FINC6010 Chap.3 Hedging with Futures and Basis Risk
Hedging with Futures and Basis Risk
A futures hedge combines a physical exposure with an offsetting contract position. This chapter selects long hedges for planned purchases and short hedges for planned sales, derives the effective price through closing basis, and sizes cross hedges with correlation and relative volatility. It then tests the limits created by quantity changes, timing mismatch, margin liquidity and governance.
Direction comes from the physical transaction: a buyer fears a rise and uses long futures, while a seller fears a fall and uses short futures. The combined effective price depends on the closing basis, defined as spot minus futures, so a hedge usually locks an approximate rather than exact result. Contract selection requires a related underlying, a suitable delivery month and an appropriate quantity.
When spot and futures changes do not move one for one, the minimum-variance ratio uses correlation and relative volatility to target risk reduction rather than full notional matching. That estimate does not remove forecast error, unstable relationships or whole-contract rounding. The chapter therefore treats hedging as a governed policy.
Quantity, timing, margin liquidity, accounting presentation and performance measurement can all turn a sensible formula into a poor operational position if they are ignored.
What this chapter covers
- 01
Long and short hedge direction
- 02
Spot-futures basis
- 03
Effective purchase and sale prices
- 04
Contract-month selection
- 05
Minimum-variance hedge ratio
- 06
Cross-hedging and residual risk
Worked example · free
Size a cross hedge
- 1Identify the planned purchase and choose long futures.
- 1Compute correlation times spot volatility divided by futures volatility.
- 1Multiply by exposure size and divide by contract size.
- 2State the continuous result before whole-contract rounding.
Key terms
- Cross hedge
- A hedge using futures on an asset related to, but not identical with, the exposure.
- Hedge ratio
- The futures exposure per unit of the physical exposure under a stated risk objective.
- Basis risk
- The uncertainty caused by spot and futures prices changing by different amounts before the hedge closes, leaving the effective price imperfectly locked.
- Contract month
- The delivery month attached to a futures contract, chosen with regard to hedge end date, liquidity and the cost of rolling.
- Minimum variance
- A hedge objective that selects a ratio intended to reduce outcome variance using estimated correlation and relative volatility rather than guaranteeing a target price.
- Effective price
- The net purchase cost or sale proceeds after combining the physical transaction with the futures gain or loss. It can be reconciled from both cash-flow legs and from the initial futures price plus closing basis under consistent signs. Residual variation reflects the closing basis.
Hedging with Futures and Basis Risk FAQ
When should a firm use a long hedge?
A long hedge fits an expected purchase when a price rise would increase the firm’s cost. Gains on long futures can offset the higher spot purchase price. The effective price still depends on the basis when the hedge is closed.
What creates basis risk?
Basis risk arises because spot and futures prices may not change by exactly the same amount before the hedge ends. Timing mismatch, location, grade and use of a related futures asset can all leave a non-zero and uncertain closing basis.
Does an optimal hedge remove all risk?
No. A minimum-variance ratio targets variance reduction using estimated correlation and volatility. Forecast quantity can change, relationships can shift, margin calls create liquidity needs and whole-contract rounding leaves residual exposure. The ratio operates inside a broader risk policy.
Why can a hedge lose money and still work?
The derivative is only one leg of the combined position. A long futures hedge can lose when the purchase price falls, but the firm then buys the physical asset more cheaply. Performance should be judged against the protected effective price or variance objective, not the derivative profit in isolation.
Exam move
For every hedge, draw two columns labelled physical and futures. Write each leg’s gain or loss and combine them only at the end. Confirm the effective price using initial futures price plus closing basis. For sizing, report the unrounded contract count before explaining the whole-contract decision. Alternate planned purchases and planned sales until direction becomes automatic.
Then vary the closing spot and futures prices independently to see how basis drives the residual result. For cross hedges, state why the chosen contract is related to the exposure before inserting correlation and volatility. Recompute the contract count after changing only the correlation, then only one volatility, and explain the direction of each change.
Add an operational paragraph to every full answer: consider whether forecast quantity can change, whether the hedge ends before contract maturity and whether margin calls arrive before physical cash flows. End by evaluating the combined position against the stated objective. A derivative loss is not evidence of failure when the physical leg gains by the amount the hedge was designed to protect.
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