Derivative instruments and pricing basics - Forwards and fut...

Learning Outcomes

After reading this article, you will be able to explain the fundamental features of forward and futures contracts, differentiate between exchange-traded and OTC derivatives, calculate fair values of forwards and futures, and analyse basis risk. You will also understand how these instruments are used for hedging and the implications of imperfect hedging using futures. This will help you answer AFM exam questions involving derivatives and risk management.

ACCA Advanced Financial Management (AFM) Syllabus

For ACCA Advanced Financial Management (AFM), you are required to understand the principles and applications of derivative contracts for managing risk. Focus your revision on the following areas:

• The core features and differences between forward contracts and futures contracts
• The mechanics of futures trading, including tick sizes, margin requirements, and daily settlement (“mark-to-market”)
• The pricing of forwards and futures contracts, including calculation of fair forward/futures prices under arbitrage-free conditions
• The concept and calculation of basis, and its reduction to zero at contract expiry
• The risks associated with imperfect hedges, especially basis risk and contract size mismatches
• The uses of forwards and futures for hedging foreign exchange and interest rate exposures

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which of the following statements about futures contracts is correct?
   1. They are always settled by physical delivery.
   2. They are traded over the counter (OTC).
   3. They are standardised contracts traded on exchanges.
   4. There is no margin requirement for futures trading.
2. What is the basis in the context of a futures hedge?
   1. The notional principal of the contract
   2. The difference between the spot price and the futures price
   3. The total value of contracts held
   4. The minimum price movement of a contract

3. True or false? At expiration, the basis between spot and futures prices will always be zero.

4. A treasurer sets up a futures hedge for a $5 million foreign currency exposure but can only hedge $4.8 million due to contract size limits. Briefly explain the consequence.

Introduction

Derivative instruments such as forwards and futures play a major role in risk management in financial management. Both instruments allow firms to fix a future price for buying or selling assets, which can reduce uncertainty about outcomes from market price movements. However, differences in contract structure and trading mechanism have significant effects on their pricing, use, and associated risks.

This article explains the main characteristics of forwards and futures, the calculation of their theoretical prices, and the concept of basis and basis risk. Understanding these topics is essential for the ACCA AFM exam, where you may be required to apply these concepts to practical scenarios and recommend risk management strategies.

Key Term: derivative instrument
A financial contract whose value is derived from the price of a reference asset, such as a currency, commodity, bond, or share.

Key Term: forward contract
A private agreement between two parties to buy or sell an asset at a specified price on a future date, typically tailored to the parties’ needs and settled at maturity.

Key Term: futures contract
A standardised contract traded on an exchange to buy or sell an asset at a specified price and future date, with daily settlement and margin requirements.

FORWARDS AND FUTURES: KEY FEATURES

Forward Contracts (OTC)

Forward contracts are privately negotiated between two parties, typically a bank and a corporate client. They provide flexibility in terms of contract amount, maturity, and settlement. No money changes hands initially, and the deal is settled at the contract expiry by physical delivery or net cash settlement. However, forward contracts expose both parties to “counterparty risk”—the risk that one side defaults.

Futures Contracts (Exchange-Traded)

Futures contracts are standardised for contract size, maturity dates, and the reference asset. They are traded on exchanges which clear and guarantee trades via a central clearing house. Both buyer and seller must deposit an initial margin, and profits and losses are settled daily (“marked-to-market”). This reduces counterparty risk because the exchange guarantees fulfillment.

Key distinctions

PRICING FOR FORWARDS AND FUTURES

The fair value of a forward or futures contract is the price that would prevent arbitrage opportunities. The standard no-arbitrage forward/futures price for an asset with spot price $S_0$, delivery after time $T$ at a risk-free rate $r$ (continuous compounding), and assuming no income from the asset, is:

If the reference asset generates a known yield (e.g., dividends, interest), the formula is adjusted for the present value of that income.

Key Term: fair value (forward/futures price)
The theoretical price of a forward or futures contract that prevents arbitrage, calculated by carrying the spot price forward at the risk-free rate minus any income from the asset.

