The Futures Price: How It Relates to the Spot Price

The futures price is the figure the two sides of an exchange traded contract are bound to transact at when the contract's date arrives. The figure is the price for delivery now, carried to that date at the cost of financing it. Rs 2,000.00/- carried across a year at 6.50 per cent a year reaches Rs 2,130.00/-. Nobody arrives at it by holding a view. The figure settles where nothing is being given away.

The idea that nothing is being given away is the one to keep. A figure agreed today for a transaction that happens months from now feels as though somebody must have guessed at something to produce it, and the guess is what almost everybody reaches for. There is no guess. Every input is visible this morning: what a unit costs for delivery now, what borrowing costs, and how long the wait runs. Multiply, then add. The financing rateWhat borrowing the money costs over a year. A rate with no period attached is not a quantity anybody can work with. The period stays attached to every rate named. does the whole of the work.

Three invented inputs carry everything below. One reference asset priced at Rs 2,000.00/- for delivery now. Financing at 6.50 per cent a year. And no payment of any sort arrives for whoever is holding that reference asset at any point before the contract's date. The third input is not a small footnote. Strip it out and every rupee figure below moves.

The object worth having is narrower than it looks and more useful than it sounds: not one futures price but a whole row of them, one for every date on the board, and the arithmetic that ties them to each other. Once the row can be built, why it slopes becomes visible too, and seeing why it slopes is what stops the slope being read as somebody's forecast.

What is the futures price, and who decides where it sits?

The futures price is a figure two parties are locked into. One of them will hand over a unit of the reference asset on the contract's date; the other will hand over the money; and the amount of money was fixed on the morning the position was opened, not on the morning it is settled. Both sides are bound from that first morning. Neither may decline, neither may renegotiate, and neither holds anything resembling a choice about going through with it.

Nothing is paid to enter, which is the property most readers carry a wrong assumption about. No fee changes hands to open a position. No amount is handed to the other side. Two obligations are exchanged, and obligations cost nothing to give. Whatever collateral has to be lodged with an exchange traded position is a separate matter, worked separately, and it is not a payment to the other side at all.

So which of the four labels does Rs 2,130.00/- belong under? Take them in the order that eliminates them. Nobody hands over a premium to open either side of this. The premium label is empty at the outset and stays empty throughout. Nothing has settled, so there is no payoff to record yet. Nothing went in at the start, so there is no profit to net anything back out of. The first label survives elimination: a figure that two parties agreed to transact at. Rs 2,130.00/- is a price, and it is nothing besides a price.

Now the part that sounds contradictory the first time and stops sounding contradictory the moment it is spelled out. Two parties who opened a position this morning are locked to Rs 2,130.00/-. A different pair opening a position tomorrow morning will be locked to whatever figure is being struck tomorrow morning, and that will be a different figure. Both are correctly called the futures price. An agreed figure belongs to the pair who agreed it and never moves again. The figure on offer to somebody opening a fresh position keeps moving all day. Both statements are true at the same instant, and neither one is loose.

Here is the ordinary version of that. A household books a hall for a wedding in November and the rate is written into the booking. The hall keeps quoting new rates to everybody who walks in afterwards, and by Thursday the quoted rate is different. Nobody thinks the household's booking has changed. The rate on the board and the rate in the booking are two different things wearing one name, and it is only the shared name that ever causes confusion.

As for who decides the level, the honest answer is nobody, in the sense readers usually mean. There is no committee and no forecaster. The level is forced by arithmetic, and the next block sets that arithmetic out in full.

How is the futures price built out of the price for delivery now?

By multiplying, and by nothing else. The starting point is the two figures that are observable this morning and the length of the wait.

Picture a delivery falling twelve months out: one unit, handed over on that morning. Two arrangements reach it. Under the first, a position is opened today and settled when the date comes. Under the second, Rs 2,000.00/- is borrowed, a unit is acquired today at that figure, and it is held until the morning arrives. The second arrangement carries a bill, and the bill can be worked out down to the paisa. Apply 6.50 per cent a year to Rs 2,000.00/- across those twelve months and the financing comes to Rs 130.00/-. Set that on top of the Rs 2,000.00/- the arrangement started from, and the second arrangement has cost Rs 2,130.00/- by the time the date arrives.

Nothing arrives along the way. Nothing is deducted from that bill. Across those twelve months, holding this reference asset earns its holder nothing whatsoever. Had something come in, the receipt would have offset the financing and the total would have been smaller. Nothing comes in, so the total stands at Rs 2,130.00/-.

