# Relativistic statistical arbitrage

on April 8, 2011 at 12:22 pm

I haven’t read this paper (pdf) yet, but the abstract is already a winner:

Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.

Hat tip goes to Robert Cottrell, and Kevin Drum pulls the map out.

1 Advocatus Diablo April 8, 2011 at 12:57 pm

(sarcasm)

So, if PY = MV, such that V == Velocity of Money
V = PY/M, but now we can introduce a relativistic component… E=mc^2, where E = energy economic output, and M = mass, c=speed of light… But as energy can be stated in another form as economic output, E = Y(constant x_1), and mass is roughly related to the size of the money supply M = m(constant x_2)…

V = PE(x_1)/m(x_2) = P(x_1/x_2)(c^2)

V = P((x_1)(c^2)/(x_2)) !!

So, the velocity of high-frequency trades is a function of the price level, the speed of light, and the constants x_1 and x_2! Stated differently, that V/P is constant is now a fundamental law of the universe!

(/sarcasm)

2 albatross April 9, 2011 at 11:42 am

I was sure, when you started these calculations, that you were going to find some way to end with \$=t.

3 Hasdrubal April 8, 2011 at 1:13 pm

I’m having problems opening the document, but I wonder if they’re looking at actual network delays or theoretical delays based on physical transmit media.

Coast to coast latencies across the Internet are on the order of 60-80MS round trip (with plenty of variability based on bandwidth in the path, carrier, time of day congestion, sunspots, etc.) This is plenty of time for a computer to act on algorithms and potentially an arbitrage opportunity if you’re clever enough, I suppose. Then again, computers aren’t consistently fast, and if you’re betting on making money by carrying out transactions in less than 60 milli seconds when your virus scanner kicks off, or you try to beat someone who has their own nation wide fiber ring…

4 A leap at the wheel April 8, 2011 at 1:26 pm

“Note that while some nodes are in regions with dense ﬁber-optic networks, many others are in the ocean or other sparsely connected regions, perhaps ultimately motivating the deployment of low-latency trading infrastructure at such remote but well-positioned locations.”
I hope this is just preliminary work. This would be of much greater value if they used actual, recorded network latencies as opposed to just assuming a fully connected abstract grid of fiber.

5 Right Wing-nut April 8, 2011 at 2:12 pm

“Assume spherical cows”.

Then refine your work. Network access costs (including long-haul transmission costs) are steadily dropping. So are non-relativistic network delays. The points they choose are the convergence points for arbitrage locations. The unrealistic points are only unrealistic today. As soon as the amount of money to be made substantially exceeds the cost of setting up the station and maintaining, the station will be set up. The offshore locations have certain advantages as well…

6 Rahul April 8, 2011 at 2:46 pm

“The offshore locations have certain advantages as well”

e.g. data center cooling costs, freedom from national regulators

7 albatross April 9, 2011 at 11:54 am

I’m no physicist, but my intuition is that I want to build a computer in a very deep well, bored down close to the center of the Earth, directly underneath the stock exchange. In the center, I should experience no net gravity, and the surface should be in fairly fast motion relative to me, so my clock should run faster than the clocks of the folks on the surface.

There must be an SF story somewhere involving this kind of effect. Put the main civilization down in a deep, deep gravity well, maybe orbiting a black hole, but put the computing devices of the “gods” up far out of the well, and the gods can do computations many times faster than the main civilization.

8 Erik Brynjolfsson April 8, 2011 at 1:30 pm

Pretty funny.

It also underscores how rent-seeking via high frequency trading is a sad waste of not only equipment, but also too much of the brainpower of my MIT colleagues and graduates.

9 Jose April 11, 2011 at 6:11 am

In which realm exactly would this be a waste? What else would anyone use such a brainpower for if not for one of these :

a) To make a ton of money

b) To fulfill a self-aggrandizing prophecy

c) both

LOL

10 Radord Neal April 8, 2011 at 1:33 pm

This phenomenon is the backdrop to the 1977 story “Good-Bye, Robinson Crusoe” by John Varley.

11 Rahul April 8, 2011 at 1:35 pm

The colored map on page-5 of the pdf confuses me. The large red dots are supposed to be locations of “major securities exchanges”. Why are there red dots in the Atlantic and the Indian ocean? Or is that Madagascar?

12 Right Wing-nut April 8, 2011 at 2:07 pm

I would assume the Atlantic point is Bermuda. I don’t know the Indian Ocean.

