The Interest Rate Swap: Two Streams, One Agreement

An interest rate swap is one agreement under which two parties exchange two schedules of payments. One schedule is computed at a fixed rate, the other at a floating benchmark reading, and both are applied to the same notional. The notional never changes hands. On each payment date only the difference between the two schedules moves, from whichever side owes more.

The instrument only makes sense once what it was reached for is in view, so the situation comes first. Two parties are sitting on money that arrives in a shape they did not choose. One of them takes in an amount that moves up and down with a published rate and would much rather it sat still. The other takes in a steady amount and would rather it moved. Neither of them wants to borrow from the other. Neither of them has anything to sell the other. The two parties have no reason to be in a room together at all, except this one.

The two parties can agree to pay each other on two different bases and settle the gap. Nothing is bought, nothing is sold, and no principal is advanced, repaid or secured, and yet after the agreement is signed the money arriving at each of them has a different shape from the one it had the day before. The trick is worth sitting with. Most of finance changes what a party holds. A swap changes only the pattern in which money reaches that party.

There is a version of this on any street. Two neighbours have electricity bills. One of them has a bill that jumps around every month because the tariff moves; the other pays a flat monthly amount on a scheme. The two neighbours agree that neighbour A will cover neighbour B's bill each month and neighbour B will hand neighbour A a flat sum back. Nobody lends anybody anything, no meter is transferred, and at the end of the month only the shortfall between the two amounts crosses the fence. Both of them now face a different pattern of outgoings than they did, and the only thing that ever actually moves is a difference.

Everything below runs on one agreement between Chitrakoot Cements Limited and Saranga Capital Limited, two invented parties, with rates and figures chosen for teaching. The numbers in a swap look institutional, and a reader will assume somebody went and measured them. Nobody did.

What actually happens when two parties enter an interest rate swap?

One document gets signed, and inside it there are two schedules of payments running in opposite directions. The picture is worth holding before a single number arrives. Everything else is a detail hanging off it.

Chitrakoot Cements Limited will pay on one basis for the whole life of the agreement. Saranga Capital Limited will pay on the other basis for the whole life of the agreement. Each of those two schedules is called a legOne of the two schedules of payments inside a single agreement. An arrangement of this kind has exactly two: one computed at a fixed rate, one computed at a floating reading., and there are exactly two of them. The schedule computed at a rate written into the document is the fixed leg. The schedule computed at a published reading taken on a stated date is the floating leg.

Both legs are applied to the same figure, and that figure is called the notionalThe figure the two rates are applied to. It turns a percentage into rupees and never changes hands, which is why it is called notional rather than principal.. Here it is Rs 1,000 crore. The word notional carries the weight of what follows. Everything below turns on the job that word does in the document, and on the jobs it does not.

Nobody lends anybody anything in an arrangement of this kind, and no principal is advanced, repaid or secured at any point in its life. A loan is what a reader's mind reaches for first, and the sentence above is the one to keep. A loan moves a sum out and then brings a sum back. A swap moves neither. The agreement computes two amounts, sets them against each other, and moves the remainder.

The picture reads from the outside in. The outer frame is one document with two signatures on it. The dashed strip near the top is the notional, drawn dashed because it is the only thing in the frame that is not a cash flow. The two panels underneath are the two schedules. The two arrows at the foot run in opposite directions on the same dates. Opposite directions on one date make everything that follows possible.

What is the notional doing in the agreement, if it never changes hands?

The notional is the idea that decides whether a swap is understood or misunderstood for years.

Rs 1,000 crore is written at the top of the agreement between Chitrakoot Cements Limited and Saranga Capital Limited. Not one paisa of it is lent. Not one paisa of it is borrowed. Nobody hands it over on the first day, nobody hands it back on the last day, and no event described anywhere in the document causes it to move in any direction. A notional is a multiplier that turns a percentage into rupees, and it is the only figure in the agreement that is never a cash flow.

