How the trading activity scales with the company sizes in the FTSE 100
  This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value per trade, transaction value per hour, tick rate), to the order queue (total number of orders, total value), and to the price dynamic (spread, volatility). The outcome is that systematic scaling relations are observed: 1) the value exchanged by hour and value in the order queue have exponents lower than 1 respectively 0.90 and 0.75; 2) the tick rate and the value per transaction scale with the exponents 0.39 and 0.44; 3) the annualized volatility is independent of the size, and the tick-by-tick volatility decreases with the market capitalization with an exponent -0.23; 4) the spread increases with the volatility with an exponent 0.94. A theoretical random walk argument is given that relates the volatility exponents with the exponents in points 1 and 2. 
Gilles Zumbach