Markets are efficient if and only if P = NP

TL;DR

This paper establishes a theoretical link between market efficiency and computational complexity, showing that market efficiency implies P=NP, and that markets could be used to solve NP-complete problems, suggesting markets are likely inefficient.

Contribution

It provides a novel theoretical framework connecting financial market efficiency with computational complexity, specifically P versus NP, and demonstrates how markets could be programmed to solve complex problems.

Findings

Markets are likely inefficient if P ≠ NP.

Market efficiency decreases with longer or more frequent data.

Empirical data supports the link between data availability and market inefficiency.

Abstract

I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.