  This paper presents a quantitative analysis of the relationship between the
stock market returns and corresponding trading volumes using high- frequency
data from the Polish stock market. First, for stocks that were traded for
suffciently long period of time, we study the return and volume distributions
and identify their consistency with the power-law functions. We find that, for
majority of stocks, the scaling exponents of both distri- butions are
systematically related by about a factor of 2 with the ones for the returns
being larger. Second, we study the empirical price impact of trades of a given
volume and find that this impact can be well described by a square-root
dependence: r(V) V^(1/2). We conclude that the prop- erties of data from the
Polish market resemble those reported in literature concerning certain mature
markets.
