Advanced Financial Management · Derivatives Analysis and Valuation

Forward and Futures Contracts for CA Final AFM

Updated 5 October 2026 · Fact-checked

A forward or futures contract fixes a price today for buying or selling an asset on a future date. Fair price = spot × (1 + cost of carry) or spot × e^((r − q)T). To solve questions, find the fair price, compare it with the quoted price, then hedge or arbitrage and compute the gain or loss.

Understand Forward and Futures Contracts

A forward contract is a private agreement between two parties to buy or sell an asset at a fixed price on a fixed future date. It is customised and traded over the counter. Its main risk is counterparty default, because nobody guarantees it. Settlement usually happens only on maturity.

A futures contract is a standardised forward traded on an exchange. A clearing corporation stands between buyer and seller, so default risk is very low. To get this safety, you post an initial margin. Every day the contract is marked to market: gains are credited and losses are debited to your account. If your balance falls below the maintenance margin, you get a margin call and must top up to the initial margin level.

The fair price comes from no-arbitrage. You can buy the asset today, hold it, and deliver it later. So the futures price should equal the spot price plus the net cost of carrying the asset. Carrying cost is the financing cost (interest) plus storage cost, minus any income received such as dividends. If the quoted price is higher than fair, you buy spot and sell futures (cash-and-carry). If it is lower, you sell spot and buy futures (reverse cash-and-carry).

For hedging, you take a futures position opposite to your spot position. If you own shares, you sell futures. If you will buy later, you buy futures. A hedge is rarely perfect because of basis risk. Basis = spot price − futures price. It is negative before expiry when futures trade above spot, and it converges to zero at expiry. If the basis changes between the time you set the hedge and the time you lift it, the hedge gains or loses.

For a stock portfolio hedged with index futures, the number of contracts depends on the portfolio beta. A higher beta means the portfolio moves more than the index, so you need more contracts. You can also use futures to change beta up or down to a target level.

Key rules to remember

Futures price (discrete, no income): F = S × (1 + r × T) or F = S × (1 + r)^T; Use the compounding style the question gives. T is in years, e.g. 3 months = 0.25.
Futures price (continuous compounding): F = S × e^(rT); Use only when the question says continuous compounding or gives e^ values.
Futures price with known dividend: F = S × (1 + r × T) − D × (1 + r × t) or F = (S − PV of D) × (1 + r × T); D is the dividend and t is the time from dividend receipt to expiry, so the dividend earns interest until expiry. Use one method consistently. With annual compounding, replace (1 + r × T) with (1 + r)^T.
Futures price with dividend yield: F = S × e^((r − q)T) or F = S × [1 + (r − q) × T]; q is the dividend yield. If the question states simple rates, use the simple form.
Cost of carry: Cost of carry = Futures price − Spot price (net of income); Includes interest and storage, less income. Basis = Spot − Futures; it is negative when futures exceed spot, and it converges to zero at expiry.
Mark-to-market (long): Daily gain = (Today's settlement price − Previous settlement price) × Lot size × Contracts; For a short position the sign reverses.
Number of contracts for beta hedge: N = (β of portfolio × Portfolio value) ÷ (Index futures price × Lot size); Sell N contracts to hedge a long portfolio. To change beta: N = (Target β − Current β) × Portfolio value ÷ (Futures price × Lot size); positive means buy.
Hedge ratio (minimum variance): h = ρ × (σS ÷ σF); Contracts = h × Exposure ÷ Value of one futures contract.

How to solve Forward and Futures Contracts questions

Use this order for almost any forward or futures question.

1Read the data: spot, quoted futures price, period, interest rate, dividends, lot size, margin. Convert the period into years.
2Identify the compounding style (simple, annual or continuous) and use that for the whole question.
3Compute the fair futures price after adjusting for dividends or storage costs.
4Compare fair price with quoted price. Quoted above fair means overpriced: sell futures, buy spot. Quoted below fair means underpriced: buy futures, sell spot.
5For an arbitrage question, build the cash flows today and at expiry, and show the net riskless profit.
6For a hedging question, decide the direction (sell futures to protect a long position), then compute the number of contracts using beta and lot size.
7Compute the outcome: spot result plus futures result, and compare with the unhedged position. Show the effective price or portfolio value.
8State the conclusion, including any basis risk or rounding of contracts.

Quickest way: Fair price, then gap, then lots

When to use it: Use when time is short, especially for 5 to 8 mark arbitrage or beta-hedge parts.

Write F = S × (1 + r × T) − dividends at once, with the numbers.
Take the difference between the quoted price and F. That gap per unit is your arbitrage profit.
Multiply the gap by the lot size and number of lots.
For hedges, write N = β × Value ÷ (Futures price × Lot size) and round to the nearest whole contract.
Skip full cash flow tables unless asked, but state the strategy in one line.

