Swap Rate and Forward Rate: What Each One Covers Ahead

A swap rate is the one fixed rate written into a swap agreement and applied to every period it runs for. A forward rate is a rate for a single stretch of time that has not begun yet. One number stands for a whole schedule; the other stands for one interval. Neither is a prediction, and neither can be recovered from the other without a quoted rate for every interval.

Two rates keep turning up in the same conversation about the same arrangement, and they get mixed up constantly. Both are percentages. Both are about time that has not happened yet. Both are written down by the same people in the same units on the same sheet of the same note. So somebody who meets one of them on a Tuesday and the other on a Friday has every reason to assume they are two names for one idea. The two rates are not the same idea. The separation is not subtle once it has been seen, and it is not a question about finance at all. The question is one about calendar.

Step away from rates for a moment. A housing society signs a maintenance contract for its lift at one flat charge a month for the coming year. The flat charge covers January, it covers December, and it covers every month in between, and nobody renegotiates it in June because the weather changed. Separately, the same society asks a contractor what it would cost to replace the lift doors in April. The replacement quotation is also a price, it is also about the future, and it covers April and nothing else. One of the two figures sits in a contract that runs all year. The other is a quotation for one job in one month. Nobody in that society confuses them. The two rates compared here are separated by exactly that difference, and by nothing else that decides anything.

The two names, before the two definitions. A swap rateThe single fixed rate written into a swap agreement and applied to every period of it. There is exactly one of them in any given agreement. is the flat charge in that analogy: one figure negotiated into a document, applied everywhere in it. A forward rateA rate for one stretch of time that has not started yet, running from one future date to another future date. A forward rate says nothing about any other stretch. is the quotation for April: one figure attached to one stretch of time that has not started yet. The full scheduleThe complete set of periods an arrangement runs over, from the first to the last. A schedule is a list of dates, not a list of values. of an arrangement is the whole run of periods it covers, and each single stretch inside it is one intervalOne stretch of time between two dates. An interval is the unit a forward rate is attached to: one rate, one interval, no more and no less.. A comparison like this one is often met cold, by somebody who has not met either rate before. Each of the two is taken apart on its own first.

Everything below that carries a number runs on one invented arrangement. Chitrakoot Cements Limited pays 7.20 per cent a year and receives the floating benchmark. Saranga Capital Limited pays the floating benchmark and receives 7.20 per cent a year. The notional both rates are applied to is Rs 1,000 crore. The floating benchmark keeps that name throughout. Putting a real name on it would date the material and would say something about a real market for which there is no basis.

One point shapes everything that follows. No forward rate for any stretch of time stands behind this worked case, and none was made up to fill the space, so the comparison runs on what the two rates cover rather than on what they equal. The missing side is not a gap somebody forgot to close. The absence is the honest shape of what exists, and a block below makes it the lesson rather than an apology.

What does a swap rate actually cover, and over how long?

A swap rate is the fixed rate two parties negotiate and write into a swap agreement. In the arrangement between Chitrakoot Cements Limited and Saranga Capital Limited it is 7.20 per cent a year. The figure was arrived at by two sides talking to each other, it went into the document on the day the document was signed, and from that moment it is a term of the agreement in exactly the way a delivery date or a notice period is a term of the agreement.

One number applies to every period of the arrangement, the first and the last alike. A move in the floating benchmark does not move it. Almost every mistake made with swap rates is a failure to hold on to that one property, so it is worth reading twice. In the first period Chitrakoot Cements owes the fixed leg computed at 7.20 per cent a year. In the second period it owes the fixed leg computed at 7.20 per cent a year. In the last period, whenever that falls, it owes the fixed leg computed at 7.20 per cent a year. Nothing happening in the world between those dates touches that figure. The agreement fixed it once.

There is a practical consequence that makes swap rates unusually easy to find, and it is worth saying plainly because readers often assume the opposite. An agreement of this kind contains exactly one swap rate, and locating it in the document takes about ten seconds. The search is not for a series, not for a table, and not for anything that has to be computed. The search is for one percentage with a period attached to it, sitting in a clause, next to the notional it is applied to. If two figures both look like candidates, one of them is the floating leg description rather than a rate, or the agreement covers something other than the plain arrangement worked here.

