Forwards and Futures — the whole chapter in plain English

Start at the goldsmith's shop

The workbook opens this chapter in a jewellery shop, and it is the cleanest way in.

On 11 May 2024 you walk in to buy gold. The market price is ₹62,130 for 10 grams of 24 carat gold. You pay ₹62,130, take the gold home. Money moved, gold moved, done. That is a cash market transaction, and ₹62,130 is the spot price.

Now change one thing. You do not want the gold today — you want it after one month. The goldsmith quotes ₹62,337 for 10 grams. You agree and walk out. No money changes hands. No gold changes hands. All that exists is a promise.

You have bought a forward contract — you are long forward. The goldsmith has sold a forward contract — he is short forward. One month later you pay ₹62,337 and collect 10 grams.

The important word is obliged. Both parties must go through with it, whatever gold is worth on that day.

• If gold is at ₹62,700 in the cash market: you buy at ₹62,337 under the contract, sell at ₹62,700 in the market — profit ₹363 per 10 grams.
• If gold is at ₹62,100: you must still pay ₹62,337 — loss ₹237 per 10 grams (buy price minus sell price).

What a forward is, formally

A forward contract is an agreement made directly between two parties to buy or sell an asset on a specific date in the future, at the terms decided today. It is used in commodities, foreign exchange, equity and interest rate markets.

Its two essential features:

• It is a contract between two parties — a bilateral contract.
• All terms — price, quantity, quality of the underlying, place of delivery, settlement procedure — are fixed on the day of entering the contract.

Forwards are bilateral over-the-counter (OTC) transactions. The terms are negotiated between the two parties, and altering any term needs both parties to agree. Corporations, traders and investing institutions use OTC deals heavily because they can be shaped to an exact requirement.

The essential idea of entering into a forward is to fix the price and thereby avoid price risk.

Why forwards keep breaking

Two problems, both named in the syllabus.

Liquidity risk. Liquidity is the ability to buy or sell the quantity you want. Forwards are tailor-made, so nobody else particularly wants your contract. They are not listed or traded on exchanges, so other participants cannot easily reach the contract or the contracting parties. Result: it is very difficult to exit a forward before maturity.

Counterparty risk. The risk of economic loss because the other side does not perform. The workbook's example: A agrees to buy 100 kg of rice at ₹40 per kg from B after 6 months.

• If rice goes to ₹50, B has every incentive to refuse delivery at ₹40.
• If rice falls to ₹35, A has every incentive to buy from the market instead.

A party defaults when there is an incentive to default. This is also called default risk or credit risk.

On top of these: lack of transparency and settlement complications, because settlement happens directly between the two parties.

The fix is obvious once stated — bring these contracts onto a centralised trading platform. That is exactly what futures do.

Futures: the standardised, exchange-traded forward

A futures contract is an agreement made through an organised exchange to buy or sell a fixed amount of a commodity or financial asset on a future date at an agreed price. In one line: futures are standardised forward contracts traded on an exchange, and the clearing corporation associated with the exchange guarantees settlement.

Buy futures and you take a long position. Sell futures and you take a short position. The workbook adds a caution worth remembering: "buy" and "sell" are figurative only — no money and no underlying asset changes hands between buyer and seller when the deal is originated.

In a futures market the exchange decides all the terms of the contract other than price. Its features:

• Contract between two parties through the exchange
• Centralised trading platform
• Price discovery through free interaction of buyers and sellers
• Margins payable by both parties
• Quality decided today (standardised)
• Quantity decided today (standardised)

Futures are not perfect either. Their limitations: limited maturities, a limited set of underlyings, lack of flexibility in contract design, and increased administrative costs on account of MTM settlement.

Contract specifications — everything except the price

The exchange fixes everything but the price. That bundle is called the contract specifications. Here is the workbook's Nifty futures quote from the NSE website as on 3 October 2025:

Underlying instrument and underlying price. The underlying is the index or stock on which the contract trades — here, Nifty 50. The underlying price is the spot price, the price in the cash market — here 24,894.25 on 3 October 2025.

