Cost of carry and the fair price of futures
Spot price plus financing cost minus dividends gives the fair futures price. Gaps from it are what arbitrageurs trade.
Cost of carry is what it costs to buy an asset today and hold it until a future date, minus any income the asset pays while you hold it. For equity, the NISM workbook defines it as the interest paid to finance the purchase less the dividend earned.
It matters because it sets the fair price of a futures contract. Buying futures and buying the shares now and holding them should cost the same. If they do not, arbitrage traders step in until the gap closes. So the fair futures price is the spot price plus the cost of carry.
The formula, in the forms the workbook uses
- Fair futures price
- Spot price + cost of carry minus inflows (dividends on equity, interest on bonds).
- Compound form
- F = S × (1 + r minus q)^T, where S is spot, r the cost of carry (financing rate), q the income yield and T the time to expiry in years.
- Continuous form
- F = S × e^((r minus q) × T). The workbook gives both and shows they produce slightly different answers.
- Basis
- Spot price minus futures price. When futures trade above spot, basis is negative. Whatever it is during the contract's life, it becomes zero at expiry, because futures settle at the closing price of the underlying.
- Convenience yield
- The benefit of physically holding an asset, mostly a commodity idea. When it outweighs the cost of carry, futures can trade below spot and the model breaks down.
Worked example: fair price of Nifty futures
Illustrative numbers. Nifty spot is 25,000, the financing rate is 7% a year, the dividend yield on the index is 1% a year, and the futures contract expires in 30 days.
- 1
1. Net carry rate
r minus q = 7% minus 1% = 6% a year.
- 2
2. Time in years
T = 30 / 365 = 0.0822.
- 3
3. Continuous form
F = 25,000 × e^(0.06 × 0.0822) = 25,123.59.
- 4
4. Compound form
F = 25,000 × 1.06^0.0822 = 25,120.02. Close, but not equal; read which form a question asks for.
- 5
5. Basis
Spot minus fair futures = 25,000 minus 25,124 = about minus 124 points, shrinking to zero by expiry.
When the market price is off the fair price
Using the example above, fair value is about 25,124. The arbitrage named in the workbook:
25,250
Mispricing
Futures too expensive
Arbitrage
Cash-and-carry
Trades
Buy the shares (spot), sell futures, deliver or square off at expiry
24,980
Mispricing
Futures too cheap
Arbitrage
Reverse cash-and-carry
Trades
Sell the shares (spot), buy futures
25,110 to 25,140
Mispricing
Inside an illustrative no-arbitrage band
Arbitrage
None
Trades
Brokerage, taxes and margins make the trade unprofitable
| Market futures price | Mispricing | Arbitrage | Trades |
|---|---|---|---|
| 25,250 | Futures too expensive | Cash-and-carry | Buy the shares (spot), sell futures, deliver or square off at expiry |
| 24,980 | Futures too cheap | Reverse cash-and-carry | Sell the shares (spot), buy futures |
| 25,110 to 25,140 | Inside an illustrative no-arbitrage band | None | Brokerage, taxes and margins make the trade unprofitable |
Free account, this exam preselected.
The model's assumptions
The workbook lists these as the important ones, and says the model suits forwards better than futures because it ignores margins.
- check_circleThe underlying is available in abundance in the cash market.
- check_circleDemand and supply are not seasonal.
- check_circleThe asset is easy to hold and maintain.
- check_circleThe asset can be sold short.
- check_circleNo transaction costs, no taxes, no margin requirements.
How Series VIII tests this
The classic question is the workbook's own: a share at ₹100, borrowing at 6% for a year, a ₹2 dividend. Net carry is 6 minus 2 = ₹4, so the breakeven futures price is ₹104. Trap answers add the dividend instead of subtracting it (₹108) or ignore it (₹106).
Other questions ask which arbitrage applies when futures trade above fair value (cash-and-carry: buy spot, sell futures), what basis becomes at expiry (zero), or whether basis is positive when futures trade above spot (no, it is negative). Check the sign convention every time: basis is spot minus futures.
FAQs
What is cost of carry in futures?expand_more
The cost of holding the underlying until the futures expiry: financing interest, less income such as dividends. Added to the spot price, it gives the fair futures price.
What is the cost of carry formula?expand_more
Fair futures price = spot + cost of carry minus inflows. As a rate: F = S × (1 + r minus q)^T, or F = S × e^((r minus q)T) with continuous compounding.
Why do futures trade above the spot price?expand_more
Usually because the cost of financing the underlying exceeds the income it pays, so the cost of carry is positive. When dividends or convenience yield are larger, futures can trade below spot.
What happens to basis on expiry day?expand_more
It becomes zero. Futures settle at the closing price of the underlying, so spot and futures converge.
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