Dynamics of observables in rank-based models and performance of functionally generated portfolios

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.