An exploration of the mathematical structure and behavioural biases of 21st century financial crises

TL;DR

This paper compares the dynamics of recent and past financial crises, introducing new mathematical tools to analyze collective market behavior, distributional differences, and portfolio optimization during crises.

Contribution

It presents novel mathematical techniques for analyzing market dynamics, distributional distances, and portfolio optimization specific to financial crises.

Findings

Market dynamics show similarities across crises.

New methods quantify distributional differences in returns.

Optimized portfolios vary in effectiveness during crises.

Abstract

In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century - the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises.