The Swap: One Agreement, Two Schedules of Payments

A swap is a single contract in which two sides promise each other payments worked out on two different bases. Both schedules sit on one shared figure that nobody hands over, and both fall due on one shared calendar. One schedule carries a rate the two sides negotiated; the other carries a published reading. Only the gap between the two is ever transferred.

The word gets used loosely, and that is exactly why it is worth taking apart properly once. People say swap when they mean an exchange of almost anything, and then they meet a real agreement and try to read it as a trade in which two objects change places. Nothing changes places. Nobody hands anything over at the start, nobody hands anything back at the end, and the large rupee figure printed near the top of the document is not a sum that anybody has or will have.

The shape comes before the vocabulary. Two sides want money to reach them in a pattern that is not the pattern it currently arrives in. Nothing is on sale that would fix the pattern, so neither side can buy its way out. Lending to each other is also out. Neither side wants the other's credit. The two sides can instead write one document that says: for the next stretch of time, the first side will pay an amount worked out this way, the second will pay an amount worked out that way, and on each agreed date whichever of the two is behind settles the difference.

The document just described is the whole object. Everything else written about these arrangements is a choice made inside that shape. Which basis the second schedule follows. How long the document runs. How a stretch of the calendar is counted. Who is on the other side and what they place as security. A change in any of those gives the arrangement a different name in the market; the shape underneath is untouched.

A version of the same arrangement exists on any street. Two stallholders sit outside the same office building. One of them sells tea and takes roughly the same amount every single day. The other sells cut fruit and takes a great deal on hot days and almost nothing on wet ones. The two stallholders agree, for a year, that at the end of each month one will pay the other a flat figure and the other will pay whatever a stated share of the fruit takings came to. Neither of them lends the other a rupee. At the end of each month they do not exchange two bundles of cash. Both amounts get worked out, one of them is bigger, and the shortfall crosses the pavement. The pavement arrangement is a swap in every structural respect, and the only thing a real one adds is a document, a stated calendar and a figure that both amounts are computed on.

Everything worked below runs on one agreement between Chitrakoot Cements Limited and Saranga Capital Limited, two invented parties. The rates, the shared figure and the benchmark reading were all chosen to teach with, so no market produced any of them.

What is a swap, once every particular type is stripped away?

Five parts, and no more than five. Two sides. One contract. Two schedules of payments running in opposite directions. One figure that both schedules are computed on and that neither side ever hands over. One calendar of dates on which the schedules fall due. A document containing those five is an arrangement of this kind, whatever the market calls it and whatever the second schedule happens to follow.

Take them one at a time. Each has a trap sitting behind it. Two sides means two specific named counterpartiesThe two named parties who signed the agreement. Each is on the other side of every payment the document produces.. Not a market, not an exchange, not the general public. Somebody signed on each end and somebody on each end has to keep paying. One contract means one document, not two arrangements sitting beside each other. The single document matters more than it looks. A reader who pictures two separate promises will start asking what happens if one promise is honoured and the other is not. The single document does not permit that question.

Two schedules of payments running in opposite directions is the part the name comes from. Each side is a payer on one schedule and a receiver on the other, at the same time, for the whole life of the arrangement. One figure both schedules are computed on is the part that gets misread hardest, and there is an entire section on it below. One calendar means the dates are the same for both schedules. Sharing the dates is what makes it possible to set the two amounts against each other at all.

The five parts are the whole of the general form, and every variety of this arrangement is a choice made inside them rather than an addition to them. Once the five are held, an unfamiliar type stops being a new thing to learn and becomes a document to fill in.

The everyday test for whether the shape is right is to ask what would be missing if one of the five were removed. Without the shared figure, neither schedule can be turned into rupees at all. A rate on its own converts to nothing. Without the shared calendar, the two amounts fall due on different days, so they cannot be set against each other and two separate transfers have to happen. Without one of the two schedules, what is left is not an exchange but a plain obligation to pay. The world already has a word for that.

What are the Swap Legs, and why does every agreement have exactly two?

