  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.
