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A review of two decades of correlations, hierarchies, networks and clustering in financial markets
Gautier Marti, Frank Nielsen, Mikołaj Bińkowski, Philippe Donnat
arXiv:1703.00485v7q-fin.ST
TL;DR
This review organizes two decades of developments in financial-market research. It finds that dynamic analyses of correlations and their derived structures may help track market changes, but remain in their infancy and are hardly exploitable in practice.
Problem
The reliability and interpretation of correlation-based trees, networks, and clusters remain uncertain, with results sensitive to methodology and correlation-estimation uncertainty.
Source: §3.1 · p. 3Method
The review tracks and organizes two decades of developments in financial-market research.
Source: §1 · p. 1Results
Dynamic analyses of correlations and derived structures may track market-structure changes, but this research remains in its infancy and is hardly exploitable in practice.
Source: §4 · p. 6Takeaways & Limitations
The authors recommend sharing code and data or synthetic datasets to support common tasks and benchmarks for correlation-network research.
Source: §8 · p. 17Evidence and practice are constrained by uncertain correlation estimates and method-sensitive clustering, weak reproducibility, difficult method comparisons, absent common benchmarks, and mostly confidential data.
Source: §3.1 · p. 3, §8 · p. 17
Abstract
from arXiv · showhide
We review the state of the art of clustering financial time series and the study of their correlations alongside other interaction networks. The aim of this review is to gather in one place the relevant material from different fields, e.g. machine learning, information geometry, econophysics, statistical physics, econometrics, behavioral finance. We hope it will help researchers to use more effectively this alternative modeling of the financial time series. Decision makers and quantitative researchers may also be able to leverage its insights. Finally, we also hope that this review will form the basis of an open toolbox to study correlations, hierarchies, networks and clustering in financial markets.
1. Introduction
Over two decades after Mantegna’s 1999 paper, research on financial time-series clustering and correlations has spread across several directions. This review organizes those developments.
1. Introduction
- Since Mantegna’s 1999 paper, work has explored statistical methodology, market fundamentals, risk, portfolio optimization, trading strategies, and alphas.The review frames its scope as developments over the following two decades.Source: §1 · p. 1
- The review aims to track and organize developments in clustering financial time series and studying their correlations.The review describes a need to bring work from different directions together.Source: §1 · p. 1
- The reviewed directions include both methodological research and applications such as risk and trading strategies.These are among the areas in which work has developed.Source: §1 · p. 1
2. The standard and widely adopted methodology
The widely adopted methodology stems from Mantegna’s 1999 work [1] and chapter 13 of [2]. It computes returns, correlations, and distances, then builds a minimum spanning tree from those distances.
2. The standard and widely adopted methodology
- The methodology derives from Mantegna’s seminal paper [1] and chapter 13 of [2], both published in 1999.The review describes it as widely adopted in the literature.Source: §2 · p. 1
- For N assets, the procedure computes log-returns from prices, then calculates pairwise correlations and converts them into distances.The text introduces the returns and then describes the correlation and distance steps.Source: §2 · pp. 1–2
- A minimum spanning tree is built from the distances; it is a connected graph with N −1 edges and no loops.When all distances differ, the tree is unique and gives an indexed hierarchy corresponding to a Single Linkage dendrogram [2].Source: §2 · p. 2
3. Methodological concerns and extensions
The review describes concerns about the standard correlation-based clustering methodology and surveys proposed alternatives in algorithms, distances, and other methodological choices. It also notes that no alternative appears to have gained broad enough acceptance for systematic empirical use.
3. Methodological concerns and extensions
- No proposed alternative appears to have gained broad enough acceptance for systematic empirical studies of market correlations.The review notes many concerns and suggested alternatives but no widely adopted replacement.Source: §3 · p. 2
3.1. Concerns about the standard methodology
- MST/SLCA clusters can be unstable under small input changes, with chaining and Pearson correlation’s outlier sensitivity and distribution limits among the cited concerns [4, 5, 6].Method changes can also produce large clustering differences and variability in portfolio formation and perceived risk [10, 4].Source: §3.1 · pp. 2–3
- King [11] questioned finite-variance and stationarity assumptions and suggested exploring distribution-free methods.The review notes that these conditions were in doubt in King’s study.Source: §3.1 · p. 3
3.2. Contributions for improving the methodology
- Proposed responses include alternative algorithms and distances, broader methodological refinements, and efforts to address statistical soundness.The review groups contributions to the field around these approaches.Source: §3.2 · p. 3
3.2.1. On algorithms
- Alternatives to MST include ALMST to address chaining, PMFG and TMFG filtered graphs, DBHT clustering, Potts models, maximum-likelihood clustering, RMT, and community detection [8, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].The review also describes a p-median construction in which every cluster is a star [22].Source: §3.2.1 · pp. 3–4
3.2.2. On distances
- Proposals include mutual-information and mutual-information-rate distances, Brownian [33], copula-based [34, 35, 36] and tail-dependence [37, 38] distances, and multivariate-dependence distances including the RV coefficient [40].Another distance accounts for both return correlations and distributions [6]; [41] attributes most apparent nonlinearity to univariate non-Gaussianity and says strong non-stationarity in a few specific stocks may also play a role.Source: §3.2.2 · p. 4
3.2.3. On other methodological aspects
- Researchers have used bootstrap methods to estimate reliability of hierarchical trees and correlation-based networks, and GANs to sample realistic artificial correlation matrices for robustness tests [42, 43, 8, 44, 45].A multi-objective evolutionary algorithm has also been proposed to explore the neighborhood of an empirical matrix [46].Source: §3.2.3 · p. 5
- Related methods assess clustering/network stability using cophenetic correlation [49], adjusted Rand index [4], or link-co-occurrence mutual information [9], preprocess returns, and use threshold, influence, partial-correlation, and Granger-causality networks [61, 62, 24, 63, 23, 64].Source: §3.2.3 · p. 5
4. Dynamics of correlations, hierarchies, networks and clustering
Research on changing financial correlations, hierarchies, networks, and clusters may track market-structure changes, but remains in its infancy and is still hardly exploitable in practice. Studies commonly use rolling Pearson correlations and independently compute networks or clusters, although sampling choices and unresolved parameter choices complicate interpretation.
