Geometrical Macroeconomics

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GEOMETRICAL MACROECONOMICS DASHBOARD

This dashboard computes Ollivier-Ricci curvature on financial correlation networks to measure structural fragility in markets. Curvature captures whether the network geometry is resilient (positive, clustered) or fragile (negative, bottlenecked)--information invisible to simple correlation statistics.

> New here? Read the tutorial to understand the theory behind curvature-based fragility analysis.

> This is an experimental research framework. Whether curvature correlates with financial stress, and whether it leads or merely accompanies crises, are empirical questions under investigation. Results should not be used as trading signals.

SAMPLE DATA LOADED

> 20 assets tracked | 42 network edges

The sample universe consists of 20 large-cap US equities spanning technology (AAPL, MSFT, GOOGL, AMZN, META, NVDA, TSLA, ADBE), financials (JPM, BAC, V, MA), healthcare (JNJ, UNH), consumer (WMT, PG, HD, DIS), energy (XOM), and fintech (PYPL). This cross-sector mix is intentional: curvature is most informative when the network includes assets from different sectors, because it can detect whether cross-sector "bridge" connections are fragile bottlenecks or robust links.

What the data shows: The system fetches the last 2 years of daily adjusted close prices from Yahoo Finance, computes logarithmic returns (dimensionless, as required by the geometric framework), estimates pairwise correlations over a 60-day rolling window, and builds a thresholded correlation network (edges kept where |ρ| > 0.3). Ollivier-Ricci curvature is then computed for each edge and aggregated into the metrics below.

  1. [1] Data - View or reload price data
  2. [2] Network - Explore correlation networks
  3. [3] Curvature - Analyze Ricci curvature time series
  4. [4] Crisis - View risk analysis and alerts
SPACETIME CURVATURE SURFACE
Explore the animated 3D curvature landscape →
Risk Gauge ? Risk Gauge Visual representation of current network curvature. Green (κ > 0) indicates stable markets. Cyan (-0.15 to 0) is normal. Orange (-0.25 to -0.15) signals elevated risk. Red (< -0.25) indicates critical fragility.

The needle shows aggregate Ollivier-Ricci curvature (κ). Positive = clustered, resilient network. Negative = bottlenecked, fragile network.

Curvature Trend ? Curvature Trend Recent history of mean network curvature. Rising trend indicates improving market stability. Falling trend suggests increasing systemic risk. Red zone (< -0.25) marks critical fragility periods.

Each point is the mean curvature across all edges for that day's 60-day rolling correlation window. The red zone marks κ < -0.25 (high fragility).

SYSTEM STATUS
0.1481
Current Curvature (κ) ? Mean Ollivier-Ricci Curvature The average curvature across all edges in the correlation network. Computed by comparing the Wasserstein transport cost between each pair of connected nodes' neighborhoods to their direct distance. Positive κ means neighborhoods overlap (clustered, resilient). Negative κ means the edge is a bottleneck (fragile).
DECLINING
Trend (7d) ? 7-Day Trend Compares today's mean curvature to 7 trading days ago. IMPROVING = curvature increased by > 0.02 (network becoming more clustered). DECLINING = decreased by > 0.02 (bottlenecks forming). STABLE = change within ±0.02.
NORMAL
Fragility Status ? Network Fragility Status Derived from current curvature level. NORMAL (κ > 0): network is well-clustered with redundant connections. CAUTION (-0.15 to 0): mild bottleneck formation. ELEVATED (-0.25 to -0.15): significant structural fragility. CRITICAL (< -0.25): network dominated by fragile bridges.
20
Assets Tracked ? Asset Universe Number of stocks in the correlation network. Each asset becomes a node; significant correlations (|ρ| > 0.3) become edges. More assets provide broader market coverage. The sample set uses 20 large-cap US stocks across multiple sectors.
UNDERSTANDING THE METRICS

The dashboard applies Ollivier-Ricci curvature from discrete differential geometry to financial correlation networks. Here is what each metric captures and how to read it:

How Curvature Is Computed

1. Log-returns: Daily prices are converted to logarithmic returns -- dimensionless quantities that make the geometric framework well-defined.
2. Rolling correlations: Pairwise correlations are estimated over a 60-day window, capturing the local correlation structure at each point in time.
3. Distance metric: Correlations are converted to distances via d = √(2(1-ρ)). Perfectly correlated assets have distance 0; uncorrelated assets have distance √2.
4. Network thresholding: Only edges with |ρ| > 0.3 are kept, filtering out noise.
5. Ollivier-Ricci curvature: For each edge, the Wasserstein-1 (earth mover's) distance between the neighborhoods of its two endpoints is compared to the direct edge distance. The ratio determines curvature: κ(i,j) = 1 - W1(μi, μj) / d(i,j).
6. Aggregation: The mean curvature across all edges gives a single scalar summarizing the network's geometric state.

What Curvature Means Economically

Positive curvature (κ > 0): The neighborhoods of connected assets overlap heavily -- the network is clustered with many redundant paths. If one connection breaks, information and risk still flow through alternative routes. This is structurally resilient.

Negative curvature (κ < 0): Connected assets' neighborhoods are far apart -- the edge is a bottleneck or bridge between otherwise disconnected regions. If this edge breaks, the network fragments. This is structurally fragile.

Why it matters beyond correlation: Two markets can have the same average correlation but very different curvature. A market where all assets are uniformly correlated (Scenario A) is geometrically different from one where clusters are connected by a few fragile bridges (Scenario B). Curvature distinguishes these cases; average correlation cannot.

CURVATURE INTERPRETATION GUIDE
Range Status Network Geometry
κ > 0.0 NORMAL Well-clustered, redundant connections. Perturbations tend to be absorbed by the network.
-0.15 to 0.0 CAUTION Mild bottleneck formation. Some edges are bridges rather than part of clusters. Standard conditions for most markets.
-0.25 to -0.15 ELEVATED Significant bottlenecks. Network depends on a few critical connections. Reduced redundancy means perturbations may amplify.
< -0.25 CRITICAL Network dominated by fragile bridges. Removing a few edges could fragment the structure. Consistent with periods of financial stress.

These thresholds are indicative. The curvature-fragility relationship is a hypothesis under empirical investigation, not a validated trading signal.

RECENT ALERTS

> No active alerts

> Curvature alerts are generated when κ crosses threshold boundaries or when the 7-day trend shows significant decline.

DATA PIPELINE

The system follows a modular pipeline matching the paper's implementation architecture:

Stage What It Does Parameters
Data Ingestion Fetches adjusted close prices from Yahoo Finance, computes log-returns 20 tickers, 2yr history
Network Construction Rolling correlations → distance metric → thresholded graph 60-day window, |ρ| > 0.3
Curvature Computation Ollivier-Ricci curvature via Wasserstein optimal transport on each edge Uniform neighborhood measure
Analysis Aggregate curvature, trend detection, threshold alerts 7-day trend, 4 alert levels