An Information Theory Approach to the Stock and Cryptocurrency Market: A Statistical Equilibrium Perspective

TL;DR

This paper compares the stochastic structures and informational efficiency of cryptocurrency and stock markets using an information theory approach and the QRSE model, revealing insights into investor behavior and market dynamics.

Contribution

It introduces the application of the QRSE model to analyze and compare the cross-sectional return distributions of cryptocurrencies and stocks from 2017 to 2022.

Findings

Cryptocurrency markets show different stochastic properties than stock markets.

Investor behavior varies significantly between bear and bull trends.

Cryptocurrencies exhibit different levels of informational efficiency compared to stocks.

Abstract

We study the stochastic structure of cryptocurrency rates of returns as compared to stock returns by focusing on the associated cross-sectional distributions. We build two datasets. The first comprises forty-six major cryptocurrencies, and the second includes all the companies listed in the S&P 500. We collect individual data from January 2017 until December 2022. We then apply the Quantal Response Statistical Equilibrium (QRSE) model to recover the cross-sectional frequency distribution of the daily returns of cryptocurrencies and S&P 500 companies. We study the stochastic structure of these two markets and the properties of investors' behavior over bear and bull trends. Finally, we compare the degree of informational efficiency of these two markets.