Vertical and Calendar Spreads: What Varies Between Legs

A vertical spread holds two legs that end on the same date at different levels. A calendar spread holds two legs at the same level that end on different dates. The difference in what varies decides everything else about each pair, including whether what it pays can be drawn at a single date from arithmetic alone. The vertical pair can be. The calendar pair cannot.

Set side by side, the two names sound like variations on one theme. The resemblance stops at the word spread. One of them produces a shape that can be worked out with a pencil at any price at all. The other produces no single shape at all. On the day that shape would be drawn, one of its two contracts has not finished. Everything in this guide comes back to that, and the whole of it can be recovered from two fields on a contract row.

The everyday version comes before the finance version. A household takes two loans in the same month. Both are due on the last day of March, and they differ only in size. Both are done, so on the first of April the household can add them up and say exactly what it paid. Now change one thing: the second loan is due in September instead. One of the two is still running, and what it will finally cost depends on things nobody has measured yet. So on the first of April the household still cannot say what the pair cost. The March pair can be totalled. The March-and-September pair cannot, not on the first of April, no matter how careful the arithmetic is. The gap between a pair that can be totalled and a pair that cannot is exactly the difference between the two spreads here, and it survives the translation into contracts without losing anything.

What is a vertical spread, before anything gets compared?

A vertical spreadTwo legs that end on the same date and sit at different levels. The word vertical comes from the levels being stacked one above the other on a screen, nothing more. is two legsOne contract held inside a larger position. A leg is complete on its own and keeps its own obligation however many other contracts sit beside it. that end on the same date and sit at different levels. The definition ends there. The name is doing nothing except describing how the two levels look stacked on a screen, one above the other. Write it out as signed primitivesOne leg written as four fields: a plus or a minus, a call or a put, one level, and one end date. The word primitive means the row cannot be broken down any further. and the pair in this guide reads: plus one call at Rs 2,000.00/- for one year, minus one call at Rs 2,200.00/- for one year. Two rows. Same last field. Different third field.

Read the obligations one row at a time. Reading a row at a time is the only approach that survives being surprised. The bought leg gives its holder a choice at the end date and obliges nothing further once the premium has been handed over: if the reference asset finishes below Rs 2,000.00/- the holder simply does not use it, and no further demand arrives. The written leg is the opposite arrangement seen from the other side. Its writer has no choice at all. Above Rs 2,200.00/- the writer must perform at the other side's choosing, and every further rupee of price is another rupee owed.

Held together, the two rows oblige something neither of them obliged alone. What the pair pays stops rising at Rs 200.00/-, the distance between the two levels, and stays at Rs 200.00/- at every price above the higher one. Neither leg on its own has that property. The bought leg keeps rising forever and the written leg keeps owing forever, and it is only their sum that goes flat. The flat stretch is worth saying carefully, and it is the one thing about a vertical pair a reader can check without any premium, any rate and any assumption. Checking it is arithmetic on two rows.

Work it at a price to see the flatness arrive rather than taking it on trust. At a price of Rs 2,400.00/- at the end date, the bought leg at Rs 2,000.00/- pays Rs 400.00/-, and the written leg at Rs 2,200.00/- owes Rs 200.00/-, so the pair pays Rs 200.00/-. Push the price to Rs 2,600.00/- and the bought leg pays Rs 600.00/- while the written leg owes Rs 400.00/-, and the pair still pays Rs 200.00/-. The extra Rs 200.00/- of price movement between those two cases arrived on one row and left on the other in the same instant, so it reached the holder as precisely nothing.

One caution about Rs 2,200.00/- before it becomes furniture. Rs 2,200.00/- is a declared levelA level chosen here purely to draw a shape. The level carries no premium anywhere and is not read off any venue or any contract., chosen at ten per cent above the spot price purely so that a second level exists to draw with. A declared level carries no premium anywhere in this guide. The levels at which contracts are actually made available, and the spacing between them, are set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in. So Rs 2,200.00/- is geometry, and Rs 2,000.00/- is the one level in this worked example that carries premiums at all.

What is a calendar spread, before anything gets compared?

A calendar spreadTwo legs at the same level that end on different dates. The word calendar points at the only field that differs, the date. is two legs at the same level that end on different dates. Written out, the pair in this guide reads: minus one call at Rs 2,000.00/- ending at the near date, plus one call at Rs 2,000.00/- ending at the far date. Two rows again. Same third field this time. Different last field.

Read the way most readers first read them, those two rows lead to a wrong answer honestly reached. The levels match. One row carries a plus and the other a minus. Everything about the shape of the thing as written says these two cancel out, and the reader moves on believing the position is nothing at all. Legs cancel only where the level and the date both match, and in this pair only the level matches, so the two rows do not cancel. GroupingSorting the legs of a position by level and by end date before reading what the position obliges. Two legs meet only when both fields agree. is done on two fields, not one, and dropping the second field is the single commonest way a calendar pair gets misread into nothing.

