Chapter 2: Unsupervised Learning II: Network Theory

Finance has always been about connections, but traditional models often oversimplify them. The 2008 global financial crisis and the COVID-19 market shock exposed how misleading those assumptions can be. The collapse of Lehman Brothers and the near-failure of AIG showed how distress spreads through linkages that conventional approaches failed to capture. What was missing was a framework to map and measure these interdependencies.

This chapter of AI in Asset Management: Tools, Applications, and Frontiers highlights how network theory, long used in data science, can be applied to practical investment problems. Traditional tools such as clustering and centrality remain essential, while machine learning (ML) techniques, including graph neural networks (GNNs), provide additional ways to uncover hidden clusters, trace contagion, and test scenarios across markets.

By combining established network tools with newer ML methods, practitioners can see how assets, institutions, and information flows are linked. This perspective helps them move beyond overly simplistic assumptions and uncover patterns that shape diversification, systemic risk, and market forecasting.

• Network theory reveals hidden connections and contagion pathways between financial institutions.
• Combining classical tools with ML improves risk detection and forecasting.
• GNNs and graph attention networks (GATs) help model complex relationships in financial markets.
• Network-based methods enhance diversification and systemic risk monitoring.
• These techniques support both investment decision-making and regulatory oversight.

At its core, network theory borrows from graph mathematics to study systems of relationships. In an investment setting:

• Nodes might be banks, firms, asset classes, factors, or analysts.
• Edges capture how those entities connect — through lending, correlation, money flows, news, gossip, services, counterparty exposure, or ownership.
• Network properties such as centrality, community structure and clustering, or density show which institutions dominate, how communities form, and where vulnerabilities lie.

By itself, network analysis is largely descriptive. Applied to investment problems, it reveals patterns of interconnectedness that traditional models miss. With the support of modern data techniques, including machine learning methods such as GNNs, network analysis can also highlight contagion pathways, asset clusters, fragility, systemic risk, and potential stress points that arise on the node level but are transmitted over the edges.

Network analysis begins with modeling interconnectedness and applying established measures such as clustering, centrality, and modularity. Modern data-driven methods, particularly machine learning, extend these foundations by making it possible to capture dynamics, scale, and prediction.

• GNNs draw on both firm-level attributes, such as balance sheets, and structural data, such as credit exposures, to model how shocks may ripple through a system.
• GATs build on this by weighting connections differently, highlighting which links matter most — a useful refinement for forecasting and asset clustering.
• Deep learning approaches can improve performance in some forecasting tasks, including returns, volatility, and spillovers, when trained on network data, though simpler models can still be competitive.
• Explainable AI (XAI) tools are being developed to make model outputs more transparent, which is important for regulators and practitioners who must act on these insights.

These approaches do not replace classical network analysis. Instead, they provide complementary ways to apply network theory to investment problems, particularly in areas where prediction and real-time monitoring are required.

Network models show how risk can spread across institutions and markets. These models can be used to trace contagion pathways, estimate the speed of transmission, and identify nodes that are critical to stability. They help to evaluate when and how a systematic risk might become systemic.

• In 2008, Lehman’s collapse and AIG’s derivative exposures froze global markets.
• During COVID-19, asset co-movement networks revealed contagion channels across asset classes in real time.

Regulators and central banks increasingly use these tools to identify systemically important institutions, monitor liquidity networks, and stress-test exposures.

Traditional mean–variance optimization depends heavily on unstable inputs. Network methods add another layer by revealing hidden structures in asset relationships.

• Community detection algorithms identify clusters of connected assets that are not visible from static classifications.
• Minimum spanning trees simplify dense correlation matrices to highlight key relationships.
• Centrality-based weighting steers portfolios away from hub assets that magnify contagion risk.
  The result is a more resilient and adaptive approach to diversification.

Forecasting asset behavior is rarely straightforward, but networks provide useful context.

• Shifts in network density can signal changes in market volatility.
• Models trained on centrality measures can anticipate cross-market spillovers.
• Graph-based machine learning methods, such as GNNs and GATs, can improve forecasts by capturing complex and evolving dependencies.
  Although no approach eliminates uncertainty, these methods provide additional signals that help investors and risk managers anticipate stress.

