Offset: How a Hedge Cancels Part of a Move Either Way

An offset is a change in one position being met by an opposite change in another. Because the contract is written on the very thing being held, the two move by the same rupee amount in opposite directions, so the pair sits still whichever way the price went. Three things stay outside it: the units not written against, the period beyond the contract, and the cash the contract calls for.

Two positions on the same thing, pointing opposite ways, add up to a number that does not move. The addition is the whole mechanism, and it is genuinely as simple as it sounds. Everything that follows is either the arithmetic of that addition or a careful list of the places where the addition stops working, and the second list is longer than most readers expect it to be.

One thing decides how the rest of the guide reads, and it is worth settling before the first figure. The word most people reach for here is protection, and protection suggests something that stops the bad and leaves the good alone: a helmet, an umbrella, a shock absorber under a bus seat. An offsetA change in one position being met by an opposite change in another, so that the two added together move by less than either of them would have moved alone. works with the same force in both directions and has no way of telling a good move from a bad one, so it is not shaped like any of those. Nothing in the arithmetic knows which way the holder was hoping the price would go. The contract simply moves against the holding, whichever way the holding moved, and it does so at the identical rate.

What is an offset, in plain terms?

An offset is a change in the value of one position being met by an opposite change in the value of another. The two taken together move by less than either would have moved on its own. The definition holds everywhere the word is used. The rest of this guide is about how much less, and about the corners of the arrangement where the word quietly stops applying.

Here is a version with no finance in it at all. A vendor on a street corner has bought a sack of onions this morning for a certain amount, and the sack is sitting behind the stall. Later that afternoon a caterer walks up and pays an advance for that same sack, at a price fixed there and then, for collection on Saturday. From that moment the vendor has two positions on one sack. If the wholesale price of onions collapses before Saturday, the sack behind the stall is worth less, and the fixed-price agreement with the caterer is worth more. The agreement commits somebody to pay the old price for something that has become cheap. The two changes are the same size and they point opposite ways.

Now run the same afternoon with the price going up instead. The upward direction is where the everyday version earns its keep. Onions become scarce, the wholesale price jumps, and the sack behind the stall is suddenly worth a great deal more than it cost. The sack has already been sold at Saturday's fixed price, so the vendor gets none of that, and the agreement that was worth having when the price fell is now standing between the vendor and the rise. Nobody has been cheated, nothing has gone wrong, and the arrangement is behaving exactly as it was written. The agreement removed the fall and removed the rise, in one motion, using the same clause.

One word in the title carries the weight, and it is there for a reason: an offset acts on the part of the exposure it was written against, in the direction it was written, and for as long as it runs. Every one of those three phrases is a boundary, and each of the three has a section further down. The vendor covered one sack, not the whole shed. The vendor covered it until Saturday, not until the end of the month. And the price the caterer agreed was a level fixed on the day. No later movement in the onion market reaches it at all.

Most of the trouble comes from the second half of the definition rather than the first, so say plainly what an offset is not. An offset is not a cushion that absorbs the bad moves and lets the good ones through, and no version of it behaves that way. A reader who takes only that sentence away has taken the useful half of the subject. An arrangement that stops falls and passes rises through does exist in this subject, but it is a different instrument with a different structure, it costs a premium paid up front, and it is settled elsewhere. The arrangement worked below costs no premium and gives no such asymmetry, and the two facts are the same fact seen from two sides.

Why does the cancellation work at all, and what is it resting on?

On one fact, and everything else here depends on it. The contract is written on the same reference assetThe invented item every figure in this guide runs on. It pays nothing at all while it is held, which is why the contract price is built from a price and a financing rate and nothing else. that is held. Not a similar one, not a related one, not one that usually moves with it. The same one. Sharing one asset is why a single price appears on both sides of the arithmetic, and why the two movements are equal rather than merely similar.

The case, set out in the words used for it throughout. A holder has bought one unit of that invented reference asset at a spot priceThe price for taking delivery of the thing today rather than on some later date. of Rs 2,000.00/-. The reference asset pays nothing at all while it is held, and that fact matters to the contract price further down. Against that unit the holder has written one unit of contract on the short positionThe side of a contract bound to sell at the agreed price on the later date, whatever the price happens to be by then., at a contract price of Rs 2,130.00/-. Financing costs 6.50 per cent a year, so that price is Rs 2,000.00/- plus Rs 2,000.00/- multiplied by 0.065.

Now watch what the shared price does. When somebody quotes the reference asset at Rs 1,920.00/- instead of Rs 2,000.00/-, that single quotation prices the unit on the shelf and measures the contract at the same time. One number, arriving once, doing two jobs at once in opposite directions. Only one thing is involved, so there is no second quotation anywhere, no second market, and nothing that has to be assumed about how two things move in relation to each other.

