We examine the validity of the power-law tails of the distributions of stock returns $P\left\{R>x\right\}\sim x^{-{\zeta }_R}$ 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 ${\zeta }_R\approx 3$ for all three markets. We perform similar analyses of the related microstructural variable, the number of trades $N\equiv N_{\Delta t}$ over time interval $\Delta t$, and find a power-law tail for the cumulative distribution $P\left\{N>x\right\}\sim x^{-{\zeta }_N}$, 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.

• Received 8 July 2007

DOI:https://doi.org/10.1103/PhysRevE.77.037101