Fixed Leg and Floating Leg: What Each One Knows When

A fixed leg pays at one rate written into the agreement and repeated in every period, so given the calendar and the counting method its whole schedule can be worked out on the day of signing. A floating leg pays at whatever a benchmark reads on each period's reset day, so its schedule becomes knowable one period at a time. Both are worked on the same notional.

A leg is two things held together: a schedule of payment dates, and a rule for filling in the amount against each of those dates. Everything that separates the two legs of an ordinary rate arrangement comes out of where that rule points. The fixed leg's rule points inward, at a number already sitting in the document. The floating leg's rule sends somebody out on a stated day to read a figure that somebody else publishes. One difference in where the rule points produces every other difference between the two legs, and there is no second difference sitting underneath it.

Putting a worth on a rate arrangement takes an expected reading of the floating benchmark for every period still to come. Only the opening reading exists behind these notes, so the arrangement is never given a worth. The opening period, on the other hand, can be worked all the way through, and it is.

One agreement carries every figure here. CHITRAKOOT CEMENTS LIMITED and SARANGA CAPITAL LIMITED, both invented for teaching, have signed a rate arrangement on a notionalThe figure both sides use as the base for working out their own amounts. The notional itself is never paid, lent or borrowed by anybody under the arrangement. of Rs 1,000 crore. Chitrakoot Cements hands over 7.20 per cent a year and takes in the floating benchmark. Saranga Capital does the mirror of that, handing over the benchmark reading and taking in the 7.20 per cent. The benchmarkA rate figure that somebody unconnected to the agreement puts out on a published timetable, and that publication is what lets two businesses work from one number instead of each producing its own. carries no name at all and is only ever called the floating benchmark. Pinning it to a real series would tie the arithmetic to one market at one moment in that market's history, and none of the arithmetic depends on which series is read.

What is the fixed leg, on its own?

The fixed leg is a schedule of payments worked out at one rate, negotiated between the two parties and written into the agreement, and that rate is the same on the last period as it was on the first. On this arrangement that rate is 7.20 per cent a year, and it belongs to Chitrakoot Cements as the side that pays it.

The rate does not respond to anything. No reading moves it. No publication moves it. No event moves it, whether that event happens in the market the two parties operate in, in the wider economy, or inside either business. The only thing that ever ends a fixed rate is the arrangement itself ending. The claim is stronger than most descriptions of a fixed leg make, and the strength is the point: no channel at all carries news to the number.

A looser version of the consequence produces the failure set out further down, under the error that gets made. The consequence therefore repays close attention. Every amount on the fixed leg is computable on the day of signing, given the calendar and the counting method. Not roughly computable, not computable subject to something later. Computable, in the ordinary sense that somebody could sit down with the document on the afternoon it was signed, work each cell out, and never have to revise one of them.

Notice what that statement is about. The statement is about amounts, and only about amounts. The statement says nothing whatever about what the arrangement will do to either party, nothing about what either party will end up transferring, and nothing about whether being on this side of it turns out well. Somebody who reads the sentence as a statement about a party's position has read a different sentence from the one written.

The opening period of the fixed leg is worth working through once. Watching the arithmetic happen teaches more than taking a finished result on trust. The notional is Rs 1,000 crore. The rate is 7.20 per cent a year. The arrangement runs on periods of one full year. A full year makes the day count fractionWhatever proportion of a twelve month stretch one period is treated as covering, fixed by a counting rule both sides agree to beforehand. A period spanning twelve full months comes out at 1.0000. exactly 1.0000. Apply 7.20 per cent to Rs 1,000 crore across a fraction of 1.0000 and the cell reads Rs 72.00 crore grossAn amount taken on its own, before anything owed in the other direction has been set against it. A gross amount can be perfectly correct and still never be transferred.. The same working for the second period gives Rs 72.00 crore. The third and the fourth are also Rs 72.00 crore, and the arithmetic is identical each time only because the fraction is identical each time.

