How the cost of carry sets a forward price
Imagine you need an asset in one year. You could wait and buy it in the spot market then, or buy it today and hold it. Holding it costs money — you tie up capital at the financing rate r and, for commodities, pay storage u — but it can also pay you back through incomeq (dividends or coupons) and a convenience yield y (the benefit of having the physical asset on hand). The forward price is simply the spot grown at that net rate, because any other price would let someone lock in a riskless profit by trading the spot against the forward. It is the same no-arbitrage logic that underpins theBlack-Scholes calculator, applied to a delivery contract instead of an option.
The cost-of-carry formula
F = S · e( (r + u − q − y)·T )
where S = spot price, r = financing (risk-free) rate,u = storage cost, q = income / dividend yield earned while holding the asset, y = convenience yield, and T = years to delivery. The bracketed term (r + u − q − y) is the net cost of carry: positive carry produces contango (F > S), negative carry produces backwardation (F < S), and the basis F − S converges to zero at delivery.
What makes this calculator different
- It breaks down the carry components. Financing, storage, income, and convenience yield are each shown separately with their sign, so you can see exactly which forces push the forward above or below the spot.
- It classifies contango vs backwardation. The result is labelled by regime and shows the basis (F − S) in dollars and as a rate, so the market structure is explicit, not something you have to infer.
- It works for financial assets and commodities alike. Set storage and convenience yield to zero for an equity index or bond; turn them on for a commodity — the same cost-of-carry engine prices both.
Frequently asked questions
What is a forward / futures price and how is it set?+
A forward or futures price is the price agreed today for delivery of an asset at a future date. It is not a forecast of where the spot will trade then — it is fixed by no-arbitrage. If you can buy the asset now, carry it to delivery, and lock in a sale, the forward must equal the spot price grown by the net cost of carrying it; otherwise a riskless profit would exist. So the price is the spot compounded at the financing rate, adjusted for storage, income, and convenience yield, with no view on the future required.
What is the cost-of-carry formula?+
For continuous compounding, F = S · e^((r + u − q − y)·T). Here S is the spot price, r the financing (risk-free) rate, u the storage cost, q the income or dividend yield earned while holding the asset, y the convenience yield, and T the time to delivery in years. The bracketed term (r + u − q − y) is the net cost of carry: costs of holding the asset push the forward up, while income and convenience yield pull it down. Multiply S by e raised to that net rate over T and you have the arbitrage-free forward.
What is the difference between contango and backwardation?+
Contango describes a market where the forward price is above the spot (F > S), which happens when the net cost of carry is positive — financing and storage outweigh income and convenience yield. Backwardation is the reverse: the forward sits below the spot (F < S), typically when a high income or convenience yield dominates. The basis (F − S) is positive in contango and negative in backwardation, and it converges to zero as the contract approaches delivery.
Why isn’t the futures price a prediction of the spot?+
It is tempting to read the futures price as the market’s best guess of the future spot, but that is not what it is. The price is pinned by the carry relationship between today’s spot and the cost of holding the asset until delivery — an arbitrage condition, not a probability-weighted forecast. If the forward drifted away from spot-plus-carry, traders would buy the cheap leg and sell the rich one until it snapped back. Expectations about the future spot are already embedded in today’s spot price, not added on top in the forward.
What is the difference between a forward and a future?+
A forward is a private, over-the-counter contract customized between two parties — bespoke size, date, and terms — and settled at delivery, which carries counterparty credit risk. A future is a standardized, exchange-traded contract that is marked to market daily through a clearinghouse with margin, largely removing counterparty risk. The two differ in structure, liquidity, and cash-flow timing, but the pricing model is the same: both are valued by the cost-of-carry, no-arbitrage relationship to the spot.
Disclaimer: This calculator is foreducation and illustration only. It applies the cost-of-carry, no-arbitrage model with simplifying assumptions (continuous compounding, constant rates, frictionless markets, and a known carry); real forward and futures prices reflect frictions, term-structure effects, and market dynamics this model omits. Its output is not a tradeable quote, and nothing here is investment, tax, or trading advice.