Futures Fair Value Calculator

Work out the theoretical futures price from spot, financing cost, storage and yield, and compare it with the traded price.

A futures price is not a prediction of where the market will be on expiry day. It is today's cash price with the cost of carry added on — the money tied up, the storage rented, and whatever the asset pays out along the way that the holder of a contract never receives. This futures fair value calculator does that sum deliberately, from rates you enter, rather than inferring it backwards from whatever the screen happens to say.

Formula: fair value = spot x e^((rate + storage - yield) x time)

Your figures

Underlying price

The cash price of the underlying today — the market the contract settles against.

Annual financing rate

The rate your own broker or treasury desk charges to fund the cash position, not a policy rate.

Annual storage cost

Storage, insurance and handling as a percentage of spot. Zero for an index or a financial contract.

Annual yield given up

What holding the asset pays that the futures holder does not receive: a dividend yield, a coupon, or a commodity's convenience yield.

Days to expiry

Calendar days from today to the contract's expiry.

Day count basis

The year length your financing is quoted on. US money-market rates and most commodity carry use 360; sterling and most index screens use 365.

Compounding convention

Continuous is the derivatives-desk form and composes cleanly across periods. Simple interest is what most cash-and-carry desks and index fair-value screens quote inside a year.

Futures price

Optional — the price the contract is actually trading at, to compare with fair value and imply a rate from it.

Results

Fair value

5,043.34

5,000.00 spot, +43.34 pts of carry over 90 days

Carry to expiryFair value less the underlying price: what the period of carry is worth in the contract's own points.: +43.34 pts · +0.867%
Net carry rateFinancing plus storage, less the yield given up. A yield larger than the financing cost turns this negative and puts fair value below spot.: +3.500%
Time to expiry90 days on a 365-day year.: 0.2466 years
Traded price against fair valueThe contract is trading above the price the entered carry implies.: +6.66 pts · +0.132%
Implied net carry rateThe annual rate the traded price corresponds to, in total, on this convention and day count.: +4.035%
Implied financing rateThe implied net carry with the storage and yield entered above taken back out, so it stands next to a financing quote.: +5.535%
Convention usedBoth figures above depend on this pair. The same rates on the other pair give a different answer.: Continuous · 365-day year

What this means

Carrying the underlying for 90 days at a net +3.500% a year moves the 5,000.00 spot price by +43.34 pts, so fair value is 5,043.34 on continuous compounding and a 365-day year. The traded price is +6.66 pts away from it, which is the same statement as saying the market is pricing a net +4.035% a year to defer the purchase — +5.535% once the storage and yield entered here are removed. Fair value is a restatement of the spot price and the rates entered, on the convention chosen. It describes the carry, not where the contract will trade.

Every rate, multiplier, margin and commission above is yours to enter. No broker's or exchange's figure is preset, because the figure that applies to a position is the one that account is actually charged; margin fields open empty for that reason, and any other number a field starts with is a round illustration. The contract specifications the site does carry — tick sizes and point values — are the exchange's published ones and are stated as such.
The two conventions are not interchangeable. Simple interest and continuous compounding, and a 360- against a 365-day year, give different answers from identical rates, which is why the pair used is printed with the result.
Assumes the carry can be transacted: cash borrowed at the rate entered, the asset bought and held, and storage rented at the cost entered. Where any of those is unavailable — a commodity that cannot be borrowed, a balance sheet that is full — a traded price can sit away from fair value indefinitely.
Excludes commission, exchange fees and the spread on both sides of a cash-and-carry, which are charged four times across the opening and closing of the two positions.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Futures Fair Value calculation

Used as a cost of carry calculator, it takes the underlying price, your own financing rate, an optional storage cost, an optional yield given up and the days to expiry, and returns the theoretical futures price those figures imply. The carry is reported in the contract's own points and as a percentage of spot, and the compounding convention and day count are printed alongside, because the same rates on the other pair of conventions give a different answer and a carry figure read without them cannot be checked by anybody.

Enter the price the contract is actually trading at and the formula runs backwards as well. The gap between that price and fair value becomes an annual rate — the financing the market is charging to defer the purchase — and a rate is something that can be set beside a quote from a broker or a treasury desk and argued with. A gap of two and a quarter points cannot be argued with, because nobody knows whether it is large.

