Relativistic Share Trading

Once upon a time, if you wanted to buy or sell shares in a company, your wishes would be conveyed by word of mouth to a broker on the trading floor of a stock exchange. Then, he’d have to find another broker on the same floor willing to match your offer. This would, of course, take some time.

Relativistic Share Trading
Relativistic Share Trading

Today, your wishes are conveyed to the stock exchange computer, and your order is electronically matched, with no human intervention. This is much faster. In fact, the most advanced stock exchange computers match orders within ten microseconds. Ten microsecond is an incredibly short time. It takes a million microseconds to say the word “microsecond”, and when you do, ten microseconds is not enough time for the sound to travel from your teeth to your lips. Say “modern share market computers” out loud, and by the time the sound of your voice reaches the ears of the person next to you, modern share market computers can have performed hundreds of trades.

What’s more, today your purchase of US equities might not happen on Wall Street – there are multiple securities exchanges around the USA, spread across the country. There’s no guarantee that the same share will have the same price at the different exchanges – and when they diverge, there’s a chance for a quick individual to make a pile of money. After all, if Apple shares cost $500 here and $600 there, you can make a quick $100 by buying one here and selling it there. Then you can do it again and again. This is called an “arbitrage opportunity”.

Arbitrageurs have to act quickly. Buy Apple shares at $500, and the price goes up. Sell them at $600, and the price goes down. Pretty soon, the prices at the exchanges match, and the opportunity is gone. The money is made by the arbitrageur who most quickly spots a price difference and most quickly reacts. Professional arbitrageurs don’t bother reading stock prices off the newspaper or Google finance. They’ll have their computer plugged directly into the stock exchanges’ live price feeds, with software running ready to pounce as soon as an opportunity is noticed.

Within microseconds.

Because there are professionals doing this with computers, normal human beings like you and me can forget about making money via stock market arbitrage. By the time you get the paper from the corner store and turn to the business section, a billion microseconds have passed. By the time you pick up the phone and your broker picks up, another hundred million. Another million passes as you say the words “buy at this price” or “sell”. For we financial mortals, prices at different exchanges always match, and there is no easy money to be had through arbitrage.

So are there no arbitrage opportunities at all? Are stock prices always in synchrony everywhere? Suppose your favourite stock drops by $1 at exactly 32.846791 seconds after 10:54am in New York. With an arbitrageur’s super-fast computer plugged directly into the exchanges, will the price in Chicago drop by the same amount 10 microseconds later? The answer is “no, the prices won;’t match” and the reason comes, not from finance or economics, but from physics – specifically, from Einstein’s Theory of Special Relativity.

His theory says that no information can travel faster than light. Light, though fantastically fast, is not infinitely fast, and 10 microseconds is a very short time. It’s only enough time for light to go about 2 miles (3km). Even 100 microseconds after the price drop on Wall Street, there’s no way people north of Manhattan could even know about it, let alone act on it. It’s a whole three milliseconds later that a signal travelling at the speed of light reaches Chicago from New York. That’s almost an eternity. Olympic swimming gold medals are sometimes decided by times this short. The trading computer can perform hundreds of trades in that time, so by the time anyone in Chicago can react, the price may have recovered, dropped further, or even rebounded beyond its original price – and nobody in Chicago can possibly know until another three milliseconds have passed.

To recap, by Einstein’s relativity, it’s not physically possible for the market in Chicago to synchronize perfectly with the one in New York. Information arriving in one exchange from the other is up to about 300 trades too late. Information about the price changes is hopelessly out of date before the laws of physics allow traders to use it.

It no longer makes sense for an arbitrageur to look for occasions when the two markets show different prices at the same time. In Einstein’s theory of relativity – that is, in the real world of high-speed trading on distant stock markets – “the same time” is a phrase that literally doesn’t makes sense. If you buy a share in New York and I buy one in Chicago when our clocks say it’s 54 minutes and 32.846791 seconds past the hour, the question of who bought whose first depends literally on who you ask – specifically, on whether they are travelling in the direction from NY to Chicago, or the other way round, or standing still. Phsycists who study relativity don’t talk about things happening “at the same time”. They use the words “spacelike separated”, which means “far enough apart in space that either might have happened first”. The opposite of this is “timelike separated”, which means “far enough apart in time that one unambiguously happens before the other”. When – if ever – computers are trading at nanosecond speeds, just hopping on a plane will get you going fast enough to muddy the order of typical trades. Stock brokers may have to pick up the terminology and strange ideas that are bread and butter for physicists studying Special Relativity.

Someone, one day, will do the hard math to understand what arbitrage means in an era of Relativistic Share Trading. They may or may not need the full power of Einstein’s equations, but there will certainly be some difficult math involved of some kind. When they work through it and see what it implies, there’s a good chance they’ll make a big pile of money for their employer and their employer’s clients – and, dare I hope, a little for themselves as well.