Advanced Financial Management · The use of financial derivatives to hedge against interest rate risk

Interest Rate Futures Hedging in AFM

Updated 11 October 2026 · Fact-checked

Interest rate futures are exchange-traded contracts priced at 100 minus the interest rate. To hedge borrowing, sell futures now and buy them back later. To hedge deposits, buy futures. Work out contracts as loan ÷ contract size × loan months ÷ contract months, then add the futures gain or loss to the cash interest.

Understand Interest Rate Futures

An interest rate future is a standardised contract traded on an exchange. It fixes an interest rate for a notional deposit or loan of a set size and period, for example a 3-month deposit of $1,000,000. You never actually lend or borrow under the contract. You use it to make a profit or loss that offsets the change in your real interest cost.

The price is quoted as 100 minus the annual interest rate. A price of 94.80 means an implied rate of 5.20%. When market rates rise, the price falls. When rates fall, the price rises. This one fact drives every hedge.

If you will borrow and fear rising rates, you sell (go short) futures today. If rates rise, the price falls, you buy back cheaper and make a gain. That gain offsets the higher interest on the loan. If you will deposit and fear falling rates, you buy (go long) futures. If rates fall, the price rises and you sell at a gain, which offsets the lower deposit income.

Futures are standard in size and date. So you rarely hedge perfectly. You round the number of contracts to a whole number. You pick an expiry date that is on or after the date the rate is fixed. The gap between today's cash price (100 minus the spot rate) and the futures price is the basis. It shrinks to zero at expiry, so a hedge closed before expiry carries some basis risk. That is why hedge efficiency is usually below 100%.

You also pay initial margin when you open a position. The exchange then settles gains and losses daily through variation margin. Margin affects cash flow and funding, but most exam calculations ignore it unless the question asks. Futures hedges are fixed: unlike options, you give up the benefit if rates move in your favour.

Key rules to remember

Futures price: Futures price = 100 − implied annual interest rate (%); A price of 94.80 implies a rate of 5.20%. Price and rate move in opposite directions.
Number of contracts: Contracts = (Amount to hedge ÷ Contract size) × (Hedge period in months ÷ Contract period in months); Round to a whole number. A 6-month loan hedged with 3-month contracts needs twice as many contracts.
Tick size and tick value: Tick value = Contract size × 0.01% × (Contract months ÷ 12); For a $1,000,000 3-month contract, one tick (0.01) is worth $25. Use the contract details given in the question.
Futures gain or loss: Profit or loss = Price movement in ticks × Tick value × Number of contracts; Seller gains when the price falls. Buyer gains when the price rises.
Basis: Basis = (100 − current spot rate) − current futures price; Cash price minus futures price. It converges to zero at expiry.
Unexpired basis: Basis at a date = Opening basis × (Months remaining to expiry ÷ Months at start); Linear convergence is an assumption. State it if you use it.
Hedge direction rule: Borrower: sell futures now, buy back later. Depositor: buy futures now, sell later.; Check the direction by asking which way the futures price must move for you to gain.
Effective rate and hedge efficiency: Effective rate for a borrower = (Cash interest − futures gain) ÷ Amount ÷ Years. Effective rate for a depositor = (Deposit interest + futures gain) ÷ Amount ÷ Years. Hedge efficiency = Futures gain ÷ Loss on the underlying position; Compare the futures gain with the extra cost caused by the rate move. A gain larger than the loss means the hedge over-compensated. If the futures position makes a loss, the sign of the futures adjustment reverses.

How to solve Interest Rate Futures questions

Use the same sequence for any interest rate futures question. It keeps the direction, number and cash flows clear and earns method marks even if one number is wrong.

1Identify the exposure: borrowing or depositing, the amount, the start date of the exposure, the length of the period and the rate basis.
2Decide the direction. Borrower fears a rate rise, so sell futures. Depositor fears a rate fall, so buy futures.
3Choose the contract. Pick the expiry on or after the date the rate is fixed, and use the nearest one if the question allows a choice. Note the contract size and period.
4Calculate the number of contracts: amount ÷ contract size × hedge months ÷ contract months. Round to a whole number and state the rounding effect on any unhedged amount.
5Find the closing futures price. If the question gives a basis assumption, apply it. At expiry the futures price is 100 minus the spot rate. Before expiry, add or subtract the unexpired basis.
6Calculate the futures gain or loss in ticks, then in money: ticks × tick value × contracts.
7Compute the cash interest at the actual rate, then net the futures result against it. Convert to an effective annual rate if asked.
8Comment briefly: hedge efficiency, basis risk, rounding, margin cash flows and the fact that you lose the benefit of favourable rate moves.

