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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Frank J. Fabozzi Series
- Sprache: Englisch
Expansive overview of theory and practical implementation of networks in investment management
Guided by graph theory, Network Models in Finance: Expanding the Tools for Portfolio and Risk Management provides a comprehensive overview of networks in investment management, delivering strong knowledge of various types of networks, important characteristics, estimation, and their implementation in portfolio and risk management. With insights into the complexities of financial markets with respect to how individual entities interact within the financial system, this book enables readers to construct diversified portfolios by understanding the link between price/return movements of different asset classes and factors, perform better risk management through understanding systematic, systemic risk and counterparty risk, and monitor changes in the financial system that indicate a potential financial crisis.
With a practitioner-oriented approach, this book includes coverage of:
- Practical examples of broad financial data to show the vast possibilities to visualize, describe, and investigate markets in a completely new way
- Interactions, Causal relationships and optimization within a network-based framework and direct applications of networks compared to traditional methods in finance
- Various types of algorithms enhanced by programming language codes that readers can implement and use for their own data
Network Models in Finance: Expanding the Tools for Portfolio and Risk Management is an essential read for asset managers and investors seeking to make use of networks in research, trading, and portfolio management.
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Seitenzahl: 667
Veröffentlichungsjahr: 2024
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Table of Contents
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
Preface
Acknowledgments
About the Authors
Part One
Chapter 1: Introduction
Network Theory, Graph Theory, and Topology
What is a Network?
Financial Markets and Financial Networks
Data
Application of Networks in Finance
Network Design
Key Takeaways
Notes
Chapter 2: The Basic Structure of a Network
Network Representations
Types of Networks
Network Visualization
Key Takeaways
Notes
Chapter 3: Network Properties
Connectedness
Components, Clustering, and Communities
Key Takeaways
Notes
Chapter 4: Network Centrality Metrics
Node Centrality Metrics
Descriptive Statistics and Network Summary
Key Takeaways
Notes
Part Two
Chapter 5: Network Modeling
Network Models
General Framework
Random Portfolio Network Simulation and Network Regime
Dynamic Network Models
Key Takeaways
Notes
Chapter 6: Foundations for Building Portfolio Networks – Link Prediction and Association Models
Portfolio Network Topology Interference and Inference
Link Prediction Models
Association Models
Key Takeaways
Notes
Chapter 7: Foundations for Building Portfolio Networks – Statistical and Econometric Models
Portfolio Network Topology Interference and Inference with Statistical and Econometric Models
Regression-Based Models
Key Takeaways
Notes
Chapter 8: Building Portfolio Networks – Probabilistic Models
Portfolio Network Topology Interference and Inference with Probabilistic Models
Probabilistic Models
An Overview of the Networks
Key Takeaways
Notes
Chapter 9: Network Processes in Asset Management
Network Evaluation
Statistical Models for Network Processes
Causal Network Interference
Key Takeaways
Notes
Chapter 10: Portfolio Allocation with Networks
General Framework
Relationship Between Portfolio Allocation and Networks
Nonoptimization Approaches for Portfolio Allocation
Portfolio Optimization with Networks
Key Takeaways
Notes
Part Three
Chapter 11: Systematic and Systemic Risk, Spillover, and Contagion
The Role of Networks in Risk Management
Risk Overview
Systematic and Systemic Risk
Spillover and Contagion
Key Takeaways
Notes
Chapter 12: Networks in Risk Management
Portfolio Volatility and Network Analysis
Risk Management Indicators
Risk Indicators on the Node level
Edge Connectivity and Spillover Indicators
Comparing Risk Metrics
Key Takeaways
Notes
References
Index
End User License Agreement
List of Illustrations
CHAPTER 1
Figure 1.1 A Network of Tested Strategies.
Figure 1.2 Network Analysis Applications in Inference, Structure, and Implementation.
Figure 1.3a A Single Hedge Funds Network with 442 Nodes and Optimized Edge Structure.
Figure 1.3b A Sample Network.
Figure 1.4 A Different Network Design with Identification of Highly Connected Nodes and P...
CHAPTER 2
Figure 2.1 Network Types.
Figure 2.2 Graphs with Different Types of Edge and Node Design.
Figure 2.3 Graph Plots with Different Design and Graph Algorithms.
Figure 2.4 An Example for a Random and MST Network Design.
Figure 2.5 A Large Network Design with Various Attributes.
CHAPTER 3
Figure 3.1 The Mathematical Expression of Connectedness.
Figure 3.2 Edges and Nodes of a Simple Graph.
Figure 3.3 A Degree Distribution of Single Hedge Funds Power-law.
Figure 3.4 Historical 10-year Bond Yields in the European Monetary Union (EMU).
Figure 3.5 A Directed Weighted Network for the European Monetary Union (EMU) Government B...
Figure 3.6 Examples of Assortative and Disassortative Asset and Factor Networks.
Figure 3.7 A Partial Correlation Single Hedge Fund Network with Bonferroni Adjustment.
Figure 3.8 The Community Structure of a Single Hedge Fund Network.
Figure 3.9 Bridge Ties of a Bond and Equity Fund Network.
CHAPTER 4
Figure 4.1 Degree Centrality for Different Asset and Factor Networks.
Figure 4.2a Bridge Ties for Degree Centrality-Weighted Directed Granger Causality.
Figure 4.2b An Undirected Asset and Factor Network.
Figure 4.3 Eigenvector Centrality for Different Asset and Factor Networks.
Figure 4.4 Bonacich Centralities for All Asset and Factor Networks.
Figure 4.5 Hub and Authority Centrality of a Directed Asset and Factor Network.
Figure 4.6 Closeness Centrality for the Asset and Factor Networks.
Figure 4.7 Betweenness Centrality for the Asset and Factor Networks.
