The Hedge: Reducing an Exposure That Already Exists

A hedge is a contract written against an exposure a holder already has. A move in the price of the thing held is met by an opposite move in the contract. A hedge does not remove the risk, it exchanges one exposure for another: the gain goes with the loss, an obligation arrives, margin has to be funded, and the gap between the two sides stays with the holder.

Somebody holds a thing, or has agreed to buy one, or has agreed to sell one, and the price of that thing will not sit still until the day it matters to them. The exposure is there before anybody has said the word contract, and it will still be there afterwards in a different shape. Everything below is the arithmetic of that reshaping and the plain list of what the reshaping costs.

What has to exist before there can be a hedge at all?

Start with the part almost every explanation skips. The first thing needed is not the contract but the exposureThe part of what somebody holds or owes whose value moves with a price they do not control.. Something is already at risk, sitting on a shelf or on a book or in a crate, and only after that is anything written against it. Reverse the order and the word stops applying: a position entered first, with a reason attached to it afterwards, is a position taken on its own whatever the ticket says. Most of the trouble in this subject starts exactly there, and it starts quietly. Nothing on a screen distinguishes the two.

Four things have to be nameable before the word means anything. The thing itself. How much of it there is. Which direction hurts. And when it stops mattering. Miss any one of them and there is nothing to write a contract against. A contract has a size, a side and a date, and every one of those has to be answering something.

Here is the everyday version, and it is worth running beside the finance one the whole way down. A snack stall outside one office building has bought its stock for the season. From the moment the stock is in the crate, the stall is exposed to the price of that stock falling, whether or not anybody at the stall has ever heard of a contract. The exposure was created by the purchase, not by any later decision about covering it. Any sensible conversation about covering it starts by writing down what is in the crate, how much of it, the direction that hurts, and by when it has to be gone.

The finance version runs on one invented thing, called the reference assetThe invented item these worked figures run on. It pays nothing at all while it is held, which is why every figure below is built from a price and a financing rate and nothing else. throughout. A holder has bought one unit of it at a spot priceThe price for taking delivery of the thing now, today, rather than on some later date. of Rs 2,000.00/-. The reference asset pays nothing at all while it is held. The absence of any income matters more than it looks, and it comes back below. So the exposure is one unit, its size is Rs 2,000.00/- because one unit at Rs 2,000.00/- is what the holder put out, a fall in the price is the direction that hurts, and it stops mattering on the day the holder no longer needs to be holding it. The price of one unit and the size of the exposure are the same number here for that reason alone, and not because one was copied from the other.

What does a holder actually have once the contract is written?

An exchange is the accurate word for it, and the exchange has three rows. Row one, before the contract: one unit of the reference asset, bought at Rs 2,000.00/-, whose value moves with a price nobody at the stall controls. Row two, after it: that same unit, plus a contract on the same reference asset written on the short positionThe side of a contract that is bound to sell at the agreed price on the later date, whatever the price happens to be by then.. The two now move against each other. Row three, what arrived with the contract: an obligation, a margin balance to fund, and a gap between the two sides.

The risk has not been removed, it has been swapped.

An exchange rather than a removal is the whole of the subject, and it is worth sitting with. The holder started with one thing to watch and finished with four. The exposure that used to be there is now met by something, and being met is the whole purpose of the arrangement. The three that arrived are new, and none of them was there on the morning before. The swap may be exactly what the holder wants. Whether it is cannot be settled from these figures, and the closing section says plainly why not.

How is the contract written against the holding, and at what price?

The holder writes one unit of the contract on the short side. The short side binds the holder to sell one unit of the reference asset on the later date at a price agreed today. The contract price is not chosen and not negotiated down. Arithmetic produces it. Financing costs 6.50 per cent a year, and the reference asset pays nothing at all while it is held, so there is nothing coming in to set against the cost of carrying it. Take the spot price of Rs 2,000.00/-, multiply it by 0.065 to get Rs 130.00/-, and add that to the Rs 2,000.00/-. The contract priceThe price agreed today for a transaction that happens on a later date. It is settled at the moment the contract is written and does not move afterwards, whatever the price of the thing does. for one year out is Rs 2,130.00/-, and the Rs 130.00/- sitting inside it is the carry.

Both of those are prices, and neither is a premium. Nothing whatever is paid to open this position. The difference between a price and a premium does real work further down. A premium is money handed over at the start for a right. Here no money is handed over at the start for anything. Two parties agree a price and a date, and the money moves at the end. The make-up of the Rs 2,130.00/-, and why it is arithmetic on a financing rate rather than anybody's view of where the price is going, is covered separately and is used here as finished work. The one thing worth carrying across is that it says nothing about where the price will be. The contract price says what carrying the unit to that date costs.

