Statistical Properties of Share Volume Traded in Financial Markets

Abstract

We quantitatively investigate the ideas behind the often-expressed adage `it takes volume to move stock prices', and study the statistical properties of the number of shares traded $Q_{Δt}$ for a given stock in a fixed time interval $Δt$. We analyze transaction data for the largest 1000 stocks for the two-year period 1994-95, using a database that records every transaction for all securities in three major US stock markets. We find that the distribution $P(Q_{Δt})$ displays a power-law decay, and that the time correlations in $Q_{Δt}$ display long-range persistence. Further, we investigate the relation between $Q_{Δt}$ and the number of transactions $N_{Δt}$ in a time interval $Δt$, and find that the long-range correlations in $Q_{Δt}$ are largely due to those of $N_{Δt}$. Our results are consistent with the interpretation that the large equal-time correlation previously found between $Q_{Δt}$ and the absolute value of price change $| G_{Δt} |$ (related to volatility) are largely due to $N_{Δt}$.