Notice what this makes the swap rate, as an object. A swap rate is not an observation of anything. Nobody read it off a screen and copied it into the document. Two parties settled on it, in the same way two parties settle on a rent, and once settled it belongs to that document and to no other. Neither figure would be a measurement, so a different pair of parties signing on the same afternoon could write a different one and neither of the two would be wrong.

What does a forward rate cover, and over how long?

A forward rate is a rate for one stretch of time that has not started yet. The rate runs from a future date to another future date, and both of those dates are part of what it is. A forward rate without its two dates is not an incomplete forward rate; it is not a forward rate at all, in the same way that a train fare without a route is not a fare. The dates are not decoration attached to the number. The dates are the half of it that says what the number is for.

A forward rate covers one interval and says nothing whatever about any other interval. This is the mirror image of the property that defines a swap rate, and it is where readers usually go wrong in the opposite direction. Learning that a forward rate is about the future, they quietly extend it over the whole future. A forward rate does not extend. A rate for the stretch running from the start of the fourth period to the end of the fourth period describes the fourth period. The fourth period rate is silent about the third, silent about the fifth, and silent about the arrangement as a whole.

The practical consequence runs the other way from the one above, and it is the reason this comparison exists at all. A forward description of a stretch of calendar is a list with one entry for every interval in it, so where a swap agreement holds one rate, a forward description of the same stretch of time holds as many rates as there are intervals. An arrangement running eight periods has one swap rate in its document and would take eight forward rates to describe in this second way. Sixteen periods, sixteen forward rates, and still one swap rate. The two descriptions are not different lengths by accident. The two answer different questions, and that is what sets their lengths.

One more thing about where a forward rate lives. A forward rate is quotedPublished with a date and a source attached to it. A figure that arrives without both of those has not been quoted; it has merely been mentioned., or it is worked out from other quoted rates, and either way it belongs to whoever published it rather than to any pair of parties. A forward rate was a rate somebody was prepared to arrange on a particular day, so it carries that day's date, and the next day there is a fresh one. Nothing about a forward rate is signed by anybody.

What is the one axis that actually separates them?

Put the two definitions on top of each other and the difference is arithmetic in shape rather than in level. One number against a list of numbers, describing the same stretch of calendar. Everything else people say about these two rates is downstream of that. A swap rate is a single figure that two parties agreed to apply everywhere in an arrangement, and a forward rate is a figure attached to one place in it.

The temptation in a comparison of this kind is to reach for a longer list of differences and to treat them as equals. The differences are not equals. Where each rate comes from, what moves it, who it belongs to and how many of them there are for a given stretch of calendar all follow from coverage. Coverage is the axis. The rest is consequence.

Take the consequences one at a time. Because a swap rate has to work across a whole schedule, it cannot be re-cut when one period turns out differently from another, so nothing moves it once the document is signed. Because a forward rate covers one interval, a fresh one can be quoted for that interval tomorrow without anything else having to change. Because a swap rate was negotiated, it belongs to the two parties who negotiated it. Because a forward rate was published, it belongs to whoever published it, and it carries their date.

A swap rate has to work across a whole schedule and a forward rate does not. The two are therefore answers to different questions, and comparing their levels without saying which stretch each one covers means nothing at all. If somebody claims that a swap rate is higher than a forward rate, the only correct first response is to ask which forward rate, covering which interval, and to keep asking until the calendar is on the table. Two figures that cover different stretches of time are not high or low relative to each other. The two figures are simply about different things.

Is either of these two rates a forecast of anything?

No, and the error is one that recurs in new clothes. Earlier in this subject area a forward price of Rs 2,130.00/- was built out of a spot price of Rs 2,000.00/- and a financing cost of 6.50 per cent a year, and the lesson of forward pricing was that the answer is carry rather than opinion. Nobody predicted a rise. The number says what it costs to buy now and hold, and nothing else. The same discipline applies to both of the rates here, and it applies just as strictly.

Take the swap rate first. The 7.20 per cent a year in this agreement is a rate two parties negotiated and wrote down. The agreed rate is not a statement that the floating benchmark will average 7.20 per cent a year over the life of the arrangement, it is not anybody's view, and it is not evidence of anything. Two sides sat down, each with its own reasons for wanting the shape of its cash flow changed, and they settled on a term of a contract. Reading a forecast out of a negotiated contract term is like reading a weather forecast out of a rent agreement because the rent was agreed in monsoon.