What did the holder give up in order to give up the loss?

Now test the arrangement. Take the reading at the spot price of Rs 2,000.00/- first. Everything afterwards is then a movement against something rather than a bare number. Then move the settlement priceThe price the obligation is finally worked out against on the last day of the contract. Until that day it is unknown, and in this guide it is tested rather than predicted. down by a 4.0 per cent move in the price of the reference asset. On Rs 2,000.00/- that move is Rs 80.00/-, and it takes the settlement price to Rs 1,920.00/-. The unit held is now worth Rs 80.00/- less than was paid for it. The payoffWhat a position produces at settlement, before anything paid to get there has been taken off. A payoff is not the same thing as a profit. on the short contract is Rs 2,130.00/- less Rs 1,920.00/-, or Rs 210.00/-.

Now move it the same Rs 80.00/- the other way, to Rs 2,080.00/-. The unit held is worth Rs 80.00/- more than was paid for it. The payoff on the short contract is Rs 2,130.00/- less Rs 2,080.00/-, or Rs 50.00/-, and Rs 50.00/- is Rs 80.00/- below the Rs 130.00/- it was at the reference reading. Every rupee the holding lost, the contract found, and every rupee the holding gained, the contract gave back. The offset runs both ways or it does not run at all, and no version of this arrangement shows up for the fall and stays away for the rise.

One line is worth leaving with. Giving up the rise is what the holder gave up in order to give up the loss. Nothing was subtracted from the holder's risk and quietly left behind: the two things left together, at the same moment, in the same movement. A reader who wanted the fall covered and the rise kept was not describing this arrangement, or any arrangement built out of a contract with two bound sides.

Look at the same three readings a second way. The first picture shows the movement and the second shows what the movement leaves. At every one of the three settlement prices, the settlement price plus the payoff comes to Rs 2,130.00/-. At Rs 1,920.00/- it is Rs 1,920.00/- and Rs 210.00/-. At Rs 2,000.00/- it is Rs 2,000.00/- and Rs 130.00/-. At Rs 2,080.00/- it is Rs 2,080.00/- and Rs 50.00/-. The total is the same at all three and the split between the two sides is different at all three. An exchange drawn out looks exactly like that. The total is the contract price, fixed on the day the contract was written. The fixed total is the whole of what the holder bought and the whole of what the holder gave away.

Every figure in that table is a payoff and not a profitWhat is left of a payoff once everything paid to get there has been taken off. Nothing has been taken off anywhere in this table, so nothing in it is a profit., and the difference is not a quibble. Nothing has been taken off for what it cost to hold the unit for the year, and nothing has been taken off for funding the margin balance that the next section is about. A reader who reads the Rs 210.00/- column as money made has skipped both.

Does that offset hold on every day, or only on one?

Only on one, and this is the point most treatments skate over. Everything in the table above is read at the final date, the day the contract settles. On that day the unit held and the unit sold forward are the same thing on the same date, so they cancel rupee for rupee and the total sits still at Rs 2,130.00/-. Before that day they do not cancel rupee for rupee, and the reason is the carry. Suppose the price of the reference asset falls to Rs 1,920.00/- while a full year still runs to the later date. The contract price for that same later date is now Rs 1,920.00/- multiplied by 1.065, or Rs 2,044.80/-. Against the Rs 2,130.00/- written into the holder's contract, the quoted price for the same date has moved Rs 85.20/-. The spot price moved Rs 80.00/-. The financing cost applies to the new price too, so the contract price moved by 1.065 times the spot move.

So the moment being read at has to be named, every time, or the arithmetic quietly changes underneath the words. The two figures in that mid life reading are not the same date's money: one is a price for today and one is a price for a day a year away, and adding them is adding two different dates together. The clean cancellation belongs to the final date for that reason alone, when both are prices for the same day. How much of a move an offset actually catches, and what the two sides do to each other in between, is covered separately and in full. The warning is the part to carry: a flat net line drawn with no moment named is teaching an equality that holds on exactly one day.

One fall, taken twice, shows it by eye. The price of the reference asset drops the same Rs 80.00/- in both readings, and the only thing that changes between them is the day the reading is taken on. At the final date the contract side answers with Rs 80.00/- and the two come to nothing. With a year still to run the contract price for the later date answers with Rs 85.20/-, and Rs 5.20/- is left standing. The offset is over complete before the end and exact only at it, so the moment is not a detail to mention afterwards but part of the reading itself.