Each of the two schedules of payments has a name. A legOne of the two schedules of payments inside a single agreement. Each leg says what rate it is computed at, what figure that rate is applied to, and which dates it falls due on. is one schedule of payments inside a single agreement, and the word is used because the arrangement stands on both of them at once. Take one leg away and the arrangement does not lean, it falls over. Nothing is being exchanged any more.

A leg is described completely by three things and by nothing else. The rate it is computed at. The figure that rate is applied to. The dates it falls due on. Rate, figure and dates are the entire specification of a leg. Filled in, those three fields price the leg for any stretch of the calendar for which the rate is held, and with one of them missing there is not enough on the table to compute anything.

The three field specification is the practical use of the idea. A reader is handed an unfamiliar document, in an unfamiliar market, referencing something never met before. Understanding the market is not required in order to read the arrangement. Finding two legs and filling in three fields each is what is required. Whatever is left over in the document is describing the contract rather than the legs.

Now the count. Why exactly two, and never one and never three? Because an exchange needs a thing given and a thing received, and each of those is a schedule. One schedule is not an exchange at all; it is somebody paying somebody. A bill, a loan repayment or a rent has that shape. Three schedules would be a different agreement doing a different job, and the market gives that a different name rather than calling it a swap with a spare leg. Two is not a convention that could have gone another way. A two sided exchange has exactly two directions in it, and two directions is what the word means.

One more piece of vocabulary discipline, and it is worth adopting because it removes an entire class of confusion. In this arrangement the two legs are called the fixed leg and the floating leg, in those words, every time. And a party is described by the leg it pays, never by the leg it receives. So Chitrakoot Cements Limited pays the fixed leg and is therefore the fixed payer. Saranga Capital Limited pays the floating leg and is therefore the floating payer. Each of them also receives the other leg. Describing somebody by the leg they receive would double the number of names for the same two positions and help nobody.

What is the Swap Rate, and which of the two legs does it apply to?

The swap rateThe single fixed rate the two sides negotiate into the agreement. The swap rate applies to the fixed leg, it does not change for the life of the arrangement, and there is exactly one of it in the document. is the single fixed rate the two sides negotiate into the agreement. The rate applies to the fixed leg. The figure does not move for the life of the arrangement. In the agreement worked here it is 7.20 per cent a year, and it was 7.20 per cent a year on the day the document was signed, and it will still be 7.20 per cent a year on the last date in the calendar.

Three properties, and each one is worth a line of its own.

The swap rate is agreed rather than observed. Nobody looked it up. Two parties negotiated it and wrote it down. The figure belongs to those two parties and to their document, and not to any market. Another pair of parties signing on the same afternoon could write a different figure and both documents would be perfectly valid.

The swap rate applies to every stretch of the calendar in the arrangement. One figure describes the entire fixed schedule, from the first date to the last. One figure for every stretch is a genuinely useful property: the whole fixed side of the arrangement can be written out in full on the day of signing, with no gaps and nothing to wait for.

And the swap rate is not a forecast of anything. Nothing about the rate gets lost faster than that, so it is worth being blunt. A rate two parties negotiated into a private document is a piece of arithmetic about what each of them can borrow and lend right now, and it is not an opinion about where anything is heading. It sits in exactly the same category as a forward price built out of a spot figure and a financing cost: a cost of carrying, not a view about the future. Reading a negotiated figure as somebody's expectation is the single most damaging misreading available in this subject, and it is available here as much as anywhere.

The household version runs like this. A building's water tanker arrives on demand and the residents pay whatever the tanker costs that week. The cost moves about. A supplier offers to charge a flat figure every month for a year instead. Whatever flat figure the two sides settle on, it is the outcome of a negotiation between one party who wants certainty and another who is willing to carry the movement. The flat figure is not a prediction of what tankers will cost. A resident who tells the neighbours that the flat figure reveals what the market thinks tanker prices will do has invented a meaning that nobody put into the number.

What does the other leg follow, and how does it get its number?

The floating leg is computed at a floating benchmarkA published rate reading taken on a stated date. The reading is looked up rather than negotiated, and a fresh one is taken for each stretch of the calendar. reading taken on a stated date. The benchmark reading is looked up rather than negotiated. Nobody in either party decides what it says. For the first stretch of the calendar in this agreement, that reading is 6.00 per cent a year, and that figure is the last thing about the floating leg that can be stated here.