Without that fact the whole treatment stops being reliable. If the contract were written on something else, the two sides would move for different reasons: one price would arrive from one place and a second price from somewhere else, the distance between them would wander about on its own, and the neat equality below would become an approximation of unknown quality. None of the arithmetic here survives that change.

Here is the absence, said out loud before a reader can generalise from what follows. The case worked above contains one priced thing and no second one beside it, and no measure anywhere of two prices moving together. So the case most parties in the world actually face, where a party holds one thing and writes a contract on something adjacent, cannot be worked from these figures at all, and how close is close enough is a question they cannot reach.

What would have to be brought before that other case could be worked in figures? Three things, and none of them is here. Two separately priced things, both of them real enough to be quoted. Both prices over the same period, on every date that matters to the holder. And some tested account of what moves the distance between them, produced from records somebody can check rather than from an assumption that they generally move together. A worked example built without those three is fiction dressed as arithmetic. A cross positionA contract written on something other than the thing actually held, used when no contract exists on the thing itself. is named here and is worked out in full elsewhere.

With that settled, the arithmetic below is safe to read, so long as the case being read is understood to be the tidiest case there is rather than the ordinary one. The tidy case is worth working precisely because it is tidy: seeing exactly what a complete cancellation looks like gives something to measure an incomplete one against.

What does the cancellation look like when the price falls, and when it rises?

The cancellation is exact at one moment and not at every moment, so state the moment before touching a single figure. Every change in the table below is taken on the final date, where the contract price and the spot price are prices for the same transaction on the same day and are therefore the same price. Naming the day is not a technicality parked in a footnote. The final date is the reason the two columns match to the rupee, and a flat line shown without naming the day would teach an equality that holds on exactly one date out of the whole life of the contract.

One glossed sentence covers what is different before that date, and the full treatment sits elsewhere. Earlier in the life of the contract the price being quoted for that later date still carries the financing left to run, so it does not move by the same rupee amount as the price today: a fall from Rs 2,000.00/- to Rs 1,920.00/- with a full year still to go moves the quoted contract price from Rs 2,130.00/- to Rs 2,044.80/-. A contract move of Rs 85.20/- against a spot move of Rs 80.00/- leaves Rs 5.20/- standing. The cancellation is over-complete before the end and exact only at it. How that distance behaves over the life of a contract, and what it leaves behind on an early close, is covered separately.

Now the arithmetic itself, worked in change in valueWhat a holding is worth now set against what it was worth before. It is not money until something is sold or somebody pays. rather than in settlement figures. An offset acts on changes. One unit of the reference asset is held, bought at the spot price of Rs 2,000.00/-. One unit of contract is written against it on the short side. Take a 4.0 per cent move in the price of the reference asset. On a base of Rs 2,000.00/- that move is Rs 80.00/- of price.

Downwards, from Rs 2,000.00/- to Rs 1,920.00/-: the unit held changes by minus Rs 80.00/-, the contract position changes by plus Rs 80.00/-, and the pair changes by Rs 0.00/-. Nothing surprising there, and this is the direction everybody remembers. A party bound to sell at Rs 2,130.00/- is better off when the thing being sold is cheaper, so the unit on the shelf lost Rs 80.00/- of value and the short position gained the same Rs 80.00/-.

Upwards, from Rs 2,000.00/- to Rs 2,080.00/-: the unit held changes by plus Rs 80.00/-, the contract position changes by minus Rs 80.00/-, and the pair changes by Rs 0.00/- again. The upward line is the one worth sitting with, and it is the line that gets skipped. The holder is in the same place whichever way the price went, and being in the same place is exactly what was arranged. Nobody was tricked. The Rs 80.00/- that did not arrive as a loss on the way down is the same Rs 80.00/- that did not arrive as a gain on the way up, and it left by the same door. The Rs 80.00/- forgone on the way up is what was handed over in order to be rid of the loss on the way down.

Every figure in that table is a change in value. Not one of them is a payoff, a premium or a profit, and the difference is not pedantry. A payoff is what an obligation delivers when it is settled. A premium is an amount paid to somebody for taking an obligation on. A forward-style contract is entered at a price rather than bought for a fee, so nothing whatever is paid. A profit is what is left after every cost of carrying a position is counted, and a change in value counts none of them. The table holds three readings of how two positions moved against each other, taken on one day.

A picture of a movement and a picture of a pair of numbers teach slightly different things, so look at the same three readings a second way, set out as two panels rather than as three lines. The lines above show that the symmetry holds everywhere across the range. The panels below show that the individual figures are literally the same figures, sitting in mirrored places.