What is the first thing that came with the contract?

An obligation. The contract is now a thing in its own right, and it does not depend on the holding surviving. If the unit is sold, damaged, delayed, or never turns up at all, the short contract is still open and still has to be settled at Rs 2,130.00/-. Nobody sends a note releasing it. There is no clause that reads: this contract expires if the reason for writing it goes away.

Picture what that leaves. A position that was written to answer something, with the something now gone, moving in one direction only, with nothing behind it. If the price of the reference asset rises after the unit has been sold, the short contract loses on that rise and there is no longer a holding rising alongside to meet it. A holding sold early is not a remote possibility that happens to careless people. Selling early is the ordinary way a covering position becomes an uncovered one, and it arrives through something going right at least as often as through something going wrong. A holding sold at a price the holder was pleased with is still a holding gone.

What is the second thing that came with the contract?

Cash to find, and a specific day on which to find it. The contract is carried against marginWhat a party posts before carrying a position, and tops up when the position moves against them. It is not a payment for the contract and it is not a fee.. On one unit, 8.0 per cent of the Rs 2,000.00/- of exposure is Rs 160.00/-. The 8.0 per cent is a teaching figure rather than a requirement anybody has set. Margin itself, and how a position is marked from one day to the next, is covered separately. The size and the timing are what belong here.

Take the two limbs together. Either one alone misleads. Rs 2,000.00/- of exposure standing on Rs 160.00/- of margin is 12.50 times. A 4.0 per cent move in the price of the reference asset is Rs 80.00/-, and Rs 80.00/- against the Rs 160.00/- posted is 50.0 per cent of it. Quote only the first and the arrangement sounds enormous. Quote only the second and it sounds like small change. Side by side, the two limbs give the feature that actually makes these contracts different to hold: a 4.0 per cent move in the reference asset takes half of what was put down.

Now the timing, the part nobody expects the first time. The short position is marked against the holder on the day the price of the reference asset goes up. The day of that mark is the day the unit sitting in the crate is worth more. So cash leaves on the good day. For a holder whose money is tied up in the holding itself, that ordering is the whole difficulty in one line: the crate cannot be spent, the crate is doing well, and the call for cash does not wait for the crate to be sold. A stall that has to find cash on the morning its stock became more valuable is not in an unusual position. The stall is in the ordinary position of anybody carrying a covering contract.

What is the third thing that came with the contract?

A gap. The two sides of this arrangement are two different things, and there is nothing in the arithmetic that forces them to line up. The two sides part company in three places, and each of the three leaves something behind with the holder. The date, when the holding stops mattering on a day the contract does not end, or the contract ends on a day the holding is still there. The quantity, when the holding is not a whole number of contract units and contracts come in sizes somebody else decided. And the thing itself, when no contract exists on what is actually being held, so whatever is written has to be written on something else.

How much each of the three leaves, and the arithmetic for measuring it, is covered separately and in full. The shape of the claim is what matters at this point: whatever is left over by any of the three is an exposure like any other exposure, with a size and a direction and a date, and it belongs on the list of things the holder is carrying rather than in a footnote.

Do these figures show whether the holder came out ahead?

No, and it is worth being blunt about why. A reader who has watched three settlement prices go past will want a verdict. Nothing in these figures says. The worked figures are one invented reference asset at one spot price with one financing rate and one invented margin percentage. There is no run of prices, no history, no distribution and nothing that actually happened. A verdict needs evidence, and there is none of it in this arithmetic.

So what are the three settlement prices in the table? The three settlement prices are points the obligation is tested at, chosen to sit either side of the spot price so the movement is visible in both directions. Testing is all they do. A tested price carries no claim whatever about where the price of anything will go, and a settlement price that was tested is not a settlement price that was forecast.

What would have to be known before anyone could say whether to do this?

Whether anybody should write a contract against something they hold cannot be settled by arithmetic like this. The question is unanswerable from anything written above, and the useful thing to do instead is to name what the answer would need.

The exposure itself, and how long it runs. Whether a contract exists on the thing held at all, and on what dates it runs to. The cash that can be posted and funded on a bad day without selling the very thing the contract was written to cover. The leftover when the dates and the quantities do not line up, and whether the holder can carry it. And what the authority requires before a position counts as a hedge rather than as a position taken on its own, set by SEBI at sebi.gov.in.

Notice what is not on that list. How well it worked last time. There is no last time in these figures. Whether covering is the careful or responsible thing to do. Care is a description of a feeling rather than of an arrangement, and the word hedge supplies the feeling free of charge. Understanding how an exchange of exposures works is not a reason to make one.

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