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

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. • We study the structure of the equity market with respect to market capitalization. • We study concentration, imbalance and differences between market cap distributions. • We introduce a framework of linear and nonlinear functionals of optimal portfolios. • We use these functionals to track various properties of portfolios over time. • A significant shift in market dynamics is detected around 2020.