One more reading of the table, and then the control below takes any size of move. The bottom row is the one to read. The unit held travelled Rs 160.00/- across the three readings, from minus Rs 80.00/- to plus Rs 80.00/-. The short contract travelled the same Rs 160.00/-, in the other order. The pair travelled nothing at all, at any point in between and at both ends. The last cell is the offset, and a cell with nothing in it is the most expensive cell in the table.

Which parts of the exposure does an offset never touch?

Three of them, and each is outside the cancellation for a different reason. The first is a matter of size, the second is a matter of dates, and the third is not a movement at all, so there is nothing there for a cancellation of movements to act on. The third one surprises people who have understood the first two perfectly. Take them in that order.

The first: the part it was not written against

Cancellation happens on the units the contract stands against and nowhere else, so a holding larger than the position written against it keeps its original exposure on the difference. If twenty units are held and fifteen units of contract are written, then fifteen units are covered and five are exactly where they were before anybody wrote anything. The five uncovered units did not become less exposed because their neighbours became covered. Nothing about the act of writing a contract reaches them.

The uncovered remainder is arithmetic rather than a defect, and the distinction is worth insisting on. Nothing leaked, nobody did it badly, and no better contract would have covered the lot. The covered unitsThe part of a holding that a contract has actually been written against. The rest of the holding is untouched by it. are the covered units and the remainder is the remainder, and any reader who has ever bought insurance for two of their three scooters already understands the shape of this perfectly. How a holding is divided between the two parts, what governs the split, and what the remainder costs are covered separately and are not reworked here.

The second: the period outside the contract

Cancellation runs for as long as both sides are in place and not one day longer. There are two ways for that to end and both of them are ordinary. If the holding is still there after the contract ends, the exposure comes back in its original form on that day, in full, with nothing carried over from the period that has just finished. If the holding goes before the contract ends, the contract carries on alone, still open, still moving in one direction, with nothing behind it any more.

Neither case is unusual, and it is worth understanding why not. The dates a contract runs to are not chosen by the holder. The dates are set by the exchange under the framework administered by the Securities and Exchange Board of India (SEBI) at sebi.gov.in, they exist because a market needs everybody trading the same dates, and they will not have been arranged to suit the month in which one particular holder stops needing to hold one particular thing. So a mismatch is the normal condition rather than the exception, and the only question is which way it runs. The figures the mismatch leaves behind are covered separately.

The third: the carry that was already in the price

One glossed sentence, and then the subject passes to the treatment that does it properly. The contract was written at Rs 2,130.00/- rather than at Rs 2,000.00/-. Money costs 6.50 per cent a year and the reference asset pays nothing at all while it is held, so the gap of Rs 130.00/- is the financing inside the price, produced by multiplying Rs 2,000.00/- by 0.065. That carryThe financing sitting inside a contract price for a later date. It is a fact about how the price is built, not a payment anybody makes or receives. is a fact about how a contract price for a later date is constructed. The carry is not something the offset produced, not something the offset can remove, and emphatically not a profit created by covering anything. The Rs 130.00/- of carry, what it is not, and why nobody banks it are covered separately and in full.

Only one thing about it matters here: the offset cancels movements, and the level the contract was struck at is not a movement. Move the price a rupee and the cancellation acts on that rupee. The Rs 130.00/- was there before any price moved and would still be there if the price never moved again, so a mechanism that works on changes has nothing at all to grip. The third item on the list feels different from the first two for that reason. The first two are parts of the exposure that the offset did not get to. The third is not part of the exposure at all.

If the two sides are equal in amount, why does the holder still need cash?

The cash question matters more than the cancellation above it. Everything so far has shown two amounts that match. The two sides below match in amount and not in kind, and the difference is settled in a bank account on a specific afternoon.

Take the day the price rises by Rs 80.00/-, from Rs 2,000.00/- to Rs 2,080.00/-, and look at the two sides one at a time rather than as a pair.

On the holding: the unit is worth Rs 80.00/- more, and that figure lives in a valuation. The Rs 80.00/- cannot be spent and cannot be sent anywhere. The figure does not pay a bill, settle a demand or reach anybody, and it does nothing at all for anybody until the unit is sold to somebody who hands over money for it. The gain is unrealisedA change in value that has not been turned into money. It exists on a statement and nowhere else until something is sold., a plain description rather than a criticism and true of every holding anybody has ever had.

On the contract: the position is Rs 80.00/- worse, and that figure is money. A short position is markedRevalued at the current price with the difference settled, so that the amount a position has moved becomes a real credit or a real demand rather than an opinion. against the party carrying it when the referenced price goes up, and once that has happened the difference stops being a view about anything and becomes a demand. Cash is called for, out of an actual bank account, on the day, by the clearing member the party deals through. There is no clause anywhere allowing that demand to be answered with a valuation, however impressive the valuation looks.

