Forward and Futures Position: Working Out the Payoff

This calculator works out what a forward or a futures position pays at a chosen settlement price. Given the side, the agreed price, the lot size, the lots held and a day by day path to the final date, it returns the payoff, the exposure, the margin posted and the cash moved at each close. The calculator prices no contract and ranks no settlement price.

Underneath all of that sits a very small sum. A position in either contract compares two numbers, the price agreed when it opened and the price on the day it falls due, and multiplies the difference by the units it stands on. Settling up day by day does not add to that: it breaks the same difference into instalments. The rest of this guide is about knowing which two numbers a position holds, where each came from, and what the answer may be called.

What does this tool work out, and where does it stop?

A reader who does not know where a tool stops will keep using it past that point and will not notice, so the edges come first. The calculator produces a payoff at settlement, on either side, at whatever settlement price is tested, together with the path the money takes to get there on a cleared position.

Three things it does not work out, and none of the three is an oversight. The calculator does not price a contract: deciding what Rs 2,130.00/- should be in the first place is built out of the price for delivery now and the cost of financing, and is handled on its own. Nor does it say which side to be on. Choosing a side turns on the purpose the position serves and on what else is already carried, and neither is a fact about the instrument. And it puts no weight on any settlement price: the control moves anywhere between Rs 1,600.00/- and Rs 2,400.00/-, and the calculator returns what the obligation produces there and nothing about which of them turns up.

The last of the three edges is the one a working tool quietly erodes. A control that sweeps a range invites the feeling that the middle is the ordinary case and the ends unusual. An invented reference asset has no history to lean on and no central case to point at.

Where does each of these numbers come from?

Four numbers describe the position itself, and they are not four decisions. Only one of them is a choice. People arrive expecting a calculator where every box is an opinion, and it is not one. Each note beside a field says where the number is found and stops there.

SIDE. The side is read off the position already held. If the position binds the holder to buy the reference asset on the due date, that is the long side; if it binds the holder to sell, that is the short side. Whichever side was taken when the price was agreed remains the side held until the position closes or falls due.

AGREED PRICE. The price fixed on the day the position opened, Rs 2,130.00/- in the worked default. Its most important property is that it does not move. Positions struck tomorrow will be struck at whatever tomorrow says, and none of that reaches back into a position already opened. A wedding caterer who fixed a rate for December in July does not get a different rate in December because July has been forgotten.

SETTLEMENT PRICE. The price of the reference asset on the day the obligation falls due. Nobody has this number until that day, and the control exists for that reason. The number typed or dragged in is a test pointA price fed in on purpose to see what the obligation produces there, chosen for the check rather than because it is expected., a price tried out to see what the obligation produces there. The settlement price is the one field that is genuinely a choice, and the four day closes above it are that same field asked five days running.

UNITS. The lot size times the number of lots gives the count of reference asset units under the position. On a bilateralAgreed directly between two parties and nobody else, with terms written to suit them rather than taken off a standard sheet. agreement the two sides write the quantity in themselves. On a cleared contract, where a clearing corporationThe body that steps into the middle of a cleared trade, so each side faces it rather than the other side. stands in the middle, the lot size is the contract sizeThe number of units one contract stands on, fixed by the exchange rather than by the two parties. read off the exchange specification under SEBI at sebi.gov.in. The 40 the field opens on is a placeholder so that a worked example runs. A real contract size is set by the exchange and changes, so it has to be read there on the day it is needed.

The margin per cent is not a fifth number of that kind. The margin per cent is an assumption, entered so the posting and the daily cash have something to be struck on, and the 8.0 per cent the field opens on is a placeholder. Real requirements, and the dates on which they change, are set by clearing corporations under SEBI.

How is the payoff on a long position worked out?

The side bound to buy takes the settlement price, subtracts the agreed price, and multiplies what is left by the number of units. Nothing else goes in. No financing, no fee, no adjustment for how long the position was held.