The limit just stated is not a stylistic flourish but the actual state of what is known. One reading is held, for one stretch of the calendar, and nothing at all for any stretch after it. No schedule of expected readings stands behind the floating leg. Every cell of the floating schedule after the first is empty, and the honest picture of the arrangement has those cells drawn empty rather than filled with something plausible.

Now notice what kind of asymmetry that is. Two candidates offer themselves and only one of them is real. The asymmetry is not one of obligation. Both sides are equally bound for the entire life of the document; neither has a choice about paying and neither has an option to walk away from a stretch that turns out badly. The asymmetry is one of knowledge. One side's amounts are all knowable today and the other side's are knowable one stretch at a time.

The fixed schedule can be written out in full on the day of signing, and the floating schedule for exactly one stretch of the calendar. A rate that was agreed and a rate that has to arrive differ in precisely that way.

The empty cells repay a moment of precision about what they mean. The cells do not mean nil. Nor do they mean small. Nor do they mean that the floating leg pays nothing in those stretches, and they are not a low bar sitting beside a tall one. Empty means unknown, and specifically unknown for a stated reason: a published reading for that stretch has not been taken, and none is held here. An empty cell that a reader mistakes for a quantity is worse than no picture at all. Each cell therefore carries the words rather than a shape.

What do the two legs have in common, and why does that matter so much?

Two things, and they are the two that make the whole arrangement work. Both legs are computed on the same figure, and both fall due on the same dates.

The shared figure has a name, and is called the notionalThe figure both legs are computed on. The notional turns a rate into rupees and never changes hands. Notional rather than principal is the right word for it.. In this agreement the notional is Rs 1,000 crore, or Rs 10,00,00,00,000/- in whole rupees. Nobody advances it, nobody repays it and nobody is ever entitled to it, and the word for a figure of that kind is notional rather than principal. The notional sits in the document doing exactly one job: turning a rate into rupees. A rate on its own converts to nothing at all, so without a figure to apply it to, neither leg produces an amount.

Sharing one figure is more convincing worked through than stated. The fixed leg over one full first stretch is 7.20 per cent a year applied to Rs 10,00,00,00,000/-. The amount is Rs 72,00,00,000/-. The floating leg over the same stretch is 6.00 per cent a year applied to the same Rs 10,00,00,00,000/-. The amount is Rs 60,00,00,000/-. One set against the other leaves Rs 12,00,00,000/-.

The same figure can be reached without computing either leg. The two rates first: 7.20 per cent a year less 6.00 per cent a year is a gap of 1.20 percentage points. The gap of 1.20 percentage points applied to the same Rs 10,00,00,00,000/- gives Rs 12,00,00,000/- again, to the last rupee. The notional cancelled out of the arithmetic entirely. An arrangement with a headline figure of Rs 1,000 crore printed on it therefore produces a first stretch difference of Rs 12.00 crore and nothing larger.

The two legs also share the calendar, and that is the second half of why this works. If the fixed leg fell due on one date and the floating leg on a date three weeks later, there would be nothing to set against anything. Two separate transfers would have to happen, three weeks apart, and every rupee of both would have to move. Sharing the dates is what makes it possible to compute both and move one.

The practice of computing both and moving one has a name. The practice is called nettingWorking out both amounts, setting one against the other, and transferring only the difference. One movement of money instead of two., and it is not exotic. A household buys milk from the dairy at the corner every morning and, at the end of the month, owes Rs 3,000/-. The person who runs the dairy sends two children to that same household for tuition and, at the end of the month, owes Rs 2,400/-. Nobody hands over Rs 3,000/- and gets Rs 2,400/- back. One of them hands over Rs 600/- and the month is closed. The dairy and the household have just netted, and a swap is that arrangement written down properly with dates in it.

The test that runs on any agreement of this kind is whether both legs are computed on the same figure and fall due on the same dates. If they are not, the netting picture set out here does not describe that document, and whatever it is doing, it is doing something else that needs reading on its own terms.

