> This page translates raw curvature numbers into a risk assessment. It does not predict crises — instead it measures a structural property of the correlation network that historically accompanies periods of market stress.
The core idea is simple: when the market's correlation network develops many bridge-like connections (negative curvature) and few well-supported clusters (positive curvature), shocks have fewer alternative paths to dissipate. The network becomes fragile in a geometric sense — not because any single correlation is alarming, but because the topology channels risk through bottlenecks.
Important caveat: curvature is a contemporaneous indicator of network structure. Whether it leads, lags, or merely accompanies market stress is an empirical question that depends on the asset universe, window size, and market regime. Treat the risk levels below as a structured way to monitor geometric fragility — not as a trading signal.
> No curvature data available
> Compute curvature first to see risk assessment
Curvature is the mean Ollivier-Ricci value across all network edges. Trend shows the direction of change. Percentile ranks the current reading against the full history — a 10th-percentile reading means curvature is lower (more fragile) than 90% of historical observations. The Risk Level maps these metrics to the thresholds in the interpretation guide below.
> No active alerts
Alerts are generated when curvature crosses predefined thresholds or when the trend shows sustained deterioration. Each alert includes a confidence score reflecting how far the reading deviates from historical norms. Multiple simultaneous alerts — for example, low curvature and a declining trend and rising network density — carry more weight than any single signal.
> Compute curvature to see risk factors
Risk factors break down what is driving the current risk level. These may include specific bottleneck edges (asset pairs with deeply negative curvature), sector-level concentration (too many edges within one cluster), or trend-based signals (curvature falling over consecutive snapshots). Understanding the factors helps distinguish between localized stress (a single fragile pair) and systemic fragility (network-wide deterioration).
| Level | Curvature | Interpretation | Action |
|---|---|---|---|
| LOW | > 0 | Stable market structure | Normal operations |
| MEDIUM | -0.15 to 0 | Slight stress indicators | Monitor closely |
| HIGH | -0.25 to -0.15 | Elevated fragility | Increase vigilance |
| CRITICAL | < -0.25 | High systemic risk | Defensive positioning |
These thresholds are calibrated from historical analysis of curvature behavior around known stress events (2008 financial crisis, 2020 COVID crash, etc.). They are not universal constants — different asset universes, window sizes, and threshold parameters will shift the distribution. Use this table as a starting framework and adjust based on your own backtesting.
The "Action" column reflects a conservative monitoring stance. Curvature is one input among many — it should complement, not replace, traditional risk measures like VIX, credit spreads, and drawdown analysis.