Title: Dynamics of observables in rank-based models and performance of functionally generated portfolios,
Abstract: In the seminal work [9], several macroscopic market observables have been
introduced, in an attempt to find characteristics capturing the diversity of a
financial market. Despite the crucial importance of such observables for
investment decisions, a concise mathematical description of their dynamics has
been missing. We fill this gap in the setting of rank-based models and expect
our ideas to extend to other models of large financial markets as well. The
results are then used to study the performance of multiplicatively and
additively functionally generated portfolios, in particular, over short-term
and medium-term horizons.