding carry is what separates informed hedgers from those who hedge blindly and wonder why the cost compounds over time.
Real-World Examples
The Refinery That Read Backwardation Before the Headlines
A mid-sized fuel buyer watched the crude futures curve flip into backwardation — quoted contracts pricing below the fair carry value this model would produce from financing and storage alone. The implied convenience yield had jumped, which the team read as the market anticipating physical tightness. They accelerated their purchasing program and locked in supply weeks before inventory data confirmed the shortage and spot prices spiked. The futures curve, decoded through carry arithmetic, had given them a usable early warning that news headlines had not yet offered. That single timing advantage paid for years of hedging overhead.
Why the ETF Holder's Returns Dragged the Index
An investor tracking a commodity index through a futures-based ETF noticed returns trailing the spot price in a rising market. Running the carry model showed the culprit: the futures curve was in steep contango, so every month the fund sold the cheap expiring contract and bought the pricier next one, bleeding value on each roll. The carry cost was roughly four percent annualized. Once the investor understood the mechanism, they switched to a spot-backed vehicle for that exposure. Contango is invisible until you compute it; once computed, it becomes a line item you can choose to avoid.
The Hedged Producer Who Locked a Premium
A wheat grower saw that new-crop futures were trading well above the fair carry value derived from current storage and financing rates, reflecting strong export demand. Rather than sell into the local cash market, she hedged most of her anticipated harvest by selling those rich futures, locking in a price that exceeded her all-in carrying cost of holding grain by a wide margin. Months later, as basis normalized, her hedge delivered more than the physical sale would have. The carry model had told her exactly when the futures market was paying above fair value — and she sold into it.
Glossary of Terms
- Cost of Carry
- The net annualized cost of holding an asset until a future date: financing plus storage and insurance, minus any yield or convenience benefit it provides while held.
- Contango
- A futures curve where deferred prices sit above spot, reflecting positive net carry costs. Buying long hedges in contango incurs recurring roll losses.
- Backwardation
- A futures curve where deferred prices sit below spot, typically signaling tight physical supply and a high convenience yield for holding the asset now.
- Convenience Yield
- The non-cash benefit of physically possessing a commodity, which rises when inventories are low and can push futures prices below spot.
Frequently Asked Questions
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Ivy Sinclair-Wren
Financial Chaos Analyst
Ivy Sinclair-Wren is a Financial Chaos Analyst covering investing, AI, wealth psychology, and the emotional consequences of opening finance apps during market crashes. Based in Melbourne, she specializes in demystifying the US tax code and helping users navigate the intersection of spreadsheet logic and human irrationality.