Work it at the default the calculator opens on. The agreed price is Rs 2,130.00/-, the settlement price being tested is Rs 2,400.00/-, and the position stands on one lot of forty units. Rs 2,400.00/- less Rs 2,130.00/- leaves Rs 270.00/- on each unit, and forty of those is Rs 10,800.00/-. The price on the due date came in above the agreed price by exactly Rs 270.00/- a unit, so the long side collects Rs 10,800.00/- at a settlement of Rs 2,400.00/-. The lines below are drawn a unit at a time.

Now push the settlement price the other way, where readers get uneasy and the arithmetic is at its most honest. Suppose settlement lands at Rs 1,600.00/-. Rs 1,600.00/- less Rs 2,130.00/- is a negative Rs 530.00/- a unit, or Rs 21,200.00/- handed over across forty. A negative payoff is a real answer and not an error state: the side bound to buy is bound at Rs 2,130.00/- whatever the day produces, and buying there when the open market is at Rs 1,600.00/- costs Rs 530.00/- a unit more. A settlement price below the agreed price gives a negative payoff, and the position performs exactly as written when it does.

A forward payoff has no floor. Nobody walks away, nobody declines, nobody exercises a choice. Neither party has an exit written into the arrangement, so the line runs straight through nil and out the other side without changing its slope.

How is the payoff on a short position worked out?

Turn the subtraction around. The side bound to sell takes the agreed price, subtracts the settlement price, and multiplies by the units. Same two numbers, same multiplication, opposite order.

At the same default, Rs 2,130.00/- less Rs 2,400.00/- gives a negative Rs 270.00/- a unit, so the short side hands over Rs 10,800.00/- across forty units. The long collected and the short handed over the very same amount, on the same agreement and the same day. The two sides are mirrors at every settlement price without exception, and the pair adds to nothing every time.

The mirror is why the tool works both sides whichever one is selected. In front of a single rising line it is easy to forget that a second party is bound to the opposite of everything shown. What one side hands over is what the other collects.

The four test points, worked out and printed

The table below covers the whole range this guide uses, worked at one unit, so the arithmetic survives even if every control were stripped away. The last column is nil on every row. The mirror is stated there as a number rather than as a picture.

The second row is the one to sit with. Settlement at Rs 2,000.00/- means the reference asset went nowhere across the whole year, and the long position still produces minus Rs 130.00/- a unit, or Rs 5,200.00/- handed over across forty. Standing perfectly still is not a break-even outcome for the side bound to buy at Rs 2,130.00/-, and what it costs is the carryThe cost of holding something from today through to a later date, mostly the interest on money tied up in it. built into the agreed price.

Does the daily settlement change what the position produces?

No, and the calculator shows it on screen rather than leaving it to be taken on trust. A forward makes one payment, on the final day, for the whole difference between the agreed price and the settlement price. A cleared position pays and collects that same difference in instalments under daily settlementSettling up for each day's movement as it happens, in daily instalments rather than one lump at the end., one for every day the price moves, and they add to the single payment exactly.

Read the day column in the build-up above. On the worked default the reference asset closes at Rs 2,050.00/-, Rs 2,010.00/-, Rs 2,180.00/-, Rs 2,260.00/- and finally Rs 2,400.00/-. Against the agreed price of Rs 2,130.00/-, that is a fall of Rs 80.00/- a unit, a further Rs 40.00/-, then rises of Rs 170.00/-, Rs 80.00/- and Rs 140.00/-. Across forty units the long side hands over Rs 3,200.00/- and Rs 1,600.00/-, then collects Rs 6,800.00/-, Rs 3,200.00/- and Rs 5,600.00/-. The five add to Rs 10,800.00/- collected, exactly what the forward pays once on the last day.

The difference is in when the money moves and what has to be sitting there while it does. Rs 6,400.00/- is posted before the cleared position may be carried. The first two days go against the long side, so by the close of the second day the running balance has fallen to Rs 1,600.00/-. A forward on the same terms would have called for nothing on either day. The path changes the timing and the cash that has to be available, and leaves the total exactly where it was. Rs 6,400.00/- posted and Rs 10,800.00/- collected leaves Rs 17,200.00/- in the account at the end, the second reconciliation the calculator prints on screen. How a top-up is worked out, and what happens if it is not met, are covered under margin and daily settlement.