Quickest way: Direction, count, ticks, net

When to use it: Use this when time is short and the question gives the opening and closing futures prices and the contract details.

Write borrower = sell, depositor = buy before anything else.
Work out contracts in one line: amount ÷ size × months ÷ contract months. Round.
Find the price move: sell price minus buy price for a seller, the reverse for a buyer. Write it in ticks (0.01 = 1 tick).
Multiply ticks × tick value × contracts. A $1m 3-month contract is $25 per tick.
Subtract the gain from the interest cost (or add it to the deposit income) and show the effective rate.
Add one line on basis and hedge efficiency to pick up the discussion marks.

Common mistakes in Interest Rate Futures

Buying futures to hedge a loan, or selling them to hedge a deposit.
Students think in terms of rates rather than prices. Rates rise, so they assume the futures position should go up too.
Fix: Remember that price = 100 − rate. A rise in rates is a fall in price. A borrower needs a gain when prices fall, so the borrower sells.
Forgetting to scale the number of contracts for the loan period.
Students divide the loan by the contract size and stop, even when the loan is 6 months and the contract covers 3 months.
Fix: Always apply the period ratio: months of exposure ÷ months of the contract. Write the formula out before calculating.
Using the wrong tick value or counting ticks incorrectly.
A move from 94.80 to 93.50 is 1.30, which is 130 ticks, not 13 ticks. Students also forget to pro-rate the tick for a 3-month contract.
Fix: Tick value = size × 0.0001 × months ÷ 12. Convert the price move by multiplying by 100 to get ticks.
Ignoring basis, or treating the closing futures price as 100 minus the spot rate before expiry.
The zero-basis shortcut is only true at expiry. Students apply it whenever the hedge is closed.
Fix: If the hedge is closed before expiry, estimate the remaining basis and adjust the closing price. State your assumption about linear convergence.
Choosing a contract that expires before the date the rate is set.
Students pick the nearest contract without checking the date. The hedge then ends before the exposure.
Fix: Select the first expiry on or after the date you borrow or deposit. Check it every time the question lists several expiry months.
Presenting the futures hedge as free of risk.
The answer focuses on the calculation and ignores margin, basis and rounding.
Fix: Add a short comment: basis risk, whole-contract rounding, margin calls, and the loss of the benefit if rates move favourably.

Worked examples

Example 1

It is 1 April. A company will borrow $12,000,000 on 1 July for 6 months at 1% above the reference rate. The current reference rate is 5.0%. September 3-month futures (contract size $1,000,000) trade at 94.80. By 1 July the reference rate has risen to 6.5%. As a simplifying assumption, the futures price on 1 July equals 100 minus the spot rate. Show how a futures hedge works, calculate the effective interest rate and the hedge efficiency.

Show the solution

Direction: the company is borrowing and fears a rate rise, so it sells September futures. September is the first expiry on or after the 1 July borrowing date. A June contract would expire before the loan starts, so it cannot be used.
Number of contracts: $12,000,000 ÷ $1,000,000 × 6 ÷ 3 = 24 contracts. No rounding is needed.
Opening position: sell 24 contracts at 94.80, an implied rate of 5.20%. The opening basis is (100 − 5.0) − 94.80 = 0.20.
Closing position on 1 July: the question assumes the futures price equals 100 − 6.5 = 93.50. This is a simplification, because the September contract has not yet expired. Buy back 24 contracts at 93.50.
Futures gain: 94.80 − 93.50 = 1.30, which is 130 ticks. Tick value = $1,000,000 × 0.01% × 3/12 = $25. Gain = 130 × $25 × 24 = $78,000.
Loan interest at the new rate: 7.5% (6.5% + 1%) × $12,000,000 × 6/12 = $450,000.
Net interest cost = $450,000 − $78,000 = $372,000. Effective rate = $372,000 ÷ $12,000,000 ÷ 0.5 = 6.2%. This equals the opening futures-implied rate of 5.20% plus the 1% margin. It works out this way because the assumed closing basis is zero, so the hedge locks in the futures-implied rate. The 1% margin is a fixed cost that the hedge does not change.
Hedge efficiency: without the hedge the rate rise from 5.0% to 6.5% costs 1.5% × $12,000,000 × 0.5 = $90,000 extra. Efficiency = $78,000 ÷ $90,000 = 86.7%. The shortfall of $12,000 arises because the cash price started 0.20 above the futures price (95.00 against 94.80) and the basis is assumed to have converged to zero by 1 July. The futures price therefore fell by only 1.30 while the cash price fell by 1.50 (0.20% × $12,000,000 × 0.5 = $12,000).