Figure 4.8 Comparison of Centrality Metrics in Network Analysis – A Directed Marko...
Figure 4.9 A Comparison of Centrality Metrics with Community Affiliation in Network Analy...
CHAPTER 5
Figure 5.1 Network Simulation for the 31 Assets and Factors Used for Asset Allocation.
Figure 5.2 An Average Degree of Simulated Networks.
Figure 5.3 An Undirected Network Using the Fisher Transformation of the Partial Correlati...
Figure 5.4 An Undirected Network Using the Fisher Transformation of the Partial Correlati...
Figure 5.5a The Barabási–Albert Preferential Attachment Network.
Figure 5.5b A Minimum Spanning Tree.
Figure 5.6a The Barabási–Albert Network with Preferential Attachment for Sin...
Figure 5.6b The Partial Correlation Single Hedge Fund Network.
Figure 5.7 The Degree Distribution and Community Distribution of a Small Hedge Fund World...
CHAPTER 6
Figure 6.1 Models for Building Portfolio Networks.
Figure 6.2 Returns Clouds for the Market Returns (Mkt.RF) and Value Factor (HML).
Figure 6.3 Connecting the Unstructured Data Points with a Distance Metric.
Figure 6.4 A Wasserstein Distance L2-Norm Asset and Factor-Weighted Network.
Figure 6.5 A Completed Asset and Factor Network.
Figure 6.6 An Undirected Correlation-Based Fischer Transformation Asset and Factor Networ...
Figure 6.7 An Undirected Asset and Factor Network Using a Correlation Test.
Figure 6.8 A Partial Correlation Asset and Factor Network.
CHAPTER 7
Figure 7.1 A Directed Asset and Factor Network.
Figure 7.2 A Directed Asset and Factor Network with a Confounder.
Figure 7.3 A Directed Asset and Factor Network with Receiver/Sender Operators.
Figure 7.4 A LASSO Asset and Factor Network.
Figure 7.5 A Granger Causality Test Asset and Factor Network.
Figure 7.6 A Directed Vector-Autoregression and Cholesky Variance Decomposition Asset and...
CHAPTER 8
Figure 8.1 Eigenvectors of a Markov Chain Probability Matrix.
Figure 8.2 A Markov Chain-Directed Asset and Factor Network.
Figure 8.3 A Markov Chain Manhattan Distance-based Directed Asset and Factor Network.
Figure 8.4 Connectedness in Bayesian Networks.
Figure 8.5 A Bayesian Asset and Factor Network.
Figure 8.6 A Bayesian Asset and Factor Network with Edge Strength.
Figure 8.7 All Asset and Factor Networks with Node Degree Centrality.
CHAPTER 9
Figure 9.1 ROC Curves Comparing the Goodness-of-Fit for the Different Eigenmodels for Ass...
Figure 9.2 Examples for AUC Curves: Bond and Equity Funds, Equity Markets, and Single Hed...
Figure 9.3 A Graph Intersection: A Directed vs. a Completed Graph.
Figure 9.4 Goodness-of-Fit Plots.
Figure 9.5 A Simulated and Original Asset and Factor Network.
Figure 9.6 ROC Curves Comparing the Goodness-of-Fit to the Undirected Network with Differ...
Figure 9.7 Network Visualizations Subject to the Different Eigenmodel Covariates.
Figure 9.8 Eigenvalues and Spectral Partitioning of Graph Laplacian for an Undirected Ass...
Figure 9.9 A Graph Laplacian with Different Eigenvectors.
Figure 9.10 An Initial Undirected Network and the Network with Selected Nodes. Note: we use...
Figure 9.11 Exposure Mappings.
CHAPTER 10
Figure 10.1 Eigen Centrality-Weighted Asset and Factor Networks.
Figure 10.2 A Degree and Eigen Centrality Relationship.
Figure 10.3 Eigen Centrality-Weighted Covariances for a Directed Markov Chain Network for ...
Figure 10.4 Eigen Centrality-Weighted Covariances of Assets and Factors.
Figure 10.5 Examples for Hierarchical Clustering in Different Markets.
Figure 10.6 Hierarchical Clustering and Allocation of an Undirected Network: Degree Distri...
Figure 10.7 A Network Plot with CFG Community Optimization and Importance Scores.
Figure 10.8 A Histogram of Simulated Returns for Assets and Factors.
Figure 10.9 Eigen Centrality-Weighted Returns of Asset and Factor Networks.
Figure 10.10 Alpha Centrality-Weighted Returns of Asset and Factor Networks.
Figure 10.11 Power Centrality-Weighted Returns of Asset and Factor Networks.
CHAPTER 11
Figure 11.1 Exogenous Beta and Alpha Centrality as Node Weights in Undirected Asset and Fa...
Figure 11.2 The Business Cycle of an Economy – Network Density and Reciprocity.
CHAPTER 12
Figure 12.1 Criticality Scores Using the Eigenvector Centrality Scores and the Asset Volat...
Figure 12.2 Eigenvector Centrality for an Undirected, Partial Correlation, and Markov Chai...
Figure 12.3 The Fragility Index of an Asset and Factor Network.
Figure 12.4 Risk Increments for All Networks with Volatility as a Compromise Vector.
Figure 12.5 A Normalized Risk Score for a Directed, Undirected, and the Undirected W2-Wass...
Figure 12.6 Nodal Entropy for a W2-Wasserstein Distance-Based Undirected Asset and Factor ...
Figure 12.7 Entropy of Asset and Factor Datasets.
Figure 12.8 A Spillover Index for Different Asset Classes.
Figure 12.9 A Spillover Index for the Assets and Factors and the Multi-Asset Factor Data S...
Figure 12.10 The Ricci Curvature for a -Wasserstein Distance Asset and Factor Network.
