Charta is on Google Play: practise on the go. Get the app
Charta

Compute the profit or loss on a long hedge or a short hedge.

FRM® Part I · Financial Markets and Products · Using Futures for Hedging · FRM1.FM.8.e

The idea

A hedge's profit or loss has two parts: the change in value of the exposure and the gain or loss on the futures. A short futures position gains when the futures price falls: Profit = (F sold − F bought back) × contract size × number of contracts. A long futures position is the reverse: it gains when the futures price rises and loses when it falls. Here F1 is the futures price at the outset, and S2 and F2 are the spot and futures prices when the hedge is lifted. A short hedge realises S2 + (F1 − F2) per unit, and a long hedge's effective cost is the same expression. Both reduce to one formula, with b2 the basis S2 − F2 at the close: Effective price = F1 + b2. If the basis is unchanged, the price is F1 plus the initial basis S1 − F1, the starting spot price S1. Apply the quantity actually hedged, which may differ from the exposure when a hedge ratio is used. In a good hedge, the futures result and the change in the exposure's value have opposite signs.

Formulas

Effective price locked in by a futures hedge

effective price = F₁ + b₂

F₁
the futures price when the hedge is set up
b₂
the basis, spot minus futures, when the hedge is lifted

It is S₂ + (F₁ − F₂) per unit for a short hedge and a long hedge alike. Multiply by the quantity actually hedged, which differs from the exposure when a hedge ratio is used.

Profit on a short futures position

short futures profit = (F₁ − F₂) × contract size × N

F₁
the futures price at which the contracts were sold
F₂
the futures price at which they were bought back
contract size
the units in one contract
N
the number of contracts

A short gains when the futures price falls; a long position's profit is the negative. In a good hedge this result and the change in the exposure's value have opposite signs.

A practice question

From the question bank, with the reason each wrong option is wrong.

A food company hedges the purchase of 100,000 bushels of corn by buying futures at USD 6.00. When it buys the corn, spot is USD 6.45 and the futures price is USD 6.50. The net price paid per bushel after the futures P&L is:

  1. USD 6.45Why not: Ignores the hedge, giving the unhedged spot cost.
  2. USD 5.95 - correct
  3. USD 6.00Why not: Assumes a perfect hedge at the opening futures price and ignores the basis change.
  4. USD 6.95Why not: Adds the futures gain to the cost instead of subtracting it.

Futures gain = 6.50 - 6.00 = 0.50 per bushel. Net price = 6.45 - 0.50 = 5.95. (Equals F1 + b2 = 6.00 + (6.45 - 6.50).)

A harder one

A farmer short hedges 100,000 bushels of corn by selling futures at USD 5.60. At the sale date the spot price is USD 5.20 and the futures price is USD 5.35. Total net proceeds are closest to:

  1. USD 560,000Why not: Assumes a perfect hedge at the opening futures price, ignoring the basis change.
  2. USD 520,000Why not: Ignores the futures profit, giving the unhedged proceeds.
  3. USD 545,000 - correct
  4. USD 495,000Why not: Subtracts the futures gain from the spot proceeds instead of adding it.

Futures gain per bushel = 5.60 - 5.35 = 0.25. Net = (5.20 + 0.25) x 100,000 = 545,000.

The hardest tier

A manager holds 100,000 units of an asset (spot 50 now) and sells 120,000 units of futures at 51 using a hedge ratio of 1.2. Later spot is 46 and the futures price is 46.5. The net profit or loss on the combined position is:

  1. a gain of 140,000 - correct
  2. a gain of 50,000Why not: Applies the futures P&L to 100,000 units instead of the 120,000 actually sold.
  3. a loss of 140,000Why not: Sign error on the net result: the futures gain exceeds the spot loss.
  4. a gain of 540,000Why not: Counts only the futures gain and forgets the loss on the underlying asset.

Spot loss = 100,000 x (46 - 50) = -400,000. Futures gain = 120,000 x (51 - 46.5) = 540,000. Net = 140,000. A hedge ratio above 1 leaves the position net long the market's fall.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Using Futures for Hedging