Basis vs Basis Risk: The Gap and Not Knowing the Gap

The basis is the spot price less the contract price at one stated moment. On these figures, with a year to run, it is Rs 2,000.00/- less Rs 2,130.00/-, being minus Rs 130.00/-. Basis risk is not a number at all. The gap on a day not yet reached is simply not known in advance, and the not knowing bites when a position ends early.

Two prices for one thing sit side by side at the same instant. The distance between them is a subtraction and nothing more mysterious than that. Every idea below grows out of that single difference: a position carried all the way to its final date never has to care what that distance was along the way, and a position that stops earlier is settled against whatever the distance happened to be on the day it stopped.

A wedding hall shows the shape. A couple walks in eleven months before the date and the manager quotes one figure to hold it, and quotes a smaller figure to anyone wanting it this coming Saturday. Both numbers are for the same hall. The difference is not the manager's opinion about how popular weddings will be next winter. The difference is what it costs him to have money tied up in a booking for eleven months, and it shrinks as the date walks closer. On the morning of the wedding there is no longer any in-between to be paid for, so the two quotes are the same quote. A shrinking distance, and the fact that nobody can know today exactly what it will be in month seven, is the whole of what follows.

What exactly is the basis, and which way round is the subtraction?

The basis is the spot price of the reference asset less the price of the contract written on it, both taken at one stated moment. Two prices go in and one number comes out. The order is SPOT LESS CONTRACT everywhere, without a single exception, and every figure below is read that way.

The opposite subtraction is written down in plenty of places, so the order has to be stated out loud before anything else. Somebody who works with these numbers daily may reach for contract less spot without thinking, and their answer will be the mirror image of the one here. The two versions differ by nothing except a sign, so a basis figure met anywhere at all carries no meaning until the order it was taken in is known. A printed minus Rs 130.00/- does not reveal whether the contract price is above the spot price or below it until somebody states the order. The order is not a subtlety. Getting it backwards is the difference between reading a market as expensive to finance and reading it as cheap.

Work it here. The reference asset used throughout pays out nothing at all, and nobody who holds it collects a single thing for doing so. With twelve months to run, its spot price is Rs 2,000.00/- and the price of the contract on it is Rs 2,130.00/-. Take the spot price first and the contract price second, and Rs 2,000.00/- less Rs 2,130.00/- leaves minus Rs 130.00/-. Minus Rs 130.00/- is the basis with a year still to run.

Be clear what kind of figure that is. A difference between two PRICES at a single instant is the whole of it. It is not a payoff, because no position has settled. Nobody has been better or worse off by it, so it is not a profit. Not one rupee has moved in either direction on account of it existing. Two prices were quoted and one of them was taken away from the other, in the same way that the difference between the fare on two taxi apps is a difference and not a payment.

Why is the sign negative here, and what one thing would flip it?

The contract price on these figures is the spot price walked forward to the later date. Begin at Rs 2,000.00/-, let financing of 6.50 per cent a year run right across twelve months, and the carryWhat it costs to keep money locked into something for a length of time. The working is covered separately and arrives here already finished. amounts to Rs 130.00/-; add the two together and Rs 2,130.00/- is the finishing point. How that walk is built step by step is worked through under the cost of carry, and the result arrives here already finished.

Now notice what is missing from the walk. Nothing comes back the other way. Across the year, no payment of any size reaches whoever happens to be holding this reference asset, so there is no income to set against the financing and no credit to knock off the total. With nothing arriving during the holding period, carry can only ever add, so the contract price sits above the spot price at every date before the last, and a basis taken spot less contract is therefore negative all the way along.

So what would turn the sign around? Exactly one thing, and it belongs to the thing being referenced rather than to the paper written over it. If the thing paid something out while it was being held, that payment would be set against the financing rather than added to it. A small payment would narrow the gap. A large enough payment would swallow the financing whole and push the contract price BELOW the spot price, at which point the basis taken this way round would come out above nil.

The reference asset here hands over nothing during the year, and that case therefore cannot be worked. Every price here is built on a thing that returns nobody anything while it is held, and quietly giving it an income would move the contract price, the ladder, the residual and the drawings all at once. Where a contract price sits under a spot price in the world, the first question is what the referenced thing pays out, not what anybody thinks of it.

What happens to the gap as the final date comes near?

One question is worth asking before any table. The spot price is held completely still. The spot price is Rs 2,000.00/- today and Rs 2,000.00/- on every line below. Nothing about the reference asset can slip into the answer. Under that condition alone, what does the basis do as the months run down?

The ladder below is the whole answer, and every rung on it is checked twice. Once by taking Rs 2,000.00/- and adding Rs 2,000.00/- times 0.065 times the fraction of the year still left. Once by removing the basis from the spot price. The second route must hand back the same contract price. Neither route is allowed to disagree with the other.

The gap does not merely tend towards nil on the final date, it has to arrive there exactly, and the reason is worth holding on to. Once the due date itself arrives, the price of taking the reference asset then and the price of taking it right now describe one and the same transaction, at one moment, over one thing. Any distance left between them would be free money for the first person to notice it, available by buying at the lower quote and immediately handing over at the higher one. Distances of that sort do not survive being noticed. The two prices are one price at the end, not merely close.

There is a second reading of the ladder, and it is the one worth carrying away. In a worked example where nothing whatsoever about the reference asset changed, the basis shrank by precisely the amount of financing that had run off. Between the nine month rung and the six month rung the basis moved from minus Rs 97.50/- to minus Rs 65.00/-, a movement of Rs 32.50/-, which is three months of financing on Rs 2,000.00/- and not one paisa besides. The spot price on both those rungs is the same Rs 2,000.00/-. Whatever moved, it was not the reference asset.

If basis risk is not a number, what is it?

