How the trading activity scales with the company sizes in the FTSE 100

TL;DR

This study reveals how various trading activity measures scale with company size in the FTSE 100, showing systematic relationships and independence of volatility from size, supported by a theoretical random walk model.

Contribution

It provides the first detailed analysis of how trading activity metrics scale with company size in a major stock index, introducing a theoretical model linking volatility and activity exponents.

Findings

Value exchanged per hour scales with an exponent of 0.90.

Tick rate scales with an exponent of 0.39.

Volatility is independent of company size.

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 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.