Figure 12.11 The Ricci Curvature for a Markov Chain Asset and Factor Network.
Figure 12.12 The Ricci Curvature Indices for Different Markets.
Figure 12.13 Comparing the Fragility and Ricci Curvature for Directed Asset and Factor Netw...
Figure 12.14 Comparing Entropy and Ricci Curvature for the W2-Wasserstein Distance Undirect...
Figure 12.15 The Combined Plot for the Ricci Curvature and Entropy of Global Equity Markets...
Figure 12.16 Spillover Index, Ricci Curvature, and Entropy for the Asset and Factor Directe...
Figure 12.17 Differences of Ricci Curvature and Entropy for an Undirected Asset and Factor ...
List of Tables
CHAPTER 1
Table 1.1 An Adjacency Matrix for the Undirected Asset and Factor Network.
CHAPTER 4
Table 4.1 Centrality Metrics for a Directed Markov-Chain Network.
Table 4.2 Descriptive Statistics for Asset and Factor Networks.
CHAPTER 5
Table. 5.1 Descriptive Statistics for the Estimated and Simulated Single Hedge Fund Netwo...
Table 5.2 Statistics for the Monte Carlo Simulation of Small Hedge Fund World.
CHAPTER 6
Table 6.1 Simple Return (%) Statistics for Three Bonds.
Table 6.2 A Distance Matrix for the Three Bonds.
CHAPTER 8
Table 8.1 An Overview of the Asset and Factor Networks.
CHAPTER 9
Table 9.1 Network Intersection for the Directed, Undirected, and Completed Asset and Fac...
Table 9.2 The Null Model Output.
Table 9.3 An ERGM Including Node-Level Attributes.
Table 9.4 Mixing Matrices for the Asset and Factor Undirected Correlation Test Network.
Table 9.5 The Model Output for Dyad-Level Attributes.
Table 9.6 An ERGM Output with Edge-Level Covariates.
Table 9.7 The ERGM Model with Local Structure Attributes.
Table 9.8 Exposure in the Four Categories: – Directed, Indirect, Combined, and No...
Table 9.9 Average Causal Effects for the Undirected Asset and Factor Network.
CHAPTER 10
Table 10.1 Community Affiliation for a Partial Correlation Network of Assets and Factors.
CHAPTER 11
Table 11.1 Results for the Alpha Centrality-Weighted Network.
Guide
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
Preface
Acknowledgments
About the Authors
Begin Reading
References
Index
End User License Agreement
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Network Models in Finance
Expanding the Tools for Portfolio and Risk Management
GUEORGUI S. KONSTANTINOV
FRANK J. FABOZZI
Copyright © 2025 by Gueorgui S. Konstantinov and Frank J. Fabozzi. All rights reserved.
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Library of Congress Cataloging-in-Publication Data
Names: Fabozzi, Frank J., author. | Konstantinov, Gueorgui S., author.
Title: Network models in finance: expanding the tools for portfolio and risk management / Gueorgui S. Konstantinov, Frank J. Fabozzi.
Description: Hoboken, New Jersey: John Wiley & Sons Inc., [2025] | Series: The Frank J. Fabozzi series | Includes bibliographical references and index. | Summary: “*Network Models in Finance: Expanding the Tools for Portfolio and Risk Management* explores the application of network theory to asset management, emphasizing how network-based methodologies can enhance portfolio and risk management. The book integrates quantitative modeling, causal relationships, and optimization within a network framework, extending beyond traditional asset management tools. It provides a comprehensive overview of graph-theoretical approaches and practical implementations using R, bridging classical methods with modern financial data science. By offering both theoretical insights and practical applications, the book aims to address complex challenges in finance, making it a valuable resource for practitioners and academics seeking advanced network-based solutions in asset management”– Provided by publisher.
Identifiers: LCCN 2024041153 (print) | LCCN 2024041154 (ebook) | ISBN 9781394279685 (hardback) | ISBN 9781394279708 (ebook) | ISBN 9781394279692 (epub)
Subjects: LCSH: Portfolio management–Mathematical models. | Financial risk management–Mathematical models. | System analysis.
Classification: LCC HG4529.5.F33455 2025 (print) | LCC HG4529.5 (ebook) | DDC 332.6–dc23/eng/20241107
LC record available at https://lccn.loc.gov/2024041153
LC ebook record available at https://lccn.loc.gov/2024041154
Cover Image: Courtesy of Frank J. Fabozzi
Cover Design: Wiley
To my family.
– Gueorgui S. Konstantinov
To the memory of the 13 courageous soldiers who gave their lives during the Afghanistan evacuation.
– Frank J. Fabozzi
Preface
Network Models in Finance: Expanding the Tools for Portfolio and Risk Management integrates network theory with asset management, delving into quantitative modeling and the simulation approaches of networks and their applications to two aspects of aspect management: portfolio and risk management. Drawing on practitioner and academic research on network theory and the theories associated with asset management, we provide a timely and comprehensive overview of innovative network-based tools and methodologies applied to asset management. The approaches discussed in this book are not necessarily novel but extend beyond traditional models and tools in asset management by incorporating causal relationships, inference, association, probabilistic structures, and optimization within a new network-based framework using time-series data.
In this book, we showcase the broad and deep knowledge of network theory and its applications. Networks provide new perspectives for asset managers, offering insights into investment management topics highly relevant for institutional investors, family offices, researchers, academics, and industry practitioners. This book stands out by providing insights that extend current knowledge in network theory to address specific needs in portfolio and risk management. It offers a unique contribution compared to the existing literature, making it a valuable resource for understanding and applying network-based methodologies in asset management.