The last clause matters more than it looks. The cells are identical because the counting produces the same fraction in every period, not because a fixed leg is automatically flat. Change the calendar so that periods cover different stretches of a year and the fixed leg produces different amounts while remaining, in every sense that counts, fixed. The rate is what stays fixed, and the rate is what the two sides negotiated.

What is the floating leg, on its own?

The floating leg is a schedule of payments worked out at whatever a named benchmark reads on the reset dateThe stated day on which the reading for the coming period is taken and locked. The reset date sits at the front of the period it governs, not at the end of it. that opens each period. On this arrangement it belongs to Saranga Capital as the side that pays it. Its first reading is 6.00 per cent a year, and applying that to Rs 1,000 crore across a fraction of 1.0000 gives a cell of Rs 60.00 crore gross.

The rule is completely fixed and the numbers are not, and readers collapse those two things constantly. The agreement is exhaustively specific about which reading is to be used, on what day it is to be taken, and from where. The agreement is entirely silent about what that reading will turn out to be. A reader who calls the floating leg vague has confused a rule with its output: the rule is not vague at all, and if it were, the arrangement would be unworkable rather than merely uncertain.

So picture the floating leg as a schedule where the method column is filled in for every single row, right to the end of the arrangement, and the amount column carries a figure only in the rows whose reset day has already come round. The schedule is not an incomplete document. The schedule is a complete document describing an incomplete set of facts, and the two things are easy to run together.

Now the household version, worth keeping because it carries straight through into far harder material further on. A household keeps two standing instructions on one bank account. The first says: pay Rs 8,400/- on the fifth of every month to the same place. Nobody has to look anything up before that payment goes; the amount was settled the day the slip was signed, and twelve months of it were settled at once. The second says: on the fifth of every month, read the electricity meter, work out what is owed on the published tariff, and pay that. The second slip is exactly as precise as the first. The second slip just happens to point at a dial that has to be looked at before a number exists.

What does each leg know, and when did it start knowing it?

The axis the whole comparison turns on is time, and that axis is sharper than the contrast most treatments reach for. The usual framing is certainty against uncertainty. The framing sounds right and teaches almost nothing, and it never says when anybody became certain of anything. Placing both legs on one timeline instead makes the real distinction appear on its own.

The fixed leg is complete from the first day. Run the timeline as far as the closing period and every cell in that row already carries Rs 72.00 crore. Advance the timeline by a period and nothing in the row changes. Nothing about the row was ever waiting to happen. Advance it to the last period and the row still reads what it read on the afternoon of signing.

The floating leg fills in from the left, one cell at a time, and the timing of that filling is the part readers get wrong. The cell for a period is filled at the start of that period rather than at its end. The reset that produces the reading sits at the front of the stretch of time the reading governs. The amount is therefore settled before the period it applies to has run at all.

The floating leg is not unknown during the period it applies to. It became known before that period started. The only unknown periods at any given moment are the ones that have not begun yet, and every description that says otherwise has quietly moved the reset to the wrong end of the period. From the middle of period two, the amount for period two is a settled fact and has been for some weeks; the amounts for periods three and four are the open ones.

The distinction earns its keep the moment somebody has to plan. A treasurer standing at the front of a period knows exactly what the floating leg will produce for that period, and can put the figure in the cash forecast for the coming months without qualification. The uncertainty is real, but it lives further out than the loose description places it, and mislocating it makes a business hold cash against a question that has already been answered.

What do the two legs have in common?

More than a reader expects, and the sharing is not a coincidence of the design. The shared base is the reason the arrangement can work at all.

Both legs are worked on the same Rs 1,000 crore of notional, in the same money, and that is exactly why the notional drops out of the settlement. Chitrakoot Cements owed Rs 72.00 crore one way. Saranga Capital owed Rs 60.00 crore the other way. Only the Rs 12.00 crore of difference is transferred, and that Rs 12.00 crore goes from Chitrakoot Cements to Saranga Capital. Take the notional out of the picture entirely and the settlement is unchanged. The notional was never in the settlement to begin with.