The amount that actually moves in the first period is Rs 12.00 crore. The figure is worth building rather than taking from a line. The fixed rate is 7.20 per cent a year and the floating benchmark reads 6.00 per cent a year for the first period, so the gap between the two rates is 1.20 percentage points. Applying that gap to the notional gives the amount that changes hands.

Rs 1,000 crore multiplied by 1.20 percentage points is Rs 12.00 crore. In whole rupees, Rs 10,00,00,00,000/- multiplied by 0.0120 gives Rs 12,00,00,000/-. A proportion means nothing until the division has been done as well as the multiplication, and the arithmetic runs back the other way too. Rs 12.00 crore divided by Rs 1,000 crore is 0.012, or 1.2 per cent. So 1.2 per cent of the headline figure moved. The other 98.8 per cent stayed exactly where it was, and where it was is nowhere. The notional was never anywhere to begin with.

Turned around once more, it gives the number worth remembering. The notional of Rs 1,000 crore is 83.33 times the Rs 12.00 crore that moved, rounded to two places. A reader who takes the headline for the amount at risk has overstated it by a factor of eighty-three.

The sliver in the middle row is not a drawing error. The sliver is Rs 12.00 crore drawn at the same scale as Rs 1,000 crore, and at that scale it is about six pixels wide against five hundred and ten. Finding it takes squinting, and that is the point. The ratio is exactly what a committee note reporting a bare notional hides.

Here is the everyday version. A household says its home is insured for Rs 60,00,000/-. The sum insured is printed on the policy in large type, and it is not money anybody has, moved or will move. The premium is what moves, and the premium is a small percentage of the sum insured. Nobody looking at the policy thinks the household is sitting on Rs 60,00,000/- of cash, or owes it, and nobody should. A notional works the same way: it is the figure the percentage is applied to, and it is quoted precisely because the percentage on its own means nothing.

What does the fixed leg promise, and for how long is it known?

Chitrakoot Cements Limited has agreed to pay 7.20 per cent a year on the notional. The 7.20 per cent is the fixed rateThe rate written into the agreement on the day it is signed. It does not change afterwards for any reason, whatever any published rate does., and the word fixed is doing real work: the rate is written into the agreement on the day it is signed and does not change afterwards for any reason. Not if published rates rise. Not if they collapse. Not if either party would prefer otherwise. The rate sits in the document.

Every fixed leg rate for the whole life of the arrangement is knowable on day one, an unusual property and exactly what one side was after. The property holds for every fixed leg anywhere and not just for this agreement, and it is worth stating that way. There is no waiting, no observation and no reset. The schedule is complete the moment the ink is dry.

Over one full first period the fixed leg comes to Rs 72.00 crore grossAn amount before the other side's amount has been subtracted from it. A gross leg figure is computed, and then usually never sent, because only the difference is transferred.. Rs 1,000 crore multiplied by 7.20 per cent is Rs 72,00,00,000/-. The word gross carries weight there. Rs 72.00 crore is a computed amount and not a transfer. Nobody is going to send it.

One honest note about the picture below. The drawing shows the rate, not the amount. Turning a rate into an amount for any period needs that period's own day count fractionHow much of a year a period counts as when a rate is applied to it. A full year counts as 1.0000; a shorter period counts as less, and how it is counted is a term the two parties agree., and the Rs 72.00 crore figure above holds because this first period is one full year and the fraction is 1.0000. How that fraction is arrived at, and why the same rate can pay differently over two periods of similar length, is covered separately. The rate itself is flat regardless, and that is what the drawing shows.

What does the floating leg promise, and where does its number come from?

Saranga Capital Limited has agreed to pay the floating benchmarkA published reading taken on a stated date and used as the rate for one period. It is not written into the agreement; only the instruction to use it is. on the same notional of Rs 1,000 crore. The floating promise is a different kind of promise from the fixed one, and the difference is the whole reason two parties bothered.

