  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.