Contract multiplier / contract size. Futures trade in lots. The exchange fixes the lot size, and it differs for every stock and index. Contract value = futures price × lot size. With a Nifty lot size of 65, the workbook computes 65 × 24,894.25 = ₹16,18,126.25.

How big must a contract be? Clause 1.1.4 and Clause 2.1.4 of the SEBI Master Circular for Stock Exchanges and Clearing Corporations dated 16 October 2023 stipulated a contract value between ₹5 lakh and ₹10 lakh. That limit was last set in 2015, and market values have risen roughly three times since. So SEBI decided a derivative contract shall have a value not less than ₹15 lakh at introduction, with lot sizes fixed so that the contract value on the review day sits between ₹15 lakh and ₹20 lakh. Effective from November 2024.

Contract cycle. The period over which a contract trades. NSE index and stock futures follow a three-month trading cycle — on 3 October 2025 you can trade the near month (Oct 2025), the next month (Nov 2025) and the far month (Dec 2025). The BSE offers monthly as well as weekly futures contracts.

Expiration day. The day the contract ceases to exist — its last trading day. On expiry all contracts are compulsorily settled. To continue a position you must roll it over: for a long position, sell the expiring contract and buy the next one, both legs executed at the same time. NSE's Nifty, Bank Nifty and stock futures expire on the last Tuesday of the month (or the day before, if that Tuesday is a trading holiday). A new far-month contract is introduced on the trading day following the expiry of the near month contract.

The uniform expiry rules (SEBI circular dated 26 May 2025), brought in to reduce market concentration risk and control expiry-day volatility:

• Each exchange may choose only Tuesday or Thursday as the expiry day for all its equity derivatives.
• Each exchange may offer only one benchmark index options contract per week, on its chosen expiry day.
• All other equity derivative contracts — benchmark index futures, non-benchmark index derivatives, single stock futures and options — must have a minimum one-month tenor.
• These expire on the last Tuesday or Thursday of the month, per the exchange's chosen day.
• Changing the expiry day needs prior SEBI approval.

NSE has chosen Tuesday. BSE has chosen Thursday.

Tick size. The minimum move allowed in the price quotation. For Nifty futures it is 5 paisa. The bid is what a buyer will pay; the ask is what a seller will accept.

Daily settlement price. Open positions are settled every day at this price, calculated by the exchange as the last half-an-hour weighted average price of that futures contract. It is therefore different for each expiry month. On 3 October the Oct Nifty futures daily settlement price is its closing price, 25,006.60.

Final settlement price. The price at which all open positions in the near-month contract are finally settled on expiry day. It is the closing price of the underlying index or stock in the cash segment on the last trading day — not a futures price at all.

Trading hours. 9.15 a.m. to 3.30 p.m., Monday to Friday. Note two different kinds of holiday: on a trading holiday the exchange is closed and no trading is possible; on a clearing holiday the exchange is open and trading happens, but no clearing and settlement takes place because banks are closed.

BSE Sensex futures differ:

Because the Sensex and the Nifty move very closely together, participants trade Nifty and Sensex futures against each other as a pairs trading strategy.

Basis — a word with a sign trap in it

Basis is the difference between the spot price and the futures price.

• If futures price > spot price, basis is negative.
• If spot price > futures price, basis is positive.

On 3 October 2025 the spot was 24,894.25 and futures 25,006.60, so basis = 24,894.25 − 25,006.60 = −112.35, a negative basis.

Two more points the exam likes:

• Basis is meaningless without naming the contract. Basis for the one-month contract differs from basis for the two-month contract. The difference between the one-month basis and the two-month basis should equal the cost of carrying the underlying between the first and second month — this is the fundamental principle linking futures prices and cash prices together.
• Whatever the basis is, it becomes zero at maturity. There can be no gap between futures and spot at expiry, because final settlement of futures on the last trading day takes place at the closing price of the underlying asset.

Cost of carry

Cost of carry is the relationship between futures prices and spot prices. It measures the storage cost (in commodity markets) plus the interest paid to finance or carry the asset until delivery, less the income earned on the asset during the holding period.

