Stock return distributions: tests of scaling and universality from three distinct stock markets.

We examine the validity of the power-law tails of the distributions of stock returns P{R>x} ~ x(-zeta(R)) using trade-by-trade data from three distinct markets. We find that both the negative as well as the positive tails of the distributions of returns display power-law tails, with mutually consistent values of zeta(R) approximately 3 for all three markets. We perform similar analyses of the related microstructural variable, the number of trades N identical with N(Deltat) over time interval Deltat, and find a power-law tail for the cumulative distribution P{N>x} ~ x(-zeta(N)), with values of zeta(N) that are consistent across all three markets analyzed. Our analysis of U.S. stocks shows that the exponent values zeta(R) and zeta(N) do not display systematic variations with market capitalization or industry sector. Moreover, since zeta(R) and zeta(N) are remarkably similar for all three markets, our results support the possibility that the exponents zeta(R) and zeta(N) are universal.