13 Jeff April 8, 2011 at 2:07 pm

I believe that red dot east of Madagascar is Mauritius

14 Rahul April 8, 2011 at 2:47 pm

Could be. I’m just skeptical if either of Bermuda or Mauritius qualify as “major exchanges”.

15 dirk April 8, 2011 at 2:02 pm

There is no great stagnation.

16 Michael F. Martin April 8, 2011 at 2:23 pm

Haven’t read anything so cool since the mathematical model of cow behavior.

17 JP White April 8, 2011 at 2:29 pm

Reminds me of a book I read a couple of years ago: “Einstein’s Clocks, Poincare’s Maps: Empires of Time.” Recommended.

18 Aristotle Democritus April 8, 2011 at 3:11 pm

(parody)
Beyond simple relativity, the Wave–Tick duality postulates that all prices exhibits both wave and tick properties. A central concept of quantum mechanics… err I mean quantitative analysis, this duality addresses the inability of classical relativistic analysis concepts like “tick” and “wave” to fully describe the behavior of ultrahigh frequency trading. Standard interpretations of quantitative analysis explain this paradox as a fundamental property of the Market, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the trader. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–tick duality is one aspect of the concept of complementarity, that a trade can be viewed in one way or another, but not both simultaneously. A profitable trader attributes profitability to “alpha”, an edge it has over the Market, while an unprofitable trader blames latency and front-running for its losses. While a trade can be viewed in one way or another, it cannot be viewed both ways simultaneously.
(/parody)

19 Heisenberg April 8, 2011 at 3:20 pm

Also, the more accurately scientists narrow down the price of a good, the more uncertain become the quantities demanded and supplied.

20 Advocatus Diablo April 8, 2011 at 6:42 pm

Tip o’ the hat to you sir!

21 JasonL April 8, 2011 at 3:17 pm

Why does this feel like a Pynchon novel to me?

22 Orange14 April 8, 2011 at 3:39 pm

Actually it was all done by William Gaddis in ‘JR’ that was written just about the same time as Gravity’s Rainbow.

23 Alek April 8, 2011 at 4:48 pm

If you want to look for arbitrage opportunities between an exchange in, say, London and another one in New York, why don’t you just place a server in London, one in NYC, connect the two and have them figure it out? What do you gain by placing a third server in the middle?

24 Heisenberg April 8, 2011 at 5:50 pm

Without having read the paper, my guess would be that information from London can be combined with information from New York and then traded on in London again in half the time if it only has to travel half the distance to New York.

25 BM April 8, 2011 at 8:21 pm

This is absurd; the exchanges could get rid of this if they wanted to.

Just announce that all trades will be queued up for one second, in random order, then executed exactly on the second. The order that arrives at 12:00:00.0000 has precisely the same “priority” (or, rather, exactly the same chance of winning the priority-deciding dice roll) as the order that arrives at 12:00:00.9999. Likewise for all of the orders between 12:00:01.0000 and 12:00:01.9999, etc. Heck, make it ten seconds or a minute.

Even better: traders can buy, at auction, government-issued “one millisecond priority-boost coupons” to bias a the random number generator. Revenue from the coupon auctions is earmarked for the newly-established federal Office of Public Shaming, whose first target is anyone who bought the coupons.

26 IVV April 11, 2011 at 10:19 am

Yes, but they don’t want to get rid of this.

27 Dan April 8, 2011 at 11:32 pm

And when quantum computers are perfected, we will be able to complete a trade before an offer is tendered.

28 Kauser April 9, 2011 at 12:40 am

Reminds me of .

29 Kauser April 9, 2011 at 12:44 am

*Reminds me of Paul Krugman’s widely acclaimed, Einsteinian magnum opus titled “Economics: the final frontier”.

30 techreseller April 11, 2011 at 3:25 pm

Long ago in my business classes it was explained to me that Wall Street existed to properly allocate capital among business opportunities. In more layman’s terms, Wall Street was overpaid because they could thru market mechanisms help determine which companies should receive new capital to best generate a return on the companie’s business activity. Now Wall Street exists merely to exploit extremely tiny, extremely short differences between exchanges or to front run orders from those otherwise known as Wall Street clients. What a waste of talent, money and energy. And we wonder why US competitiveness is declining. Even while I disagree with the China model, at least they are investing in things that create lasting value to others outside the investment banks.