The scale, stated carefully

The headline figure and the moving figure set side by side is where a great many notes go wrong. The notional is Rs 10,00,00,00,000/-. The amount that moved in the first stretch is Rs 12,00,00,000/-. The second divided by the first is 12 over 1,000. Reduced, that is 3 over 250, or 0.012, or 1.2 per cent exactly. The 1.2 per cent multiplied back by the notional lands on Rs 12,00,00,000/- again with nothing left over. The division in that direction is an equality.

Turned around, something different happens. Rs 10,00,00,00,000/- divided by Rs 12,00,00,000/- is 1,000 over 12. Reduced, that is 250 over 3, and 250 divided by 3 does not end. The figure 83.33 is commonly used for it, and it is a perfectly reasonable working figure, but it is a rounding rather than an equality. 83.33 multiplied by Rs 12.00 crore gives Rs 999.96 crore. The shortfall against the notional is Rs 4,00,000/-. Multiplying by 250 over 3 lands on Rs 1,000 crore exactly. 250 over 3 belongs wherever the exact figure matters, and 83.33 is shorthand rather than the answer.

What actually settles between the two parties on a date?

Both amounts get computed. The two amounts are set against each other. One transfer happens. Three steps, and only the third one moves money.

Work it once, slowly, with every figure named. Over one full first stretch the fixed leg comes to Rs 72,00,00,000/-, or Rs 72.00 crore. The fixed leg amount is grossAn amount computed on one leg before the other leg has been set against it. A gross figure is a real computation, but it is not what moves.: it is a real computation on a real leg, but it is not a sum anybody sends. Over the same stretch the floating leg comes to Rs 60,00,00,000/-, or Rs 60.00 crore, and that is gross too. Set the two against each other and what is left is Rs 12,00,00,000/-, or Rs 12.00 crore, and that figure is the netWhat remains after the two legs have been set against each other. The net is the only amount that actually changes hands.. Chitrakoot Cements owed more over that stretch, so Chitrakoot Cements Limited pays the net to Saranga Capital Limited.

Two habits of vocabulary hold this together, and they are worth adopting for good. The two gross figures are payments that were computed. The transferred figure is a net. And not one of the three is a price. Nothing was bought and nothing was sold, so the word price has nothing at all to attach itself to, and using it merges three distinct things into one vague number in somebody's note.

The direction is a consequence, not a rule. Whichever side owed more over that stretch is the side that pays, and the document does not fix which side that will be on any date after the first. If a later reading of the floating benchmark came in above 7.20 per cent a year, the floating leg would be the larger of the two and the transfer would run the other way, from Saranga Capital Limited to Chitrakoot Cements Limited. No reading is held for any stretch after the first, so whether that happens cannot be said. The direction was never written into the document, so the arrangement handles a reversal without any amendment.

The multiple of eleven that follows is exact rather than approximate, and worth holding for that reason. The two gross figures added give Rs 1,32,00,00,000/-. Divided by the net of Rs 12,00,00,000/-, that comes to exactly eleven, with no remainder. Settling gross would move eleven times the money to achieve the same closing position. Nobody does it, and the reason is arithmetic rather than convention.

What is a swap not, and which three objects does it get confused with?

Three, and a cold reader tends to arrive carrying all three at once. Each one can be killed in a line.

A swap is not a loan. Nobody advances anything at the start, nobody repays anything at the end, and no principal is at stake at any point in between. The absence of principal is precisely why two parties who would never lend each other money can still sign one of these: neither is being asked to trust the other with a sum, only to keep settling a difference. The word notional exists to mark this. The figure is called notional and not principal because the rates are applied to it and it does nothing else.

A swap is not a sale. Nothing changes hands in the sense a sale means, and neither side finishes holding something the other side used to hold. There is no article, no delivery, no transfer of title and nothing to inspect. The pattern in which money reaches each side is what changed, and a pattern is not an object that can be sold.

A swap is not a forecast. The fixed rate in it was negotiated between two parties, and a negotiated figure is not anybody's expectation of anything. The fixed rate is the outcome of what each side could borrow and lend at the time they sat down, worked into a figure they were both willing to sign. Reading it as a prediction attributes an opinion to a document that contains none.

