NISM-Series-VIII: Equity Derivatives · Strategies using Equity Futures and Equity Options

Hedging with Futures and Basis Risk Explained

Updated 11 October 2026 · Fact-checked

Hedging with futures means taking a futures position opposite to your cash position so losses on one offset gains on the other. To hedge a stock portfolio with index futures, sell contracts = β × portfolio value ÷ (futures price × lot size). Basis risk is the risk that the basis changes before you close the hedge.

Understand Hedging with Futures and Basis Risk

A hedge reduces risk from price moves in something you already hold or will buy. If you own shares and fear a fall, you sell (short) futures. If the market falls, you lose on the shares but gain on the futures. If you will buy shares later and fear a rise, you buy (long) futures.

For a single stock, you can short that stock's futures. For a diversified portfolio, you usually use index futures such as Nifty futures. Index futures remove market (systematic) risk. They do not remove stock-specific (unsystematic) risk, so the hedge is not perfect unless the portfolio mirrors the index.

Portfolios do not move one-for-one with the index. Beta (β) measures how much the portfolio tends to move for a 1% move in the index. A portfolio with β of 1.2 tends to move 1.2% for a 1% index move. So you need more futures value than the portfolio value when β is above 1, and less when β is below 1. The number of contracts is the beta-adjusted portfolio value divided by the value of one futures contract (futures price × lot size).

Basis = spot price − futures price. Before expiry, futures usually trade above spot, so basis is usually negative under this definition. Basis moves towards zero at expiry because futures converge to spot. Basis risk is the risk that the basis changes in an unexpected way between the time you set the hedge and the time you close it. A hedge held to expiry of the same contract has little basis risk. A hedge closed early, or one using a different asset or expiry, carries basis risk.

A hedge therefore locks in the movement, not a guaranteed price. The result depends on how spot and futures move relative to each other.

Key formulas to remember

Number of futures contracts to hedge a portfolio: N = β × Portfolio value ÷ (Futures price × Lot size); Round to the nearest whole contract. Short if you hold the portfolio, long if you will buy it.
Hedge ratio (value basis): Hedge ratio = Value of futures position ÷ Value of the exposure; With beta hedging, this equals β. A ratio of 1 is a full hedge only if β = 1.
Portfolio beta: β = Σ (weight of stock i × beta of stock i); Weights are each stock's share of total portfolio value, adding up to 1.
Basis: Basis = Spot price − Futures price; Some texts use futures minus spot. Read the question's definition. Basis converges to zero at expiry.
Value of one futures contract: Contract value = Futures price × Lot size; Use the futures price, not the spot price, unless the question says otherwise.
Net result of a hedge: Net result = Gain or loss on cash position + Gain or loss on futures position; Short futures gain = (Entry futures price − Exit futures price) × quantity.

How to solve Hedging with Futures and Basis Risk questions

Use this order for any hedging question. It works for number-of-contracts, outcome and basis questions.

1Identify the exposure: do you hold the asset (go short futures) or will you buy it (go long futures)?
2Find the portfolio value and its beta. If the beta is not given directly, compute it as the weighted average of stock betas.
3Compute the value of one futures contract: futures price × lot size.
4Apply N = β × portfolio value ÷ contract value. Round to the nearest whole number of contracts.
5For an outcome question, compute the change in the portfolio value and the futures profit or loss separately.
6Add the two to get the net result. Check the sign: a good hedge shows the two moving in opposite directions.
7For basis questions, compute basis at the start and at the end. Basis risk is the change between them.

Quickest way: Beta-times-ratio shortcut

When to use it: Use it for number-of-contracts MCQs when time is short and the options are well separated.

Divide portfolio value by contract value first to get the unadjusted ratio.
Multiply that ratio by beta.
Round to the nearest whole number.
Check the direction: holders of shares sell futures, planned buyers buy futures.
Eliminate options that use spot instead of futures price or ignore beta.