The pairing of the two terms invites a search for a second figure of the same kind, and there is not one. So the place to begin is with what basis risk is not. The basis is minus Rs 32.50/- with three months left. Basis risk is not minus anything. Basis risk has no units, it cannot be printed in a column, and asking for its value is asking the wrong shape of question.

Basis risk is the plain fact that the gap on a day not yet reached is not knowable in advance, and that a position ending on such a day gets settled against whatever the gap turns out to be when it arrives. Basis risk is a statement about a future moment, not a measurement of the present one.

Basis risk does not touch a position carried the whole way to its final date. The gap there is nil by construction, as the ladder showed, so there is nothing left to be uncertain about. Somebody who opens a position with twelve months to run and simply holds it through to deliveryThe point at which the referenced thing itself changes hands rather than being settled in money. The trigger for it and the time it takes are set by the authority named further down. has taken on many things, and the size of the gap on some intervening Tuesday is not among them.

Basis risk does touch a position that ends before the final date, for any reason at all. Perhaps the thing being protected got sold. Perhaps the money is wanted somewhere else. Perhaps somebody just changed their mind. The reason does not matter to the arithmetic. The position gets closed at a contract price that still has unspent financing sitting inside it, and the unspent amount is the gap on that day.

Where does basis risk bite, on the one case these notes can work?

Here is the case, and it is worked in full. A long positionThe side bound to take the referenced thing and pay for it on the later date. How the two sides behave when prices move is worked through elsewhere. is opened when the contract has twelve months to run, at a price of Rs 2,130.00/-. Three months before the final date, whoever holds it decides to get out.

The spot price on the day of that close is Rs 2,000.00/-, exactly where it began. Nothing at all has happened to the reference asset. So the position closes at Rs 2,000.00/-? The close does not happen at Rs 2,000.00/-, and the reason is the whole of the basis.

With three months still to run, three months of financing have not yet been spent, so the contract price is not Rs 2,000.00/-. Three months of the 6.50 per cent, worked on Rs 2,000.00/-, comes to Rs 32.50/-; lay it beside the starting price and the contract stands at Rs 2,032.50/-. The basis on that day is therefore minus Rs 32.50/- rather than nil, so the close is settled against a price that sits Rs 32.50/- away from the spot price, and that Rs 32.50/- is precisely the financing that has not yet run off.

The general shape to carry away is this: stop early and the unspent financing is still inside the price, and the earlier the stop, the more of it is left there. Stop with nine months left instead of three and the residual is minus Rs 97.50/-. Stop on the final date and there is nothing left at all. The residual is not a penalty and nobody charged it. The residual is what remains of a walk interrupted before it finished.

Readers slide at exactly this point, so the two halves have to be separated carefully. Here the residual is arithmetic, flat and predictable, and it can be read straight off the ladder. Out in the world neither price sits still, so nobody knows in advance what the gap will be on the particular day they turn out to need it, and the not knowing is what makes it a RISK. The arithmetic here shows the shape of the thing. A spot price held still cannot show the uncertainty. Only two prices that both move can do that.

Why can the commoner case not be worked here at all?

Most people who go looking for basis risk are looking for a case that needs two separately priced things, and saying so plainly is more useful than working a near miss. The usual case runs like this. No contract exists on the exact thing a party holds, or none exists with a date they can use, so the party offsets it with a contract written on a DIFFERENT thing. A miller sitting on one grade of grain protects it with a contract on another grade. A borrower exposed to one rate offsets it against a contract on a rate that moves nearby.

The two things are genuinely different, so the gap between their prices wanders for reasons entirely of its own, and that wandering is exactly what the party is carrying. The wandering is not financing running off a clock but two prices that usually travel together, occasionally not doing so.

THERE IS ONE REFERENCE ASSET HERE AND NO SECOND ONE. There is no other thing to hold, no second price anywhere, and consequently no relationship between two prices that could be measured, drawn or moved. So the usual case stays unworked here, and no second referenced thing gets conjured up to make it look otherwise.

Say what would actually be needed before anybody could work it honestly. Two separately priced things. A record of how far apart those two prices have run in the past. And some tested account of what drives that distance, so a reader knows whether they are looking at something stable or something that can come apart at exactly the wrong moment. Not one of those three exists here, and made-up versions of all three would teach somebody to trust a relationship assembled for the occasion.

The one case that can be worked here is the residual left behind by a stop before the final date. The residual case is smaller than the general one, and completely honest with it. The idea that matters survives intact: a gap nobody chose is sitting in the price on the day the position ends.

What does a basis refuse to say about the future?

Should a position be closed early, and what has to be known first?

The make-up of the gap, and the residual it leaves when a position stops short, are now settled. The next question forms by itself: should the position be closed early, when should it be closed, and should it have been opened at all?

None of those three can be answered from arithmetic, and the reason is structural rather than cautious. An answer would need a record of what actually happened, somebody's account of having done it, a likelihood attached to each outcome and a spread of possible results. One frozen spot price and one financing rate supply not a single one of the four.

A list comes before the question is even well formed, and nobody gets to skip it. First, what the position exists to do at all. Second, how long that reason is expected to run. A reason that ends in March and a contract that runs to December have already created the residual on their own. Third, what is already held against the position. A residual on one side may be met by something on the other. Fourth, what has been posted and to whom. Money already lodged with a clearing corporationThe body that stands between the two sides of a cleared position so that neither faces the other directly. How it is funded and governed is worked through elsewhere. is not money available elsewhere. Fifth, what the authority requires before a position counts as protection for something held rather than as a stake taken on its merits, the row left blank above.

Knowing what a residual gap is made of is not, by itself, any kind of reason to take on a position that would carry one. Grasping how something works and having a reason to reach for it are separate accomplishments, and only the earlier of the two is on offer here.