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

ArXiv ID: 2310.04907 “View on arXiv”

Authors: Unknown

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.

Keywords: Quantal Response Statistical Equilibrium (QRSE), Cross-sectional distributions, Cryptocurrency returns, Informational efficiency, Bear and bull trends, Cryptocurrency

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced statistical equilibrium models and information theory (Shannon entropy) to analyze market structure, indicating high mathematical complexity. It also demonstrates strong empirical rigor with a detailed, multi-year dataset of 46 cryptocurrencies and S&P 500 companies, including data processing, cross-sectional analysis, and comparisons of market efficiency.
  flowchart TD
    A["Research Goal: Compare Stock & Crypto Markets<br>via Cross-Sectional Distributions & Efficiency"] --> B["Data Collection: Stocks S&P 500 & 46 Major Cryptos<br>Jan 2017 - Dec 2022"]
    B --> C["Methodology: Apply Quantal Response<br>Statistical Equilibrium (QRSE) Model"]
    C --> D["Process: Recover Cross-Sectional<br>Return Frequency Distributions"]
    D --> E["Analysis: Stochastic Structure &<br>Investor Behavior in Bull vs. Bear Trends"]
    E --> F["Outcome: Comparative Analysis of<br>Informational Efficiency"]
    F --> G["Key Findings:<br>Structural differences in markets<br>Efficiency disparities"]