Is the number a payoff or a profit, and when do the two split apart?

Four words do all the work in this guide and cannot be swapped for one another. A PAYOFF is whatever the obligation throws off on the day it falls due, counted before anything spent on getting into it; a PROFIT is that figure once everything spent on getting into it has been taken off; a PREMIUM is money handed over in exchange for taking on a position; and a PRICE is a number two sides agree or a market quotes. So Rs 2,000.00/- and Rs 2,130.00/- are prices, and Rs 10,800.00/- is a payoff. Whether it is also a profit turns on the third word.

Neither a forward nor a futures position is bought for a premium. Two sides agree a price and both are bound; nobody has paid anybody for the privilege. Margin is not a premium either. Margin is posted as security and comes back. Because no premium is paid to enter either contract, the payoff and the profit are the same number here, and that coincidence is a trap rather than a simplification.

Here is why it is a trap. There is an instrument, covered separately, that is acquired for a premium. On it the payoff and the profit are two figures separated by exactly the amount paid at the start, and a reader who used the two words interchangeably here will carry the habit across and overstate every result by the premium. So the tool labels its output PAYOFF.

There is a household version that makes the distinction obvious. Two people each end a month with Rs 5,000.00/- more in hand. The first was handed Rs 5,000.00/-. The second was handed Rs 6,000.00/- but paid Rs 1,000.00/- for the ticket that let them collect it. The payoff of each is the same. The profit of each is not.

Is one unit on screen Rs 2,130.00/- or Rs 2,000.00/-?

Both, and the two are not the same reading of the same thing. Notional against exposure is the second labelling habit, and it catches more readers than the first. A quantity on a derivative position has two respectable sizes, they answer different questions, and using one where the other belongs misdescribes the position by a wide margin.

One unit at the agreed price of Rs 2,130.00/- is Rs 2,130.00/- of NOTIONAL, and none of it has changed hands anywhere. Nobody has paid it, nobody has received it, nobody is holding it in an account. The notional is the amount written on the face of the agreement, and its job is to say how large the obligation is. An obligation is not a balance.

The same single unit measured against the price for delivery now of Rs 2,000.00/- is Rs 2,000.00/- of EXPOSURE, and that is the figure a margin requirement gets struck on. Exposure answers a different question: how much of the referenced thing is being stood on. A move in the reference asset then gives the move in the position.

The two differ by Rs 130.00/-, and that gap is not a rounding. The gap is the carry sitting inside the agreed price, so the notional sits above the exposure rather than beside it. Nothing reaches whoever holds the reference asset during the year, so the carry is the whole of the difference.

Scale it up and the discipline earns its keep. Forty units at the agreed price carry Rs 85,200.00/- of notional. The exposure those same forty stand on is Rs 80,000.00/-. Report the first without saying which it is and a reader believes Rs 85,200.00/- has moved or is at stake, and neither is true. The payoff meanwhile scales plainly: Rs 270.00/- a unit becomes Rs 10,800.00/- collected across forty, and Rs 530.00/- a unit handed over becomes Rs 21,200.00/-. The line does not change shape; only the numbers along its side do.

One last use of exposure. A cleared position has to post something before it can be carried, and it is struck on the exposure rather than the notional. Take an initial marginMoney put up before a position may be carried, held as security against it moving the wrong way. of 8.0 per cent, a placeholder for the arithmetic: 8.0 per cent of Rs 2,000.00/- is Rs 160.00/- a unit, so forty units call for Rs 6,400.00/-. Set that Rs 2,000.00/- of exposure against the Rs 160.00/- put up and the leverageHow much value a position sits on compared with the money put up to carry it, as a multiple. is 12.50 times, so a four per cent move against the position is Rs 80.00/- a unit, or Rs 3,200.00/- across forty, and that is 50.0 per cent of everything posted. A four per cent move takes half of what was put down, and that ratio, rather than the exposure or the notional, is what makes these positions different to hold. Day one of the worked default is exactly that move, so the margin account drops from Rs 6,400.00/- to Rs 3,200.00/- before anything has gone wrong.