The everyday check is quick. Two people agree to swap the same thing on two different dates, and no amount of matching on the thing makes those two agreements one agreement. Somebody still has to turn up twice. Contracts behave exactly the same way, and the reason is not subtle: settlement happens on a date, and two different dates are two different settlements whatever else agrees between them.

At the near date the calendar pair stops resembling anything else in this guide. On the near date the written leg is settled and finished. If the reference asset stands at Rs 2,400.00/- on that date, that leg settles owing Rs 2,400.00/- less Rs 2,000.00/-, or Rs 400.00/-, and the figure is exact. The written row is now closed and will never be reopened. The other row is not closed. The bought leg at the far date is still running, with time left in it, and it has not paid anything and will not pay anything until its own date arrives.

So what the holder has at the near date is a settled amount beside a live legA leg that has not reached its end date, so it has a value rather than a payoff. A value is a price; a payoff is arithmetic on the price., and that combination is not a payoff at all. It is minus Rs 400.00/- settled, plus one contract still running. A settled amount and a live leg are not the same kind of object, and they do not add. One is arithmetic on a price. The other is a price. Working out what a contract with time left in it is worth needs an input covered separately.

Notice how little of that depended on anything clever. No rate was applied, no premium was needed, and nothing was assumed about where the price might go. The two rows were read, the dates were compared, and the near date was walked to. Reading the rows and comparing the dates is the whole method, and grouping by field is set out below before it is used on both pairs at once.

What actually varies between the legs, and why does nothing else matter until that is settled?

Two legs written out in full can differ in the level, in the end date, or in both. The list ends at three. Each case behaves so differently from the others that naming the pair before sorting out which case applies is the wrong order of work.

Differ on the level alone and the pair has one end date. Both rows finish on the same day, both settle into amounts on that day, and adding two amounts is arithmetic. There is one shape and it can be drawn at every price on the axis. One end date is the vertical case, and everything worked out above follows from that single fact.

Differ on the end date alone and the pair has two ends. One row finishes while the other is still running, and there is no single day on which both are amounts. Two ends is the calendar case, and every blank cell further down follows from that single fact.

Differ on both and the pair is in the second case with an extra complication bolted on. The date difference is what stops the pair having one end, and the level difference does not undo it. So the second case is the one that decides: if the dates differ at all, no single-date shape exists, whatever the levels are doing. That is why the date field is the senior field, not out of preference, but because it is the field that can remove a whole picture.

Which gives the reading habit worth carrying to any position at all. Before a pair is named, its legs are grouped by level and by end date, and only then does what it obliges get decided. The name is a label somebody attached afterwards. The grouping is the thing itself. Names are attached loosely in practice. Fields are not.

What does each pair oblige at the end of its legs?

The two sit side by side on obligation rather than on outcome. An obligation is what each side must do. An outcome is what each side ended up with. The distinction is not pedantry. Obligations can be read off contract rows today. Outcomes cannot be read off anything at all until prices arrive, and this guide has none of those.

The vertical pair obliges three things across the range of prices, and they are three because the pair has two levels and levels cut a number line into three pieces. Below Rs 2,000.00/- nothing is owed by anyone and nothing is received: both rows are silent. Between Rs 2,000.00/- and Rs 2,200.00/- only the bought row is doing anything, so a rising amount is received, one rupee for each rupee of price above the lower level. Above Rs 2,200.00/- each further rupee arriving on the bought row leaves on the written row, so a fixed Rs 200.00/- is received and no more.

The calendar pair obliges two things and they sit on two different dates rather than in three price regions. On the near date, whatever the written leg owes at that date is settled and finished, and that figure is arithmetic on the price on that date. From that date onward, one bought contract is still running to the far date, and what happens to it happens later.

The same exercise attempted for the calendar pair runs differently, and the second column is where the difference shows. At Rs 2,400.00/- on the near date, the written leg settles owing Rs 400.00/-, exactly, with no rounding and no assumption. The bought leg has a value at that moment, and producing it needs an input covered separately. So the row reads minus Rs 400.00/- in the settled column and an honest blank in the other, and the pair total is not a number at all.

Both tables describe obligations rather than results. Neither one says which pair a reader should hold, which pair pays more, or which pair did better in any stretch of time. No stretch of time appears in this guide. There is a reference asset with a price and two ways of writing contracts against it, and the tables say what each arrangement requires of each side. Requirements on each side are the whole content, and the temptation to read a preference out of a shape is exactly what the closing sections interrupt.