Both arrangements put the same unit into the same hands on the same morning. The equivalence of the two arrangements pins the figure in the first to the bill in the second, and it pins rather than suggests. Any figure other than Rs 2,130.00/- for that date hands somebody a certain gain, and a level that hands out certain gains does not survive the morning. Run it both ways to see why.

Below Rs 2,130.00/-, say at Rs 2,090.00/-. Somebody agrees to buy at that figure, then borrows Rs 2,000.00/-, takes a unit this morning, sits on it, delivers it into the contract on the date and collects. Their bill is Rs 2,130.00/- and their receipt is Rs 2,090.00/-, so the person on the other side of that agreement has handed over Rs 40.00/- for nothing whatever. Above Rs 2,130.00/-, the argument reverses and runs through somebody who already holds a unit: they sell it this morning for Rs 2,000.00/-, put the money to work at 6.50 per cent a year, agree to buy a unit back on the date at the inflated figure, and finish the year with the unit back in hand and a difference in their pocket. Either way, somebody is collecting free moneyA gain that can be locked in with certainty by transacting at a level that has been set wrongly. The gain requires no view about anything and no luck. for taking on nothing at all.

One warning about that expression before it gets used. The record behind these figures gives one rate for one year and nothing finer, so the financing runs straight across the period rather than compounding inside it. A half year therefore enters as exactly half the financing.

Is there a different futures price for every date, and how do they relate?

Yes, one for every date, and they relate in the plainest possible way: they are the same price for delivery now, carried different distances. The row of dates is the part of the subject that gets skipped, and skipping it is what leaves the misreading below standing unchallenged.

The row is built here rather than handed over. Hold the price for delivery now perfectly still at Rs 2,000.00/-, hold financing at 6.50 per cent a year, and change nothing except how far away the date is. Twelve months of financing on Rs 2,000.00/- is Rs 130.00/-, putting that rung at Rs 2,130.00/-. Take away a quarter of the wait and a quarter of the financing goes with it: nine months costs Rs 97.50/-, putting that rung at Rs 2,097.50/-. Halve the wait from the top and the financing halves with it: six months costs Rs 65.00/-, so Rs 2,065.00/-. A quarter of a year costs Rs 32.50/-, giving Rs 2,032.50/-. And on the date itself there is no wait left at all, so the rung sits at Rs 2,000.00/-.

Read the last column downwards before anything else. The step it holds does not move. Every three month step buys the same extra quarter of a year of financing on a base that was never allowed to move, and so every three month step adds the same Rs 32.50/-. Equal steps for equal distances is exactly what a straight line is, which is why the shape below is a straight line and not a curve, a hump or anything with a story in it.

Something worth pausing on: the line begins at exactly the price for delivery now. The starting height is not a drawing convention chosen to look tidy. Put T at nil in either expression and the financing term vanishes, leaving the price for delivery now standing alone. The next block is about what that means on the ground.

Moving the price for delivery now, and watching the wedge close as the date approaches, are each worked with a control separately. The five rungs can be compared against one another and checked with a single multiplication each. A row that can be audited line by line beats a control that redraws faster than it can be followed.

What happens to the futures price as the date gets closer?

The figure bound for a date walks down the row towards the price for delivery now, and on the date itself the two are the same number. Do not take that as a tendency or a habit. The walk is arithmetic, and the arithmetic is worth doing rather than reciting the word for it.

A date twelve months away carries twelve months of financing, Rs 130.00/-. Three months later, the same date is nine months away and carries Rs 97.50/-. Three months after that, Rs 65.00/-. Then Rs 32.50/-. On the morning the date arrives there is no wait left to finance at all. Applied across a wait of nothing, 6.50 per cent a year gives nothing, and the figure bound for that date is Rs 2,000.00/- plus nothing, or Rs 2,000.00/-.

On the final morning the contract and a transaction in the reference asset itself have become the same transaction, and one transaction cannot carry two prices at once, so the walk has to end there rather than merely tend towards it. Buying the reference asset under the contract on its own date is money paid and a unit received, today. The purchase is a transaction for delivery now, wearing a contract's name. If the two figures differed by a single rupee on that morning, somebody would do the cheap one and undo the dear one within the minute and take the difference. The difference therefore is not there.

Two things are named and left alone. Each is worked properly on its own elsewhere. The named distance between an exchange traded figure and the price for delivery now on any day before the date, including which sign it carries, belongs to a separate treatment. So does what somebody is left holding when they shut a position ahead of the date rather than seeing it through. Neither is needed to follow the arithmetic above.

Does daily settlement pull the two prices apart?

