This post is inspired mostly by semi-informed intuitions** about recent trends in economics and finance what have intrigued me, and my application of systems and complexity theory to the discussion.

High-frequency trading

Over the past year, I've seen a number of news stories on high- frequency trading (HFT). A number of companies engaged in this practice have clustered around "hotspots" determined by the maximizing information flow between points on a fiber optic network. Their strategy is to receive high- throughput data as fast as possible from the trading floor and (with very short latency) turn it into trades. This results in the buying and selling of shares at a very high rate (on the order of seconds).

This practice is based in part on a paper [1] called "Relativistic statistical arbitrage" (algorithmically-assisted trading -- statistical arbitrage [2] -- near the speed of light -- relativistic). This paper advocates high-frequency trading purely from the standpoint of data transfer. The potential advantage of this approach is twofold. One is that the "winner" (e.g. the highest-frequency trader) can take advantage of larger trends in the market as they emerge, or exploit disequilibria (fluctuations that deviate from the mean) in a way that minimizes the overall risk. They are at the root of a cascade, so to speak. The real advantage of this is not quite clear, however, it is suspected that the flash crash experienced on the New York Stock Exchange (NYSE) during May, 2010 was caused by a critical mass of high-frequency traders all converging on the same set of trades. This may have created a false signal that lower-frequency investors interpreted as a sell-off.

I am not formally trained in finance or economics, so my criticism of HFT stems from a fundamentally different view as to what constitutes "information". I think of information more formally in terms of information content, or distinct regularities embedded in a signal. Furthermore, I suspect that proponents of HFT believe that they are extracting information from very short timescales. However, there is a fundamental difference between data and information, and what HFT amounts to is an aliasing of information contained in market dynamics. As people familiar with time-series analysis know, aliasing is an oversampling of the true information content embedded in a series of events.

For example, we cannot extract yearly performance information out of data from two days worth of hourly intervals. In fact, any subsampling of the of the yearly (global) time-series would only serve as an instance of stochastic flux, or random deviations from a linear equilibrium which actually govern time-series dynamics locally. In short, very short timescales in the stock market serve as stochastic flux and do not contain very much information content in and of themselves. The main advantage of high-frequency trading with respect to information is being at the root of a cascade, and limiting your exposure to a stock if its value suddenly declines.

Cascades, Stochastic Flux, and Bubbles

While the information content HFT operates on seems to be minimal, the effects of HFT in the form of trading cascades and ultimately false information can be very real. A related problem is that of market volatility at moderate time-scales (in this case on the order of hours or days). One aspect of statistical arbitrage is the assumption of regression to the mean, or that all fluctuations are noise and can be disregarded when the size (and diversity) of one's portfolio is sufficiently large. However, stochastic fluctuations may not be normally-distributed (e.g. Gaussian) nor contain uniform information content that can be easily approximated. I suspect that aliasing and these factors plays a role in triggering volatility at this time-scale as well. With quick trades becoming increasingly common and the 24-hour news cycle providing large volumes of informational "fragments", an open-loop, entirely reactive system has developed. For example, a series of news articles concerning weather-related production problems or speculation about future political developments, this can be enough to trigger a large-scale increase or decrease in value that is corrected only after the fact. This may be why the market jumps in extreme ways whenever a trend is sensed, while information related to long-term observation can often dampen this volatility. It could also be an unexplored factor in "bubble" formation seen in commodities markets, with the open-loop operating over a much longer timescale.

Two additional things

1) I recently re-read Benoit Mandelbrot's book "The (mis)behavior of markets", which is an application of fractal theory to financial markets[3]. Mandelbrot was a vocal critic of the movement towards relying on deterministic models and risk minimization in finance. While my critique of HFT was not directly inspired by Mandelbot's book, I feel that these ideas are very similar. Anyone intrigued by the ideas I have presented here should read this book.

2) there was a recent installment of Paul Solman's "Making Sen$e" segment on the PBS Newshour in which the "shape" [4] of our fledgling economic recovery was debated (video).The main idea was that the time-series of economic recovery, based on the context, took on a specific shape (e.g. a "U" shape or an "L" shape function). In the video, the shapes they debate are based on comparisons of GDP (gross domestic product) against time. However, what would happen if multiple functions (e.g. unemployment, purchasing power with respect to time) were compared and/or integrated? Would they reveal a greater truth? And what would the shape of an economic recovery be then?

References:

[1] Wissner-Gross, A.D. and Freer, C.E. (2010). Relativistic statistical arbitrage. Physical Review E, 82, 056104. Paper.

[2] Pole, A. (2007) Statistical arbitrage: algorithmic trading insights and techniques. Wiley Finance, New York. Google book.

[3] Mandelbrot, B. (2004). The (mis)beheavior of markets.

[4] Solman, P. (2011) U,V,W, or L. How Is the Economic Recovery Shaping Up, Literally? YouTube. Video.

* economic trace refers to the graphical representation of time-series data related to economics.

** although I am pretty good at understanding complex systems....

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