FRM Exam Part I · How Do Firms Manage Financial Risk?

Hedging Instruments: Forwards, Futures, Swaps and Options

Updated 11 October 2026 · Fact-checked

Hedging instruments are derivatives a firm uses to offset an exposure to interest rates, currencies or commodities. Forwards and swaps are custom OTC contracts, futures are standardised and margined, and options protect against one-sided moves for a premium. To solve questions, identify the exposure, take the opposite position, then compare cost, flexibility and residual risk.

Understand Hedging Instruments: Forwards, Futures, Swaps, Options

A firm has an exposure when a change in a market price changes its cash flows or value. A company that will receive euros in six months loses if the euro falls. A airline that must buy fuel loses if fuel rises. A borrower on a floating rate loses if rates rise. Hedging means taking a derivative position whose gains offset those losses.

Forwards fix a price today for a trade at a future date. They are OTC, so you can match the exact amount and date. The trade-offs are counterparty (credit) risk and limited liquidity. A forward locks in the rate: you give up gains as well as losses.

Futures do the same job but are exchange-traded, standardised and marked to market daily with margin. This nearly removes credit risk and gives easy exit. The costs are basis risk (the futures price may not move one-for-one with your exposure, or the contract date may not match), rigid contract sizes, and interim cash flows from margin calls that can create a liquidity strain.

Swaps exchange a series of cash flows. In a plain vanilla interest rate swap, one party pays fixed and receives floating. A firm with floating-rate debt that pays fixed and receives floating turns its debt into effectively fixed-rate. A currency swap does the same across currencies. Swaps are like a strip of forwards and are used for long-dated exposures.

Options give the right, not the obligation, to trade. A bought put on an asset you own sets a floor while keeping the upside. A bought call on something you must buy sets a cap on cost. You pay an upfront premium for this one-sided protection. Forwards cost nothing upfront but remove the upside. Options cost money but keep it. That trade-off is the most tested idea in this topic.

Key formulas to remember

Forward hedge outcome (long exposure to buy): Effective price = S_T − (S_T − F) = F; S_T is the spot price at maturity. The payoff to a long forward bought at F is S_T − F. Subtracting it from the spot price paid gives an effective purchase price of F whatever the spot price, ignoring credit risk and basis.
Futures hedge number of contracts: N = h × (Exposure size ÷ Contract size); h is the hedge ratio. Exposure size and contract size must be in the same units, either both in units (such as barrels) or both in value (such as dollars). Do not mix them. With h = 1 the futures position matches the exposure in size. This removes price-level exposure only when the futures asset matches the exposure and the futures maturity matches the hedge date. Otherwise basis risk remains. Short futures hedge a long exposure; long futures hedge a future purchase.
Minimum variance hedge ratio: h* = ρ × (σS ÷ σF); ρ is the correlation between spot and futures price changes. σS and σF are the standard deviations of those changes.
Basis: Basis = Spot price − Futures price; Basis risk is uncertainty in the basis when the hedge is closed. Let F1 be the futures price when the hedge is set up and b2 the basis (S2 − F2) when it is closed. With this definition, a short hedge on an asset you hold and sell at the close gives effective price = F1 + b2.
Fixed-for-floating swap, payer's net cost: Net cost = Floating paid to lender + Fixed paid − Floating received = Fixed rate + loan spread; If the swap floating leg matches the loan's floating rate, the floating receipt cancels the floating loan payment. The borrower pays the swap fixed rate plus the loan spread.
Protective put floor: Minimum net proceeds per unit = K − premium (ignoring financing); with financing, K − premium × (1 + r)^T (annual compounding) or K − premium × e^(rT) (continuous compounding); K is the strike, r the financing rate and T the time in years. Use the compounding convention the question states: (1 + r)^T for annual compounding, e^(rT) for continuous compounding. This is per unit of asset held. The upside stays open but is reduced by the premium.
Duration-based hedge (DV01 matching): N = DV01 of exposure ÷ DV01 of one hedging contract; Use a short position in the contract to hedge a long bond position.

How to solve Hedging Instruments: Forwards, Futures, Swaps, Options questions

Use the same sequence for any hedging question, whether it asks for a calculation or a choice of instrument.

1Identify the exposure: what asset or liability, which market variable, what date, and whether you lose when the price rises or falls.
2Take the opposite position: short or sell a derivative to hedge a long exposure, long or buy for a future purchase, pay fixed to turn floating debt into fixed.
3Choose the instrument using the question's cues: exact amount and date favour forwards or swaps, liquidity and low credit risk favour futures, keeping upside favours options.
4Size the hedge: use contracts = hedge ratio × exposure ÷ contract size, or match DV01 for bonds. Round to whole contracts.
5Compute the outcome: effective price or rate, including premium for options and basis for futures.
6State what remains: basis risk, credit risk, margin liquidity risk, forgone upside, or premium cost.
7Check the sign and units, and see whether your answer matches the intended direction of the hedge.

