Detecting imbalanced financial markets through time-varying optimization and nonlinear functionals

TL;DR

This paper investigates the dynamic structure of equity markets by analyzing market capitalization distributions and introduces a mathematical framework for studying time-varying portfolios using nonlinear functionals, revealing market imbalances.

Contribution

It presents a novel mathematical framework for analyzing time-varying portfolios with nonlinear functionals, applied to market capitalization and portfolio exposure.

Findings

Distribution of top 100 companies' market caps varies over time.

New framework for analyzing portfolios with nonlinear functionals.

Insights into market imbalance and concentration dynamics.

Abstract

This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies' market capitalizations over time, in terms of inequality, concentration at the top, and overall discrepancies in the distribution between different times. In the next section, we introduce a mathematical framework of linear and nonlinear functionals of time-varying portfolios. We apply this to study the market capitalization exposure and spread of optimal portfolios chosen by a Sharpe optimization procedure. These methods could be more widely used to study various measures of optimal portfolios and measure different aspects of market exposure while holding portfolios selected by an optimization routine that changes over time.