Trading volume: Definitions, data analysis, and implications of portfolio theory

We examine the implications of portfolio theory for the cross-sectional beh avior of equity trading volume. Two-fund separation theorems suggest a natu ral definition for trading activity: share turnover. If two-fund separation holds, share turnover must be identical for all securities. If (K + 1)-fun d separation holds, we show that turnover satisfies an approximately linear K-factor structure. These implications are examined empirically using indi vidual weekly turnover data for NYSE and AMEX securities from 1962 to 1996. We find strong evidence against two-fund separation, and a principal-compo nents decomposition suggests that turnover is well approximated by a two-fa ctor linear model.