Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory - Lo, Andrew W.; Wang, Jiang (Review of Financial Studies, 2000)
"We examine the implications of portfolio theory for the cross-sectional behavior of equity trading volume. Two-fund separation theorems suggest a natural definition for trading activity: share turnover...We find strong evidence against two-fund separation, and a principal-components decomposition suggests that turnover is well approximated by a two-factor linear model" – Abstract.