Short Hedge

Q: A short hedge is most appropriate for which of the following participants?

An Australian wheat grower expecting to sell at harvest. The grower has natural long exposure to wheat through the standing crop and faces a fall in spot prices before harvest. Shorting futures offsets that risk and locks in a sale price near F_1. Option A describes a buyer who needs a long hedge. Option C describes pure speculation, not hedging. Option D conflates risk neutrality with risk management.

Q: An oil producer sells crude futures at US80 per barrel. At delivery, spot is US74 and futures are US$75. The effective price received per barrel is closest to:

US79. Effective price= F_1 + b_2 = 80 + (74 - 75) = US79. The hedger sells physical for US74 and gains 80 - 75 = US5 on the short futures, netting US$79. Option D would only be exact if the realised basis at close were zero.

A short hedge sells futures contracts today to lock in a future selling price. It suits anyone with long cash exposure, such as a commodity producer, an exporter holding foreign currency receivables, or a fund manager planning to liquidate equity. If the spot price falls, the gain on the short futures offsets the loss in the cash market. The effective price received equals $F_1 + b_2$ , where $F_1$ is the futures price at hedge inception and $b_2$ is the basis at the close date.

Try it yourself

Minimum-variance hedge ratio

You hold an asset and short futures to offset its price moves. The hedge ratio h is how many units of futures you short per unit of exposure. The variance of the hedged position is a parabola in h, minimised at h* = ρ · σ_spot / σ_futures. The deeper the correlation, the more variance the hedge removes — exactly ρ² of it.

Hedge effectiveness 64%. At h* the hedge removes 64% of the unhedged variance, leaving 0.52 of residual (basis) risk you cannot diversify away.

Hedge ratio h*0.96

Optimal contracts N* (exact)19.2

N* rounded to whole contracts19

Hedge effectiveness ρ²64%

Unhedged variance σ_spot²1.44

Minimum variance at h*0.52

Correlation ρ0.8

σ_spot (spot change std dev)1.2

σ_futures (futures change std dev)1

Exposure Q_A (units to hedge)10,000

Contract size Q_F (units per contract)500

h* = ρ · σ_spot / σ_futures · N* = h* · Q_A / Q_F · Var(h) = σ_spot² + h²·σ_futures² − 2·h·ρ·σ_spot·σ_futuresσ_spot and σ_futures are standard deviations of price changes over the hedge horizon. Effectiveness ρ² is the share of spot variance the hedge removes; the rest is basis risk. Contracts are discrete, so N* is rounded to whole contracts in practice.

Why it matters

A grain farmer owns wheat that will only be sold at harvest. The risk is that wheat prices fall before then. Selling wheat futures today fixes the receivable at $F_1$ . If wheat drops by $20 per tonne, the futures short gains roughly $20 per tonne and the two cancel. The price lock is not exact because basis at close is uncertain, but residual risk is far smaller than outright exposure. The hedger gives up upside as the cost of removing downside.

Before you read on — recall

A short hedge is most appropriate for which of the following participants?

Formulas

Effective price received under a short hedge

P_{\text{eff}} = S_2 + (F_1 - F_2) = F_1 + b_2

Here

S_2

is the spot price at close,

F_1

and

F_2

are the futures prices at open and close, and

b_2 = S_2 - F_2

is the basis at close. Source: Hull (2022) §3.4.

Worked examples

Scenario

An Australian wheat grower expects to harvest 5,000 tonnes in November. In August she sells 100 ASX Eastern Wheat futures (50 tonnes each) at A$330 per tonne. At delivery in November the spot price is A$300 and the futures settle at A$303.

Solution

Spot revenue $= 5{,}000 \times 300 =$ A$1,500,000. Futures gain per tonne $= 330 - 303 =$ A$27, so total futures gain $= 5{,}000 \times 27 =$ A$135,000. Total received $=$ A$1,635,000, or A$327 per tonne. This equals $F_1 + b_2 = 330 + (300 - 303) =$ A$327, which is close to but not exactly the locked-in A$330 because of the realised basis $b_2 = -3$ .

Scenario

An oil producer shorts 1,000 WTI crude futures at US$80 per barrel to hedge October output. By delivery, spot crude has fallen to US$72 and futures to US$72.50.

Solution

Loss on physical $= 80 - 72 =$ US$8 per barrel. Gain on futures $= 80 - 72.50 =$ US$7.50 per barrel. Net price received $= 72 + 7.50 =$ US$79.50, equal to $F_1 + b_2 = 80 + (72 - 72.50) =$ US$79.50. Basis weakened by $0.50, so the hedger underperforms the locked rate by that amount.

Common mistakes

✗A short hedge guarantees you the futures price $F_1$ . It only guarantees you $F_1 + b_2$ . The realised basis at close is unknown when the hedge is set, so basis risk remains. If you hold to delivery and the futures underlying matches your physical, basis converges to zero and the lock becomes nearly exact.
✗A short hedger profits when prices fall. The futures leg profits, but the physical position loses an offsetting amount. The whole point is that the net position is approximately flat. Treating the futures gain as profit is a confusion of cash flow with economic outcome.
✗Short hedges remove the need for inventory management. Hedging price risk does not hedge storage costs, deterioration, or counterparty risk on the physical buyer. A producer still bears all operating risks of the underlying business.

Revision bullets

•Sell futures today, lift them at the close date
•Suits anyone holding or producing the underlying asset
•Effective price received $= F_1 + b_2$
•Removes price risk but leaves basis risk
•Gives up upside in exchange for downside protection
•Hedge effectiveness highest when held to delivery

Quick check

A short hedge is most appropriate for which of the following participants?

An oil producer sells crude futures at US$80 per barrel. At delivery, spot is US$74 and futures are US$75. The effective price received per barrel is closest to:

Connected topics

Hedge / Spec Long/Short Eff. Price Hedge vs Spec Long Hedge Beta Hedge Basis Risk

More in Hedging & Basis Risk

Change Beta Basis Cross Hedge Min Var. HR Tailing

In learning paths

Hedging & Risk Path

Sources

Hull (2022), §3.1 and §3.4
Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
Section 3.1 introduces the short hedge with the textbook oil-producer example. Section 3.4 derives the effective price expression.
CME Group, How to Hedge Grain Risk
CME Group. How to Hedge Grain Risk. CME Education Centre, accessed 2026.
Walks through a producer short hedge in grain futures and explains how basis changes affect realised price.
ASX 24 Contract Specifications
Australian Securities Exchange. ASX 24 Contract Specifications. ASX, version 11, December 2025.
Reference for ASX Eastern Wheat and Western Wheat futures contract sizes used by Australian producers.
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.
Quantifies how much variance a short hedge removes and shows that effectiveness depends on the spot-futures correlation.

How to cite this page

Dr. Phil's Quant Lab. (2026). Short Hedge. Derivatives Atlas. https://phucnguyenvan.com/concept/short-hedge