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V-D · Chapter 6 of 13

Forwards and futures

Forward versus futures contracts, basis and contango, cost-of-carry pricing with a worked example, margins…

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Futures are the workhorse of every SIF strategy: the cheapest way to go short, to hedge a portfolio, or to add exposure without buying stock. The exam wants you to price a futures contract from the spot price and the cost of carry, read a mark-to-market statement, and explain why the futures price is usually above spot. All three appear here with numbers.

Forwards and their limitations

A forward contract fixes today the price at which two parties will trade an asset on a future date. A jeweller who needs gold in three months can lock the price with a bullion dealer. The trouble is that each party depends on the other to perform (counterparty risk), the contract is hard to transfer or cancel (illiquidity), and the price is negotiated privately so nobody else can see it (no price discovery). Forwards still dominate in currency and interest rate markets among banks, but for retail and fund use the exchange-traded futures contract solves all three problems.

Futures: the standardised forward

A futures contract specifies the underlying, the lot size (for Nifty futures currently 75 units, revised by the exchange from time to time), the expiry date (as set by the exchange for weekly and monthly contracts), the tick size and the settlement method. Index futures are cash settled: at expiry the difference between your trade price and the final settlement price (the closing index value) is paid in cash. Single-stock futures are physically settled on expiry. Three monthly series trade at any time: near, next and far month.

Key terms:

  • Spot price: the current cash market price of the underlying.
  • Futures price: the price agreed today for delivery at expiry.
  • Basis = Futures price − Spot price. When the basis is positive the market is in contango; when negative, backwardation. The basis shrinks to zero at expiry because the futures price converges to spot.
  • Cost of carry: what it costs to hold the underlying until expiry (financing) less what you earn from holding it (dividends).
  • Open interest: the number of contracts outstanding; it rises when new positions are created and falls when they are closed.

Pricing a futures contract: cost of carry

The fair futures price is what it would cost to buy the underlying today, borrow the money to do so, and hold it until expiry. If the futures price were higher, an arbitrageur would buy spot, sell futures and lock in a riskless profit (cash-and-carry); if lower, the reverse. Arbitrage keeps the futures price close to this fair value.

Formula
F = S × (1 + r × T) (simple interest) or F = S × e^(r × T) (continuous compounding)
Formula
With a dividend yield q: F = S × e^((r − q) × T)

Here S is the spot price, r the annual risk-free rate, T the time to expiry in years, and q the annual dividend yield of the underlying. Dividends reduce the fair futures price because the holder of the cash asset receives them and the holder of the futures does not.

Worked example
Spot price of share₹1,000
Risk-free rate (annual)8%
Time to expiry3 months = 0.25 year
Fair futures (simple) = 1,000 × (1 + 0.08 × 0.25)₹1,020.00
Fair futures (continuous) = 1,000 × e^(0.02)₹1,020.20
If dividend yield is 2%: 1,000 × e^((0.08 − 0.02) × 0.25)₹1,015.11
Market futures quoted at ₹1,030: overpriced by about ₹10Cash-and-carry arbitrage

With the futures at ₹1,030 against a fair ₹1,020, the arbitrageur borrows ₹1,000 at 8%, buys the share, sells the futures at ₹1,030, and at expiry delivers (or cash settles) for ₹1,030, repays ₹1,020, and keeps ₹10 before transaction costs. If the futures were at ₹1,010 instead, the reverse cash-and-carry applies: sell the share (or borrow and sell it), invest the proceeds, buy the futures. In practice the cost of carry also includes transaction costs and, for stocks that are hard to borrow, a lending fee, so a small band around fair value is not arbitrageable.

Exam trap
Exam trap. T must be in years. A three-month contract uses T = 0.25, not 3. And the formula gives the fair price; if the question asks for the cost of carry itself, it is F − S (₹20 in the example), often expressed as a percentage annualised.

Margins and mark-to-market

When you buy or sell a futures contract, you post initial margin, computed by the clearing corporation's SPAN system to cover the worst likely one-day move. Each evening, every open position is marked to market: the day's change in the futures price is debited from losers and credited to winners in cash. The result is that a futures position never accumulates an unsettled loss. If your margin balance falls below the maintenance level, you get a margin call and must top up, or the broker squares off the position. Exposure margins and extreme loss margins are collected on top of SPAN.

Worked example
Buy 1 lot Nifty futures at 25,000 (lot 75); contract value₹18,75,000
Day 1 close 24,900: MTM = (24,900 − 25,000) × 75−₹7,500
Day 2 close 25,150: MTM = (25,150 − 24,900) × 75+₹18,750
Day 3 sold at 25,080: MTM = (25,080 − 25,150) × 75−₹5,250
Net profit = (25,080 − 25,000) × 75+₹6,000

Each day's settlement happens in cash from the margin account. The total equals the simple difference between exit and entry price times the lot, which is a handy check on exam arithmetic.

Reading the futures market

A futures price well above fair value signals strong demand to be long (bullish positioning); a discount to spot near a dividend season is normal, not bearish. Rising price with rising open interest suggests new longs; rising price with falling open interest suggests short covering. For an SIF manager, the cost of carry is the running cost of staying short: a short index futures position in contango "earns" the carry as the basis decays, while a long position pays it. Rolling a position from one month to the next before expiry incurs the spread between the two contracts, which is part of the strategy's cost that a distributor should be able to explain.

Remember

  1. Forwards are private, customised and carry counterparty risk; futures are exchange-traded, standardised, cleared and marked to market daily.
  2. Basis = futures − spot; positive is contango, negative is backwardation; basis converges to zero at expiry.
  3. Fair futures price F = S(1 + rT) or S·e^(rT), with T in years; dividends lower the fair price: F = S·e^((r − q)T).
  4. If the market futures price is above fair value, cash-and-carry arbitrage (buy spot, sell futures) pulls it back; below, reverse cash-and-carry.
  5. Initial margin (SPAN) is a deposit; daily mark-to-market settles each day's gain or loss in cash so losses never pile up unsettled.
  6. Index futures are cash settled; single-stock futures are physically settled; open interest shows whether positions are being built or closed.
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