Where you are. Last lesson named the module’s two halves. This one builds the simplest amplifier there is, and it is older than every institution in this course: an agreement today about a price tomorrow.
A price agreed in March for a harvest in September
A farmer will have wheat in September and no idea what it will fetch. A miller will need wheat in September and the same ignorance. Both can plan a business around a known price and neither can plan around a guess.
So they agree in March: in September, this much wheat at this price. Both are now certain, and both have given something up. If the price soars the farmer sells below the market anyway; if it collapses the miller pays above it. Neither is speculating. Both are buying certainty with the possibility of regret.
That agreement is the whole instrument, and every futures market in the world is a machine for making it between strangers.
The idea in one paragraph
A future obliges both parties to trade a specified thing at a specified price on a specified date. Because the obligation is unconditional, the payoff is linear: for every unit the settlement price sits above the agreed price, the buyer gains and the seller loses exactly that amount, and below it the reverse. Nothing about the instrument is complicated, and two things about it are important. It is zero sum: the two sides’ payoffs always cancel, so a futures market creates no wealth and only moves it. And it tracks the underlying without anybody holding it, which is why a small deposit can control a large exposure - the amplifier from lesson 1, in its plainest form.
Both sides, computed
The exercise computes the two payoffs across a grid of settlement prices, alongside the payoff of simply owning the asset from the same starting price.
Three things fall out, and the assertions check all three. The two sides always sum to zero. The long side’s payoff is identical to owning the asset - the same gains, the same losses - and the long never touched the asset. And the relationship is a straight line in the settlement price, with no kinks and no caps, which is precisely what the next lesson’s options will not have.
The same promise, two venues
A forward is that agreement made privately between two parties: the farmer and the miller, or two banks. It is bespoke, so it can be for an odd quantity on an odd date, and it is nobody else’s business.
A future is the same economics standardised and moved onto an exchange: fixed contract sizes, fixed dates, and - the part that matters for this module - a clearing house standing between the two sides, collecting margin from both.
Why anybody with no view trades one
The farmer and the miller both wanted certainty. A speculator wants the opposite: exposure to the move, with no interest in wheat at all.
Both are necessary. Hedgers arrive with lopsided needs - all the farmers want to sell September wheat, all at once - and without somebody willing to take the other side, the price they get would be terrible. The speculator is paid, in expectation, for absorbing that imbalance, which is lesson 12 of module 4 wearing different clothes: the person standing in the middle is compensated for the risk of being there.
Check yourself
1. The farmer sells wheat forward at 200 and the price is 260 in September. Did the farmer lose 60?
Not in any sense that matters to the business. The farmer receives 200 as agreed, which is the number the whole year was planned around, and forgoes 60 of upside that was never counted on. What was bought in March was certainty, and certainty has a price whichever way the market moves - which is why hedging is judged against the plan, not against hindsight.
2. A long futures position and owning the asset have identical payoffs. What differs?
The capital. Owning the asset means paying for it and holding it; the future gives the same exposure for a margin deposit that is a fraction of the value. It also has an expiry date and no ownership rights along the way. Identical payoff, entirely different funding - which is the amplifier.
3. A forward and a future have the same payoff diagram. Why does anybody prefer the exchange-traded one?
Because of who they depend on. A forward leaves you exposed to your counterparty’s solvency until the settlement date. A future puts a clearing house in the middle, which collects margin from both sides daily so no large unpaid loss can accumulate. The economics are identical; the counterparty risk is not.
4. Futures are zero sum. Why is a futures market nevertheless useful rather than a casino?
Because moving risk is valuable even when it creates no wealth. The farmer and the miller both end up with something they wanted - a known price - and the speculator is paid for absorbing the imbalance between them. Zero sum in money does not mean zero sum in usefulness.
Do this
Compute both sides across a grid and check the symmetry.
python3 code/futures_payoff.pyThe starter leaves you payoffs, returning the long’s profit, the short’s, and the payoff of simply holding the asset. The assertions check that the two sides always cancel, that the long tracks the holder exactly, and that a thirty-point move produces a thirty-point payoff in each direction. Success prints the grid and the line:
a future is a promise about a price: symmetric, zero sum, and it tracks the asset without anybody holding itThe completed version is in solutions/futures_payoff.py.
What you can now do. You can compute both sides of a future, explain why the private and exchange-traded versions differ in risk rather than economics, and say what a hedger buys. The payoff is a straight line and the exposure is large. The next lesson puts a small deposit behind it and asks what that multiplies.