Answer: Sell 24 September futures. The futures gain is $78,000, the net interest cost is $372,000, the effective rate is 6.2% (the futures-implied 5.20% plus the 1% margin) and the hedge efficiency is about 86.7%. The gap from 100% arises because the basis is assumed to converge from 0.20 to zero.

Example 2

It is 1 June. A company expects to receive $5,300,000 on 1 September and will deposit it for 3 months. It fears interest rates will fall. September 3-month futures (contract size $1,000,000) trade at 95.40. On 1 September the deposit rate is 3.5% and the futures price is 96.50. Recommend and evaluate a futures hedge, ignoring margin.

Show the solution

Direction: the company is depositing and fears a fall in rates, so it buys September futures. A fall in rates raises the futures price, giving a gain on the long position.
Number of contracts: $5,300,000 ÷ $1,000,000 × 3 ÷ 3 = 5.3, which rounds to 5 contracts. $300,000 stays unhedged. Rounding up to 6 would over-hedge.
Futures result: bought at 95.40 and sold at 96.50, a gain of 1.10, which is 110 ticks. Tick value is $25. Gain = 110 × $25 × 5 = $13,750.
Deposit interest at the actual rate: $5,300,000 × 3.5% × 3/12 = $46,375.
Total income = $46,375 + $13,750 = $60,125.
Effective annual rate = $60,125 ÷ $5,300,000 × 12/3 = 4.54% (to two decimal places). The closing futures price of 96.50 equals 100 minus the 3.5% deposit rate, so the closing basis is zero and the hedge locks in the 4.60% implied by the opening futures price (100 − 95.40) on the hedged $5,000,000. Check: $5,000,000 × 4.60% × 3/12 = $57,500, which equals $43,750 interest at 3.5% plus the $13,750 futures gain. The unhedged $300,000 earns only 3.5%: $300,000 × 3.5% × 3/12 = $2,625. Total = $57,500 + $2,625 = $60,125. The gap between 4.54% and 4.60% is therefore fully explained by the unhedged $300,000.
Comment: the hedge protects most of the income but fixes the outcome. If rates had risen instead, the futures would have lost money and cancelled the benefit. Margin payments on the long position would be needed on days when prices fall.

Answer: Buy 5 September futures. The futures gain is $13,750, total income is $60,125 and the effective rate is about 4.54%. The closing basis is zero, so the hedged $5,000,000 locks in 4.60%. The rate is lower overall because the unhedged $300,000 earns only 3.5%.

Exam tips

Write the direction (sell for borrowers, buy for depositors) and the reason in one sentence at the start. Examiners award marks for the logic, not only the numbers.
Show the contract formula, the tick value and the tick count as separate lines. A single arithmetic slip then costs you one mark, not the whole calculation.
Check every contract detail the question gives: size, period, expiry month and any basis assumption. Do not use the figures from this page if the question differs.
Add a short discussion paragraph with basis risk, rounding, margin and the loss of upside. Professional skills marks reward a clear recommendation and a balanced view of the risks.
If the question asks you to compare futures with other tools such as FRAs, options or swaps, tailor the comparison to the case. Mention that futures are standardised and exchange-traded, with daily margin.

Practice questions from The use of financial derivatives to hedge against interest rate risk

Interest Rate Futures in other exams

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

Interest Rate Futures: frequently asked questions

Do I buy or sell futures to hedge borrowing?

Sell futures. If interest rates rise, the futures price falls, so you buy back at a lower price and make a gain. That gain offsets the higher interest on your loan.

How do I calculate the number of interest rate futures contracts?

Divide the amount by the contract size, then multiply by the hedge period in months divided by the contract period in months. For $12,000,000, a $1,000,000 contract and a 6-month loan hedged with 3-month contracts, that is 12 × 6 ÷ 3 = 24. Round to a whole number.

What is basis in interest rate futures?

Basis is the cash price minus the futures price, where the cash price is 100 minus the current spot rate. It falls to zero at expiry. If you close the hedge before expiry, the remaining basis causes basis risk and the hedge will not be perfect.

Why is hedge efficiency not 100%?

Basis can change differently from what you assumed. Whole-contract rounding leaves some exposure unhedged, and the futures period may not match your loan or deposit exactly. Hedge efficiency compares the futures gain with the loss on the underlying position.

Do I include margin in AFM futures calculations?

Only if the question asks. Initial margin and variation margin affect cash flow and funding, so mention them in discussion. Most numerical answers ignore them and just calculate the futures gain or loss.