The motivation for this book comes from our proven track record and practical experience with network models in asset management. We have successfully implemented network-based asset allocation across a broad set of portfolios. Scientifically, our motivation and background are influenced by numerous seminal works reported in the literature that highlight the connectedness in various organizational, biological, informational, financial, social, economic, technological, and physical fields. These works suggest that traditional reductionist approaches in science may benefit from more holistic methods that preserve and explain complexity. This foundational perspective drives our exploration of network theory in the context of asset management.
In this line of thought, the underlying assumption in the book is that there is a relationship between the interacting entities in financial markets. In finance, several studies have embraced these themes, where researchers have argued that economics is a science of relations and finance needs new tools to investigate financial market complexity. These works gave birth to this book.
This book distinguishes itself by implementing several graph-theoretical frameworks in asset management. Specifically, it provides an overview of various types of networks that can be investigated, implemented, and validated in practice. The techniques covered are the product of rigorous theoretical research and development by many experts and researchers in network theory, graph theory, economics, finance, mathematics, and the physical sciences. Concepts borrowed from diverse scientific research are adapted to fit the asset management framework, representing a unified approach to quantitative portfolio and risk management that extends traditional models to modern financial data science and analytics.
In addition to offering a solid theoretical foundation for network science, we emphasize the practical implementation of network modeling approaches that can be successfully applied in real-world multi-asset, bond, equity, and alternative asset allocation. This book bridges traditional investment methods, such as optimization approaches and variance-covariance frameworks, with modern financial data science applications, integrating the domain of networks into asset management.
Covering a wide range of applications relevant to both practitioners and academics, we guide the reader by first developing a robust theoretical framework, and then providing practical illustrations and codes in the programming language R for actual portfolios comprising traditional and alternative asset classes, factors, and other economic variables like payments and transaction data. A major objective is to shed light on the problems faced by practitioners in portfolio management and risk management, considering that asset classes and factors are integrated into a holistic framework. Potential solutions to these problems are provided.
The primary distinction of Network Models in Finance, compared to other books on network modeling, lies in its comprehensive coverage of the visualization, analysis, research, estimation, and computation of a wide range of networks applied in asset management. This book focuses specifically on evaluating portfolio networks and investigating their properties.
Related literature has been published that explore various aspects of networks in finance and economics. For instance, some books provide network analysis and models applied to economics, finance, corporate governance, and investments, focusing on analytical modeling and the econometric and statistical analysis of properties emerging from individual-level interactions. These authors combine observational and theoretical insights in networks and agent-based models, which are valuable for understanding nonlinear and evolving complex systems.
Other works explicitly focus on networks’ risk management advantages, discussing the risk propagation, contagion, and spillover effects that networks provide to different asset classes. Additionally, while some books offer a broad and detailed analysis of networks and their relation to markets, they often need a more focused view of asset management.
In contrast, our book integrates these various approaches to provide a detailed and specific examination of network-based methods in asset management, which makes it a unique and valuable resource in the field.
CENTRAL BOOK THEMES
A network consists of nodes and links between them. The nodes and links are the central fields of investigation. The chapters of this book cover different topics related to nodes and links and describe, explain, and apply various tools used to model and analyze financial networks in asset management. The datasets include a broad set of asset classes and factor time series. Additionally, we use datasets from country payments and other transaction data.
Network Models in Finance contains 12 chapters, which are divided into three parts. Part One comprises Chapters 1–4.
Chapter 1
introduces the basic concepts of real networks, network science, and different network types. The importance of understanding the interactions among economic variables, individuals, and financial institutions to capture and explain complex market behaviors is explained. The chapter’s focus then shifts to data, detailing the types of datasets used in network analysis within finance.
Chapter 2
covers network structure and description, network representation, types, and visualization. The chapter begins with an overview of both basic and complex network types and the definition of connectedness. Specific topics include metrics that explain, describe, and capture the complex relationships underlying graphs, as well as importance scores and specific node and edge properties that describe networks. The chapter features numerous examples of networks across different asset classes and topics in asset management, providing a broad overview of modeling networks at both the node and edge levels.
Chapter 3
investigates descriptive network metrics and their application in asset management, offering descriptive statistics that characterize networks. These metrics refer to a network’s overall properties and aim to describe its underlying structure.
Chapter 4
focuses on centrality and other importance scores, which are among the most critical nodal characteristics of networks.
Part Two comprises Chapters 5–10, focusing on the network construction for portfolio management.
Chapter 5
provides an overview of networks and how they are constructed using mathematical models. It explains the various approaches to modeling real networks, including topics such as the Erdös–Renyi random graph model, the Albert–Barabasi preferential attachment model, and the small-world model.
Chapter 6
covers the most widely used networks in finance, focusing on association network models constructed using statistical tests. The chapter’s primary focus is on link prediction models, which aim to use existing data and observations to generate scores that indicate the likelihood of links between vertices. While these links are not directly observable, observable market data can be leveraged to model these relationships effectively.
Chapter 7
discusses statistical and econometric models, focusing on network construction used in portfolio allocation models based on different types of regression models. The regression models applied are both linear and nonlinear. These models may consist of multifactor or single-factor structures, incorporating one or multiple explanatory variables and possibly interaction terms governing cross-relationships between these variables.
Chapter 8
describes probability models used to construct portfolio networks. Probability theory offers a straightforward approach to implement mathematical and statistical tools for edge prediction and simulation. The probabilistic models discussed in this chapter include Markov chain network models and Bayesian networks, which enable model generation without requiring prior information about the underlying network structure.
Chapter 9
, one of the most advanced chapters in this book, covers model selection and network manipulation using three statistical models: the Exponential Random Growth model, the Latent Network Model, and the Laplacian Spectral Partitioning model. This chapter also includes discussions and visual examples of causal network interference models, which estimate the network impact of preselected nodes under treatment. Key topics include network inference, mathematical models for network simulation using unobserved and observed data, and their implementation within nonoptimization and optimization algorithms. Additionally, it discusses data science models that help evaluate the goodness-of-fit of networks.