The question is left open where the price for delivery now is set beside the forward figure, and it deserves the mechanism rather than a confident answer. The mechanism comes first, then an account of exactly how far these figures can take it.

An exchange traded position is settled every single day. Its value is struck against a fresh figure each day and the difference is moved in cash, into or out of a margin balanceA running collateral account attached to an exchange traded position. Cash arrives in it and leaves it while the position is open, and what sits in it is not a payment to the other side. held for the position. On a day the position gains, cash arrives. On a day it loses, cash leaves. The margin balance was opened with initial marginCollateral lodged before a position may be carried at all. The 8.0 per cent used here was invented for teaching and is not anybody's actual requirement. before the position could be carried at all, and on these figures that opening amount is Rs 160.00/- a unit, being 8.0 per cent of Rs 2,000.00/-, a percentage invented for teaching and not a requirement of any authority. The account faces a clearing memberWhoever stands in front of the institution in the middle on a participant's behalf. Participants deal through one rather than facing that institution personally., who in turn faces the clearing corporationOnce a trade has been struck on an exchange, this institution takes the place of each original side, so neither of them any longer faces the other. Its funding and its governance are treated separately. sitting in the middle of every position.

Now compare that with a bilateral agreement between two named parties. Nothing moves. Not on the first day, not on any day after, not until the final date. There is no account, no daily figure and no cash crossing anywhere.

So here is where a difference could come from, stated carefully. Cash that arrives in a balance early can be put to work; cash that has to be found early has to be financed. The timing of those flows is therefore worth something rather than nothing. Suppose what the flows do were connected to what financing costs, with money tending to arrive when it could be put to work well and to leave when replacing it was dear. The two arrangements would then not be worth the same, and the figures attached to them would part company.

Notice how much of that sentence is a condition rather than a fact. It says the two prices could differ. The sentence does not say they do, it does not say in which direction, and it certainly does not say by how much. Getting from could to does needs two quantities, and neither of them exists anywhere in the figures behind these rungs.

What would be needed before that could be answered properly?

Two quantities, both of them absent, and naming them is more useful than a plausible figure would be.

The first is a rate earned or paid on whatever is sitting in a margin balance. Without it, cash arriving in the balance and cash leaving it are worth precisely the same as each other and there is nothing to compute. The second is a stated relationship between the financing rate and the price of the reference asset, telling anybody whether cash tends to arrive on the days when financing is dear or on the days when it is cheap. Without that, the flows have no systematic tilt at all and their timing carries no value in one direction rather than the other.

Neither quantity exists in the figures behind these rungs, and no substitute is manufactured to finish an argument tidily. There is no series of past rates, no relationship between anything and anything, and no distribution from which either could be drawn. The absence is a hard limit, stated as a limit rather than worked around.

One consequence follows. Every figure above and below treats the exchange traded price and the bilateral price as one and the same number, Rs 2,130.00/-. The equality is an assumption, and it is named as one each time it matters.

Something does stand in place of an answer. The difference between the two figures is a real question with a real answer somewhere, and the answer is not available from these figures. A number made up to plug the hole could not be checked. The absence can be checked in a single glance at the two empty rows, and knowing exactly which two quantities would produce the answer is worth more than the made up number.

Does the futures price say where the reference asset is going?

No. And that deserves an argument rather than an assertion, so here it is in three moves that each stand on their own.

Move one: nothing in the build ever consults an opinion. Look back at what went into Rs 2,130.00/-. The Rs 2,000.00/- a unit fetches this morning. Financing quoted at 6.50 per cent a year. A wait running twelve months. Every one of those three can be read off today. The expression has no term with that shape in it, so there is no step in the calculation at which somebody's view could be inserted, even by a person determined to insert one.

Move two: the figure moves when financing moves, and the reference asset is never mentioned while it does. Change the financing rate and every rung of the row shifts, upwards for a dearer rate and downwards for a cheaper one, and the whole row pivots around the point where it meets the date. Nobody has said a syllable about the reference asset while that happens. A quantity that swings on somebody else's borrowing costs while every opinion in the room holds perfectly still is a cost. The figure was never an opinion.

Move three: run the subtraction and look at the size of what comes out. Take a long position struck at Rs 2,130.00/-. Reach the date with the reference asset still changing hands at Rs 2,000.00/-, exactly where it started. The position hands over minus Rs 130.00/-. Minus Rs 130.00/- is a payoff, not a price, and keeping the two labels apart matters. Now notice the size of it. The carry was the entire content of the figure that was struck, so the loss is the carry to the paisa and could not have been any other number.

