Futures payoffs and hedging
◈ 8 cardsLinear both ways: the long gains (S_T − F) × size, the short gains (F − S_T) × size; the producer sells to lock a price, the consumer buys — and each gives up the favourable move.
Two lines through F
At expiry a futures position is worth the difference between the price it was struck at, , and the spot price then, , times the contract size:
Both are straight lines through zero at . The long line rises one-for-one with the spot; the short line falls one-for-one. There is no cap and no floor on either — a futures payoff is linear and symmetric, unlimited both ways. That is the difference from an option (Lesson 12.4), whose payoff bends at the strike.
The producer's hedge — Northshore sells
Northshore Timber will sell 110 mbf (thousand board feet) of lumber in three months. Lumber futures for that month trade at 520 per mbf. Northshore sells 110 mbf of futures — a short hedge, because it is short the futures against the physical it is long.
Suppose spot at expiry is 480. The futures gain is =(520-480)*110 = +$4,400. The physical lumber sells at 480 × 110 = 52,800. Add the futures gain: 57,200, which is =480+4400/110 = 520 per mbf — the price it locked in June. The fall was hedged.
Now suppose spot is 560. The futures lose =(520-560)*110 = −$4,400; the lumber sells at 560 × 110 = 61,600; net 57,200 — again 520 per mbf. The rise was hedged away too. A futures hedge does not remove the downside and keep the upside; it removes both. Northshore traded uncertainty for a known price, and the price of that certainty is the rally it will not enjoy.
The consumer's hedge — Halton buys
Halton Dairy will buy 5,000 bushels of feed grain in three months. It fears a rise, so it buys futures at 6.40 — a long hedge.
Spot at expiry 6.90: futures gain =(6.90-6.40)*5000 = +$2,500, which exactly offsets the extra 0.50 a bushel it now pays for the physical. Effective cost: 6.40.
Spot 6.10: futures lose =(6.10-6.40)*5000 = −$1,500. Feed is cheaper — but the hedge gives that saving back. Effective cost: still 6.40.
Which side hedges which risk
| You are… | Your risk is… | Hedge with… |
|---|---|---|
| a producer — will sell the underlying | a price fall | short futures |
| a consumer — will buy the underlying | a price rise | long futures |
The rule: take the futures position that gains when your physical position loses. A gold miner sells gold futures; a jeweller buys them. An exporter who will receive US dollars sells USD futures; an importer who must pay them buys.
Basis and the imperfect hedge
The examples assume the futures price converges exactly to spot at expiry and that the contract matches the physical in size, grade and date. In practice the basis (spot − futures) is not always zero, and a hedger in 110 mbf with contracts of 27.5 mbf each holds four contracts, not 4.0 exactly. Those are refinements; the paper marks the linear arithmetic.
Recompute
Northshore at a spot of 560: futures =(520-560)*110 = −4,400; effective price 520. Cold: producer → sells futures → short hedge; consumer → buys futures → long hedge.