Chapter 10
summarizes how different networks can be applied to asset management. This chapter, which is central to the book, focuses on portfolio construction using networks. It uses concrete asset class and factor networks to demonstrate the advantages and versatility of networks in asset management, providing tools and practical examples for simulating, estimating, and applying networks to asset allocation. It also discusses the role of networks in financial markets and their advantages for the asset management industry, including examples of portfolio allocation using networks with both nonoptimization and optimization approaches.
Part Three of the book comprises Chapters 11 and 12, focusing on risk management with networks.
Chapter 11
discusses various frameworks for risk management, differentiating between spillover, contagion, and financial stress. A major topic in this chapter is the impact of risk on nodes and edges.
Chapter 12
is dedicated to portfolio risk management, providing readers with an advanced framework for implementing networks in risk management. The chapter begins with a detailed description of spillover and contagion risks and how these risks can be modeled using networks. Key themes include the computation of risk, fragility, and other metrics that help manage portfolio risk using a graph-theoretical framework. This chapter also features network-based risk indicators for modeling and predicting spillover and contagion risks in global asset markets. Using a broad set of examples, the advantages of novel time-varying metrics such as entropy, Ricci curvature, and spillover indices are demonstrated.
THE AUDIENCE FOR THIS BOOK
This book’s intended audience includes portfolio managers, risk managers, chief investment officers, consultants, researchers/analysts, investors (i.e., beneficial owners), sales managers, and academic researchers.
For portfolio managers, the book provides insights into a holistic approach to quantitative network-based portfolio management, including risk analysis, monitoring and control, portfolio optimization, and asset allocation. Portfolio managers can utilize networks to simulate and validate asset networks, capture asset interconnectedness in portfolios and benchmarks, and apply methods from financial data science like cross-validation, goodness-of-fit estimation, statistical inference, optimizations, allocation, and backtesting.
Risk managers within the portfolio management team will benefit from tools designed to investigate the risks associated with interconnected asset classes and factors in the market rather than isolated risk drivers of risk. These tools can actively monitor, predict, and identify time-varying spillover and contagion associated with portfolio assets, helping to identify risk scores using different metrics to explain interconnectedness, fragility, risk increment, and the criticality of asset classes and portfolios.
Chief investment officers (CIOs) seeking to expand the role of networks in portfolio and risk analysis, allocation, and management within their organizations will gain a deeper understanding of interconnectedness risks and how portfolio managers apply network theory to quantitative asset management. The book provides valuable insights beyond traditional allocation methods and analysis, offering CIOs a new perspective on asset management.
Consultants will find the book useful for analyzing and investigating managers’ investment processes applying network theory to quantitative portfolios. It helps consultants evaluate the merits of network-based and traditional portfolio managers and their investment processes, broadening their knowledge of network and financial data science-based portfolio management tools that are less familiar to asset owners and prospective clients. Researchers and analysts seeking to expand their and understanding of the risks associated with networks and interconnected asset classes and factors will benefit from the book’s coverage. It provides insightful information on constructing networks in portfolio and risk management.
Investors (i.e., beneficial owners) should understand the construction process of network-based portfolios and the resulting risk attributes for fund selection, holistic analysis, and interconnectedness. The book covers the functionality and relationships of the network constituents and risks, demonstrating how portfolio managers apply analytical tools to generate alpha.
Sales managers (i.e., “asset gathers”) must explain to clients how their firm’s asset manager performed and added value using novel and alternative capital allocation and investing techniques. This requires a deep understanding of network science, how network-based portfolios are managed, along with the benefits of incorporating network analysis into investors’ portfolios.
Academic researchers need to understand network theory and the application of network-based portfolio models, recognize the potential for added value, limitations of theoretical frameworks, and how practitioners address the challenges of network theory applied to portfolios. The book provides practical examples and codes, offering insightful information for asset allocation and risk management, which may differ from mainstream approaches in investment textbooks that treat asset risk more as separable and isolated rather than holistic, integrated, and interconnected.
Acknowledgments
This book was inspired by Professor Otto Loistl of the Vienna University of Economics and Business, whose insights, vision, and work on the analysis and applications of interactions in financial markets have been profoundly influential.
We are deeply grateful for the feedback, suggestions, constructive criticism, and shared experiences of our colleagues who collaborated with us on previous projects. Their invaluable insights, inspiration, and encouragement were instrumental in the development of this book. In particular, we would like to thank:
Irene Aldridge of AbleMarkets
Atanas Angelov of ResTec
Eduard Baitinger of FERI Trust
Jennifer Bender of State Street Global Advisors
Andreas Chorus of LBBW Asset Management
Alexander Denev of Turnleaf Analytics
Alexander Fleiss of Rebellion Research
Daniel Giamouridis of Qube Research & Technologies and Bayes Business School
Petia Zeiringer of Union Invest Real Estate Austria
Frank Hagenstein of Hagenstein Real Estate
Hossein Kazemi of CISDM/Isenberg School of Management and the University of Massachusetts at Amherst
William Kinlaw of State Street Global Markets
Panagiotis Patzartzis of LBBW Asset Management
Momtchil Pojarliev of Wellington
David Primik of Wiener Städtische Versicherung
Jonas Rebman of LBBW Asset Management
Mario Rusev of d-fine
Axel Sima of Generali
Joseph Simonian of Autonomous Investment Technologies
Andreas Otto St. Vogelsinger of Astro-Pharma
Ronny Weise of Societe Generale
Christoph Witzke of Deka Investments
We extend our special thanks to Marcos Lòpez de Prado for his insights and for pushing financial data science forward.
We also thank AQR Capital Management, LLC, and Professor Kenneth French for providing their data libraries, which were invaluable to our research.