The 2008 financial crisis highlighted the paradox of networks: They can absorb small shocks, but under extreme stress the same interconnections accelerate collapse. Network models make it possible to quantify this tipping point, identify institutions that are “too connected to fail,” and run contagion simulations in advance. Networks provide information on how risk propagates and help to determine the individual impact as well as the outcome of financial architecture. Recent advances, including machine learning techniques, are helping transform these models into real-time monitoring tools that are increasingly used by practitioners and regulators.

A variety of tools from network science are already widely applied in investment analysis:

• Centrality measures such as degree, betweenness, closeness, and eigenvector identify influential institutions or assets.
• Community detection methods reveal hidden clusters of assets or groups of institutions that move together. Communities reveal structures omitted by a priori classifications.
• Entropy and fragility indicators help gauge hidden risks and system vulnerabilities.

Building on these foundations, newer data-driven approaches are being used to extend prediction and scalability:

• Graph-based machine learning models, including GNNs and GATs, incorporate both node attributes and structural information to support forecasting and contagion analysis.

Together, these tools allow practitioners to move from static descriptions of market relationships to adaptive, scenario-based modeling.

Future progress in network analysis for investment will come from both richer network structures and advances in data-driven methods. Likely directions include the following:

• Multiplex networks that capture multiple types of relationships, such as ownership, lending, and sentiment.
• Alternative data integration, bringing ESG metrics, news flows, and social signals into network models.
• Graph-based machine learning techniques, including GNNs and GATs, which support large-scale prediction and dynamic stress testing.
• Explainability tools that improve transparency in complex models, an important requirement for practitioners and regulators.

As financial systems grow more interconnected, these approaches are moving from academic research into the infrastructure of practice, shaping how risks, contagion, and diversification are managed.

This chapter demonstrates how network theory, long established in data science, can be applied to investment problems in ways that reveal connections and risks missed by traditional models. Classical measures such as clustering and centrality remain central, while modern data techniques, including machine learning, extend the analysis to larger and more dynamic settings.

For practitioners, the takeaway is practical: Conventional models still matter, but today’s interconnected markets call for a network perspective that can capture systemic risk, contagion, diversification, and forecasting. Network analysis, supported by modern data techniques, provides a clearer framework for managing complexity and uncertainty in investment practice.

This summary is based on the CFA Institute Research Foundation and CFA Institute Research and Policy Center chapter “Unsupervised Learning II: Network Theory,” by Gueorgui S. Konstantinov, PhD, and Agathe Sadeghi, PhD, which demonstrates how network theory, extended with modern data methods, can be applied to practical investment problems.

How does network theory help manage systemic risk?
Network analysis maps institutions, assets, and markets as nodes and edges. Measures such as centrality, density, and clustering reveal how shocks spread and help identify institutions that are systemically important.

How do modern data techniques extend network analysis?
Classical measures remain the foundation, but methods such as GNNs and GATs add predictive power. They support contagion modeling, portfolio analysis, and large-scale forecasting.

Can network analysis improve portfolio diversification?
Yes. Community detection and filtering methods uncover hidden clusters of interconnected assets, allowing investors to diversify across groups. Advanced techniques refine these models to adapt to evolving market structures.

Why are regulators interested in network models?
Supervisors use network analysis to identify systemically important institutions, stress-test exposures, and monitor liquidity flows. Advanced methods strengthen these applications and support macroprudential policy.

Clauset, Aaron, Mark E. J. Newman, and Cristopher Moore. 2004. “Finding Community Structure in Very Large Networks.” Physical Review E 70 (6): 6–11. doi:10.1103/PhysRevE.70.066111.

Konstantinov, Gueorgui S., and Frank J. Fabozzi. 2025. Network Models in Finance: Expanding the Tools for Portfolio and Risk Management. Hoboken, NJ: John Wiley & Sons.

Wu, Xian. 2025. “Trading Graph Neural Network.” Working paper (10 April). doi:10.48550/arXiv.2504.07923.

Zareei, Abalfazl. 2019. “Network Origins of Portfolio Risk.” Journal of Banking & Finance 109 (December). doi:10.1016/j.jbankfin.2019.105663.