Towards Understanding the Predictability of Stock Markets from the Perspective of Computational Complexity

TL;DR

This paper explores stock market predictability through computational complexity, showing that market predictability depends on the number of strategies used by traders and introducing complexity classes that characterize prediction difficulty.

Contribution

It introduces a simple agent-based market model and proves complexity-theoretic results linking the number of strategies to prediction feasibility and hardness.

Findings

Basic model generates realistic price graphs.

Prediction is feasible with few strategies in polynomial time.

High strategy diversity leads to computationally hard prediction problems.

Abstract

This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, which are between P^NP[O(log n)] and PP. These computational completeness results open up a novel possibility that the price graph of an actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.