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Hedging & Basis Riskintermediate

Long Hedge

A long hedge buys futures today to lock in a future purchase price. It suits anyone with short cash exposure, such as a manufacturer that will buy raw materials, an importer with future foreign-currency payables, or a fund manager who knows that new cash will need to be invested in equities. If the spot price rises, the gain on the long futures offsets the higher purchase cost. The effective purchase cost equals F1+b2F_1 + b_2, where F1F_1 is the futures price at inception and b2b_2 is the basis at the close date.

Why it matters

A copper smelter that needs ore next quarter is structurally short copper. The risk is that copper prices rise before purchase. Buying copper futures today locks the cost at roughly F1F_1. If spot rises by $500 per tonne, the futures long gains about $500 per tonne and offsets the higher invoice. A long hedger gives up the benefit of a price fall in exchange for protection against a price rise.

Formulas

Effective price paid under a long hedge
Peff=S2−(F2−F1)=F1+b2P_{\text{eff}} = S_2 - (F_2 - F_1) = F_1 + b_2
Here S2S_2 is the spot price paid at close, F1F_1 and F2F_2 are the futures prices at open and close, and b2=S2−F2b_2 = S_2 - F_2 is the basis at close. Source: Hull (2022) §3.2.

Worked examples

Scenario

A Sydney-based copper cable manufacturer needs to buy 250 tonnes of copper in three months. The current LME 3-month future trades at US$8,000 per tonne. The firm buys 10 LME copper futures (25 tonnes each). Three months later, spot copper is US$8,500 and futures are US$8,480.

Solution

Spot purchase =250×8,500== 250 \times 8{,}500 = US$2,125,000. Futures gain per tonne =8,480−8,000== 8{,}480 - 8{,}000 = US$480, total =250×480== 250 \times 480 = US$120,000. Net cost =2,125,000−120,000== 2{,}125{,}000 - 120{,}000 = US$2,005,000, or US$8,020 per tonne. This equals F1+b2=8,000+(8,500−8,480)=F_1 + b_2 = 8{,}000 + (8{,}500 - 8{,}480) = US$8,020. The basis widened from zero (an assumed initial alignment) to US$20, raising the effective price by US$20.

Scenario

An Australian super fund will receive A$50 million of new contributions in two months that must be invested in ASX 200 equities. To avoid being left behind if the market rallies, it buys 100 SPI 200 futures at an index level of 8,000. Two months later the index is 8,400 and the SPI future also at 8,400.

Solution

Futures gain per point =8,400−8,000=400= 8{,}400 - 8{,}000 = 400. Each contract pays A$25 per point, so total gain =100×400×25== 100 \times 400 \times 25 = A$1,000,000. The fund pays a higher price for the equities by roughly the same percentage, but the futures gain offsets the cost of waiting. This is a textbook anticipatory long hedge.

Common mistakes

  • ✗Only commodity buyers use long hedges. Any entity that will buy an asset in the future can lock in the price. Importers buy currency forwards, bond desks buy bond futures before a coupon reinvestment, and equity fund managers buy index futures to bridge new cash. The mechanic is identical.
  • ✗A long hedge guarantees the initial futures price. It guarantees F1+b2F_1 + b_2. If basis weakens or strengthens, the realised cost moves with it. Holding to delivery removes most of this risk because basis converges to zero.
  • ✗Buying futures replaces the eventual purchase. The hedger still buys the physical asset at the spot price in the cash market. Futures transfer the price risk during the waiting period and are usually closed out before delivery.

Revision bullets

  • •Buy futures today, sell them at the close date
  • •Suits any party planning a future purchase
  • •Effective cost paid =F1+b2= F_1 + b_2
  • •Protects against rising prices, gives up benefit of falls
  • •Anticipatory hedge when cash arrives later
  • •Basis converges to zero if held to delivery

Quick check

A long hedge would be most useful for which of the following?

A long hedger bought futures at US$100. By close, spot is US$110 and futures are US$108. The effective purchase cost per unit is:

Connected topics

Eff. PriceShort Hedge

In learning paths

Hedging & Risk Path

Sources

  1. Hull (2022), §3.2 and §3.4
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Section 3.2 introduces the long hedge with a copper-fabricator example and derives the effective cost in §3.4.
  2. CME Group, Self-Study Guide to Hedging
    CME Group. Self-Study Guide to Hedging with Grain and Oilseed Futures and Options. CME Education Centre, accessed 2026.
    Detailed worked examples of buyer long hedges with explicit basis treatment, suitable for student reference.
  3. ASX, ASX SPI 200 Futures
    Australian Securities Exchange. ASX SPI 200 Futures product brochure. ASX.
    Confirms the A$25 per point multiplier used in the anticipatory equity long-hedge example.
  4. Ederington (1979)
    Ederington, Louis H. The Hedging Performance of the New Futures Markets. Journal of Finance, Vol. 34, No. 1, March 1979, pp. 157-170.
    Provides the variance-reduction framework that quantifies how a long hedge cuts uncertainty in the future purchase cost.
How to cite this page
Dr. Phil's Quant Lab. (2026). Long Hedge. Derivatives Atlas. https://phucnguyenvan.com/concept/long-hedge
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