How trading activity scales with company size in the FTSE 100

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Abstract
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 of less 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 of −0.23; (4) the spread increases with the volatility with an exponent of 0.94. A theoretical random walk argument is given that relates the volatility exponents to the exponents in points 1 and 2.
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