FRM Exam Part I · Introduction to Derivatives

Uses of Derivatives: Hedgers, Speculators and Arbitrageurs

Updated 11 October 2026 · Fact-checked

Derivatives are used in three ways. Hedgers take a derivative position to cut an existing risk. Speculators take a position to bet on price moves, using leverage. Arbitrageurs lock in a riskless profit from price gaps between markets. To solve questions, identify the existing exposure first, then the direction of the derivative position.

Understand Uses of Derivatives: Hedging, Speculation, Arbitrage

A derivative is a contract whose value depends on an underlying asset, rate or index. People trade derivatives for three different reasons. The same contract can serve any of the three, depending on who holds it and what other exposure they have.

Hedgers already face a risk and want to reduce it. An airline that must buy jet fuel in six months is hurt if prices rise. It can go long a fuel futures contract. If fuel rises, the futures gain offsets the higher cost. A hedge fixes the price. It removes the downside, but it also removes the upside.

Speculators have no underlying exposure. They take a view and open a position to profit if it is right. Derivatives need little upfront cash (margin or an option premium), so a small price move gives a large percentage gain or loss on the money put up. This is leverage. It works in both directions. A speculator can lose more than the margin posted on a futures or short option position.

Arbitrageurs look for a riskless profit with no net investment. They buy the cheap version of an asset and sell the expensive one at the same time. A classic case is a forward price that differs from spot price compounded at the financing rate. Arbitrage trades push prices back into line, which is why forward and futures prices follow no-arbitrage relationships.

For the exam, classify the trader by purpose, not by instrument. A trader with an offsetting underlying exposure is a hedger. A trader with a one-way bet is a speculator. A trader locking in a risk-free gain is an arbitrageur.

Key formulas to remember

Long hedge (futures): Hedged cost = Spot at purchase − Gain on futures = Initial futures price + Final basis; Basis = Spot − Futures. A long hedge protects a planned purchase. Gain on a long futures = (F_end − F_start) × quantity.
Short hedge (futures): Hedged proceeds = Spot at sale + Gain on short futures = Initial futures price + Final basis; A short hedge protects an asset you own or will sell. Gain on a short futures = (F_start − F_end) × quantity.
Basis: Basis = Spot price − Futures price; If the basis at close is zero, the hedge is perfect. Otherwise basis risk remains.
Return on margin (leverage): Return on margin = Profit or loss ÷ Initial margin; Leverage multiplies percentage returns. The same ratio applies to losses.
Cost-of-carry forward price (no income): F₀ = S₀ × e^(rT); Continuous compounding. If the market forward differs from this, an arbitrage exists.
Option payoffs at expiry: Long call = max(S_T − K, 0); Long put = max(K − S_T, 0); Buyers risk only the premium. Option sellers keep the premium but face large possible losses.

How to solve Uses of Derivatives: Hedging, Speculation, Arbitrage questions

Use this method for any question on hedgers, speculators or arbitrageurs.

1Read the scenario and write down the trader's existing exposure: owns the asset, will buy it, owes money, or has none.
2Classify the purpose: offsetting exposure means hedge, one-way view means speculation, simultaneous offsetting trades with a riskless gain means arbitrage.
3Choose the direction: a long hedge for a future purchase, a short hedge for a future sale or an asset held.
4Compute the derivative gain or loss using contract size × price change, with the correct sign for long or short.
5Combine with the spot result to get the net outcome, such as the effective price or the hedged cost.
6For speculation, divide profit or loss by margin or premium to get the leveraged return.
7For arbitrage, compare the market price with the no-arbitrage price and name the trades that capture the gap.
8Check the answer: a perfect hedge should leave the result close to the initial futures price.

Quickest way: Effective price shortcut

When to use it: Use for futures hedging questions that ask for the net price paid or received.

Effective price = Initial futures price + Final basis (final spot − final futures).
If the question says the basis is zero at close, the answer is simply the initial futures price.
For speculation, return on margin = (price change × contract size) ÷ margin. Do not add margin to the profit.
For arbitrage, compare F market with S × e^(rT). If market F is higher, sell the forward and buy the asset. If lower, buy the forward and short the asset.

