  This note complements the inspiring work on dimensional analysis and market
microstructure by Kyle and Obizhaeva [18]. 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, then -- up to a
constant -- 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.
