The financial market and its instruments are subject to numerous studies all over the world. Special attention is duly earned by the multifaceted research and analysis of the behavior of rates of return on shares, as well as shares’ other statistical properties including the beta parameter. Stock stability is considered by dividing the whole market into the bull and bear categories, and the rate of return is studied according to different frequencies of measurement. The purpose of this article is to examine the statistical properties of monthly rates of return for the biggest companies in terms of capitalization and turnover, which were listed on the stock exchange in Frankfurt, Paris, and Warsaw between 2005 and 2015. The basic descriptive statistics of the rates of return as well as the normality and stationarity of their time series undergo analysis. Moreover, hypotheses about equality of the expected value of the rate of return and its variance are subject to verification. This study is also conducted considering the division of the whole market into the bull and bear categories according to two definitions. The obtained results serve to conduct a comparative analysis of the three stock markets enumerated above. The results constitute an introduction to further and more advanced research on the beta parameter and its properties.