One more thing about those tables. Three figures in this guide are all Rs 2,000.00/-, and a careful reader will suspect a copying error. The spot price of the reference asset is Rs 2,000.00/-. The level both premiums sit at is Rs 2,000.00/-. And the exposure one of these contracts carries is Rs 2,000.00/-. The three agree for two separate reasons, not by accident and not by mistake. The first two agree because the option pair in the working example is struck at the money, and struck at the money is exactly what it means for the level to equal the spot. The third is the same quantity looked at a third way. Exposure here is the value of one unit of the reference asset the contract is written on, so it is the spot price again, and it is not an amount either side has paid or ever will pay. Three appearances, one price, two reasons.

Why can one of these be drawn at a single date and the other cannot?

A payoff diagram makes one promise to whoever reads it: at each price on the horizontal axis, the height of the line is what the position pays. For that promise to be keepable, every leg in the position has to have finished by the date being drawn. A finished leg pays an amount, and an amount is a straightforward function of the price. A leg still running does not pay an amount. A running leg has a value, and a value is a price of its own, arrived at by whatever process prices are arrived at by, and no arithmetic recovers it from the price on the axis.

So there is exactly one test, and it is about the date rather than about the shape: on the date to be drawn, has every leg finished? Everything else about the position, the number of legs, the levels, the signs, whether it has a name in a book, is downstream of that answer.

The test applied to the vertical pair: both legs end on the same date, one year out. On that date both are finished. Both pay amounts. Adding two amounts at each price is arithmetic that runs off the end of a pencil, so the line exists at every price, and the figure above prints it with a marker at Rs 2,200.00/- and at Rs 2,600.00/- to show it going flat. Nothing in that drawing rests on an assumption anybody could disagree with.

Now run the test on the calendar pair at the near date. Almost every published picture of a calendar pair is drawn at that date. The written leg has finished. The bought leg has not. So the test fails, and it fails on the second leg alone. Working out what a contract still running is worth needs a figure for how far the reference asset might move over the time it has left. No such figure has been given, so the far leg carries no stated value at the near date. There is therefore no diagram for the calendar pair, and that absence is the finding.

What would have to be known before the calendar pair could be drawn?

Naming what is missing is more useful than gesturing at it, so here are the two things, and they are different in kind from each other rather than two versions of the same gap.

The first is a figure for how far the reference asset might move over the life of the surviving leg. A figure for movement is the input that turns time left into value, and it is the reason a contract with six months to run is worth something rather than nothing even when the price sits exactly at its level. Without it, time left is just time left, and no amount of care with the price on the axis produces a value from it. No such figure appears in the working example, and how far a reference asset might move is covered separately, in full, where it belongs.

The second is the premiums of both legs. One premium appears in this guide, Rs 180.00/- for the call at Rs 2,000.00/-, and it is a given figure rather than a derived one. Costing a vertical pair needs a second premium at its second level, and costing a calendar pair needs one at its second date. Even if the first gap were closed, two of the four money figures would still be missing, so neither pair could be costed.

Both of those are absences with names. An absence with a name is a different thing from an answer nobody has bothered to look up. The reason is what gets named, not the shortage.

The consequence for the reader is the most transportable thing here. Every calendar diagram ever published was drawn with an assumption inside it, and in almost every case the assumption was not printed anywhere near the picture. A different assumption changes the shape of the curve. An unstated assumption does not make those pictures dishonest, and it does not make them useless. A calendar picture is simply a different kind of object from the vertical pair's line, and the difference is worth being able to see from across the room.

What happens when one control drives a panel that cannot answer?

The calculator below is built to show a blank. Building a calculator for a blank is odd, so it is worth saying in advance what happens. One control moves: the price of the reference asset. Two panels sit beside each other. Everything in the left panel is arithmetic on that price, so the left one redraws completely. The settled leg is also arithmetic on that price, so the right panel moves one bar and then stops. The second half of that position has no stated value to redraw from. The empty area is not waiting for the slider to reach the right value. The area stays empty at every setting from one end of the range to the other, and it carries the reason inside it.

Moved slowly from one end to the other, the control forms two habits at once. On the left, the marker climbs from Rs 2,000.00/-, reaches Rs 200.00/- at Rs 2,200.00/-, and then refuses to climb any further however far the control is pushed. The flat stretch arrives under the hand rather than being asserted. On the right, the written leg's settled amount has no ceiling of its own, so the bar grows past Rs 2,000.00/- and keeps growing. Beside it the dashed area does nothing at all. The contrast between one panel that answers and one that will not is the whole comparison in a single gesture.

What cannot be compared between the two pairs, and why is that the useful part?

The two pairs are now defined, their obligations read, and the question of which can be drawn is answered. Which pays more, which does better, which suits a particular holder, and which is cheap or dear are separate questions. The reason is arithmetic rather than caution. The arithmetic runs like this.