The same Rs 12.00 crore can be reached without working either row. Taking 6.00 per cent a year away from 7.20 per cent a year leaves 1.20 percentage pointsThe plain difference between two figures that are each already expressed as a percentage. Saying a rate is 1.20 percentage points above another is not the same as saying it is 1.20 per cent above it.. Apply 1.20 percentage points to Rs 1,000 crore and Rs 12.00 crore falls out directly. Two routes, one answer, and the second route never mentions Rs 72.00 crore or Rs 60.00 crore at all. The notional has cancelled, and the two routes show the cancelling rather than asserting it.

Set the Rs 12.00 crore against the notional and it is 1.2 per cent of it. Twelve rupees changed hands in the opening period for every Rs 1,000/- of notional. In full rupees the difference is Rs 12,00,00,000/- against a notional of Rs 10,00,00,00,000/-, and writing both out at that length is a useful once-only exercise in seeing how much smaller the moving figure is than the figure everybody quotes.

The sharing runs past the notional. In the ordinary case both legs run on the same calendar, so both reach a payment date on the same day. Both sit in the same document, so one set of definitions governs both. And both obey the same discipline of a rate applied to a figure across a fraction of a year. The two amounts are therefore comparable quantities rather than two different kinds of thing.

With one notional, one currency and one date shared between them, the two legs can be set against each other, and a single transfer discharges both. That operation is called nettingSetting two amounts owed on the same day between the same two sides against each other, leaving a single transfer of the leftover to discharge both of them.. Had the two legs been worked on different figures, or in different currencies, or reached their dates on different days, nothing would cancel and both amounts would have to be paid in full in both directions.

Is one of the two legs the risky one?

Almost every reader arrives with this question, and it deserves better than a hedge. Neither leg is the risky one in the abstract, and the refusal comes out of how the thing is built rather than out of caution: a leg is never held on its own.

Look at what a party actually holds. Chitrakoot Cements does not hold the fixed leg. Chitrakoot Cements pays the fixed leg and receives the floating leg, and after netting it is left carrying the difference between them. In the opening period that difference ran to Rs 12.00 crore going out. Saranga Capital is in the mirror position. Neither of them is exposed to a leg. Both are exposed to a gap, and that gap is then set against whatever each business's own money was already doing before either of them signed anything.

The illustration that makes this land needs no recommendation in it at all. Take two parties. The first has receipts that already rise and fall with a published reading. Its own contracts are written that way. The second has receipts that arrive at the same size every month regardless of what any reading does. Now put both of them on the identical side of the identical arrangement, paying fixed and receiving floating, on the identical notional, at the identical rate.

The two parties are in completely different situations. For the first party, receiving an amount that moves with a reading may sit alongside receipts that move the same way, so the whole picture is calmer than the arrangement alone would suggest. For the second, receiving an amount that moves alongside receipts that do not means the picture has become less predictable, not more. Nothing about the arrangement distinguishes the two cases. Everything about the parties does.

The question cannot be answered from the arrangement alone. Answering it would need the party's own receipts and payments, the periods they arrive over, what the party owes and on what basisThe thing a rate follows. For a fixed rate it is the document itself; for a floating rate it is a figure produced outside the document on a published schedule., and what the whole picture looks like in a period where the difference runs the other way. None of that is in the agreement, and none of it is in these notes.

What does paying a leg do to the shape of a party's cash flow?

Something, certainly, and the honest description of that something is narrower than the words most readers reach for.

A party paying the fixed leg and receiving the floating leg has turned a steady outgoing into one that moves. A party on the other side has done the reverse: it has turned an outgoing that moved into one that does not. Both statements are about the shape of one stream of money, and both are true of the arrangement in isolation.