Common mistakes in Hedging with Futures and Basis Risk

Ignoring beta and dividing portfolio value by contract value only.
Students remember the basic idea of matching values and forget the beta adjustment.
Fix: If beta is given, multiply by it. Beta of 1 is the only case where it makes no difference.
Using the spot index value to compute contract value.
The spot level is more familiar and often quoted in the question.
Fix: Use futures price × lot size unless the question says to use the index level.
Going long futures to hedge a share portfolio.
Students confuse hedging with taking a view.
Fix: A holder of shares fears a fall, so sells futures. A future buyer of shares fears a rise, so buys futures.
Believing an index futures hedge removes all risk.
The word hedge sounds like full protection.
Fix: It removes mainly market risk. Stock-specific risk and basis risk remain.
Thinking basis risk exists even when the hedge is held to expiry of the same contract.
Students link basis risk to every hedge.
Fix: At expiry futures converge to spot, so basis risk is small for a same-contract hedge held to expiry. It matters when you close early or use a different contract or asset.
Mixing up the sign of basis.
Books define it as spot minus futures or the reverse.
Fix: Use the definition in the question. Remember the key point: basis tends to zero at expiry.

Worked examples

Example 1

You hold a portfolio worth ₹60,00,000 with a beta of 1.2. Nifty futures trade at 24,000 and the lot size is 50. How many Nifty futures contracts should you sell to hedge fully against market risk?

Show the solution

Contract value = 24,000 × 50 = ₹12,00,000.
Beta-adjusted exposure = 1.2 × ₹60,00,000 = ₹72,00,000.
N = 72,00,000 ÷ 12,00,000 = 6.
You hold shares, so you sell futures.

Answer: Sell 6 Nifty futures contracts.

Example 2

A portfolio worth ₹30,00,000 has a beta of 1. You short 5 Nifty futures contracts at 24,000 (lot size 25). Nifty futures fall to 23,400 and the portfolio falls exactly in line with the index, by 2.5%. What is the net result?

Show the solution

Check hedge size: contract value = 24,000 × 25 = ₹6,00,000. Five contracts = ₹30,00,000, matching the portfolio.
Portfolio loss = 2.5% of ₹30,00,000 = ₹75,000.
Futures gain on short = (24,000 − 23,400) × 25 × 5 = 600 × 125 = ₹75,000.
Net = −₹75,000 + ₹75,000 = ₹0.

Answer: Net result is ₹0, because the loss on the portfolio is exactly offset by the futures gain.

Exam tips

Read whether the question asks for contracts to sell or buy. Direction is a common trap option.
Always check whether beta is given. If it is, it must be used in the formula.
Remember the definition: basis risk is the risk of the basis changing unpredictably. Expect conceptual MCQs on when it is lowest.
Work contract value first. It makes the later division simple and reduces arithmetic errors.
NISM Equity Derivatives has negative marking of 25% of the marks of a question, so skip a calculation only if you cannot narrow the options.

Practice questions from Strategies using Equity Futures and Equity Options

Hedging with Futures and Basis Risk in other exams

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

Hedging with Futures and Basis Risk: frequently asked questions

How do I hedge a portfolio using index futures and beta?

Find the portfolio beta, multiply it by the portfolio value, and divide by the value of one index futures contract. Sell that many contracts if you hold the portfolio. This hedges market risk but not stock-specific risk.

What is the formula for the number of futures contracts to hedge a portfolio?

N = β × Portfolio value ÷ (Futures price × Lot size). Round to the nearest whole contract. Use the futures price for contract value.

What is basis risk in futures hedging?

Basis is spot price minus futures price. Basis risk is the chance that this gap changes unexpectedly before you close the hedge. It is low when you hold the same contract until expiry, because futures converge to spot.

Why can a hedge with index futures still leave me with losses?

Your portfolio may not move exactly with the index, so stock-specific risk remains. Beta is also an estimate. Basis risk can add further differences if you close before expiry.