NISM PracticeFutures: profit and loss, pricing, basis and margins
A futures position gains or loses rupee for rupee with the price. The rest of the arithmetic follows from that and from the cost of holding the asset until expiry.
1. Profit and loss on a futures position
Buyer (long): Profit = (Exit price − Entry price) × Lot size × Number of lots
Seller (short): Profit = (Entry price − Exit price) × Lot size × Number of lots
Example. A trader buys one contract at ₹1,000, lot size 100, and it expires at ₹1,040. Profit = 40 × 100 = ₹4,000. Had the price fallen to ₹970, the loss would be 30 × 100 = ₹3,000.
Example. A trader sells one contract at ₹500, lot size 200, and the price at expiry is ₹520. Loss = 20 × 200 = ₹4,000. A seller gains when the price falls.
Unlike an option, a futures contract has no premium and no limit on loss for either side.
2. Contract value
Contract value = Futures price × Lot size
Example. An index future at 20,000 with a lot size of 50 has a contract value of 20,000 × 50 = ₹10,00,000. Lot sizes are fixed by the exchange and revised periodically; use the figure given in the question.
3. Fair price by cost of carry
Someone who needs the asset at a future date can buy it now and hold it, or buy a future. Holding costs interest on the money, and earns any dividend. In a fair market the future is priced so that neither route is cheaper.
With simple interest: F = S × (1 + r × t) − Dividend expected before expiry
where S is the spot price, r the annual interest rate and t the time to expiry in years.
Example. Spot ₹1,000; interest 12% a year; one month to expiry; no dividend. F = 1,000 × (1 + 0.12 × 1/12) = ₹1,010.
Example with dividend. Same share, but a dividend of ₹4 is expected before expiry. F = 1,010 − 4 = ₹1,006 (ignoring interest on the dividend).
Some texts use continuous compounding, F = S × e^(r × t). For short periods the answer is almost the same: here 1,000 × e^0.01 is about ₹1,010.05. Use the form your workbook uses.
4. Basis and convergence
Basis = Spot price − Futures price
In the example, basis = 1,000 − 1,010 = −₹10. When futures trade above spot, as the cost of carry normally implies, the market is said to be in contango; when below, in backwardation. As expiry approaches, the time left for carrying falls towards zero, so the futures price and the spot price converge and the basis tends to zero.
5. Arbitrage, in one example
If the future in the example traded at ₹1,020 instead of its fair ₹1,010, an arbitrageur could borrow ₹1,000 at 12%, buy the share, and sell the future at ₹1,020. At expiry he delivers at ₹1,020, repays ₹1,010, and keeps ₹10 a share with no price risk (before costs). Such trades push the futures price back towards fair value. This is cash-and-carry arbitrage; the opposite trade applies when the future is too cheap.
6. Hedging a portfolio with index futures
Value of index futures to sell = Portfolio value × Portfolio beta
Number of contracts = Value to sell ÷ Contract value
Example. A portfolio worth ₹10,00,000 has a beta of 1.2. Futures to sell = 10,00,000 × 1.2 = ₹12,00,000. If one index contract is worth ₹4,00,000, sell 3 contracts.
If the market then falls 5%, the portfolio is expected to fall about 6%, a loss of ₹60,000, while the short futures gain 5% of ₹12,00,000 = ₹60,000. The hedge removes market risk, not the risk specific to the shares held.
7. Margins and daily settlement
- Initial margin is collected upfront when a position is opened, to cover the likely loss over the next day. The rate is set by the clearing corporation's risk system and varies with volatility.
- Mark-to-market (MTM) settlement: each day the position is valued at the daily settlement price. Losses are collected from, and gains paid to, the participant.
- Leverage: because only the margin is paid, a small price move is a large percentage of the money put up.
Illustration, with an assumed margin of 10%. One contract bought at ₹1,000, lot 100: contract value ₹1,00,000; initial margin ₹10,000.
| Day | Settlement price (₹) | MTM for the buyer (₹) |
|---|---|---|
| 1 | 1,015 | +1,500 |
| 2 | 990 | −2,500 |
| 3 | 1,040 | +5,000 |
| Total | +4,000 |
The daily amounts add up to the same ₹4,000 as (1,040 − 1,000) × 100. A gain of ₹4,000 on a margin of ₹10,000 is 40%, from a 4% move in price: that is leverage, and it works equally against the trader when the price moves the other way.
8. Open interest and volume
Volume is the number of contracts traded in a period. Open interest is the number of contracts outstanding at a point in time. When a new buyer and a new seller trade, open interest rises by one; when two existing holders close out against each other, it falls by one.
Common slips
- Forgetting to multiply by the lot size.
- Giving a seller's result as a profit when the price rose.
- Using the annual rate for a one-month future without scaling the time.
- Writing basis as futures minus spot; the usual convention is spot minus futures.
- Treating initial margin as a cost. It is a deposit; the profit or loss is the price difference.
Practise in the Equity Derivatives question set, and see option payoffs.
Questions candidates ask
How is the fair price of a futures contract calculated?
By the cost of carry: spot price plus the interest cost of holding the asset to expiry, less any dividend expected. With simple interest, F = S × (1 + r × t).
What is basis in futures?
The spot price minus the futures price. It tends to zero as the contract nears expiry.
How many index futures are needed to hedge a portfolio?
Sell futures worth the portfolio value multiplied by its beta, and divide by the value of one contract to get the number of contracts.
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