Michael Lewis has been in the news for his new book, Flash Boys, decrying the problems brought about by a system ill equipped to deal with high frequency trading. The core problem can be stylistically summarized by this picture:

I place an order from the location of the red square to the green and purple exchanges on which trades occur. My communication capability on the gray “public” channel is slower than the communication capability of some competing agent on the blue “private” channel. Therefore, triangle inequality notwithstanding, the competing agent observes my actions at the green exchange and reacts at the purple exchange before my order arrives there. It appears to me exactly like I have been scooped by somebody acting anti-causally, so what happened?
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Is there a standard definition? Does it have a unit? Is it even a number?

I’m going to take a stab. Without loss of generality I’ll define liquidity availability for buying (selling is analogous), as a unitless function \(L($,s)\) over transaction amount \($\) and time limit \(s\). Operationally, it means to take \($\) amount of a tradable asset, convert into number of shares \(N\) at the current price (assume it exists) and request to transact \($\) using all possible algorithms that complete in \(s\) seconds and find the one that got the most shares \(N^*\), then \(L($,s) = N^*/N\), a number between 0 and about 1 (for most cases). The larger it is, the more liquidity there is at the \(($,s)\) pair. \(L\) is monotonically decreasing in \($\) and monotonically increasing in \(s\).
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Stories like this about the sudden unwinding of the yen carry trade had me thinking.

Financial markets are some kind of dynamical system. This system has stable and unstable modes. Clearly, the unstable modes are best not to be touched, yet there are few (or not enough) regulations or systematic constraints to keep a path from falling into those.

Common experience from systems design seems to say that you have to be willing to give up some efficiency in exchange for stability. That’s why there are currency pegs (or trading bands), reserves ratios, and interest rate targets. But these are too crude. There needs to be systematic tools in all markets to damp system dynamics to a time constant on the same order as that of economic reality. You cannot have capital flooding in and out of markets and currency flooding in and out of countries at rates that cannot be absorbed or sustained by the national economies. Sure, that is “efficient”, but it also makes no sense. This is the point at which free market and market efficiency fundamentalists need to take a step back and look at the big picture and see where they are so obviously wrong.

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