Of the three, the loan reading is the one that does real damage. A reader who has decided it is a loan then decides the notional is the amount lent, and every judgement made after that is about a sum nobody has.

How does somebody reading one of these actually work through it?

The mechanism is not the job. The steps below are what a person does with an agreement of this kind in front of them, whether they sit in a treasury team, in a credit team, in an audit file review or on the analysis side looking at somebody else's disclosure. Every step is a reading step. None of it is an instruction to do anything.

1. Find the shared figure and label it in the margin. Write beside it: multiplier, never moves. Do this before reading anything else in the document, because every later misreading in the chain starts from this line being taken for a sum. In the agreement worked here that line reads Rs 10,00,00,00,000/-.
2. Find the two legs and fill in three fields each. The rate, the figure it is applied to, and the dates. Six boxes in total. A box that cannot be filled is the thing to go and ask about, and it is a more useful question than any general one about the market.
3. Check that both legs sit on the same figure and the same dates. This is a thirty second check and it decides whether the netting picture applies at all. If the two legs are computed on different figures, the arrangement is doing something this reading does not describe.
4. Count the fixed rates. There should be exactly one, and it should appear once. More than one means two arrangements, or a document that steps its rate, which is a different object needing its own reading.
5. Compute the first stretch on both legs, then difference them. Then reach the same answer the other way, by differencing the two rates and applying the gap to the shared figure. If the two routes disagree, something in the fields has been read wrong, and finding out which is the whole value of doing it twice.
6. Write down what cannot be computed, and what would have to arrive first. On this arrangement that is every stretch after the first, and what would have to arrive is a published reading for each of them. A note that says this is worth more than a note that quietly fills the gap with something plausible.
7. Route the conditions rather than answering them. What has to be reported and what collateral is placed are set by an authority and they move. Write the name of the authority next to the question and confirm it at source on the day it is needed.

The sixth line is the single most valuable one in that whole sequence. A reader who writes down what cannot be computed has protected every conclusion that follows from it. A note with a stated gap in it is a note somebody can act on carefully. A note with the gap filled in silently is a note that looks complete and is not.

What cannot be said about the arrangement?

Every worked figure above belongs to the first stretch of the calendar and stops there. The first stretch is the actual limit of what exists behind the illustration.

The general form runs for many stretches. Only one floating benchmark reading is held, for the first of them. So the second stretch, the third and everything after are blank, and any figure attached to them would have to have been invented. Filling them would take a published schedule of expected readings for every remaining stretch, and that is not something anybody should construct from memory, borrow from a neighbouring subject or interpolate between two points.

So the value of the agreement today cannot be stated. A value needs a reading for every remaining stretch, and exactly one is held. There is no mark, no present value, no rate for any maturity, and no difference for any stretch after the first. Against those absences stands the first stretch difference of Rs 12,00,00,000/-, computed two ways that agree, and an honest set of empty cells after it.

The reading habit that follows is this: any treatment that sets out a general form and then quietly produces a valuation has smuggled a set of readings in somewhere, and the only question worth asking is where they came from. If the answer is that they were assumed, the valuation is an assumption wearing a rupee sign. If the answer is that they were published, the next questions are who published them and on what date, and the ground is solid again.

Does any of this suggest that anybody ought to enter one?

No. Knowing the general form of an arrangement is a reading skill. The skill allows a document to be picked up and read for what it obliges each side to do. Reading a document well does not indicate that anybody ought to be in one.

Four concrete things would have to be known first, and the four make clear why the question cannot be answered from a general form. The position the reader already holds, and the shape in which the money currently reaches them. The change they actually want, stated as something other than a wish. Who would be on the other side of the document, by name, and what that side is like. And what happens if that side stops paying partway through, a question about the other party rather than about the mechanism.

None of those four is settled by the general form, and no amount of clarity about how the arrangement works substitutes for a single one of them. No outcome is held for any arrangement of this kind, so none can be compared against another on how it turned out. Neither leg is the better side to be on as a general matter. That judgement needs the four things just listed.

Chitrakoot Cements Limited, Saranga Capital Limited and every rate and figure used with them are invented.
Educational material. Not advice on any investment, tax, budget or market position.