Wall Street is sharpening our nanoseconds

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By Matt Levine

LET’S SAY you and I both want to buy 100 shares of Microsoft Corp. stock. Let’s say that 100 shares are currently listed for sale on the exchange at $100. There are more shares listed for sale at $100.01, $100.02, etc., but the first 100 shares are all that are available at $100.00. We both think the stock will go up, so whoever doesn’t get the 100 shares listed at $100 will have to spend more — at least $100.01 — to buy them. Which one of us should get the shares?

The answer, traditionally, is “whoever puts in an order to buy them first.” It’s a pretty good answer!

For one thing, it rewards us for making prices more informative: Whoever moves more quickly to synthesize information into a view on the stock price is rewarded with the (cheaper) stock. For another thing, how else could it work?

If someone is willing to sell the stock at $100, and I come in to buy it at $100, why would the seller wait around to see if some later bid comes in at the same price? How long should she have to wait? What if you want to buy the stock a week later? The seller wants to sell at $100 now because she wants to sell at $100 now; if I’m available to buy at $100 now and you aren’t, then I get the stock.

But what if we put in our orders at the same time? Then neither of us is more informative than the other, and the seller doesn’t lose anything by waiting around until both of our orders are in.

You could imagine lots of good answers there. Maybe we’d each get 50 shares. Maybe priority would go to the one of us who is, I don’t know, a retail customer, or an institutional investor, or a good client of the exchange, or something. Or the exchange could run a little auction to see which of us is willing to pay more.

But the answer in actual US market structure is, come on, there is no such thing as “the same time.”

Do you know how many nanoseconds there are every single second? (A billion.) The odds that each of us would hit the “Buy” button at the exact same nanosecond are infinitesimal. So if I put in my order to buy the stock at 10:45:06.543210876 a.m., and you put in yours at 10:45:06.543210987 a.m., then I got there first and I win.

Is this a good answer? It has a simple appeal. It just gets rid of the question “who gets the stock if we put our orders in at the same time?” It replaces an economic question about how to allocate the stock with an empirical question of who got there first.

It is consistent with our intuitions about the regular case where I got there, like, a week earlier: It rewards people for moving quickly to synthesize information and update prices, and it gives the seller immediacy rather than requiring her to wait.

Of course on a nanosecond timeframe, those intuitions feel silly. It is probably socially beneficial to update prices now rather than a week from now; it’s hard to see how it matters whether you update prices now or a nanosecond from now. Making the seller wait a week imposes a hardship on her; she can’t possibly notice if you make her wait a nanosecond.

Still it is a nice continuous answer.

Who decides that, say, a second matters but a nanosecond doesn’t, or that a week matters but a second doesn’t? “Whoever gets there first gets the stock” is an easy rule to state and justify, and has the feeling of fairness. “Whoever gets there at least five seconds earlier than anyone else gets the stock, but people within each five-second block are batched together and then run an auction to allocate the stock” is more complicated, and someone needs to decide what time increments matter and how to allocate the stock within those increments, and however they decide someone will probably think it’s unfair.

Plenty of people think the system of time priority is unfair too, because it privileges high-speed traders, and because they pay for co-location and direct feeds and fast connections to exchanges; the term “front-running” is sometimes thrown around; there are speed bumps; etc. etc. etc. etc. etc.; you know all of this.

But even if you are a total believer in time priority, it is somewhat problematic because, at some scale, that empirical problem of figuring out who got there first is hard.

A nanosecond just isn’t very much time! If we both look at our watches and write down when we put our orders in, we won’t be accurate to the nanosecond. Even if our computers write down when we put our orders in, and frequently synchronize their clocks with the exchange’s clocks, they won’t match up to within a nanosecond.

But that’s just a problem of basic physics and so perhaps solvable.

Here is a story about how “computer scientists at Stanford University and Google have created technology that can track time down to 100 billionths of a second,” and about how stock exchanges are working to get that level of precision in timestamping orders:

Because the orders are placed from locations around the world, they frequently arrive at the exchange’s computers out of sequence. The new system allows each computer to time stamp an order when it takes place.

As a result, the trades can be sorted and executed in correct sequence. In a networked marketplace, this precision is necessary not only to prevent illicit trading on advance information known as “front-running,” but also to ensure the fair placement of orders.

It seems like most people who write about market structure — outside of exchanges and high-frequency trading firms, anyway — are not total believers in time priority; to them, this level of accuracy seems misplaced. (“The technology might be interesting, but the worldview in which it would be necessary for finance is pathological, rendering ever more elaborate, ever less meaningful sorts of tournaments practical,” tweeted Steve Randy Waldman.) Who cares who got there a hundredth of a nanosecond earlier?

I do not have a great response. No one really should care.

The social benefits of updating prices every second, of letting people sell stock the second they want to, are plausibly large; the marginal social benefits of updating prices every hundredth of a nanosecond, of letting people sell stock the hundredth of a nanosecond they want to, seem likely to be very small.

The best response seems like a laissez-faire one: The benefits of immediacy and constant price discovery in general are probably large, and who are you — as a regulator or academic or journalist or whatever — to decide where to cut them off? If people want to trade stocks every hundredth of a nanosecond, why not let them?

But the other standard objection to this focus on nanosecond-level trading is that it creates a socially wasteful arms race, that brilliant minds are wasted on developing high-speed trading systems rather than curing cancer. And I don’t know! This particular problem — of accurately timestamping data and figuring out the order in which to process it — seems to have deep applications beyond trading:

Because software and data are no longer in the same place, correctly calculating the order of the events that may be separated by feet or miles has become the dominant factor in the speed with which data can be processed.

“So much of our expectation about computing being correct depends essentially on knowing this order,” said Krishna Palem, a theoretical computer scientist at Rice University.

The thing about the elaborate meaningless tournaments of finance is that they give out large monetary prizes. So people have incentives to participate in them and work hard to do well. When the tournaments are about, say, who can read credit-default swap documentation most cleverly, they do seem rather socially wasteful. (Though not always!) But when they are about, say, who can best harness machine-learning techniques to evaluate masses of data and predict the future — or who can build the fastest communications infrastructure to connect far-flung places — or who can solve difficult technical problems of timing events accurately to the hundredth of the nanosecond — then they might have benefits outside of the financial tournaments.

On its own it is perhaps a little bizarre that stock exchanges would need to sequence orders down to the hundredth of a nanosecond, but if that meaningless-seeming competition between high-frequency trading firms helps subsidize basic research to improve our understanding of time itself, isn’t that kind of cool?