For equity derivatives it simplifies to: interest paid to finance the purchase minus dividend earned.

The workbook's worked case: ABC Ltd trades at ₹100. A person wants the share but has no money, so he borrows ₹100 at 6% per annum. He holds it a year and expects a 200% dividend on a face value of ₹1 — that is ₹2.

Net cost of carry = interest paid − dividend received = 6 − 2 = ₹4.

His break-even futures price is ₹104.

And a line to memorise: cost of carry may be different for different participants. Different people borrow at different rates.

Margins — how the exchange protects itself

Because the exchange guarantees settlement of all trades, it must protect itself against default. It charges margins from brokers; brokers charge margins from their clients.

Initial margin is the amount deposited in the margin account at the time of entering into a futures contract.

The workbook's case: on 14 May 2024 a person expects the market to rise and goes long one Nifty May futures at 22,250, lot size 25.

• Contract value = 22,250 × 25 = ₹5,56,250
• Broker charges 10% as initial margin = ₹55,625

Both buyers and sellers pay initial margin, because both parties are obliged to honour the contract. And initial margin depends on the price movement of the underlying — high volatility assets carry more risk, so the exchange charges higher initial margin on them.

Marking to Market (MTM). Futures may have months to run, but profits and losses are settled day to day. The exchange collects MTM margins from the loss-making participants and pays the gainers, on a day-to-day basis.

Continuing the case: that evening Nifty futures closed at 22,308.70 — a gain of 58.70 points. The trader's MTM gain = 58.70 × 25 = ₹1,468. It is credited to his account, and the next day his position starts from 22,308.70 for MTM purposes.

Open interest versus volume

Open interest is the total number of contracts outstanding — yet to be settled — for an underlying asset. The number of long futures equals the number of short futures, always, so only one side is counted. The level of open interest indicates depth in the market.

Volume traded tells you market activity over a period — a day, a week, a month, or the whole life of the contract.

The workbook's table makes the difference concrete:

Read row 3 carefully. Volume happened, but open interest did not change because one short simply replaced another.

Price band

A price band is the price range within which a contract may trade during a day. It is calculated on the previous day's closing price of that specific contract. Previous close ₹100 with a 10% band means the contract may trade between ₹90 and ₹110.

On the first trading day of a contract there is no previous futures close, so the band is set on the previous day's closing price of the underlying in the cash market. Bands are stated in the contract specifications so everyone knows them in advance, and exchanges may expand them at their discretion with specific trading halts.

Position vocabulary

• Long position — an outstanding, unsettled buy position.
• Short position — an outstanding, unsettled sell position.
• Open position — any outstanding, unsettled position, long or short. Short 5 Infosys futures and long 3 Reliance futures is one open position with two legs; buy back 2 Infosys of the same maturity next day and it becomes short 3 Infosys, long 3 Reliance.
• Opening a position — a buy or sell that increases the open position.
• Closing a position — a buy or sell that reduces it. Selling what you bought, or buying what you sold.
• Naked position — a long or short in a futures contract without any position in the underlying asset.
• Calendar spread — long one maturity and short a different maturity, on the same underlying. A short near-month plus a long far-month is a calendar spread. It is always defined with respect to the relevant months (August–September, August–October, and so on), is computed with respect to the near month series, and becomes an open position once the near month expires or either offsetting leg is closed.

Payoff charts

Payoff is the likely profit or loss that accrues with a change in the price of the underlying at expiry. The chart puts the price of the underlying on the X-axis and profit/loss on the Y-axis. The X-axis increases to the right and is not drawn to the left, because prices cannot go below zero.

Futures payoffs are linear, and both long and short have unlimited profit or loss potential.

Long futures at 100. Underlying ends at 150: you buy at 100 under the contract, sell at 150 — profit ₹50. Underlying ends at 70: you must still buy at 100 and can only sell at 70 — loss ₹30.