Worked Example 1.1

A commodity’s spot price is $100. The risk-free rate is 4% per year (continuous). Calculate the 6-month fair value of a futures contract if the asset pays no income.

Answer:
F_0 = 100 \times e^{0.04 \times 0.5} = 100 \times e^{0.02} = 100 \times 1.0202 = \102.02
The fair futures price is $102.02.

Margin and Daily Settlement in Futures

Futures transactions require an initial margin deposit with the clearing house. Each day, the contract is “marked to market”—that is, gains or losses from price movement are settled daily by adjusting margin balances. If the balance falls below a threshold (“maintenance margin”), a margin call is made to restore funds.

Key Term: margin (futures)
An amount of money required as collateral by the exchange to ensure contract performance, adjusted daily as market prices move.

BASIS AND BASIS RISK

The Concept of Basis

The “basis” is defined as the difference between the spot price of the reference asset and the futures price:

Key Term: basis
The difference between the spot price and the futures price of an asset: Basis = Spot price − Futures price.

As a futures contract approaches its maturity date, the futures price and spot price converge, and the basis tends to zero at expiry.

Worked Example 1.2

Suppose today’s spot price for EUR/USD is 1.1000, and the three-month EUR/USD futures price is 1.1050. What is the basis? What will the basis be at expiry?

Answer:
Basis = 1.1000 − 1.1050 = −0.0050.
At expiry, the futures price and spot price will be equal, so basis = 0.

Basis Risk and Imperfect Hedging

When using futures to hedge real exposures, two main sources of risk can arise:

• Contract size may not match the exact exposure, resulting in a “mismatch.”
• The expiry date of the future may not precisely coincide with the exposure’s settlement date, so the basis may not be zero when the hedge is closed out.

The result is imperfect correlation and the possibility of over- or under-hedging, known as basis risk.

Key Term: basis risk
The risk that the change in the value of a futures contract does not perfectly offset gains or losses in the hedged asset, due to changes in the basis.

Worked Example 1.3

A treasurer hedges a known future foreign currency payment due in 2¾ months using a 3-month futures contract. Why might the hedge not perfectly offset the risk?

Answer:
Since the payment occurs before the futures expiry, the company must close out the hedge early. The basis may not be zero at that point, resulting in residual currency risk—this is basis risk.

Exam Warning

In the ACCA exam, always be clear whether the hedge will be closed out before contract expiry. If so, mention basis risk in your answer and explain its potential impact on hedge effectiveness.

PRACTICAL ASPECTS OF FUTURES HEDGING

Standard Contract Sizes and Tick Values

Futures contracts are standardised in amount and minimum price movement (tick size). Tick value is the smallest gain or loss per contract for the minimum allowed price movement.

Marking to Market and Margin Calls

The daily adjustment of margin balances means that losses must be settled immediately. Failure to top up margin leads to forced closure of the position.

Choosing the Number of Contracts

The number of contracts required for a hedge is:

Adjustments may be needed for cross-hedging or nonstandard settlement dates.

Summary

Forwards and futures are essential tools for managing financial risks in modern treasury operations. Their pricing is based on no-arbitrage principles, and proper use can greatly reduce uncertainty over future prices. However, mismatches in contract size or timing lead to basis risk, so perfect hedges are rare. Understanding how basis narrows to zero at expiry and impacts imperfect hedging is critical for accurate exam answers.

Key Point Checklist

This article has covered the following key knowledge points:

• Identify the main differences between forward and futures contracts
• Calculate the fair value of forwards and futures using the risk-free rate
• Explain margin requirements, daily settlement, and tick values in futures markets
• Define basis and demonstrate how it converges to zero at expiry
• Recognise and explain basis risk caused by mismatches in hedging
• Apply hedging calculations and explain practical limitations

Key Terms and Concepts

• derivative instrument
• forward contract
• futures contract
• fair value (forward/futures price)
• margin (futures)
• basis
• basis risk