About the Authors
Gueorgui S. Konstantinov is senior portfolio manager FX and Fixed Income at DekaBank in Frankfurt, Germany. For more than 18 years, he held senior portfolio manager roles at several asset management companies where he managed global bond portfolios and currencies for institutional investors and pension funds. He is an advisory board member of The Journal of Portfolio Management, The Journal of Alternative Investments, and The Journal of Financial Data Science. He has authored articles in both academic and practitioner journals and is a coauthor of Quantitative Global Bond Portfolio Management. He earned the Chartered Alternative Investments Analyst (CAIA) and Financial Data Professional (FDP) designations. He received his MA in economics in 2005 and a doctoral degree in 2008 from the Vienna University of Economics and Business Administration (WU).
Frank J. Fabozzi is a Professor of Practice in the Carey Business School at Johns Hopkins University. He is the editor of The Journal of Portfolio Management, co-editor/ co-founder of The Journal of Financial Data Science, and an editor of Annals of Operations Research. Over the past 50 years, he has held professorial positions at MIT, Yale, Princeton, EDHEC Business School, New York University, Carnegie Mellon, and Rutgers. From 1988 to 2023, he was a trustee of the BlackRock closed-end fund complex. Dr. Fabozzi is the CFA Institute’s 2007 recipient of the C. Stewart Sheppard Award and the CFA Institute’s 2015 recipient of the James R. Vertin Award. He was inducted into the Fixed Income Analysts Society Hall of Fame in November 2002. He has earned the designations of Chartered Financial Analyst (CFA) and Certified Public Accountant (CPA). He received his bachelor’s and master’s degrees in economics in 1970 from the City College of New York, where he was elected to Phi Beta Kappa. He received his doctorate degree in economics in 1972 from the City University of New York. In 1994, he was awarded an Honorary Doctorate of Humane Letters from Nova Southwestern.
PART One
Chapter 1Introduction
Contents
NETWORK THEORY, GRAPH THEORY, AND TOPOLOGY
WHAT IS A NETWORK?
Technological and Infrastructure Networks
Information Networks and Financial Markets
Social Networks and Financial Markets
Biological Networks and Financial Markets
FINANCIAL MARKETS AND FINANCIAL NETWORKS
DATA
Assets and Factor Returns
Hedge Fund and Mutual Fund Returns
Global Equity Market Returns
European Multi-Asset and Bond Market Data
Country Bond Market Index Returns
Payments and Transaction Data
APPLICATION OF NETWORKS IN FINANCE
Network Application in Investment Management
Inference, Structure, Process, Implementation, and Visualization
Network Modeling
Processes and Implementation
Visualization
Programming Codes and Implementation
NETWORK DESIGN
KEY TAKEAWAYS
The main purpose of this book is to provide a broad overview of how to build financial networks used in investment management. In general, finance is a discipline in which all aspects of real-life networks can be found. Collaboration and exchange of services, financial transactions, and contractual obligations represent connections. These connections and the interacting entities can be considered as networks. Finance is not a system that resides in a state of chaos but is characterized by organized complexity. These networks represent the underlying structures and organization. Applying statistical, econometric, and mathematical models when building financial networks helps reveal the often-hidden underlying architecture of financial markets.
In this chapter, we provide a comprehensive introduction to the various types of networks and their relevance to financial markets. We begin with a general overview of networks, covering technological and infrastructure, in addition to information, social, and biological networks. The chapter emphasizes the unique characteristics of financial networks, particularly their proprietary nature, which necessitates specific modeling and estimation techniques.
The chapter further describes how different network properties, such as dyads and triads, apply to financial markets. It explains the importance of understanding the interactions among economic variables, individuals, and financial institutions to capture and explain complex market behaviors. The chapter focus then shifts to data, detailing the types of datasets used in network analysis within finance, including assets and factor returns, hedge fund and mutual fund returns, global equity market returns, and country bond market index returns.
Finally, the chapter delves into the application of network theory in asset management. It discusses how networks can be used for risk and portfolio management, data analysis, trading, risk management, and performance evaluation. The chapter concludes with a discussion on the design of financial networks and the key takeaways from understanding and applying network theory to finance.
NETWORK THEORY, GRAPH THEORY, AND TOPOLOGY
Network theory is a field of mathematics with roots tracing back to the works of some of the world’s most famous mathematicians, such as Leonhard Euler, Bernhard Riemann, and Henri Poincaré. It offers a framework for understanding and analyzing the relationships and interactions among interconnected entities. This theory extends the graph theory principles, founded by Euler’s solution to the Königsberg bridge problem.1 Graph theory involves studying graphs (or mathematical structures) used to model pairwise relations between objects. In graph theory, graphs consist of vertices (or nodes) and edges (or links) that connect pairs of vertices. Euler’s work laid the groundwork for network theory by introducing these basic components and demonstrating the connection between topology and network theory.
Network theory builds on these concepts to study more complex and large-scale networks, which can be found in various fields that will be discussed later in this chapter. It looks at how nodes (which can represent anything from people in a social network to computers in a technological network) are interconnected and how these connections affect the behavior and properties of the entire network.
Topology, another branch of mathematics, studies how shapes and spaces can change by stretching or bending without breaking apart or sticking together. At its core, topology is a study of how objects are connected, shaped, and arranged in space. Topology shares similarities with network analysis, especially in understanding how different elements are connected and how these connections affect the overall structure (i.e., the arrangement and organization of the elements) and behavior (i.e., how the system operates, reacts, or changes based on these connections).
WHAT IS A NETWORK?
