  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.
