*"Thus the relative velocity of two particles as measured in a frame in which both move can be as much as 2c." *Wolfgang Rindler* *(1960)

Midpoint colocation takes advantage of the 2c speed limit of light against light as observed from the ground. To take advantage of the 2c speed limit one needs a midpoint colocation data center.

The speed of light going in the opposite direction of a particle moving at 0.99c is still only c as observed from the particle frame using Einstein synchronized clocks. This speed follows the Einstein velocity addition theorem. The speed of light realtive to the particle moving at 0.99c realtive to the ground as observed from the frame measuring the speed of the particle to be 0.99c is c+0.99c=1.99c. The speed of light or any other object relative to another object as observed from another frame follows Galilean velocity addtion rules and not the Einstein velocity addition theorem. Einstein used his velocity addtion theorem correctly.

See my working paper for a overview of the hsitory of the 2c speed limit related to this topic

Illustration by Line Halsnes based on draft by Espen G. Haug, Copyright 2015

We have three main categories of colocation set-ups for high speed trading, see Howorka (2015). First, let us consider a trader in an exchange colocation that is only focusing on local trading. With local trading I am thinking only of comparing assets that are trading inside the same exchange. The trader can compare securities listed on the same exchange almost instantaneously (or at least extremely fast compared to someone located outside the exchange). Assume that the distance between two exchanges is d. The trader set-up in this case will use t = d/c to compare the price of the assets on the two exchanges. Then the trader will use 2d/c = 2t to compare and execute on both exchanges.

Next assume a trader who only has a midpoint colocation. For the midpoint colocation, comparing assets on the same exchange and executing the trades will take 0.5d/c + 0.5d/c = d/c = t. Clearly the exchange colocation is superior for comparing assets on the same exchange (local trading). When it comes to comparing the price of assets on two exchanges, the midpoint colocation uses d/2c = 0.5t. In addition, to execute trades on that information, the midpoint colocation uses 2d/2c = t. So a midpoint colocation is clearly superior to a single exchange colocation for such trading; actually it is twice as fast, given t versus 2t. This is due to the fact that the speed of light relative to light as observed from a third frame (the ground in this case) is 2c. Bear in mind the speed of light realtive to light as observed from one of the light beams follows Einstein's velocity addtion theorem and is only c.

However, we can have a third type of set-up, where we have exchange colocations at each exchange. When dealing with two exchanges, we can call this set-up “twin exchange colocation.” From these twin colocations, local trading can naturally be done almost instantaneously. To compare assets from the two exchanges takes now d/c = t and to execute trades based on this information basically will not add any time (when, for simplicity sake’s, we assume that the distance from the exchange colocation to the exchange is 0).The table below summarizes the three trading strategies.

Except for line one, the other lines have to do with what happens when we are comparing prices between two exchanges. Only the lines in bold are of real importance; for trading it does not help to get information first if you are not taking into account the time it takes to act (execute) on that information.

Most firms involved in statistical arbitrage between exchanges will also be involved in local trading strategies at each exchange. In general, this means that they do not need midpoint colocation. It could however be that midpoint colocation has cheaper rental space than exchange colocation. Firms that are only involved in arbitrage trading between two exchanges could prefer midpoint colocation for this reason. There could also be some exchanges that do not offer exchange colocation. It is not necessarily that cheap to buy or get access to the building next door to the exchange (to use for colocation), so in such situations midpoint colocation could potentially be superior for arbitrage trading between exchanges, as compared to nearby exchange colocations. Also having a colocation building close to the exchange do not necessary ensure that the communication path is short, read flashboys for examples on this.

For a more general discussion on midpoint colocations versus exchange colocation see in particular the excellent article below by Ed Howorka.

It is naturally important to think about the carbon footprint, so me and Albert are working on some interesting designs :-)

2015 Mark Buchanan: Physics in finance: Trading at the speed of light, Nature 518

2015 (MarketWatch): Physicist says it is possible to use ships to facilitate high-frequency trading

2015 Ed Howorka: Colocation beats the speed of light

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