The Amazing Power of Dimensional Analysis: Quantifying Market Impact

This paper complements the inspiring work on dimensional analysis and market microstructure by Kyle and Obizhaeva (2017). Following closely these authors, our main result shows, by a similar argument as usually applied in physics, the following remarkable fact. If the market impact of a meta-order only depends on four well-defined and financially meaningful variables, and some obvious scaling relations as well as the assumption of leverage neutrality are satisfied, then there is only one possible form of this dependence. In particular, the market impact is proportional to the square-root of the size of the meta-order. This theorem can be regarded as a special case of a more general result of Kyle and Obizhaeva. These authors consider five variables which might have an influence on the size of the market impact. In this case, one finds a richer variety of possible functional relations which we precisely characterize. We also discuss the analogies to classical arguments from physics, such as the period of a pendulum.