A Theory of Market Efficiency

We introduce a mathematical theory called market connectivity that gives concrete ways to both measure the efficiency of markets and find inefficiencies in large markets. The theory leads to new methods for testing the famous efficient markets hypothesis that do not suffer from the joint-hypothesis problem that has plagued past work. Our theory suggests metrics that can be used to compare the efficiency of one market with another, to find inefficiencies that may be profitable to exploit, and to evaluate the impact of policy and regulations on market efficiency. A market’s efficiency is tied to its ability to communicate information relevant to market participants. Market connectivity calculates the speed and reliability with which this communication is carried out via trade in the market. We model the market by a network called the trade network, which can be computed by recording transactions in the market over a fixed interval of time. The nodes of the network correspond to participants in the market. Every pair of nodes that trades in the market is connected by an edge that is weighted by the rate of trade, and associated with a vector that represents the type of item that is bought or sold. We evaluate the ability of the market to communicate by considering how it deals with shocks. A shock is a change in the beliefs of market participants about the value of the products that they trade. We compute the effect of every potential significant shock on trade in the market. We give mathematical definitions for a few concepts: • The tension and energy of the network are related concepts that measure the strength of the connections between sets of participants that trade similar items. They measure the amount of trade that is affected by significant shocks. They are high when there are many paths of high rate of trade that connect those with differing beliefs about the value of items. They are low when information from some large set of participants must take a long time to reach some other large set via trade. • A bottleneck in the network is a small set of nodes that monopolizes an unusually large share of the trade in the network. The nodes in the bottleneck have an incentive to set prices incorrectly and interfere with the fair transmission of information in the market. We give explicit mathematical definitions that capture these concepts and allow for quantitative measurements of market inefficiency. 1 ar X iv :1 70 2. 03 29 0v 1 [ qfi n. E C ] 9 F eb 2 01 7