The agreement writes down no number for this leg, only an instruction: take the published reading on a stated date and use it for the period that follows. The benchmark here is called the floating benchmark throughout and is not a named one. For the first period it reads 6.00 per cent a year, so the floating leg comes to Rs 60.00 crore gross over one full period. Rs 1,000 crore multiplied by 6.00 per cent is Rs 60,00,00,000/-.

Only one floating payment is knowable at any time, the one for the period that has just been fixed, and every period after it is genuinely unknown until its own reading is taken. Set beside the fixed leg, that gives the two halves of the arrangement: one side has bought certainty about its own schedule and the other has taken it on.

A careful reader will have noticed something and should not be left to wonder about it. Rs 60.00 crore is 6.0 per cent of Rs 1,000 crore, and the benchmark reads 6.00 per cent a year. The two figures agree, and they agree only because this first period happens to be one full year at a day count fraction of 1.0000. Over a period that is not a full year they would not agree, and reading the agreement of the two as a general rule is a mistake waiting to happen. The same premise sits under the Rs 72.00 crore on the fixed leg.

The two drawings belong side by side. Identical axes, identical periods, and one line is complete while the other is a single dot followed by empty boxes. The empty boxes are not a shortcut in the drawing. The empty boxes are the honest picture of what is known, and they matter again when somebody asks what a swap is worth today.

Why does only one payment move when two payments have been computed?

Both legs are struck on the same notional and both fall due on the same date. So there are two computed amounts sitting on the table on the same morning: Rs 72.00 crore owed by Chitrakoot Cements Limited and Rs 60.00 crore owed by Saranga Capital Limited.

Sending both would move Rs 132.00 crore of money across a banking system to achieve Rs 12.00 crore of effect. Two payment instructions, two sets of charges, two chances for one of them to go missing, and an identical outcome. So the two sides settle the difference instead, and that is called nettingComputing both payments and transferring only the difference between them. The two gross amounts are still worked out; they are simply never sent.. A difference cannot be found without both gross amounts, so both are still computed. The two gross amounts are just never sent.

Chitrakoot Cements Limited hands over Rs 12.00 crore of netWhat is left after the two sides' amounts have been set against each other. It is the only figure in an arrangement of this kind that is actually transferred. difference to Saranga Capital Limited, and it does so because Chitrakoot Cements owed more this period. Note the reason carefully, because it is not a rule about who pays.

The direction is not written into the agreement: the side paying is whichever side owes more in that period, and nothing settles that in advance. Chitrakoot Cements pays this period because 7.20 per cent a year is above 6.00 per cent a year. Let the benchmark reading come in above 7.20 per cent a year for some later period and the money runs the other way, from Saranga Capital to Chitrakoot Cements, with no amendment to the document and no negotiation. The simulation below carries the reading through that crossing, and the arrow turns round.

The size of what netting saves is not obvious until it is drawn, and the two routes belong beside each other. Settling gross moves Rs 132.00 crore. Netting moves Rs 12.00 crore. Rs 132.00 crore divided by Rs 12.00 crore is exactly eleven, so one route moves eleven times as much money as the other to produce an identical result for both parties.

How does the first period work out, step by step?

Here is the whole of the first period in four steps, worked through rather than presented as a result. Every figure belongs to the agreement between Chitrakoot Cements Limited and Saranga Capital Limited.

Step three is written twice. The second version is the check worth running every time. Subtracting the two computed legs and applying the rate gap to the notional directly are two different routes, and they have to land on the same rupee. Rs 72,00,00,000/- less Rs 60,00,00,000/- is Rs 12,00,00,000/-. Separately, Rs 10,00,00,00,000/- multiplied by 1.20 percentage points is Rs 12,00,00,000/-. Same figure, two roads, and if they ever disagree in a working then one of the legs has the wrong day count fraction or the wrong notional under it.