A rupee figure on its own says nothing about whether it hurts, so the day is worth pricing against what was actually put down. Carrying that one unit of contract needs an initial margin. The figure used is 8.0 per cent of the Rs 2,000.00/- of exposure, or Rs 160.00/- on one unit. That 8.0 per cent is a teaching figure, not a requirement anybody has published. Real margin is set by clearing corporations under SEBI's framework at sebi.gov.in, it varies by contract and by day, and it moves.

Against that Rs 160.00/-, the Rs 80.00/- called for today is 50.0 per cent of what was put down. Half the margin posted, gone in a single day, on a day when the holding is worth more than it was yesterday and every screen the holder looks at is green. Half the margin is the ratio the holder actually feels, and notice that it is struck on a different base from the 4.0 per cent. The 4.0 per cent is struck on the Rs 2,000.00/- of exposure and gives Rs 80.00/- of price. The 50.0 per cent is struck on the Rs 160.00/- of margin posted. Two percentages, two bases, and reading one as the other is how a small move gets filed as a small problem.

The sentence that names the whole cost is this: one side is a number and the other side is money, so the two sides are equal in amount and the holder still has to find cash. Nothing is wrong with the arrangement. The arithmetic did what it said it would do. The arithmetic never claimed to turn one of its two limbs into something spendable on the afternoon the other limb comes due.

And here is the sharpest version, for anybody whose money is inside the holding rather than beside it. On the day the margin callA demand for more cash, made when a position has been revalued and has moved against the party carrying it. arrives, the only asset that went up is the one thing that cannot be sold without ending the arrangement. Every other asset the holder has is exactly where it was. The one that improved is the one that is spoken for.

What does an offset not say about how well anything worked?

Nothing whatever, and this section exists because by now a reader is looking at a flat line and quietly converting it into a verdict. How much of a real move gets caught in practice is a measured quantity, and measuring it takes a record of both sides across a period rather than an identity struck at one moment.

Look at why the cancellation came out complete. The two reasons are both features of the setup rather than findings about anything. The contract references the very thing that is held, a condition imposed on the example rather than a discovery about the world. And every figure is worked at a single named moment, the final date, where the contract price and the spot price are the same price. Change either of those two and the arithmetic changes. Neither of them is evidence.

Say the absence plainly. Reporting how much of any movement was met takes a run of prices, a record of what happened on each day, and a measure of two sides moving together. An equality struck on a single date supplies none of the three. A score built by inventing that evidence is not a measurement at all, and an invented score is more dangerous than an honest gap.

What would a reader have to bring? Three things again. A stated period with a start and an end. Both sides' movements inside that period, the holding and the contract, day by day or at whatever interval the party actually uses. And the fact that both were recorded at the time rather than reconstructed afterwards from what would have been convenient. Given those three, a measure of how well two sides moved together becomes computable, and what that measure means and where it misleads is covered separately.

What would have to be true before any of this held on something real?

Six things, and every one of them is checkable in an afternoon by somebody with the records in front of them, so read them as a list of conditions rather than as a warning.

1. A contract exists on the thing itselfNot on something adjacent, not on an index that includes it, not on something that has historically moved with it. On the thing. Without this the arithmetic here is not an approximation of the truth; it is a different question.
2. The number of units written against is known and written downBecause the cancellation reaches exactly that many units and no more, and the remainder is exposed exactly as it was before. How the split is arrived at is covered separately.
3. The moment of the reading is namedOn the final date the two sides match to the rupee. Before it they do not. The contract price still carries the financing left to run. A figure quoted without its moment is a figure that might be right on one day out of hundreds.
4. The cash for a bad day is identified and sized in advanceFrom a source that is not the holding. The holding is the one asset that cannot be sold without ending the arrangement. Rs 80.00/- against Rs 160.00/- on one unit is the shape of what has to be fundable.
5. The dates on both sides are set against each otherThe contract ends when the exchange says it ends. The holding ends when the holder no longer needs it. Where those two differ, there is a stretch with one side in place and the other gone.
6. The rules that carry a value are looked up rather than recalledContract size, margin and the method behind it, the further margin called during a day, settlement by delivery or in cash, and the conditions for treating a position as a hedge are all set by SEBI at sebi.gov.in and all of them move.

Notice what is not on that list, and notice it deliberately. Whether the arrangement is worth making is not there. How it turned out for somebody else is not there. Whether the price is more likely to rise than fall is not there, and could not be. The contract price of Rs 2,130.00/- is arithmetic on a financing rate rather than a view about anything. Whether to arrange an offset is not a question these figures answer. The figures settle exactly how the arrangement behaves in both directions and what it leaves untouched.

The reference asset, the holder, the vendor and the caterer are invented.
Educational material. Not advice on any investment, tax, budget or market position.