The short is the exact mirror of the long, because one person can only go long if another goes short. A short at 100 with the price falling to 60 buys from the market at 60 and delivers at 100 — profit ₹40.

Pricing a futures contract

There is no single way to price futures contracts, because different assets have different demand and supply patterns, characteristics and cash flows. The syllabus covers two models.

1. Cost of Carry model — also called the no-arbitrage model

It assumes that in an efficient market, arbitrage opportunities cannot exist. The moment mispricing appears, arbitrageurs trade until prices realign.

The logic: you can acquire an asset for a future date in two ways — enter a futures contract, or create a synthetic futures position by buying the stock in the cash market and carrying it to that date. Both routes must cost the same.

Fair price of futures = spot price + cost of carrying the asset from today until delivery.

Carrying a financial asset involves transaction cost, custodial charges and financing cost; for commodities, add warehousing and insurance.

The gold arbitrage. Spot gold ₹62,130 per 10 grams. Financing, storage and insurance for three months = ₹100 per 10 grams. So the expected value after 3 months is ₹62,230. Now suppose the 3-month gold futures trades at ₹62,280.

Buy gold in the cash market and simultaneously sell 3-month futures. Borrow the money, take delivery, hold three months, deliver against the futures, repay the financier from the futures proceeds. Risk-free profit of ₹50 per 10 grams (transaction costs ignored).

• Futures above fair price triggers cash and carry arbitrage — buy cash, sell futures.
• Futures below fair price triggers reverse cash and carry arbitrage — buy futures, sell cash. Traders borrow gold, deliver it into the cash market, earn interest on the sale proceeds, and return the gold to the lender after three months when they receive it in the futures market.

Either way the arbitrage runs until the prices align.

No-arbitrage bounds. Margins, commissions and taxes create friction. They form a band around the fair price inside which arbitrage will not happen — the futures price must fall outside the bounds for arbitrage to be worth doing. Every component of carrying cost widens these bounds, and the wider they are, the further the market is from equilibrium. For efficient markets, costs of operating must be as low as possible.

With income from the asset. Equity pays dividends and debt pays interest during the holding period, and these inflows are subtracted:

Fair futures price = Spot price + Cost of carry − Inflows

F = S(1 + r − q)^T, where F is the fair futures price, S the spot price, q the expected return during the holding period, T the holding period in years, and r the cost of carry. With continuous compounding, F = Se^((r−q)×T).

The index worked case. Buy the index in the cash market at 17,500 (that is, buy every constituent in index proportion). Cost of financing 12%, return on index 4% per annum spread uniformly. Fair price three months out:

= 17,500 × (1 + 0.12 − 0.04)^(90/365) = ₹17,835.26

Using the exponential form: 17,500 × e^((0.12 − 0.04) × 90/365) = ₹17,848.63

If index futures trade above 17,848.63, buy the index stocks in the cash market and simultaneously sell index futures to lock in the difference. Transaction cost, taxes and margins are not considered in this calculation.

Assumptions of the Cost of Carry model:

• The underlying asset is available in abundance in the cash market
• Demand and supply in the underlying are not seasonal
• Holding and maintaining the underlying is easy and feasible
• The underlying can be sold short
• There are no transaction costs
• There are no taxes
• There are no margin requirements

Because margins are not considered, the workbook makes a sharp point: this model is suitable for pricing forward contracts rather than futures contracts. And no generalised statement can be made about using it — the assumptions and the asset's characteristics decide whether it applies at all.

Convenience yield. Sometimes the inflow from holding an asset is intangible — the comfort of simply having it. In a flood, people hoard grain, vegetables and heating oil far beyond real consumption. Everyone doing this creates demand and lifts the cash price. That perceived benefit of holding is the convenience yield (or convenience return). It is different for different people, varies over time, subjective, and very difficult to price.

When convenience yield dominates the cost of carry, futures trade at a discount to cash — and reverse arbitrage is then impossible, because nobody will lend you the asset to sell short. The cash and carry model breaks down. Convenience yield arises mainly when a commodity is scarce and inventory is low, so it is seen in consumption assets (commodities), not in financial assets such as equities, bonds or currencies.