Quickest way: Exposure, direction, instrument, residual risk

When to use it: Use this for conceptual multiple-choice questions on which instrument fits or what risk remains.

Write the exposure as long or short in one phrase, such as 'long EUR receivable'.
Flip it: long exposure means sell forward, short futures or buy a put.
Eliminate options that cost nothing or promise full upside plus full protection. Only options keep upside, and they cost a premium.
Eliminate answers that call futures credit-risk-heavy. Futures have low credit risk because of the clearing house; forwards and swaps carry counterparty risk.
Pick the answer naming the correct residual risk: basis for futures, counterparty for OTC, premium for options.

Common mistakes in Hedging Instruments: Forwards, Futures, Swaps, Options

Taking the same direction as the exposure instead of the opposite.
Students think 'hedge a loan' means 'take a loan-like position'.
Fix: Ask what hurts you first, then choose a derivative that gains in that scenario.
Saying forwards have no cost so they dominate options.
The premium is visible, but the forgone upside in a forward is not.
Fix: Compare outcomes in both price scenarios. The forward locks the rate and removes gains. The option keeps gains for a premium.
Claiming futures eliminate all risk because the exchange guarantees them.
Confusing credit risk with market risk and basis risk.
Fix: Futures remove most counterparty risk but leave basis risk, rounding and margin-call liquidity risk.
Forgetting the premium when finding an option hedge outcome.
Focus on the payoff at expiry.
Fix: Net the premium (and interest on it if given) against the payoff before stating the effective price.
Mixing up pay-fixed and receive-fixed in a swap.
Direction is described from the swap's perspective, not the borrower's.
Fix: A floating-rate borrower fears higher rates, so it pays fixed and receives floating.
Using ρ × σF ÷ σS for the minimum variance hedge ratio.
The two standard deviations are inverted from memory.
Fix: Remember h* = ρ × σS ÷ σF. The thing you hedge goes on top.

Worked examples

Example 1

A US company will pay €2,000,000 in three months. The three-month forward rate is $1.1000 per €. Spot in three months turns out to be $1.1500. Using a forward hedge, what is the USD cost, and how much better or worse off is the firm than if it had not hedged?

Show the solution

Exposure: a future payment in euros, so the firm loses if the euro rises. Hedge by buying euros forward.
Hedged cost = €2,000,000 × 1.1000 = $2,200,000.
Unhedged cost = €2,000,000 × 1.1500 = $2,300,000.
Difference = 2,300,000 − 2,200,000 = $100,000 in favour of the hedge.

Answer: The hedged cost is $2,200,000, which is $100,000 lower than the unhedged cost of $2,300,000.

Example 2

A fund holds 1,000,000 barrels of a refined product and wants to hedge. The standard deviation of spot price changes is 0.30 and of futures price changes is 0.25, with correlation 0.80. Each futures contract covers 1,000 barrels. How many futures contracts should it short for the minimum variance hedge?

Show the solution

Hedge ratio h* = ρ × σS ÷ σF = 0.80 × 0.30 ÷ 0.25 = 0.96.
Exposure in barrels = 1,000,000, so futures needed in barrels = 0.96 × 1,000,000 = 960,000.
Contracts = 960,000 ÷ 1,000 = 960.
The fund holds the asset, so it shorts the contracts.

Answer: Short 960 futures contracts.

Exam tips

Questions often ask which instrument best fits a stated need such as flexibility, low credit risk or keeping upside. Match the keyword to the instrument.
Always state the residual risk: basis for futures, counterparty for forwards and swaps, premium for options.
For hedge ratio questions, check the formula direction and round contracts to the nearest whole number.
Read swap questions from the borrower's side. Write the three cash flows before computing net rate.
Options do not remove the downside cost: the premium is the price for keeping the upside.

Practice questions from How Do Firms Manage Financial Risk?

Hedging Instruments: Forwards, Futures, Swaps, Options in other exams

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

Hedging Instruments: Forwards, Futures, Swaps, Options: frequently asked questions

What is the difference between forward and futures hedging?

Forwards are customised OTC contracts settled at maturity and carry counterparty risk. Futures are standardised, exchange-traded, marked to market daily and backed by a clearing house. Futures bring basis risk and margin cash flows, while forwards can match exposure exactly.

How do firms use swaps to hedge interest rate risk?

A firm with floating-rate debt can enter a swap where it pays a fixed rate and receives floating. The floating receipt offsets the floating loan interest, leaving a net fixed cost. A firm with fixed-rate assets can do the opposite.

What are the pros and cons of hedging with options versus forwards?

Options keep upside while protecting against adverse moves, but you pay a premium. Forwards cost nothing upfront but fix the rate, so you give up favourable moves and face counterparty risk if OTC.

Why do hedges using futures not remove all risk?

The futures price may not move exactly with the price you are exposed to, which is basis risk. Contract size and maturity may not match your exposure. Margin calls can also cause liquidity strain.