Common mistakes in Uses of Derivatives: Hedging, Speculation, Arbitrage

Calling any derivative trader a hedger.
Students focus on the instrument, not on whether an underlying exposure exists.
Fix: Ask what the trader owns or owes. No offsetting exposure means speculation.
Choosing the wrong hedge direction.
Mixing up who loses when prices rise.
Fix: Who gets hurt by rising prices (a buyer) goes long. Who gets hurt by falling prices (a seller or holder) goes short.
Assuming a hedge removes all risk.
Textbook examples often assume zero basis at close.
Fix: State that basis risk remains when the futures and spot prices do not converge or when the asset differs.
Treating leverage as extra return only.
Focus on gains on a small margin.
Fix: Leverage scales losses equally. A futures position can lose more than the initial margin.
Calling a trade arbitrage when it carries risk.
Students confuse a profitable bet with a riskless profit.
Fix: Arbitrage needs no net investment, no risk and a positive payoff. If the outcome depends on a future price move, it is speculation.

Worked examples

Example 1

A manufacturer will buy 10,000 barrels of oil in three months. Today's futures price for that date is $80 per barrel. In three months the spot price is $86 and the futures price is $85.50. The manufacturer hedged by going long 10 contracts of 1,000 barrels each. What is the effective price per barrel paid?

Show the solution

The manufacturer buys oil later, so a long hedge is correct.
Futures gain per barrel = 85.50 − 80 = $5.50.
Total futures gain = 5.50 × 10,000 = $55,000.
Cost of buying at spot = 86 × 10,000 = $860,000.
Net cost = 860,000 − 55,000 = $805,000.
Effective price = 805,000 ÷ 10,000 = $80.50 per barrel.
Check: initial futures 80 + final basis (86 − 85.50 = 0.50) = $80.50.

Answer: $80.50 per barrel

Example 2

A speculator buys one futures contract on an index with a multiplier of $250 per index point. The index is at 4,000 and the initial margin is $20,000. The index falls to 3,900. What is the loss and the return on margin?

Show the solution

Price change = 3,900 − 4,000 = −100 points.
Loss = 100 × $250 = $25,000.
Return on margin = −25,000 ÷ 20,000 = −125%.
The loss exceeds the initial margin, so the speculator must add funds.

Answer: Loss of $25,000, which is −125% of initial margin

Exam tips

Look for the key phrase that reveals purpose: 'to protect', 'to lock in' means hedge; 'expects prices to rise' means speculation; 'riskless profit' means arbitrage.
Write the sign of every gain and loss. Many wrong answers come from reversing long and short.
When the question gives final spot and futures prices, use effective price = initial futures + final basis. It saves time.
Leverage questions often include a loss larger than margin. Do not cap the loss at 100%.
Remember that a hedge gives up gains as well as losses. Options hedges keep the upside but cost a premium.

Practice questions from Introduction to Derivatives

Uses of Derivatives: Hedging, Speculation, Arbitrage in other exams

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

Uses of Derivatives: Hedging, Speculation, Arbitrage: frequently asked questions

What is the difference between a hedger and a speculator?

A hedger holds an underlying exposure and uses a derivative to reduce it. A speculator has no such exposure and takes a derivative position to profit from a price view. The same contract can be used by either.

Why do derivatives create leverage?

A futures contract needs only margin, and an option needs only a premium, far less than the value of the underlying. A small price move therefore produces a large percentage gain or loss on the money invested.

Is arbitrage completely risk free?

In theory, yes: it needs no net investment and has no chance of loss. In practice, execution, financing and counterparty risks can remain. Exam questions usually treat it as riskless.

Does a futures hedge remove all risk?

No. Basis risk remains if the spot and futures prices do not move together, or if the hedged asset differs from the futures underlying. The hedge also gives up gains from favourable price moves.