2. Expectations model

The expectations hypothesis says it is not the spot–futures relationship but the relationship between expected spot and futures prices that moves the market — especially where the asset cannot be sold short or cannot be stored. The futures price is the expected spot price of the asset in the future.

• Futures can trade at a premium or a discount to spot.
• The futures price indicates the expected direction of the spot price.

Contango — futures price higher than spot; participants expect spot to rise. Backwardation — futures price lower than spot; participants expect spot to fall.

Price discovery and convergence

If the May 2024 index futures trades at 22,308.70 on 14 May 2024, the expectations model reads it as: the market expects the spot index to settle at 22,308.70 at the close on the contract's last trading day. Every participant is predicting the spot index level at a single point in time. That is price discovery.

And it explains convergence: futures and spot prices converge at maturity, because at that instant there cannot be a difference between them. All futures contracts on expiry settle at the underlying cash market price. This holds for every underlying.

Who uses futures, and why

Three categories: hedgers, speculators (traders) and arbitrageurs.

Hedgers reduce exposure to market variables — interest rates, share values, bond prices, exchange rates, commodity prices. The classic case is the farmer who sells futures to lock a price for a future crop, with a food-processing company on the other side fixing its purchase price. In equities, an investor with a diversified portfolio who fears a temporary correction can sell index futures.

Speculators / traders. It is much less expensive to create a speculative position using futures than by trading the underlying, so potential returns are much greater. A trader expecting good quarterly results can buy the shares or go long the stock futures. But leverage is a double-edged sword — the workbook is explicit that futures positions, being leveraged, are riskier than buying or selling the underlying asset itself.

Arbitrageurs. An arbitrage is a deal that produces risk-free profits by exploiting a mispricing. Buy cheap in one place, simultaneously sell dear in another. Such opportunities do not persist, because arbitrageurs rush in and close the gap.

How the three fit together: hedgers aim to hedge their risk, traders take the risk hedgers want to offload, and arbitrageurs establish an efficient link between different markets. Traders provide depth — hedgers may not be able to hedge if traders were not present in the system.

The arbitrage worked case. Underlying ₹100, May futures ₹110, lot size 50. Buy cash at 100, sell futures at 110 — ₹10 locked per share.

Both give ₹10 per unit and ₹500 for the lot — the profit does not depend on where the price ends. That is what "locked in" means. Transaction and impact costs are ignored here; in real life brokerage, service tax and STT must be counted.

But arbitrage is not free of risk. Both legs execute in different markets, and there can be a time lag between the two orders. If either leg is illiquid, only one leg may get filled and the arbitrageur is left with a naked exposure. If the contracts are not cash settled in one or both markets, trades must be reversed, adding unwinding risk.

These traders and arbitrageurs bring liquidity, which in turn brings better price discovery, lower transaction cost and less manipulation.

Using index futures to manage risk

Total price risk = systematic risk + unsystematic risk.

Unsystematic (specific) risk is unique to a company or industry — a strike stopping production, the sudden exit of key management, loss of market share to a strong competitor. It is inseparable from investing in securities but can be reduced by diversifying.

Systematic (market) risk is what is left after diversification — variability in returns directly associated with overall movements in the general market or economy. Examples: a sudden change in monetary or fiscal policy, depreciation of the domestic exchange rate, declaration of war. Every portfolio is exposed to it, and it is separable and tradable with index-based derivatives.

Single stock futures hedge the total risk of that stock, because they are comparable with the underlying position. The only real difference between the underlying position and stock futures is settlement: cash transactions settle immediately, futures settlement is deferred.

Index futures are what you use to mitigate the systematic risk of a portfolio.

Beta measures systematic risk — the sensitivity of a stock or portfolio to index movement, based on historical prices. Beta of 2 means the stock moved 20% when the index moved 10%. Stocks or portfolios with beta above 1 are aggressive; below 1 are conservative.

Portfolio beta is the weighted average of the individual betas, weighted by investment proportion:

βp = W₁β₁ + W₂β₂ + … + Wnβn, with the weights summing to 1.