The word for what happened is changed, not reduced and not removed. Neither of those two stronger words follows from the arrangement, and reaching for them is where description turns into recommendation without anybody deciding to make one. Reduced compared with what? Removed from whose overall position? Both questions need information about the party that the agreement does not carry.

Here is the test a reader can actually apply. After the arrangement, is the party's total cash flow steadier than it was before, or less steady? Not the leg. Not the arrangement. The total. The answer depends entirely on what the party's other cash flows were doing, and neither the arrangement nor these notes carry that information.

Run the household version to feel it. A household on one salary swaps a steady rent for one that moves with a published index. Its month is now less predictable. The money coming in did not move and now the money going out does. A street vendor's takings swing hard with the season. Swap a steady stall fee for one that rises and falls with those same takings and the vendor's month becomes more predictable. The two now move together. Identical swap. Opposite result. The swap did not decide it; the rest of the picture did.

Can both legs float, or both be fixed?

Almost nothing written about swaps asks this question, and that is a pity. Answering it settles what a leg actually is.

Both floating is an ordinary structure and gets written all the time. Two legs, each following a benchmark, each referencing a different reading, both worked on one shared notional. The arrangement is then about the gap between two moving numbers rather than the gap between one moving number and a still one. Nothing in the arithmetic objects: once both readings for a period have been taken, both amounts exist and their difference is a single figure, exactly as it is here.

Both fixed is perfectly possible to write and almost pointless to write. Two schedules of already-known amounts on a shared notional produce a known series of transfers, in a known direction, of known sizes, from the day of signing. The two parties could have skipped the arrangement and simply agreed that schedule of transfers directly. Nothing is being exchanged that they did not already know they were exchanging.

So a leg is a rule for filling in a schedule, and fixed and floating are two kinds of rule rather than the only two things a swap can be built out of. That reframing does real work later. The reframing is what lets a reader meet an arrangement whose legs follow something other than a rate without needing a new mental category for it. The shape has not changed at all: two schedules, two rules, one shared base, one difference.

What do both legs look like when they are drawn out in full?

Everything above has been about rules. Here is the arrangement itself, both legs and the settlement beneath them, on one timeline of four full periods.

The fixed leg belongs to Chitrakoot Cements, the side paying 7.20 per cent a year. At a day count fraction of 1.0000 every cell in that row reads Rs 72.00 crore gross, from the opening period to the closing one, and every one of them was filled in on the day of signing.

The floating leg belongs to Saranga Capital, the side paying whatever the benchmark reads at each reset. Its opening cell reads Rs 60.00 crore gross, from a reading of 6.00 per cent a year. Every other cell in that row is empty, and it carries the words no reading taken rather than a dash or a zero. A dash suggests nothing was due and a zero suggests nothing was owed, and neither of those is true. The reading that would fill the cell has not been taken, and this record holds no reading for that period at all.

Beneath both rows sits the settlement. Its opening cell reads Rs 12.00 crore of net difference, paid by Chitrakoot Cements to Saranga Capital. Every later cell is empty for exactly the reason the floating row's are.

Now count the filled cells in each row. The shape is the lesson. The fixed row has four out of four. The floating row has one. The settlement row also has one, and it could not have more: a settlement can be no more complete than the less complete of the two legs above it, since a difference needs a figure on both sides before it exists at all.

Knowing the whole of one leg tells a party what it will pay gross and tells it nothing at all about what will change hands. Chitrakoot Cements knew on the day of signing that its gross obligation was Rs 72.00 crore in each of the four periods. Chitrakoot Cements knew, on that same day, precisely nothing about the four transfers, and it still knows only the first of them.

Why does the floating leg here stop after one cell?

The row stops because the readings stop, and the readings stop because this record contains exactly one of them.