According to Wasserman and Faust (1994), nodes often represent actors in social sciences. The term nodes and actors can be used interchangeably in network science because actors represent social (investors, individuals, corporate or institutional units, countries, and economic entities) that interact. Interaction might be a transfer of goods and services, physical connection, relation, association, or any type of material or non-material movement. When interacting, actors are linked by ties, edges, or links. The basic properties of a network, denoted by , include the number of nodes (or vertices) and the number of links (or edges) , where and . Throughout this book, we will use the terms “nodes” and “vertices” interchangeably.
In an undirected network, represents the number of nodes and links or edges (connections) , where and . The nodes or actors in a network are connected by relational ties, links, or edges, which we also use interchangeably. The edges between the nodes govern the relations, which might be directional or unidirectional. These relations can arise from social connections, information exchange, biological ties, transportation, financial transactions, economic intermediation, social interactions, physical laws, or other forms of interaction. The term “catallactics,” meaning exchange, can be used to describe networks in general. In this book, we will explore various types of relationships within networks, summarized into several major categories.
Increased computer power and data processing capabilities have enhanced personal and collective data recording. For example, data collection by smartphones and apps extends the datasets available for analysis. Data gathering using satellites, web scraping, text analysis, social networks, transactions, market data, and the like has grown tremendously. The term “alternative data” refers to novel methods of gathering data. Financial market research is evolving by applying not only traditional methods of analysis, but also tools capable of analyzing and describing a huge amount of data and possible relationships within the data. A shift from traditional methods of analysis like calculus, differential equations, and regression models to new techniques is inevitable and desirable for investigating underlying economic relationships, as stressed by Focardi and Fabozzi (2012).2
While traditional methods and procedures rely broadly on statistical correlations, the era of Big Data and significant computing power necessitates new pragmatic tools grounded in both mathematics and economics to enable efficient financial research. Modern finance is evolving, with financial markets, individual actions, and investor behavior and sentiment continually changing, leading to the emergence of new structures. As new data emerges, patterns, transmission channels, and causality also shift. Graph theory aids in identifying and exploring the underlying structure in the data, revealing relationships and connections between economic players and their interactions.
Network theory is dedicated to the science of connections between objects, and as Focardi and Fabozzi (2012) argued, economics is the science of relations. Therefore, network theory is an essential tool for analyzing relationships among actors, institutions, and instruments in financial markets. Within this framework, the nodes in a graph, applied to financial markets, represent various entities such as asset classes, individual security (i.e., stocks, bonds, and funds), countries, factors, financial institutions, trading partners, derivative contracts, or similar financial entities or instruments. The primary focus of graph theory is to identify relationships between these nodes and model the edges based on robust statistical, economic, and mathematical principles. This book aims to model financial networks and the edges between the nodes, which are typically known, but the links between them are often not observable.
Real-world networks might be observed, but networks in financial markets are mostly model-based as opposed to being sample-based. Having said that, it is worth discussing the common characteristics of the major types of real networks, how their properties relate to financial networks used in portfolio and risk management, and what the necessary model specifications are to model such networks. The most interesting and decisive property of real-world networks like biological, informational, technological, or social networks is the underlying flow process of transmitting information between the nodes.3 In the upcoming sections, we provide details of some of the existing and well-known real networks, highlighting the principles that apply to financial markets and asset management.
Technological and Infrastructure Networks
Technological networks include power grids, infrastructure, industrial, and water supply networks.4 The most interesting property of such networks is the existence of numerous Micro-Nets, which are locally autonomous networks yet form part of an entire global network. According to Newman (2010), examples of technological networks include the Internet, power grids, telephone networks, and other networks underlying physical infrastructure.
Technological networks, such as subway systems in cities, connect stations of other transport routes. Package delivery networks exemplify networks using the shortest path between nodes for efficient delivery. In these networks, information is not duplicated. Rather, each package or delivery is fixed, with a known receiver, which ensures that the goods arrive at the correct node. Additionally, the information or goods are indivisible. Borgatti (2005) illustrates that the delivery of goods follows the shortest possible path between two points within a given space or network, which minimizes the number of edges transversed (referred to as a geodesic path), ensuring the most efficient route is taken. This is a critical concept for optimizing routes and efficiently connecting points in various types of networks, including transportation, communication, and logistics systems. Minimizing distance is the goal, thereby reducing the time and resources needed to move from one node to another. A similarity in financial markets can be observed in transactions.
Although physical delivery no longer applies to all financial market transactions as it did in the early twentieth century when physical delivery was customary, the financial assets bought by an investor still follow a direct path, arriving from the seller to the buyer. Additionally, financial markets might contain local networks that are part of the entire financial landscape. Consider, for example, a network comprising highly connected private equity managers who build a local network. They might be part of a global network of limited and general partners within their private equity network.
Information Networks and Financial Markets
Many types of information networks exist.5 The most important and well-known are citation networks and the World-Wide Web (WWW). Whereas the citation network links all available bibliographic works already published and there is a specific order when establishing the links between the nodes, the WWW is a network linking the pages available on the Internet. Newman (2010) stresses that the WWW is different from the Internet, which is a physical network connecting computers. The WWW connects pages, enabling information to travel without any specific order. Among the most interesting examples of information networks are email communications and the spread of electronic information. Emails, for example, can reach numerous places and numerous receivers both simultaneously and concurrently. The information is spread through replication.
The relationship of such networks to financial markets highlights two important aspects of modern social and economic life: information processing and information efficiency as well as the exchange of goods, services, or financial instruments. While information processes refer to how information is processed, the transmission or movement of financial assets involves a different dynamic. As we shall see, information can be copied or replicated, but financial assets are indivisible.
Grossman and Stiglitz (1980) investigated the information process in financial markets and discussed the impossibility of achieving information efficiency. They demonstrated that markets cannot be fully efficient because new information is constantly arriving. As a result, equilibrium can only be momentarily achieved until new information arrives or the decision-making context changes.6
Importantly, information travels by replication, functioning as a “copy” mechanism, in contrast to a “move” mechanism. The move mechanism applies to money transfers, where the money transfer or payments have a fixed receiver – the buyer of the goods or services.