Futures Fair Value formula

t              = days to expiry ÷ day count
net carry      = financing % + storage % − yield %

fair value     = spot × e^(net carry ÷ 100 × t)        (continuous)
               = spot × (1 + net carry ÷ 100 × t)      (simple)

carry          = fair value − spot
carry %        = carry ÷ spot × 100

against a traded price:

premium        = traded price − fair value

implied net carry = ln(traded ÷ spot) ÷ t              (continuous)
                  = (traded ÷ spot − 1) ÷ t            (simple)

implied financing = implied net carry − storage % + yield %

spot: The cash price of the underlying today — the market the contract settles against, not the price of a nearer contract month.
financing %: The annual rate your own broker or treasury desk charges to fund the cash position. Not a policy rate, and not a screen quote for somebody with a better balance sheet.
storage %: Annual storage, insurance and handling as a percentage of spot. Zero for an index or any purely financial contract, and never negative.
yield %: What holding the asset pays that a futures holder does not get: a dividend yield, a coupon, or a physical commodity's convenience yield. It may be negative when holding is a burden.
day count: The year length the rates are quoted on. 360 for US money-market financing and most commodity carry; 365 for sterling and most index screens.
t: The period to expiry expressed as a fraction of a year on that day count. 73 days is 0.2000 years on 365 and 0.2028 on 360.

The shape of the fair value futures formula comes from an arbitrage argument rather than from any view about the market. Somebody who needs the asset in three months has two routes to it. They can buy the future, or they can borrow the cash today, buy the asset outright and carry it until then. The second route has an all-in cost that can be worked out exactly: the interest on the borrowing, plus the storage, minus anything the asset pays while it is held. Fair value is the futures price at which neither route is cheaper, which is why it is the spot price multiplied by the carry rather than added to some estimate of future value.

The yield is subtracted because it accrues to whoever owns the asset, and that is not the futures holder. On an equity index it is the dividend stream the shareholder collects and the contract holder forgoes; on a bond it is the coupon; on a physical commodity it is the convenience yield, which is the value of having the barrel in the tank rather than a promise of one in December. When that yield exceeds the financing cost the net carry goes negative and fair value sits below the cash price, which is not an anomaly — it is the ordinary state of an index future in a high-dividend, low-rate market, and a large convenience yield is the mechanism behind a backwardated commodity curve.

The two conventions are offered rather than chosen because careful practitioners genuinely disagree. Continuous compounding, spot × e^(r t), is the derivatives-desk form and composes cleanly when periods are chained together. Simple interest, spot × (1 + r t), is what most cash-and-carry desks and index fair-value screens quote inside a year. Over a quarter at ordinary rates the two differ by a few hundredths of a percent, which is invisible in points and audible in an implied rate; over a year at a high rate the gap is real money. The day count matters for the same reason: dividing by 360 rather than 365 moves the carry by about 1.4%.

Inverting the formula against a traded price is where the page earns its keep. Feeding the traded price back through the logarithm returns the net carry the market is pricing, and stripping out the storage and yield already entered leaves an implied financing rate. That figure is directly comparable with a borrowing quote in a way the raw premium never is. It also explains why a contract trading away from fair value is not automatically an opportunity: the gap is usually the cost of the arbitrage itself, sitting in the borrow, in the balance sheet nobody has spare, in storage that cannot actually be rented, or in the plain fact that a physical commodity often cannot be sold short at all.

Futures Fair Value: a worked example

An equity index quoted at 4,800.00 in the cash market with 73 days to a quarterly expiry, funded at 5.20% on a 365-day year, no storage cost, and 1.80% of dividends given up by holding the contract instead of the shares. The contract itself is trading at 4,835.00.

Time to expiry73 ÷ 365 = 0.2000 years
Net carry rate5.20% + 0.00% − 1.80% = +3.40% a year
Fair value4,800 × e^(0.034 × 0.2000) = 4,800 × 1.006823 = 4,832.75
Carry to expiry4,832.75 − 4,800.00 = +32.75 pts, or +0.682% of spot
Traded price against fair value4,835.00 − 4,832.75 = +2.25 pts (+0.047%)
Implied net carry rateln(4,835 ÷ 4,800) ÷ 0.2000 = +3.633% a year
Implied financing rate3.633% − 0.00% + 1.80% = +5.433% a year

Fair value is 4,832.75 and the contract sits 2.25 points above it. Restated as a rate, the market is deferring the purchase at 5.433% a year against the 5.20% entered — twenty-three basis points, which is the entire 2.25-point gap expressed in units a financing quote can be measured against. Whether those twenty-three basis points are worth anything depends on whether the cash-and-carry behind them can be transacted at 5.20% after commission on four fills and the spread on both sides.

