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 ${Q}_{\ensuremath{\Delta}t}$ for a given stock in a fixed time interval $\ensuremath{\Delta}t.$ 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 ${P(Q}_{\ensuremath{\Delta}t})$ displays a power-law decay, and that the time correlations in ${Q}_{\ensuremath{\Delta}t}$ display long-range persistence. Further, we investigate the relation between ${Q}_{\ensuremath{\Delta}t}$ and the number of transactions ${N}_{\ensuremath{\Delta}t}$ in a time interval $\ensuremath{\Delta}t,$ and find that the long-range correlations in ${Q}_{\ensuremath{\Delta}t}$ are largely due to those of ${N}_{\ensuremath{\Delta}t}.$ Our results are consistent with the interpretation that the large equal-time correlation previously found between ${Q}_{\ensuremath{\Delta}t}$ and the absolute value of price change $|{G}_{\ensuremath{\Delta}t}|$ (related to volatility) are largely due to ${N}_{\ensuremath{\Delta}t}.$