Now the other side. A forward rate is a rate at which something can be arranged now for an interval that has not started, and reading it as a prediction of what that interval will turn out to be is the single most common error anybody makes with rates. It is arithmetic on what can be borrowed and lent today, in exactly the way the forward price of Rs 2,130.00/- was arithmetic on a spot price and a financing cost. A forward rate is a cost, not an opinion.

There is a third kind of figure that gets swept into the same confusion, so name it and put it in its place. A benchmark readingThe value a published benchmark takes on a stated date. A benchmark reading is an observation of one date, and it describes that date rather than any date after it. is the value the floating benchmark takes on a stated date, and in this arrangement it is 6.00 per cent a year for the first period. The reading of 6.00 per cent a year is an observation. The reading describes a date that has already arrived. A benchmark reading is not a forecast either, and it is not the same kind of object as either rate above. Three different kinds of figure, none of them an expectation, all of them regularly read as one.

What can be said about one rate if the other is known?

Very little from one alone, and the honest answer is worth more here than a satisfying one. The relationship itself comes first, stated in words rather than in symbols. Building it is covered separately, and it is used here rather than rebuilt. A swap rate is the one fixed rate that makes the whole schedule of fixed amounts balance against the whole schedule of floating amounts. The rate therefore depends on every interval in the arrangement rather than on any one of them.

Read that again with the emphasis on the last clause. Not on the first interval, not on the middle one, not on the longest one. On all of them, together, as a set. The one figure has to do a job across the entire run of the arrangement, and it is settled by the whole set of intervals working on it at once.

Two consequences fall out, and they run in opposite directions. One interval out of many barely moves a figure that has to answer to all of them, so knowing one forward rate says almost nothing about the swap rate. And in the other direction the loss is total rather than partial. The arithmetic that produced the swap rate collapsed a whole set of figures into one, and a collapse of that kind cannot be run backwards. Knowing the swap rate says nothing at all about any individual forward rate.

An everyday version makes the second half obvious. A shopkeeper reports that the average bill across every customer who came in today was Rs 340.00/-. How much did the fourth customer spend? The average was built by throwing away exactly the information now being asked for, so nobody can say, and no amount of thinking about it will help. The swap rate did the same thing to the intervals, and it did it on purpose. A single figure that both sides can live with for the whole arrangement is the entire point of writing one.

The trap this kills is the reader who assumes the swap rate is roughly the forward rate for the middle of the arrangement, and that reader has invented a relationship nobody ever stated. It feels reasonable. A single number standing for a set feels like it ought to sit somewhere in the middle of that set, and sometimes it might. But no arithmetic anywhere puts the swap rate near the middle of the set, and a reader who acts on the feeling is acting on an assumption they made up and then forgot making.

Why can no side by side arithmetic be worked here?

Because a forward rate is a rate for a stretch of time that has not started yet, and there is not one of those written down anywhere behind this worked case. The record here holds one benchmark reading, 6.00 per cent a year for the first period, and it holds no reading and no rate for any period after that. A single reading for a period that is already fixed is not a forward rate, and calling it one would not make it one.

So the comparison runs on what the two rates cover rather than on what they equal. A set of forward rates produced here would have been produced from nowhere, and no reader would have any way at all to tell that set apart from a real one. The absence is itself the lesson. Made-up figures do not arrive labelled. Such figures sit in a note in the same font as everything else, they add up, they look reasonable, and a reader three steps downstream repeats them to somebody who repeats them again.

The missing input can be stated exactly. For each future interval in the arrangement, a rate covering that interval, from a source that publishes such rates, carrying the date on which it was published. Eight intervals, eight rates, eight dates, one named source. With that in hand the comparison could be worked, and the block above about what one rate says of the other could be shown rather than described. Without it, nothing honest can be put in the column.

One route is the obvious wrong idea, and it is worth closing off before anybody tries it. The forward rates cannot be worked back out of the swap rate. The block above is exactly why: the dependency runs one way, from the whole set of intervals into the one rate, and a set cannot be recovered from the single figure it collapsed into. Anybody who fills the empty column that way has not sourced the figures. The figures were made up, with an extra step in front.