How to use the Futures Fair Value calculator

Enter the cash price of the underlying in Underlying price. This is the market the contract settles against, not the price of a nearer contract month — using one future to value another is what the calendar spread page is for.
Put your own funding cost in Annual financing rate. The figure that decides whether a carry trade works is the rate the account is actually charged, which for most readers sits above any headline rate and differs between brokers.
Leave Annual storage cost at zero for an index, a single stock or any financial contract. Fill it in only for something that occupies physical space and has to be insured while it does.
Use Annual yield given up for the dividend yield on an index, the running yield on a bond, or an estimated convenience yield on a commodity. A yield larger than the financing rate turns the net carry negative and puts fair value below spot, which the calculator will show without complaint.
Set the day count and compounding convention to match how your financing is actually quoted, then read them back off the Convention used row before comparing the answer with anybody else's.
Add the traded price last. Fair value stands on its own without it; the traded price is what turns the page from a theoretical figure into an implied financing rate you can take to a desk.

Limitations of the Futures Fair Value calculator

Every calculation makes assumptions. These are the ones that matter here.

It assumes the carry can actually be transacted — cash borrowed at the rate entered, the asset bought and held, and storage rented at the cost entered. Where any leg of that is unavailable, a traded price can sit away from fair value for months without anything correcting it.
Commission, exchange fees and the bid-offer spread are excluded. A cash-and-carry pays them four times across opening and closing two positions, and on a gap of a few basis points that is frequently larger than the gap itself.
The rates are treated as constant across the whole period. In practice financing is repriced, dividend estimates are revised and a convenience yield moves with inventories, so the carry cost this page puts on a futures position is a snapshot of today's assumptions rather than a fixed target.
Nothing here models the daily variation margin that separates a futures contract from a forward. Marking to market every session creates interest on the cash flows themselves, which matters when rates are volatile and is invisible in this arithmetic.
The dividend yield entered is a smooth annual rate, whereas real dividends arrive on specific dates. For an index future spanning a heavy dividend month the smoothed figure will misprice the carry noticeably in both directions either side of that month.
Fair value describes the carry, not the destination. A contract can trade above or below it for as long as the market is willing to, and the figure carries no implication about which direction either price moves next.

Frequently asked questions about Futures Fair Value

Why is fair value below the spot price in my result?

Because the yield entered is larger than the financing plus storage, which makes the net carry negative. Holding the asset pays more than it costs to fund, so the right to buy it later is worth less than the asset itself. This is the ordinary state of an equity index future when dividend yields exceed short rates, and it is the arithmetic working rather than an error.

Should I choose continuous or simple compounding?

Match whichever your own financing is quoted on, and if it is a money-market borrowing that is almost always simple interest. Continuous is the derivatives-desk convention and chains cleanly across periods, which is why it is the default here. Over a quarter at ordinary rates the two differ by a few hundredths of a percent, so the choice matters far more for the implied rate than for the fair value in points.

What is the implied financing rate telling me?

It is the traded price translated into an annual borrowing cost, with the storage and yield you entered taken back out so it stands beside a financing quote. If it comes back at 5.4% and your broker funds you at 5.2%, the market is paying you twenty basis points to carry the asset and sell the contract — before the costs of doing so, which usually eat most or all of a gap that size.

Does a price above fair value mean the contract is overpriced?

No. It means the market is pricing a higher net carry than the rates you entered imply. That can be because your financing assumption differs from the marginal participant's, because the borrow is expensive, because dividends have been revised, or because the arbitrage that would close the gap cannot be put on at any sensible cost. The calculator measures the difference; it does not attribute it.

Why does the answer change when I switch between 360 and 365 days?

Because the period is expressed as a fraction of a year, and a shorter year makes the same number of days a larger fraction. Seventy-three days is 0.2000 of a 365-day year and 0.2028 of a 360-day year — about 1.4% more carry from identical rates. It is invisible in points on a short-dated contract and it moves an implied rate enough to change a decision.

Can I use this for a single stock rather than an index?

Yes. Enter the share price as the underlying, the expected dividend yield over the period as the yield given up, and zero storage. The one thing to watch on single names is the stock borrow: if the reverse arbitrage requires shorting a hard-to-borrow share, the fee on that borrow belongs in the financing rate and can be several percent a year on its own.

Last reviewed 29 August 2026. See our methodology and editorial policy.

More futures calculators