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

TL;DR

This paper develops a mathematical framework to describe the dynamics of market observables in rank-based models and evaluates the performance of functionally generated portfolios over various time horizons.

Contribution

It provides a concise mathematical description of market observables' dynamics in rank-based models, enhancing understanding of their behavior and portfolio performance.

Findings

Mathematical description of observable dynamics in rank-based models

Analysis of portfolio performance over short- and medium-term horizons

Extension potential to other large financial market models

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.