Cost of Carry

Q: What is cost of carry in futures?

The net cost of holding the underlying from today until the futures expiry: interest on the money tied up, less income such as dividends. The fair futures price is the spot price plus this carry, so index futures normally trade above spot by roughly the risk-free rate for the period.

Q: How is the fair value of Nifty futures calculated?

F = S × e^((r − q) × T), where S is the spot index, r the financing rate, q the dividend yield over the period and T the time to expiry in years. At 24,000, 6.5% and 30 days with no dividends the fair value is about 24,129.

Q: What does a negative cost of carry mean?

That the future is trading below spot. It happens when expected dividends in the period exceed the interest cost, or when the market is net short futures, for example when arbitrageurs holding the basket are joined by directional sellers. The implied carry turns negative.

Q: What is the difference between cost of carry and basis?

Basis is the actual difference between the futures price and spot. Cost of carry is what that difference should be from interest and dividends. When basis exceeds carry the future is at a premium to fair value; when basis is below carry it is at a discount.

Q: Why does the futures premium shrink as expiry approaches?

Because the carry is proportional to the time left. With 30 days to go at 6.5% the fair premium on 24,000 is about 129 points; with 7 days it is about 30 points; at expiry it is zero and the future settles at the index value.

A future should cost what it costs to buy the index today and hold it to expiry. That holding cost is the carry, and the gap between the actual future and that fair value is the market’s opinion.

In short: Cost of carry is the net cost of holding the underlying asset from today until the futures expiry: the interest on the money tied up, less any income the asset pays, such as dividends. The fair futures price equals the spot price plus the cost of carry, so index futures normally trade above spot by roughly the risk-free rate for the period, less expected dividends. The difference between the actual future and spot is the basis, and carry expressed as an annualised percentage is what traders quote as the cost of carry on a contract.

The intuition

There are two ways to own NIFTY at expiry: buy the basket of shares today and hold it, or buy the future and pay at expiry. The first ties up cash for a month, which costs interest, but collects any dividends the stocks pay. The second ties up only margin. For the two routes to cost the same, the future must be priced above spot by the interest cost and below it by the dividends. That net amount is the cost of carry. When the future trades above its fair value, buyers are paying a premium for leverage or for bullish exposure; when it trades below, the market is either expecting dividends or is net short.

Formula

Fair futures price F = S × e^{(r − q) × T}, or approximately F = S × (1 + (r − q) × T)

where S is spot, r the annual financing rate, q the annual dividend yield over the period, and T the time to expiry in years

Cost of carry (in points) = F_fair − S; annualised carry (%) = ln(F ÷ S) ÷ T, computed from the actual futures price to read the market’s implied carry

Worked example (illustrative prices and rates)

Suppose NIFTY is at 24,000, the financing rate is 6.5% a year, and the monthly future has 30 days to expiry.

Case	Calculation	Fair future	Carry
No dividends in the period	24,000 × e^{0.065 × 30/365}	24,128.6	128.6 points, 6.5% annualised
Dividend yield 1.2% in the period	24,000 × e^{(0.065 − 0.012) × 30/365}	24,104.8	104.8 points, 5.3% annualised
7 days to expiry, no dividends	24,000 × e^{0.065 × 7/365}	24,029.9	29.9 points
Actual future trades at 24,160	ln(24,160 ÷ 24,000) ÷ (30/365)		8.1% implied carry: a premium of about 31 points over fair value
Actual future trades at 24,020	ln(24,020 ÷ 24,000) ÷ (30/365)		1.0% implied carry: a discount of about 109 points to fair value

In the last row the future is far below fair value. Either heavy dividends fall in the period, or the market is net short futures, often because arbitrageurs who hold the basket and are short the future have been joined by directional sellers. The implied carry is read by comparing the actual future with spot; the fair value is what it should be in the absence of any view.

The fair futures value sits above spot by the cost of carry and converges to spot at expiry. An actual future above the curve is trading at a premium to fair value, below it at a discount.

Why it matters

It is the futures trader’s theta. A long future bought at a 129-point premium loses those points to convergence by expiry if spot is unchanged; that is the cost of the leverage.
It prices the roll. Rolling a long position from the current month to the next means paying the next month’s carry; rolling a short means receiving it. The rollover spread is the carry between the two contracts.
Deviations carry information. A future well above fair value shows leveraged buying; one below it shows short positioning or dividend expectations. Watching implied carry across the month is a positioning read.
It links to options. Put-call parity contains the same carry term: a synthetic future built from a call and a put prices at the same fair value as the actual future.

Common mistakes

Reading a futures premium as bullish on its own. Most of the premium is simply interest; only the excess over fair value says anything.
Ignoring dividends. In the dividend-heavy months, index futures trade at a smaller premium or at a discount purely because of expected payouts, not because of bearishness.
Using the wrong rate. The relevant rate is the market’s short-term funding rate, close to the overnight and treasury-bill rates, not a bank deposit rate.
Comparing carry across contracts of different tenor in points. Annualise it, or the three-month contract will always look more expensive than the one-month.

Indian specifics

NSE index futures on NIFTY, BANKNIFTY, FINNIFTY, MIDCPNIFTY and NIFTYNXT50 are cash settled on the last Tuesday of the month, so the carry period runs to that date and the futures price converges to the index closing value at expiry. NSE publishes the daily cost of carry for each futures contract in its reports, computed from the futures and spot closing prices. Stock futures carry can diverge sharply from the index because of stock-specific dividends, buybacks and the physical settlement obligation in expiry week, and stocks under securities lending demand can trade at a discount. On MCX, the carry on commodity futures also includes storage and insurance for deliverable metals, so gold and silver futures curves embed a storage cost on top of interest.

FAQ

What is cost of carry in futures?

Interest cost of holding the underlying to expiry, less dividends; the fair future equals spot plus this amount.

How is the fair value of Nifty futures calculated?

F = S × e^((r − q) × T). At spot 24,000, 6.5% and 30 days with no dividends: about 24,129.

What does a negative cost of carry mean?

The future is below spot: heavy expected dividends, or net short positioning pushing the future under fair value.

What is the difference between cost of carry and basis?

Basis is the actual future-minus-spot; cost of carry is the fair amount. Their difference is the premium or discount to fair value.

Why does the futures premium shrink as expiry approaches?

Carry is proportional to time to expiry, so the fair premium falls to zero at expiry.

See the live chain next to the futures

TradePulse shows spot, VWAP and the option chain with per-strike data, so the relationship between the index, the futures and the synthetic from the chain is visible in one place.

NIFTY option chain Futures vs options

Related terms

Basis, the actual futures-minus-spot gap
Contango, a futures curve above spot
Backwardation, a curve below spot
Rollover, paying or receiving the next month’s carry
Put-call parity, the same carry inside options
Futures contract, the instrument being priced