The Amazing Power of Dimensional Analysis in Finance: Market Impact and the Intraday Trading Invariance Hypothesis

A basic problem when trading in financial markets is to analyze the prize movement caused by placing an order. Clearly we expect - ceteris paribus - that placing an order will move the price to the disadvantage of the agent.... [ view full abstract ]

A basic problem when trading in financial markets is to analyze the prize movement caused by placing an order. Clearly we expect
- ceteris paribus - that placing an order will move the price to the disadvantage of the agent. This price movement is called the market
impact. Following the recent work of A. Kyle and A. Obizhaeva we apply dimensional analysis - a line of arguments well known in classical
physics - to analyze to which extent the square root law applies. This universal law claims that the market impact is proportional to the
square root of the size of the order. We also analyze the dependence of the trading activity on a stock, i.e. number of trades per unit of time, in dependence of some suitable explanatory variables. Dimensional analysis leads to a 2/3 law: the number of trades is proportional to the power 2/3 of the exchanged risk.