Set beside each other honestly, the two legs give this picture. The fixed leg is knowable for every period from the day the agreement is signed. The floating leg is knowable one period at a time, and one period is what exists here. So the truthful statement of the pair is that one leg is fully specified and the other is specified once, and completing the second would take readings this material does not hold.

The lopsided picture is the truest picture anybody could draw of this arrangement from a single reading, so it is worth drawing rather than apologising for. An account that filled the remaining cells with plausible-looking figures would look more finished and would be a fabrication, and worse, a fabrication a reader has no way of detecting. The blank cells are doing honest work: they mark exactly where the record ends.

The missing item is specific and worth naming. Naming it makes the gap checkable rather than vague. Each later cell needs a reading of the named benchmark for that period, read on the reset day belonging to it, and put out carrying the date it was read. Four such readings and the arrangement's whole floating row is complete. Three of them are missing, and that is why three settlement cells are missing too.

None of the three missing readings is estimated, and the agreement is never given a worth. Valuing it would take the whole run of expected readings rather than the four actual ones, and this record holds neither.

Who decides what a floating leg is allowed to follow?

Somebody other than the two parties, and that fact is not paperwork. The routing question is the last evidence that the two legs are not equal in what they depend on.

A fixed leg references nothing outside the document it is written in, so it needs nobody's permission in this respect. The rate was negotiated between the two sides, written down, and that is the end of the matter as far as any outside reference goes. A floating leg references something a third party publishes on a schedule. The outside reference immediately raises two questions the fixed leg never raises: which readings may be referenced at all, and who is answerable for administering them.

The two legs are not symmetrical in what they lean on, and the routing row below is the evidence rather than the boilerplate. It is here for the same reason the timeline is: it shows a structural difference between the legs that a description in adjectives would miss entirely.

How does somebody reading a set of accounts use any of this?

A credit analyst opens the notes to a set of accounts and finds a rate arrangement disclosed. How does the distinction drawn here change the work?

Three things, and each of them is a question the analyst can ask out loud. The first: which leg is this business paying? The answer fixes the direction, and it is the one fact the disclosure almost always gives plainly. The second: how far out is the floating leg already settled? If the reset for the current period has happened, then the amount for that period is a known figure and belongs in the near-term cash forecast as a number rather than as a range. Getting the timing right pays off exactly there, and analysts who carry the loose picture of a floating leg leave a settled figure sitting in the uncertain column for months.

The third question is the one this guide exists to force: what is the disclosure telling the analyst about, the legs or the difference? A note that prints Rs 1,000 crore of notional beside 7.20 per cent a year has told the analyst about a leg. The figure that will reach the business's bank account is the difference, and on the opening period of this arrangement that was Rs 12.00 crore rather than Rs 72.00 crore or Rs 1,000 crore. An analyst who puts the notional in a table of obligations has mis-stated the business by a factor of more than eighty, using nothing but figures the disclosure genuinely contained.

A lender doing the same reading asks a fourth question, and it is about the counterpartyThe other named side of a privately agreed arrangement. Each side depends on that specific business turning up on the day a payment falls due. rather than the legs: who is standing on the other end, and what happens to this borrower if that side does not pay. The counterparty question belongs elsewhere in this material and is not opened here, but it is worth knowing that it exists and that neither leg answers it.

Which side of an arrangement is right for a given party?

Not answered here, and not answered anywhere else in these notes.

Neither leg is presented as preferable to the other. Comparing outcomes would take a run of past readings, a distribution, probabilities and a record of how things turned out, and one opening period of one agreement supplies none of them. Every figure in this guide belongs to one invented agreement over one opening period.

Setting out what somebody would need in hand before answering turns an unanswered question into a mechanism rather than a hedge. The party's own receipts and payments, and the periods they arrive over. The party's own borrowings, and the basis each one carries. The party's position in a period where the difference runs the other way and the transfer arrives rather than departs. Whether the party could carry that period. None of that is in this guide, and none of it is anywhere in these notes.