Stock Returns, Market Trends, and Information Theory: A Statistical Equilibrium Approach

This paper attempts to develop a theory of statistical equilibrium based on an entropy- constrained framework, that allow us to explain the distribution of stock returns over di erent market trends. By making use of the Quantal Response Statistical Equilib- rium model (Scharfenaker and Foley, 2017), we recover the cross-sectional distribution of daily returns of individual company listed the S&P 500, over the period 1988-2019. We then make inference on the frequency distributions of returns by studying them over bull markets, bear markets and corrections. The results of the model shed light on the microscopic as well as macroscopic behavior of the stock market, in addition to provide insights in terms of stock returns distribution.