Social Networks and Financial Markets
Social networks are perhaps the most compelling types of networks that attract interest due to the rise of social platforms that connect individuals.7 The nodes in these social networks are called actors and are connected by ties, or links. Where the actors are connected or the basic property of social networks, is the dyad, which represents the connection between two actors establishing a social relationship.
An important characteristic of social relations is the existence of triads, which involve the relationships among three actors. A triad consists of three dyads – one between each pair of actors. Unlike dyads, which are simply connections that either exist or do not exist between two actors, triads are more complex due to their potential directions of connections. With 16 possible configurations, triads enable the modeling of intricate social interactions, revealing patterns and local structures.
Wasserman and Faust (1994), Robins et al. (2007), and Robins et al. (2005) emphasized that in social sciences, local structures shape the global structure. The knowledge of these local structures provided by analyzing triads helps to understand the overall network dynamics. Thus, triads represent the global structure of an actor network.8 A real-life example of a triad this would be the social interactions between individuals on social media platforms.
Facebook, X (formerly Twitter), LinkedIn, and Instagram are not only social network platforms but also successful companies. However, the underlying mechanism is for two actors to be connected. The major principle is that “friends of my friends are also my friends.” Social networks are central to how people are influenced by others. An essential property is that connections coincide simultaneously rather than sequentially from individual to individual. However, social networks also possess the distinctive property of directedness, meaning that the links between nodes have specific directions. This directedness implies that an edge between two nodes does not always translate into an edge between a third node and the other two nodes. In other words, the principle “friends of my friends are also my friends” is often violated, and a direct connection between nodes may not necessarily exist.
A simple example provided by Konstantinov, Aldridge, and Kazemi (2023) illustrates the difference. Consider the social network Facebook. Once two people are connected, the link is symmetrical in any direction; if person A connects to person B, then the link is symmetrical, and individual B is a connected “friend” of individual A. Alternatively, consider the social networks X or Instagram. An individual might be linked to or following another, but that does not mean the latter person is linked to the former. This principle is not limited to social networks but also applies to financial markets where transactions, orders, and money flows follow a certain direction because of causal principles within a market framework.
Of essential interest are the flow processes in social networks and their application to financial markets. Unfortunately, the principle “friends of my friends are also my friends” does not work in financial markets. To model financial markets influenced by social networks, it is necessary to use a statistical approach that employs probability models. The reason for this is that in financial markets with heteroscedastic volatility, the edge connectivity is associated rather with large degree of uncertainty than depending on trajectories or steady-state conditions. While the set of nodes is fixed, the connections are modeled probabilistically. In this context, the edges in social networks applied to financial markets arise from realizing probabilities related to the “social aspect” of a network. In other words, the interaction between nodes is governed by probabilities rather than specific node and edge properties, known as covariates, trajectories, or attributes.9
A flow principle from social networks that might apply to financial markets is information replication, which underlies the influence approach. Influencing financial markets and investors is a phenomenon that can be traced back to the early years of investment history. The result of social influence observed in financial markets is the phenomenon of crowdedness, as documented by Charles Mackay (1980).10 Convincing investors has a long tradition in financial markets and can significantly influence investment behavior.11
Biological Networks and Financial Markets
Biological networks are among the most interesting and widely studied types of networks.12 Many examples have attracted research, including food networks, ecology, protein–protein interaction networks, metabolic networks, signaling networks, and intraspecies and interspecies networks. The most widely used biological networks in finance are neural networks. However, the primary purpose of discussing biological networks in the context of the topological structure of financial markets in this book is to understand the underlying information transmission process between the nodes.
According to Borgatti (2005), the process of spreading an infection in biological networks is characterized by duplication. Consider, for example, an infection impacting a specific population. The infection spreads by duplication but does not immediately reinfect the initial nodes because they might have developed immunity. The relevance of infection spread in a biological context to financial markets can be seen in the example of duplication of information such as gossip. Specifically, negative information about a company with an elevated risk of default can be transmitted through the network via news, gossip, company announcements and press releases, negatively impacting holders of that risky asset or company. Consider a portfolio initially impacted and then fully hedged against, say, the depreciation of a specific exchange rate. In this case, the spread of negative information cannot affect that portfolio, to how an infection cannot reinfect immunized nodes.
FINANCIAL MARKETS AND FINANCIAL NETWORKS
After a brief overview of the general types of networks that exist and are detectable in nature, it is logical to focus on the primary type of networks covered in this book: financial networks that model, explain, model, and simulate financial market interactions using time series data. Perhaps the major difference between all other networks and financial markets is that financial networks are often not observable. Structures emerge to stay persistent or transitory based on intrinsic and external conditions. The dynamics of the financial market and financial networks are not governed by nodes in isolation but by the interactions that never cease. Financial markets are an unstable system operating by interactions coined by the arrow of time, whose dynamics operates at the statistical level. Therefore, probabilistic thinking applies to edge formation in financial networks. They must be specified, estimated, or simulated because financial markets generate substantial amounts of hidden or proprietary data. Consider, for example, a stock exchange that generates enormous transaction data in milliseconds, but these data are not available to the public because asset prices are formed by the transactions that occur. In contrast, data availability estimates a bipartite network – a type of network in which the set of nodes can be divided into two distinct groups – possible for scientific publications, citation networks, or actor–movie records.
Once data are gathered, a network can be observed. Financial networks can be easily estimated using various data, such as payments between countries. Generally, the availability of data and directional exchange of information between the nodes makes network construction possible. However, financial market data become increasingly proprietary, and the availability of time series data are one of the most common sources of information.