What does moving the settlement price control not mean?

As the control moves, the line stays exactly where it is while a marker travels along it. The honest reading is narrow: the marker visits points on a description of an obligation, one at a time. Sweeping the settlement price from Rs 1,600.00/- to Rs 2,400.00/- shows what the position produces at each of those prices and says nothing about which of them arrives.

The range runs from Rs 1,600.00/- to Rs 2,400.00/- because those are round numbers on either side of the agreed price, and for no other reason. If it ran from Rs 1,000.00/- to Rs 3,000.00/- the line would be the same line, and the middle would have moved.

The most tempting reading is the crossing point at Rs 2,130.00/-, where it is natural to conclude that the line touches nil because somebody formed a view. The block below is about exactly that.

Who actually reaches for a payoff line, and what do they do with it?

Rather than four job titles, walk the four fields again: each is filled in from a different place, often by a different pair of hands, and most errors happen at the joins rather than in the arithmetic.

The side field is where a records problem becomes an arithmetic problem. Somebody keeping a book of positions has to know which way round each one is, and two positions on the same reference asset held in different places are easy to net wrongly. The everyday version: a household that has agreed to buy sixty kilos of rice next month at a fixed rate and separately agreed to supply forty kilos is not holding a hundred kilos of anything. The household is holding twenty kilos one way round. The tool computes whichever side it is given, so the button that turns the position round is worth pressing.

The agreed price field is where somebody checking a statement does their real work. If a statement says a position produced a certain amount, the check is to reproduce it: take the agreed price off the position record, the settlement price off the reference asset for the due date, subtract, multiply by the units, and see whether the same number comes back. When it does not, the disagreement is almost never in the subtraction. The disagreement is in somebody having used a newer agreed price, a different day, or a different unit count.

The settlement price field is where the honest description of the check lives. Somebody sizing what a position could produce runs it at several settlement prices precisely because none is a prediction. The street vendor who has agreed a price for next month's onions already knows what a collapse in the onion price will cost, and knowing it is not the same as expecting it.

And the units field is where the labelling discipline pays for itself in front of somebody else. Say Rs 85,200.00/- with no label and the listener hears money at stake. Say Rs 85,200.00/- of notional, none of it moved, standing on Rs 80,000.00/- of exposure, and the listener knows both the size of the obligation and what a move does to the position. The number that decides how a position is understood from outside is almost never the payoff; it is the label attached to the quantity.

Which parts of this are set by an authority in India?

The arithmetic above is jurisdiction free: subtracting one price from another and multiplying by a count works identically everywhere. Where several of the fields get their contents is not jurisdiction free, and the split is worth drawing out as rows.

Which side to be on, and why the arithmetic cannot say

Once the arithmetic is working, one question arrives on its own, and it is reasonable: which side to be on. The arithmetic cannot get anywhere near it.

Answering it would need the purpose the position is being put on for, and whatever is already sitting on the other side of it: a position that looks alarming alone can be the quiet half of something already held. Then what has been posted against it, and what happens on the morning the money has to move. None of those is a fact about an instrument. Each is a fact about one particular arrangement, and cannot be read off a general account.

There is a second reason, and it is more absolute. Judging whether a position turned out well needs a record of how things actually landed, and a set of teaching figures has no such record behind it. The reference asset, its price for delivery now of Rs 2,000.00/-, its financing of 6.50 per cent a year, the agreed price built out of the two and the five closing prices were all chosen so that an arithmetic could be taught.

A tool that works out a payoff is not a tool that recommends one, and the whole of what this calculator will and will not do sits in the distance between those two statements. Nothing above describes either side as attractive or as safe. The payoff is one line reflected, so there is nothing to rank the two on. Understanding how the arithmetic works is not a reason to enter anything.