The workbook's example: betas 0.5, 1.1, 1.30 and 0.90 with weights 35%, 15%, 20% and 30% gives 0.87.

Hedge ratios.

• For a single stock hedged with its own stock futures: 1:1. An investor holding 550 shares of HDFC Bank where the contract size is 550 uses exactly 1 futures contract.
• For a portfolio hedged with index futures: 1:1 does not work. The hedging instrument is not the thing being hedged — a 10-stock portfolio against an index of 30 or 50 stocks, with a portfolio beta different from the index. So:

Number of contracts = Vp × βp ÷ Vi

where Vp is the value of the portfolio, βp its beta, and Vi the value of one index futures contract (futures index level × contract multiplier). For simplicity the beta of the futures index against the spot index is taken as one.

Two cautions: the hedge depends on the portfolio's relationship with that particular index, so the hedge ratio changes if you change the index; and the model assumes the past relationship continues in future, which may leave a gap between actual and expected outcomes.

Hedging vocabulary

Long hedge — hedging a cash-market position by going long futures. You expect funds later and want to invest in securities, but fear the market will rise before the money arrives. Buy index futures today; when the money comes, invest in cash and unwind the futures. The higher purchase price is partly or fully compensated by the futures profit. The same trick handles the problem that rushing to invest all your money at once drives prices up against you — buy futures today, invest gradually, unwind gradually.

Short hedge — hedging by going short futures. You hold a portfolio you plan to liquidate soon and fear prices will fall. Short index futures of an equivalent amount today; the cash-market loss is partly or fully compensated by the futures profit.

Cross hedge — when no futures contract exists on your asset, you hedge using futures on a closely associated asset. With no jet fuel futures, hedgers use crude oil, heating oil or gasoline. And note the workbook's own remark: using index futures to hedge a portfolio is, in a crude sense, itself a cross hedge, because you are not using the exact underlying.

Hedge contract month — the maturity month of the contract you hedge with. The thumb rule is to select the futures contract that expires just after the date on which you wish to unwind the exposure. On 10 May, planning to sell the portfolio on 20 June, you short the June contract, not the May one.

Trading and arbitrage strategies

Traders take naked positions — long when they expect a rise, short when they expect a fall — or spread positions.

A spread is two opposite positions, either in two contracts of the same maturity on different products (an inter-commodity / inter-product spread) or in two contracts of different maturities on the same product (a calendar spread, also called time spread or horizontal spread). In the equity derivatives segment only calendar spreads are available for trading. Inter-commodity spreads — gold and silver, or soybean, soybean meal and soybean oil — exist in the commodity derivatives segment.

The workbook's calendar spread count: Mr A is short 3 one-month contracts, long 2 two-month contracts and long 3 three-month contracts. That is 2 calendar spreads between months 1 and 2, 1 calendar spread between months 1 and 3, and the remaining 2 three-month contracts are naked. A calendar spread becomes a naked/open position when the near month expires or either leg is closed. Because they are combinations of two opposite positions, spreads are treated as conservatively speculative positions.

Three types of arbitrage in futures:

• Cash and carry arbitrage — long the cash/underlying market, short futures.
• Reverse cash and carry arbitrage — long futures, short the cash/underlying market.
• Inter-exchange arbitrage — two positions on the same contract in two different exchanges. If August futures on stock Z trade at ₹101 on NSE and ₹100 on BSE, buy at BSE and sell at NSE, then reverse when the difference squeezes.

In symbols: F = S + C (spot plus holding cost); in percentage terms F = S(1 + r)^T; with continuous compounding F = Se^(rT).

Futures above fair price → cash and carry arbitrage. Futures below fair price → reverse cash and carry arbitrage. And practically, an arbitrage is only undertaken if it gives a net cash inflow after transaction costs, brokerage and margin deposits.

The chapter's closing thought: futures are a quick and less expensive way to alter portfolio composition to reach a desired level of risk. They can add risk or reduce risk, which makes them risk management and portfolio restructuring tools.