The Price That Never Traded

There are prices at which nobody bought any­thing. They are not rare, and they are not errors. Some of the most impor­tant numbers in finance are of this kind, and most people who rely on them have never noticed.

An index level is one. So is the mark price an exchange uses to decide whether your futures posi­tion has run out of margin. So is the net asset value of a fund, struck once a day from some­body else's prices. So is a volume-weighted average price, the bench­mark a broker is judged against, and a fair value an auditor signs off for an asset that has not traded in months. Each is com­puted. None needs a buyer and a seller to have met at that figure.

Here is one from our second. Take every print on the four tether venues between 07:24:04.000 and .999, weight each by its size, and average. The answer is $75,822.48. It is a per­fectly rea­son­able descrip­tion of where bitcoin changed hands in that second, and it is the kind of number an exe­cu­tion desk would be mea­sured against. Of the 651 prints that pro­duced it, none crossed at that price. 8 came within fifty cents of it.

No paradox there: the average of 3 and 5 is 4, and nobody had to hold a four. It does raise the ques­tion this article is about, though. Can a price be real if nobody ever paid it?

Why a trade is not enough

The obvious answer is that the last trade is the only honest price, and every­thing else is mod­el­ling. Our own second shows why nobody who runs a market believes that.

Remember the quarter-cent trade from page 13. Had it crossed a few dollars away from every­thing else, it would have been the last trade for a moment. If futures posi­tions were settled against the last trade, a quarter-cent trans­ac­tion on a thin venue could decide whether some­body else's posi­tion worth mil­lions was liq­ui­dated. That is exactly the attack mark prices are built to resist.

So a deriv­a­tives exchange does not mark to its own last trade. It builds a mark from an index of spot venues, usually several, usually with out­liers dis­carded and stale sources dropped, and then smooths it. The mark is designed to be harder to push around than any single print. It is a price at which nobody traded, delib­er­ately, because a traded price was too easy to fake.

A fund faces a dif­fer­ent version of the same problem. Its investors need one number a day to buy and sell units at. The assets inside it trade at dif­fer­ent times, in dif­fer­ent places, and some hardly at all. The fund's admin­is­tra­tor takes a set of chosen ref­er­ence prices at a chosen moment, applies them, sub­tracts fees, divides by units out­stand­ing, and pub­lishes. SPDR Gold Shares, the largest gold fund, values its metal once a day at the LBMA Gold Price set in the after­noon auction in London. The fund's NAV is a price nobody paid, built on a bench­mark that, as page 29 describes, is itself a small machine.

Sources, filters, weights, output

Every con­structed price, from an index to an oracle feeding a lending pro­to­col, is built the same way. Somebody chooses sources. Somebody writes filters that decide which obser­va­tions to throw away: too old, too far from the others, too small, from a venue that has stopped answer­ing. Somebody chooses weights. A cal­cu­la­tion runs, and a number comes out with a time­stamp on it.

Each of those choices is a judge­ment, and each can be defended. A median ignores one crazy venue; a mean does not. A volume weight­ing follows where the money is; it also follows where wash trading is. A tight stal­e­ness filter pro­tects against frozen feeds and throws away honest quiet ones. The choices are pub­lished for the bench­marks that matter most, and it is worth reading them, because they are the dif­fer­ence between two numbers that both claim to be the price of the same thing.

CF Benchmarks, which cal­cu­lates the bitcoin ref­er­ence rate CME futures settle against, is a useful example of how spe­cific those rules get. Its daily rate takes trades from a set of con­stituent exchanges over one hour, splits the hour into twelve five-minute par­ti­tions, takes a volume-weighted median in each, and aver­ages the twelve equally. No trade needs to have hap­pened at the result. Several billion dollars of futures settle on it anyway.

Our own number

We should declare our inter­est here, because our own systems make con­structed prices, and our capture of this second con­tains one.

One of our col­lec­tors records a ref­er­ence price for bitcoin every ten seconds, for risk checks. For 07:24:04 it recorded $75,807.195. The source field reads binance-fallback: the oracle we would prefer was not the one used. The figure is the mid­point of Binance's best bid and ask at the start of the second, and it has half a cent in it. Binance quotes in whole cents, so no trade could ever have hap­pened at that price. The row reached our data­base 1.227 seconds after the instant it described, by which time Binance's best offer was $75,844.01.

Nothing about that is broken. The row is labelled hon­estly: where the number came from, when it was pub­lished, how old it was on arrival, and whether it passed our checks. Often the most useful price has no trans­ac­tion behind it at all, only a state­ment with its prove­nance attached, and it deserves exactly as much trust as that prove­nance is com­plete.

The accoun­tants got there first

Accounting stan­dards settled this argu­ment long ago, and their answer is worth bor­row­ing. Both the inter­na­tional and the American rules for fair value sort every mea­sure­ment into three levels. Level 1 is a quoted price in an active market for an iden­ti­cal asset: a traded price, used as it stands. Level 2 uses observ­able inputs that are not quite that, such as quotes for similar assets or prices from markets that trade rarely. Level 3 uses inputs that cannot be observed at all, and relies on a model and the judge­ment of whoever runs it.

Every one of the three levels pro­duces a number called fair value, and all of them end up on a balance sheet in the same column. The stan­dards insist that the level is dis­closed, pre­cisely because the numbers look iden­ti­cal once printed. A reader of a bank's accounts who does not look at how much of its assets are valued at Level 3 is reading a list of prices without the one piece of infor­ma­tion that says how much each deserves to be believed.

Market screens could learn from it. This issue borrows it for its own figures: observed, cal­cu­lated, reported, argued. Attach the level and a number tells you how far to trust it. Leave it off and the number asks for trust it has not earned.

So is it real?

A con­structed price is real in the only sense a price can be: people act on it. Positions are liq­ui­dated at marks, fund units are bought and sold at NAVs, tril­lions of dollars of loans have reset against bench­mark rates. Nobody paid the number, but a great many people paid because of it.

What changes is where the risk sits. With a traded price, the ques­tion is whether the market was deep enough to mean any­thing. With a con­structed price, the ques­tion is who chose the sources, who wrote the filters, and what they stood to gain from the answer. That second ques­tion has an unhappy history, and it is the subject of page 27.

Before that, one more thing a price is sup­posed to be unable to do.