Common mistakes in Forward and Futures Contracts

Using the full-year interest rate for a 3 or 6 month contract.
Rates are quoted per annum and students forget to scale them.
Fix: Always multiply by T in years first, such as 3/12 = 0.25, before computing.
Adding dividends to the futures price instead of subtracting them.
Students treat the dividend like a cost of holding the share.
Fix: Dividends are income from holding the asset, so they reduce the cost of carry and the fair price.
Hedging a long portfolio by buying futures.
Direction gets confused with the sign of the exposure.
Fix: Hedge means taking the opposite position. Long shares means sell index futures; future purchase means buy futures.
Ignoring beta and using the portfolio value ÷ index value alone.
The beta is given in a different part of the question and gets missed.
Fix: Multiply the portfolio value by its beta before dividing by the value of one futures contract.
Treating margin as the profit or loss rather than a deposit.
Mark-to-market entries in the margin account look like cash flows to the reader.
Fix: Track the margin balance: opening balance plus daily gain or minus daily loss, and top up only when it falls below maintenance margin, back to the initial margin.
Saying a futures hedge removes all risk.
Students ignore that basis can change before the hedge is lifted.
Fix: Mention basis risk in the conclusion and show the effective price using the actual closing basis.

Worked examples

Example 1

A share of XYZ Ltd trades at ₹500. A 3-month futures contract on it is quoted at ₹520. The risk-free rate is 12% per annum (simple), and the share is expected to pay no dividend before expiry. The lot size is 1,000. Is there an arbitrage? If so, show the strategy and profit.

Show the solution

T = 3/12 = 0.25 year.
Fair futures price = 500 × (1 + 0.12 × 0.25) = 500 × 1.03 = ₹515.
Quoted price ₹520 is above the fair price ₹515, so the future is overpriced.
Strategy: borrow ₹5,00,000 (500 × 1,000), buy 1,000 shares at spot, and sell one futures contract at ₹520.
At expiry: deliver the shares and receive 520 × 1,000 = ₹5,20,000.
Repay the loan with interest = 5,00,000 × 1.03 = ₹5,15,000.
Net profit = 5,20,000 − 5,15,000 = ₹5,000, with no risk.

Answer: The future is overpriced. Buy the share and sell the future with borrowed money to earn a riskless profit of ₹5,000 per lot (₹5 per share).

Example 2

A fund manager holds a portfolio worth ₹2,10,00,000 with a beta of 1.2. The Nifty futures price is 21,000 and the lot size is 50. The manager wants to fully hedge against a fall in the market over the next month. (a) How many contracts should be sold? (b) If the index falls by 5% to 19,950 and the portfolio falls in line with its beta, find the net result of the hedge. Assume the futures price falls with the index to 19,950 (basis ignored).

Show the solution

Value of one futures contract = 21,000 × 50 = ₹10,50,000.
Number of contracts = (1.2 × 2,10,00,000) ÷ 10,50,000 = 2,52,00,000 ÷ 10,50,000 = 24 contracts.
Index fall = 5% of 21,000 = 1,050, so the index goes to 21,000 − 1,050 = 19,950. Assume the futures price also falls by 1,050 to 19,950 (basis ignored).
Portfolio fall = 5% × 1.2 = 6%. Loss = 6% × 2,10,00,000 = ₹12,60,000.
Futures gain on 24 short contracts = (21,000 − 19,950) × 50 × 24 = 1,050 × 1,200 = ₹12,60,000.
Net result = −12,60,000 + 12,60,000 = ₹0.

Answer: Sell 24 Nifty futures contracts. Because the futures price is assumed to fall with the index to 19,950 (basis ignored), the futures gain of ₹12,60,000 exactly offsets the portfolio loss of ₹12,60,000, so the net change is nil. In practice, basis risk could leave a small difference.

Exam tips

Write the fair price formula first with numbers. Marks are given for the method even if the arithmetic slips.
If the question does not state compounding, use the style used in its other data, and say which one you chose.
In hedging answers, always state the position (long or short futures), the number of contracts, and the net outcome.
For margin questions, draw a small table of day, settlement price, gain or loss, and balance. Show the margin call amount clearly.
Add one line on basis risk in the conclusion. Examiners often give a mark for it in theory-linked parts.

Practice questions from Derivatives Analysis and Valuation

Forward and Futures Contracts in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Forward and Futures Contracts: frequently asked questions

What is the difference between forward and futures contracts?

A forward is a customised over-the-counter contract settled at maturity, with counterparty default risk. A futures contract is standardised, exchange-traded, cleared by a clearing corporation and marked to market daily with margins. Futures are more liquid and carry much lower default risk.

How do I calculate the futures price with dividend yield?

Use F = S × e^((r − q)T) for continuous compounding, or F = S × [1 + (r − q) × T] for simple rates, where q is the dividend yield. The dividend lowers the cost of carry, so the futures price is lower than without dividends.

What is cost of carry?

It is the net cost of holding the asset until the futures expiry. It includes interest and storage costs, less any income such as dividends. It explains why the futures price differs from spot.

What is basis risk in hedging?

Basis is spot price minus futures price. If the basis changes between the start and end of the hedge, the hedge does not fully offset the spot movement. This leftover gain or loss is basis risk.

How do I hedge a share portfolio using index futures?

Sell index futures when you hold the portfolio. The number of contracts equals beta × portfolio value ÷ (futures price × lot size). Round to a whole number of contracts.