Forwards and futures
Cost-of-carry pricing, basis, contango and backwardation, payoff lines, initial and maintenance margin, daily…
Futures are where the exam does most of its arithmetic. You will be asked to compute a fair futures price from spot and interest, to read the basis, to settle a mark-to-market statement and to work out profit on a lot. Each of these is a two-line calculation once the formula is in your head, and this chapter puts it there.
From forward to future
A forward fixes a price today for delivery later. Two problems stop it scaling: each side must trust the other to pay (counterparty risk), and the contract is hard to exit because its terms suit only the two who wrote it. A futures contract solves both. The exchange standardises the underlying, lot size, expiry and settlement; the clearing corporation steps between buyer and seller and guarantees both; and gains and losses are settled every evening so that no large unpaid loss ever builds up. The price of this convenience is that you cannot customise the contract and you must keep margin money with your broker.
Three monthly series trade at any time: near month, next month and far month. On expiry of the near month a new far-month contract is introduced. For Nifty, weekly contracts also exist, with the expiry day as specified by the exchange.
Pricing: the cost of carry
If you can buy the underlying today with borrowed money and hold it to expiry, the futures price should equal spot plus the net cost of holding: interest paid less any income (dividends) received. Any gap is an arbitrage.
S is spot, r the annual risk-free rate, T time to expiry in years. The exam tells you which convention to use; if it says nothing, simple interest is acceptable and the two agree to within a few rupees for short maturities.
| Nifty spot | 24,000 |
| Risk-free rate | 7% a year |
| Days to expiry | 30 days, T = 30 ÷ 365 = 0.0822 |
| Fair futures (simple) = 24,000 × (1 + 0.07 × 0.0822) | 24,138.1 |
| Fair futures (continuous) = 24,000 × e^(0.005753) | 24,138.5 |
| With dividend yield 1.2%: 24,000 × e^((0.07 − 0.012) × 0.0822) | 24,114.6 |
| Cost of carry = F − S (simple, no dividend) | 138.1 points |
If the market quotes the future at 24,200 against a fair value of 24,138, an arbitrageur buys the index basket (or an ETF) in the cash market, sells the future, and at expiry earns the 62-point excess less transaction costs. This is cash-and-carry. If the future trades below fair value, a holder of the basket sells it, invests the cash, and buys the future: reverse cash-and-carry. These trades keep the future tethered to its fair value.
Basis, contango and backwardation
A positive basis, future above spot, is contango; this is normal for index and stock futures because interest usually exceeds dividend yield. A negative basis is backwardation, seen when a large dividend is due before expiry, when the stock is hard to borrow, or when the market is heavily short. Whatever its sign, the basis shrinks to zero on expiry because the final settlement price is the spot price. A trader who buys a future in contango and holds to expiry pays the basis as a cost; a short in contango earns it.
Payoffs: a straight line
A futures payoff is linear. If you buy at F and the underlying settles at S_T, your profit per unit is S_T − F; the seller's is F − S_T. Drawn as a payoff diagram, the long is a straight line rising at 45 degrees through zero at F, and the short is its mirror image. There is no cap on either side.
| Trader A buys 1 lot (75) at 24,140; Trader B sells 1 lot at 24,140 | Payoff at expiry |
| Settles at 23,600: A gets (23,600 − 24,140) × 75 | A −₹40,500, B +₹40,500 |
| Settles at 24,140 | A ₹0, B ₹0 |
| Settles at 24,500: A gets (24,500 − 24,140) × 75 | A +₹27,000, B −₹27,000 |
| Settles at 25,000: A gets (25,000 − 24,140) × 75 | A +₹64,500, B −₹64,500 |
Futures are a zero-sum game between the two sides before costs; every rupee one makes the other loses.
Margins and mark-to-market
To open a futures position you deposit initial margin with your broker, who passes it to the clearing corporation. It is computed by the SPAN system to cover the largest likely loss over one day at 99% confidence, and for Nifty it is in the region of 10% to 12% of contract value, higher in volatile periods. An exposure margin is collected on top as a further cushion. The textbook concept of maintenance margin is the level below which the account may not fall; if it does, a margin call requires you to top up to the initial level, failing which the broker squares off the position.
Every trading day the clearing corporation marks every open position to market at the daily settlement price (the closing price of the futures contract, computed as the last half-hour weighted average). The day's gain is credited to your account and the day's loss debited, in cash, that evening or the next morning. Your position is then treated as if re-entered at the settlement price. On expiry the contract is marked to the final settlement price, the closing value of the underlying index in the cash market.
| Buy 1 lot Nifty futures at 24,140; contract value 24,140 × 75 | ₹18,10,500 |
| Initial margin at 11% | ₹1,99,155 |
| Day 1 settles 24,060: MTM = (24,060 − 24,140) × 75 | −₹6,000 |
| Day 2 settles 24,210: MTM = (24,210 − 24,060) × 75 | +₹11,250 |
| Day 3 sold at 24,180: MTM = (24,180 − 24,210) × 75 | −₹2,250 |
| Net = (24,180 − 24,140) × 75 | +₹3,000 |
The net of the daily settlements always equals exit price less entry price times the lot, which is a quick check in the exam. The leverage is what makes futures dangerous: a 2% move in Nifty is ₹36,000 on one lot, about 18% of the margin posted.
Remember
- Futures are standardised forwards with exchange trading, clearing-corporation guarantee and daily cash settlement of gains and losses.
- Fair price F = S(1 + rT) or S·e^(rT); dividends reduce it to S·e^((r − q)T). T is always in years.
- Basis = futures − spot. Positive is contango (normal), negative is backwardation; basis goes to zero at expiry.
- Future above fair value: cash-and-carry (buy spot, sell future). Below: reverse cash-and-carry.
- Long futures profit = (settlement − entry) × lot; short is the mirror image; both unlimited.
- Initial margin (SPAN) is a deposit; daily MTM settles each day's change in cash; net MTM equals exit minus entry times lot.