Step four is the one that carries the argument. The net of Rs 12.00 crore divided by the notional of Rs 1,000 crore is 1.2 per cent, so 98.8 per cent of the headline figure stays exactly where it is. Stated the other way round, the notional is 83.33 times the amount that moved, rounded to two places. The premise sitting under all four steps is that the day count fraction is 1.0000, this first period being one full year.

Three findings come out of that control, and the third is the one to keep. First, the net difference falls as the reading rises, reaches nil at exactly 7.20 per cent a year where the two legs are equal, and then grows again with the payer reversed. Second, at the low end of the declared range the net is Rs 32.00 crore and at the high end it is Rs 28.00 crore paid the other way, so even at the extremes of a six percentage point sweep the amount moving stays under Rs 32.00 crore. Third, and this is why the control was drawn to refuse to move, the notional bar stands at Rs 1,000 crore at every single setting. Nothing about the reading, the gap or the direction has anything to do with it.

How Interest-Rate Swaps Exchange Cash-Flow Exposure, and what changes for each side?

The honest answer to what a swap is for is best taken one party at a time, twice each: once before and once after.

Chitrakoot Cements Limited had an outgoing that moved with the benchmark. Every period it paid an amount it could not work out in advance, and planning around it meant planning around a range rather than a figure. After the arrangement, Chitrakoot Cements receives the benchmark and pays a fixed rate. The moving part it pays out and the moving part it now takes in are computed on the same notional and fall on the same date, so they cancel, and what is left is a steady outgoing.

Saranga Capital Limited went the other way. Saranga Capital had a steady incoming, and after the arrangement it pays fixed and receives the benchmark, so its receipts now move. The new position is not worse and not better, only different, and it is the one Saranga Capital signed up for.

Nothing was bought, nothing was sold and no principal moved, and yet the shape of what each side holds has changed. The sentence is worth reading twice. Most financial transactions change what a party holds. A swap changes only the pattern in which money reaches or leaves each party, and it does so by adding an agreement rather than by moving an asset.

Now the second finding, and readers skip it constantly. The cancellation is only as good as the match between the arrangement and the thing it sits against. Chitrakoot Cements has a moving outgoing cancelled by a moving incoming only if the two are computed on the same notional, on the same benchmark, over the same periods, falling on the same dates. Loosen any one of those and something is left over. How an existing exposure is chosen, how much of it is offset and what happens to the remainder is covered separately. The cancellation is a design outcome and not an automatic one.

Look at the four panels as two diagonals rather than as four boxes. The uneven shape starts on the left and ends on the right. The even shape starts on the right and ends on the left. The two sides traded shapes, and that is exactly what the word swap points at. The bars carry no readings because only the first period reading has been set.

What does it mean that this is an OTC Derivative, agreed privately rather than bought?

An arrangement of this kind is not bought. No screen carried a price, no order was placed, and there was no venue and no queue. Two named parties negotiated terms and signed one document. Most documents would call an arrangement reached that way a privately agreedNegotiated and signed between two named parties rather than bought from an exchange. Most documents call this an over the counter arrangement. one, or an over the counter (OTC) derivative.

Three things follow from that, and at this stage they are the whole of it. Take them one at a time.

First, the terms are whatever the two sides agreed, so no two arrangements need look alike. The notional, the fixed rate, the choice of benchmark, the length of a period and every date in the schedule were negotiated rather than handed down. The flexibility is the reason a privately agreed arrangement exists at all, and it is also why one cannot be read by pattern recognition. The document has to be read.

Second, the other side is a specific named party rather than a market. Saranga Capital Limited is the counterpartyThe specific named party on the other side of a privately agreed arrangement. Who they are matters, in a way it does not when a contract is bought on an exchange. to Chitrakoot Cements Limited, and who they are matters in a way it does not when a contract is bought on an exchange. If a payment is due in some later period, it is due from that party.

Third, somebody has to be told the arrangement exists. Reporting a privately agreed arrangement is a condition placed on the parties by an authority, and that authority is named below rather than its requirements written out.

Who sets the conditions the two parties work under?

