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This paper presents a quantitative analysis of the relationship between thestock market returns and corresponding trading volumes using high- frequencydata from the Polish stock market. First, for stocks that were traded forsuffciently long period of time, we study the return and volume distributionsand identify their consistency with the power-law functions. We find that, formajority of stocks, the scaling exponents of both distri- butions aresystematically related by about a factor of 2 with the ones for the returnsbeing larger. Second, we study the empirical price impact of trades of a givenvolume and find that this impact can be well described by a square-rootdependence: r(V) V^(1/2). We conclude that the prop- erties of data from thePolish market resemble those reported in literature concerning certain maturemarkets.

Stock returns versus trading volume: is the correspondence more general?