Then finish the thought. If Rs 2,130.00/- had been a prediction, and if that prediction had come true to the rupee so that the reference asset arrived at the date changing hands at Rs 2,130.00/-, the position would have finished exactly level. Nothing earned for being perfectly right. A number whose reward for perfect accuracy is nil was never in the prediction business, and this one loses its holder the carry precisely because the carry is all it ever was.

Knowing how the figure is built is not a reason to take a position. The record holds no account of how anything turned out and no odds on anything happening, so there is nothing whatever with which to compare one course of action against another.

Who actually uses the row of dates, and what for?

A row of figures is worth carrying around only when it alters somebody's next move, so here are four people whose next move it alters.

A treasurer facing a delivery on a known morning uses the row to price that morning, and refuses to read anything else out of it. Their question is narrow: what does having the thing available on the fifteenth of whatever month actually cost? The row answers that and declines every other question. If the need falls six months out, Rs 2,065.00/- is the figure that applies and the rest of the row is simply not about them. Treating the three month rung as a bargain because the number printed is smaller confuses a shorter wait with a discount, and those are not the same thing at all.

Somebody reading a note written by another person can use the row to audit the writer. Suppose that note claims a rising row shows what the market expects. The claim can be tested by anybody holding the note, and the test runs two operations deep. Subtract what a unit fetches today from the quoted figure. Divide what remains by that same amount. Then ask whether what comes back looks like a cost of borrowing. Here it comes back as 0.065. Over the twelve months the quote was struck across, 0.065 is the 6.50 per cent a year that started everything, so the quote closes and leaves no residue behind. A result nowhere near the financing rate means the quote is carrying something the carry cannot account for, and establishing what that is comes ahead of everything else.

A lender looking at a business that carries a number of these reads the row for its dates rather than its levels. What matters to a lender is when obligations fall due and what has to be found on each of those mornings, which is a calendar question. The rungs themselves are close to irrelevant for that purpose, and the Rs 130.00/- of financing sitting inside the furthest one is the least interesting figure here to somebody asking who has to pay what and when.

And a household meets the same row without ever calling it one. Ask a caterer what a plate costs for a function next month and then for one in December, and two different figures come back. The December figure is higher, and nobody at that table imagines the caterer is forecasting food prices. The caterer is pricing a longer wait, in which ingredients must be secured and money tied up. The caterer's two figures are the row of dates at a domestic scale, and the useful question there is the useful question everywhere: does the extra look like the cost of waiting, or does it look like something else?

A vocabulary trap sits at the end of this block, and it springs the moment a position runs to more than a single unit. Multiply forty by the struck figure of Rs 2,130.00/- and Rs 85,200.00/- appears. Rs 85,200.00/- is a notional: a headline size arrived at by multiplication, behind which nothing has travelled anywhere. Multiply forty by Rs 2,000.00/- instead and Rs 80,000.00/- appears. Rs 80,000.00/- is the exposure: the amount which genuinely shifts when the reference asset shifts. Swap the two names over and the position has been misdescribed in wording precise enough to go unchallenged.

Which parts of this are set by an authority in India?

Which question do these figures not answer?

Having built the row and taken it apart, somebody will next ask whether anybody ought to be taking one of these positions. No answer to that exists in these figures.

The reason is an inventory. The record behind these rungs holds no realised result. There is no run of past years and no series of any kind. There are no odds attached to anything happening, and no probability and no distribution appear anywhere. A judgement about whether an arrangement suits one person and not another is made out of exactly those three things, so with all three missing there is nothing to support one. The refusal here is not squeamishness about the subject. The ingredients for an answer are simply not present.

Nowhere above is any arrangement made to sound attractive. Ranking two of them by how they turned out is impossible here, there being no outcomes on hand to rank. Knowing precisely how a figure is assembled is understanding, and understanding is a wholly different thing from a reason to use one.

Something useful can go in its place, though, and it takes the form of prior questions. Why is the position there at all? What else sits alongside it, offsetting it or compounding it? What collateral went in, and into whose keeping? What lands due on the morning cash finally crosses? Work those four out and the original question begins to have an answer. Leave them unworked and it never will. Notice that not one of the four asks for anybody's opinion of a price, and that not one of them is reached by comparing Rs 2,000.00/- against Rs 2,130.00/- and inspecting what is left.

The reference asset, its price of Rs 2,000.00/-, the 6.50 per cent a year of financing, the 8.0 per cent of initial margin and every party to every position described are invented.
Educational material. Not advice on any investment, tax, budget or market position.