DP
Futuresintermediate

Effective Price

The effective price is the net price a hedger actually realises after combining the physical market transaction with the offsetting futures hedge gain or loss. For a short hedge, it equals the initial futures price F1F_1 plus the basis at close-out, Peff=F1+(S2−F2)P_{\text{eff}} = F_1 + (S_2 - F_2). For a long hedge, Peff=F1−(F2−S2)P_{\text{eff}} = F_1 - (F_2 - S_2). The effective price equals F1F_1 only when basis is zero at close-out, which happens automatically at expiry for a matched contract but rarely at any earlier date.

Why it matters

A hedger has two trades. The physical market transaction settles at the spot price S2S_2 on the close-out date. The futures hedge generates a profit or loss equal to the change in the futures price between F1F_1 and F2F_2. The combined net price is the spot received or paid, adjusted by the futures gain or loss. Algebra collapses this to F1F_1 plus residual basis. Basis risk is therefore the only uncertainty left in a properly weighted hedge.

Formulas

Effective price for a short hedge
Peff=S2+(F1−F2)=F1+(S2−F2)=F1+b2P_{\text{eff}} = S_2 + (F_1 - F_2) = F_1 + (S_2 - F_2) = F_1 + b_2
Hull (2022) §3.4 derives this for an asset seller hedging with short futures.
Effective price for a long hedge
Peff=S2+(F2−F1)=F1+(S2−F2)=F1+b2P_{\text{eff}} = S_2 + (F_2 - F_1) = F_1 + (S_2 - F_2)= F_1 + b_2
Cost form for a buyer hedging with long futures. The basis term appears the same way.
Closing basis
b2=S2−F2b_2 = S_2 - F_2

Worked examples

Scenario

A NSW wheat grower expects to sell 200 tonnes in three months. She shorts ASX wheat futures today at F1=F_1 = A$340 per tonne. At harvest, spot is S2=S_2 = A$320 and the offsetting futures price is F2=F_2 = A$322.

Solution

Closing basis b2=320−322=−2b_2 = 320 - 322 = -2. Effective price Peff=340+(−2)=P_{\text{eff}} = 340 + (-2) = A$338 per tonne. She receives A$320 in the cash market and a futures gain of $340 - 322 = AA18 per tonne, totalling A$338. The lock-in target of A$340 missed by A$2 because of non-zero closing basis.

Scenario

A wholesale flour mill plans to buy 100 tonnes of wheat in two months and hedges with long futures at F1=F_1 = A$320. At purchase, spot is S2=S_2 = A$345 and futures settle at F2=F_2 = A$348.

Solution

Closing basis b2=345−348=−3b_2 = 345 - 348 = -3. Effective cost Peff=320+(−3)=P_{\text{eff}} = 320 + (-3) = A$317 per tonne. The mill pays A$345 in the cash market but gains $348 - 320 = AA28 per tonne on the long futures, net A$317. Negative basis made the hedge slightly better than the target lock-in of A$320.

Common mistakes

  • ✗Hedging always locks in the exact futures price. It locks in F1F_1 only if b2=0b_2 = 0. Most close-outs occur before expiry, so residual basis is the rule, not the exception.
  • ✗Positive closing basis always hurts the hedger. For a short hedge, positive b2b_2 raises the effective price, which is good. For a long hedge, the effect is symmetric in the same direction, which is also good. The relationship depends on whether the hedger is buying or selling the underlying.
  • ✗Basis risk means the hedge is broken. A hedge converts price risk into basis risk, which is typically smaller. A wheat grower without a hedge faces full spot risk; with a futures hedge she faces only the residual gap between cash and futures movements.

Revision bullets

  • •Peff=F1+b2P_{\text{eff}} = F_1 + b_2 for short hedge
  • •Peff=F1+b2P_{\text{eff}} = F_1 + b_2 for long hedge in the same form
  • •Perfect lock-in requires b2=0b_2 = 0, true only at expiry of matched contract
  • •Basis risk is the residual uncertainty after hedging
  • •Strengthening basis raises PeffP_{\text{eff}}, weakening basis lowers it

Quick check

For a short hedge, if closing basis b2=S2−F2b_2 = S_2 - F_2 is positive, the effective price is:

A farmer shorts futures at F1=500F_1 = 500. At close-out spot is S2=480S_2 = 480 and futures F2=485F_2 = 485. The effective price per unit is:

Connected topics

ConvergenceShort Hedge

In learning paths

Futures Path

Sources

  1. Hull (2022), §3.4 and §3.5
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Develops the effective price formula for short and long hedges and decomposes residual uncertainty into basis risk.
  2. Ederington (1979)
    Ederington, Louis H. The Hedging Performance of the New Futures Markets. Journal of Finance, 34(1), 1979, pp. 157 to 170.
    Classic empirical paper on hedge effectiveness and the basis decomposition of realised hedged prices.
  3. CME Group, Basis and Hedging
    CME Group. Understanding Basis and Hedging Effectiveness. CME Group Education, 2024.
    Worked numerical examples showing how realised effective prices depend on the basis at close-out in agricultural markets.
How to cite this page
Dr. Phil's Quant Lab. (2026). Effective Price. Derivatives Atlas. https://phucnguyenvan.com/concept/effective-price
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