Where is each rate found, and what comes attached to it?

Knowing where to look, and what to demand on arrival, is where the distinction earns its keep. Take the swap rate for a particular arrangement first. The rate is in the agreement, negotiated and signed, sitting in a clause beside the notional it is applied to. There is nowhere else to look for it, and a swap rate sent for an arrangement without the arrangement itself is a figure with no home.

A swap rate for the market generally is a different object with the same name, and this is where careful readers get careless. A market swap rate is quoted, by somebody, on a date. The quoted rate did not come out of any particular agreement, and it does not belong to any particular pair of parties. When somebody says the swap rate moved today, they are talking about the second kind, and when somebody says the swap rate on a named arrangement is 7.20 per cent a year, they are talking about the first. The first one does not move at all, so the two never move together.

A forward rate is quoted, or it is worked out from other quoted rates, and how that working is done is covered separately in the fixed income material. Two things come attached, every time and without exception: a date and a source. A rate without its date and its source attached looks usable, and looking usable makes it worse than no rate at all. No rate at all is obviously a gap and somebody goes and fills it. A bare number is quietly copied into a note, then into a second note, and by the time anybody asks where it came from the trail is three documents long and cold.

One routing matters enough to state separately. Which rate may be used as a reference rateA rate used for valuing or for reporting rather than for paying. An authority sets what may serve as one, and that is not the same question as what two parties may agree to pay each other on. for valuation and for reporting, and which benchmark readings may be referenced in an arrangement at all, are both set by the Reserve Bank of India at rbi.org.in. Both conditions are named here and neither is stated here, and the block below on authorities explains exactly why that line is drawn where it is.

What does a rate say until what it is applied to is known?

Nothing. The same confusion arrives wearing a percentage sign, so the notional point from the opening of this sequence returns in the language of rates. An arrangement quoted by its notional has been quoted by its multiplier rather than by its money. On this agreement the multiplier is Rs 1,000 crore. For the first period the two sides settle a net difference of Rs 12,00,00,000/-, or Rs 12.00 crore.

The build matters more than the total. The fixed rate of 7.20 per cent a year less the floating benchmark reading of 6.00 per cent a year is 1.20 percentage points. Applying 1.20 percentage points to a notional of Rs 1,000 crore over one full period gives Rs 12,00,00,000/-. The check runs the other way. Rs 12,00,00,000/- divided by the notional is three two-hundred-and-fiftieths, or 1.2 per cent of the notional exactly. The two routes land on the same rupee, and landing together is the only reason to trust either.

Now put the two figures beside each other and look at the size of the gap. The notional divided by the net difference is two hundred and fifty thirds. Written as a decimal that is about 83.33 times. The division does not come out even, so 83.33 is a rounding rather than an equality, and printing it as though it were exact teaches a reader to stop checking. Either way, a figure quoted as Rs 1,000 crore describes something roughly eighty three times the size of the money that actually moved.

One more ratio, and this one is exact. The two legs gross were Rs 72,00,00,000/- and Rs 60,00,00,000/-. Between them they come to Rs 1,32,00,00,000/-. Divided by the net difference of Rs 12,00,00,000/-, that comes to eleven, with no remainder at all. Eleven times the money would have moved if the two sides had settled gross instead of netting, to achieve exactly what one transfer achieved.

So the habit is a pair of questions, and they cost nothing to ask: when somebody quotes a rate, the question is what it is applied to and over what period, and when somebody quotes an amount, the question is whether it is a multiplier or a payment. Neither question is clever. Both of them stop the most expensive misreadings in this subject area before they reach a note.

How does the one fixed rate work out, period after period?

The worked instance has a shape worth noticing before a single figure in it is read. One side of this comparison is worked in full. No values exist for the other, so it is described in full with the values left out.

The swap rate side first. The fixed rate is 7.20 per cent a year, written into the agreement between Chitrakoot Cements Limited and Saranga Capital Limited. The notional it is applied to is Rs 1,000 crore. Over one full first period that gives a gross fixed leg of Rs 72,00,00,000/-, or Rs 72.00 crore. And the sentence that makes it a swap rate rather than a reading is this one: the same rate applied to the same notional over the same period length gives Rs 72,00,00,000/- again in the second period, and again in the third, and again in every period after that until the arrangement ends.

