Toward a Theory of Marginally Efficient Markets

TL;DR

This paper proposes a theoretical framework for understanding marginal market efficiency, suggesting that markets are not perfectly efficient but contain exploitable probabilistic edges, which are quantifiable via conditional entropy.

Contribution

It introduces a novel entropy-based method to measure market predictability and models market participants as producers and speculators affecting price dynamics.

Findings

Market prices exhibit residual predictability measurable by entropy.

Perfect efficiency would require infinite arbitrage capital.

Market participants influence price entropy through their actions.

Abstract

Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it favorable games}, in the sense that there is a small probabilistic edge that smart speculators can exploit. We propose to identify this probability using conditional entropy concept. A perfect random walk has this entropy maximized, and departure from the maximal value represents a price history's predictability. We propose that market participants should be divided into two categories: producers and speculators. The former provides the negative entropy into the price, upon which the latter feed. We show that the residual negative entropy can never be arbitraged away: infinite arbitrage capital is needed to make the price a perfect random walk.