The Geometry of Risk

Correlation is a comfortable number right up until the moment it isn't. This project builds a four-layer framework for detecting systemic stress in the structure of a market, rather than in its returns.

The four layers

• Network topology — represent the market as a graph and watch it tighten. Stress shows up as the network collapsing toward a single cluster.
• Granger causality — trace who moves whom. In calm markets the causal graph is sparse; under stress it densifies and reverses direction.
• Tail-risk quantification — measure the fat end directly instead of trusting a variance number to describe it.
• Hidden-Markov regime detection — infer the unobserved state the market is actually in, and date the transitions.

Each layer is a weak signal on its own. Stacked, they identify the moments when a portfolio's diversification is quietly evaporating — which is precisely when the risk report still looks fine.