Now the forward rate side. This record contains no forward rate for any interval of this arrangement, so the forward rate side carries no worked figures at all. What such a rate would carry can be named exactly: a start date, an end date, and a value. The first two are structural and could be written down from the agreement. The value is the part that no source supplies here. So one side stands fully worked and the other fully described, and the shape is an honest one.

Who sets the conditions on which rates may be referenced?

The authority printed inside each row below sets the condition in that row. Each of those conditions moves, and writing one of them out here would be wrong rather than merely out of date on the day it changed. Wrong and confident is a worse thing to hand somebody than empty and honest, so every row below is labelled and routed to the authority that sets it.

How does somebody actually use this distinction at work?

The mechanism is not the job. People do five things with the distinction once they have it, in the order set out below, and every one of them is a reading habit rather than a decision about whether to be in anything.

1. Anybody writing a rate into a note writes the coverage beside it in the same line. Not in a footnote and not in the next paragraph. A rate on a line by itself invites the reader to compare it with the next rate they see, and the coverage is the only thing that says whether those two are comparable. One extra clause saying what stretch of time it covers does the whole job.
2. An analyst reading somebody else's note asks what each rate covers before asking whether it is high or low. High and low are questions that only make sense once two figures are known to be about the same thing. Asked in the other order, the analyst has already agreed to a comparison nobody established, and every conclusion after that inherits the fault.
3. A lender reading a borrower's arrangement takes the fixed rate out of the document and does not go looking for it on a screen. The rate that decides what the borrower pays on the fixed leg is a term of that agreement, and a market rate carrying the same name is a different figure entirely. Reading the second where the first was needed produces a number that is plausible, sourced, and about the wrong thing.
4. Anybody preparing a committee paper attaches a date and a source to every rate that came from outside the document, and states in one line where the ones inside the document came from. Two kinds of rate in one document need two kinds of provenance, and mixing them is how a figure ends up in a paper with nobody's name behind it.
5. The household version, which is the same discipline in a smaller frame: read the annual maintenance contract and the one-off quotation as two different kinds of price. The flat monthly charge covers the whole year and does not change because a repair happened. The quotation covers one job in one month. Anybody who can hold those two apart on a society notice board can hold a swap rate and a forward rate apart in a note.

Where does this reading go wrong, and what does the mistake cost?

The failure is treating a swap rate as a prediction of the benchmark, and it is made most often by somebody who has just learned what a swap rate is. The timing of the mistake matters. Ignorance does not produce it. A reader who has understood one thing correctly extends it one step too far, and that is why it slips past people who would have caught something cruder.

Does knowing all this settle what to do?

No, and the limit is worth stating in full. Understanding what each rate covers is a reading skill. The skill allows a reader to take somebody else's note apart, ask the right question about a figure in it, and notice when two numbers are being compared that were never about the same stretch of time. The reading skill gives that much and no more, and it is genuinely useful.

Three questions stay open: which of the two rates anybody ought to be paying, whether a swap rate quoted today sits at a level anybody should sign at, and whether any particular reader ought to be in an arrangement of this kind at all. None of those can be answered here, and the reason is structural rather than cautious. An answer would need the reader's own position, and no reference material holds it.

The missing facts can be named, so that the gap is described rather than shrugged at. The reader's existing holdings, and the shape in which their cash arrives. The change the reader wants in that shape, and the reason for wanting it. Who the other side would be and what happens if that side stops paying. The collateral that would have to be placed, on what terms, and the cost of leaving early. The reporting that has to be done, and to whom. Not one of those is held here, and no reference material can hold them. They are facts about the reader rather than about the instrument.

One last point belongs here rather than anywhere else. This record holds no outcome, no track record and no probability of any kind, so the two rates are not compared on outcome. Neither rate is better than the other, and neither side of the arrangement did well or badly. Somebody who was on the paying side of a period has not failed at anything, and treating that as failure reads a result into an obligation.

Which neighbouring subjects are covered elsewhere?

A comparison earns its length by holding one axis rather than drifting into the neighbouring subjects that would blur it, and those subjects are set out below. Each of them is worked in full elsewhere.

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