  This paper introduces a novel approach to financial risk assessment by
incorporating topological data analysis (TDA), specifically cohomology groups,
into the evaluation of equities portfolios. The study aims to go beyond
traditional risk measures like Value at Risk (VaR) and Conditional Value at
Risk (CVaR), offering a more nuanced understanding of market complexities.
Using last one year daily real-world closing price return data for three
equities Apple, Microsoft and Google , we developed a new topological
riskmeasure, termed Topological VaR Distance (TVaRD). Preliminary results
indicate a significant change in the density of the point cloud representing
the financial time series during stress conditions, suggesting that TVaRD may
offer additional insights into portfolio risk and has the potential to
complement existing risk management tools.
