PAPER: A Computational View Of Market Efficiency

An interesting paper showed up on arXiv, "A Computational View Of Market Efficiency". I find it interesting for two reasons. First, it is one of the rare papers in finance that observes that seemingly complex market behaviors have elegant and relatively simple descriptions in the context of computational information theory, a significant oversight in finance literature generally. Second, the paper makes no references to the existing work in algorithmic information theory that would show their result to be trivial and obvious, which demonstrates that a big cross-disciplinary gap in understanding still exists.

From the abstract:

We propose to study market efficiency from a computational viewpoint. Borrowing from theoretical computer science, we define a market to be efficient with respect to resources S (e.g., time, memory) if no strategy using resources S can make a profit. As a first step, we consider memory-m strategies whose action at time t depends only on the m previous observations at times t-m, ..., t-1. We introduce and study a simple model of market evolution, where strategies impact the market by their decision to buy or sell. We show that the effect of optimal strategies using memory m can lead to “market conditions” that were not present initially, such as (1) market bubbles and (2) the possibility for a strategy using memory m' > m to make a bigger profit than was initially possible. We suggest ours as a framework to rationalize the technological arms race of quantitative trading firms.