Ranking two obligations needs a view about which prices arrive and how likely each one is. The working example holds no outcome, no past run of prices and no probability, so neither side carries a likelihood of any kind and there is nothing available to rank with. A payoff table is a description of what each side must do. A payoff table becomes a comparison of results only when somebody supplies the missing half, a distribution over prices. Supplying one from memory would be inventing the most consequential figure in the whole comparison.

Calling either pair cheap or dear runs into a second wall, and it is a shorter one. A judgement about price needs a price. Only one premium appears in this guide, Rs 180.00/- at Rs 2,000.00/-, and either pair needs a second one before it can be costed at all. For the vertical pair the missing premium sits at a second level. For the calendar pair it sits at a second date. Neither exists here. So no profitThe payoff after every premium is counted and carried to the same date. A payoff and a profit are different figures and only one of them appears in this guide. figure appears anywhere in this guide for either pair, and the tables above are payoffWhat a position pays at the end, before anything paid to put it on is counted. A payoff is arithmetic on the price on that one date. tables rather than profit tables. Reading Rs 200.00/- as what somebody made would be reading a payoff as a profit. The two differ by exactly the amount that cannot be produced here.

Structure survives those two refusals. What varies, what settles when, what can be drawn from arithmetic and what cannot are all still standing. Structure stays true whatever the missing figures turn out to be, and that is precisely why it is the part worth teaching first and the part worth carrying furthest.

How does somebody reading a position statement tell these two apart?

Four habits, each a direct consequence of something above rather than general advice. The name arrives last and misleads first, so the most useful thing anybody does with a two-leg position is refuse to name it until the two rows have been grouped. A lender looking at a borrower's disclosed positions, an analyst reading a note, and a household member reading a statement from an intermediary are all doing the same four things in the same order.

1. Write both legs in four fields before reading anything elseSign, call or put, level, end date. A statement that shows a name and one level has given a quarter of what is needed. Reconstructing the rest from the name is guessing, and the two pairs in this guide are the reason: they share a level, they share the word spread, and they behave nothing alike.
2. Compare the fourth field first, then the thirdIf the end dates differ, there is no single shape to look for, and any picture claiming otherwise has an input in it that has not been shown. Only when the end dates match does the level difference get to decide the shape. Date first, level second: that order is the finding of this guide compressed into one instruction.
3. Work the payoff at both levels and one price beyond the higher oneFor a pair that passes the date test, three evaluations settle the shape completely and each is arithmetic on the rows. In this guide those are Rs 0.00/- at Rs 2,000.00/-, Rs 200.00/- at Rs 2,200.00/-, and Rs 200.00/- again at Rs 2,400.00/-. The third one is the test that matters: if the figure has not stopped moving, the shape is not the shape that was described.
4. Write not produced rather than filling a cell with something plausibleWhere a leg is still running, the honest entry is the reason rather than an estimate, unless the estimate arrives with its assumption printed beside it. A household that budgets around a figure it made up is in exactly the same position as a statement that does it, and the damage shows up at the same moment: when somebody adds the column and believes the total.

What those four habits are not matters as much. None of them is a view on where the price is going, none is a preference between the two pairs, and none of them gets easier once it is known which pair somebody else chose. The four are reading instructions, and they work identically on a pair somebody has named correctly, a pair somebody has named carelessly, and a pair nobody has named at all.

Should a reader who can now tell them apart hold either?

Two contract rows do not answer that, and the reason is arithmetic rather than caution. Three things would have to be known before anybody could answer it, and not one of the three appears in this guide or in the working example behind it.

The first is a view on how far the reference asset might move and how likely each move is. A view on movement is the same missing input that stopped the calendar pair being drawn above, arriving a second time in a different disguise, and it is no coincidence that it blocks both questions. Movement and its likelihood turn a description of obligations into a statement about results, and without them a payoff table and a decision are separated by the whole of the interesting part.

The second is the reader's own circumstances, and no general account can see them. Holdings already carried, what can be absorbed, what money is needed for and when, and everything else going on around a person all bear on the question, and none of it is visible from here.

The third is what each assembly would cost to place, to hold and to unwind. For the vertical pair that cost cannot be produced. The declared level carries no premium. For the calendar pair it is worse than missing: valuing a leg that has not ended needs an input covered separately, for the reasons set out above.

So what has this guide actually handed over? A test that fits in one sentence, a habit of reading two fields before reading a name, and a clear sense of which pictures on this subject are arithmetic and which ones carry an input somebody did not print. Telling two obligations apart is a reading skill, and a reading skill is not a reason to take either one on. The two things sit in different rooms, and only the first is settled here.

The reference asset, its spot price and every premium in the worked example are invented.
Educational material. Not advice on any investment, tax, budget or market position.