Three conditions sit over Chitrakoot Cements Limited and Saranga Capital Limited, and all three are named below.

The first condition is whether an arrangement of this kind may be entered into at all, and by whom. The second is what has to be reported about a privately agreed arrangement, to whom, and by when. The third is what collateral a counterparty places against one. All three go to the Reserve Bank of India at rbi.org.in, and where a contract is instead bought on an exchange the conditions on that side sit with the Securities and Exchange Board of India (SEBI) at sebi.gov.in.

Each condition is set by the authority printed inside the row, and each of them moves, so a figure written out here would be wrong rather than merely old. A stale figure is annoying. A confidently stated figure that changed last quarter is worse. Somebody would act on it.

How does somebody actually use this, and what do they do with it first?

The mechanism is not the job. The steps below are how people whose work touches a swap handle it, and every one of them is a reading step rather than an instruction to do anything.

1. A treasury team separates the notional from the cash flow before anything else. The first line written on any internal note about an arrangement of this kind is the net figure, not the notional, and the notional goes on a second line clearly labelled as a multiplier. The ordering is not a style preference. Putting the net first is the difference between a note that gets read correctly and a note that gets read as Rs 1,000 crore of something.
2. A credit analyst reads the counterparty before the arithmetic. Because the other side is a specific named party rather than a market, a future period's difference is owed by them and by nobody else. Who owes it is the question an analyst asks first about a privately agreed arrangement, and it does not arise in the same form for a contract bought on an exchange.
3. A lender looking at a borrower reads the two legs against what the borrower already holds. An arrangement that turns a moving outgoing into a steady one changes how predictable the borrower's cash cover looks. The reading is about the match: same notional, same benchmark, same dates. A mismatch leaves a residue, and finding the residue is the whole of the reading.
4. Anybody preparing a committee paper writes the period, the day count fraction and the direction on the face of it. Rs 12.00 crore means nothing without the period it belongs to, and 1.2 per cent means nothing without the base it is a percentage of. Writing both in the same sentence is the habit that prevents almost every error of this kind.
5. A household version of the same discipline: read the premium, not the sum insured. A policy for Rs 60,00,000/- and a premium of a few thousand rupees are two different kinds of number, and confusing them is the identical mistake in a smaller frame. Anyone who can keep those two apart on a policy can keep a notional and a net apart on a swap.

What cannot be answered about the arrangement from one reading, and why?

One question cannot be answered from a single benchmark reading: what a swap of this kind is worth today. The reason is worth stating plainly.

Valuing it needs a reading for the floating benchmark in every future period, not one. Only one reading has been set, the 6.00 per cent a year that applies to the first period, and every period after it is one of those empty boxes drawn earlier. No schedule of future readings has been fixed. So the first period net of Rs 12.00 crore is computable and nothing beyond it is.

Supply the missing readings and the question becomes answerable. Until then it is not. A figure produced without them would be somebody's assumption wearing the clothes of a calculation, and a number in those clothes looks finished. No shape a number can take is more dangerous.

The habit worth building is this: when a note or a screen states a value, the question to ask is what schedule of future readings produced it, and unease is warranted if nobody will say. The question is not pedantic. Asking it separates a computed value from an asserted one, and the difference is invisible on the face of the number.

What would have to be known before anybody could answer whether this fits?

A reader who has followed the mechanism this far will ask a reasonable question: is an arrangement of this kind worth being in? The mechanism does not answer that question.

The refusal is not modesty and not a legal reflex. The question is unanswerable in the abstract, and the reason is exact. Six things would have to be known before anybody could answer it, and not one of the six is knowable in advance.

The six boxes have something in common. Every one of them is a fact about a specific reader and a specific counterparty on a specific day. None of them is a fact about interest rate swaps. So the mechanism can be set out completely while neither leg turns out to be the better side to be on. Understanding how something works is not a reason to use it.

Chitrakoot Cements Limited and Saranga Capital Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.