Parameters and sampling choices
- Sampling frequency affects observed cluster organization; daily-return clusters resemble weekly and, to some extent, monthly results, while higher frequencies bring asynchronous-data and Epps-effect challenges [74, 53, 4, 78].At intraday frequency, time is needed for cluster organization to emerge, and intrasector correlation decreases faster than intersector correlation as frequency increases [74].Source: §4 · p. 6
- Rolling-window length is often arbitrary, with small windows yielding noisy data and large windows smoothing it; asset count also matters because T/N affects correlation estimates and clustering [72, 79, 43, 80, 81].No clear-cut window-length answer is reported; criteria may include investment horizon, regulation, cluster stability, convergence rate, or economic regimes [20, 17].Source: §4 · p. 6
Dynamics of correlations
- Dynamic-correlation studies monitor eigenvalue entropy using 22-day stock-return windows and identify three regime shifts during 1989–2011 from housing-market eigenvalues and eigenvectors [27, 82].The housing-market matrices use quarterly recorded prices for 51 US states with T=60 [82].Source: §4 · p. 7
Dynamics of the MST and other hierarchical trees
- The MST shrinks during stock-market crises, while optimal Markowitz portfolios lie near the tree outskirts and normalized tree length strongly correlates with diversification potential [72].The review also reports dynamic-tree findings for Asia-Pacific markets and Japan and Korea.Source: §4 · p. 7
- The dynamic spanning tree shrinks over time; Hong Kong is identified as the key financial market, and removing it leaves no clear key market and significantly reduces tree stability [54].The tree's stability also significantly increased in recent years [54].Source: §4 · p. 7
- Japanese and Korean stock markets show decreased grouping by industry categories [87].Source: §4 · p. 7
Empirical studies
- Average sovereign-bond correlation within the COVID-19 period falls from its 2019–2020 peak, a trend also reflected across network-filtering methods [88].Source: §4 · p. 7
Dynamics of clusters
- Cluster studies report greater stability during crises [22], finite-lived evolving clusters [75], and merging, splitting, birth, death, contraction, and growth [48].Source: §4 · p. 7
5. Clusters, hierarchies, and networks based on alternative data
The section extends correlation-based analysis to alternative data on company and investor relationships, including textual co-occurrence and supply-chain, payment, and trading networks.
5.1. Based on textual data
- Text-derived networks link media attention to market-premium forecasts, news sentiment to company-risk signals, and financial-discussion co-mentions to analysis of bank systemic risk [89, 90, 91, 92].The media attention index has 5.97% in-sample and 5.80% out-of-sample monthly R2; high quarterly risk values correlate with a higher chance of stock-price decline up to 70 days later. Using an entire post as co-mention context reduces reliability while yielding more relations.Source: §5.1 · p. 8
- Combining past financial-network structure with Twitter sentiment networks improves prediction of future financial networks over a persistence benchmark, while SEC product-text network features improve predictions of firm success or failure when combined with financial data [93, 95].The social networks are harder to predict and less persistent than financial networks.Source: §5.1 · pp. 8–9
5.2. Based on supply chain data
- Supplier-network centrality portfolios tend to predict overall stock-market movements [96], while cash-flow network centrality is associated with lower P/D ratios and higher expected returns [97].Supply-chain analysis also finds significant credit-risk propagation along supply chains using credit default swap spreads [98].Source: §5.2 · p. 9
5.3. Based on transaction data
- In a payment network linking around 2.4 million Italian firms, local network properties correlate with firm risk, and network-only classifiers outperform random assignments [99].Risk homophily concentrates similar-risk firms in particular network areas, so an idiosyncratic shock's propagation may vary with local structure and community.Source: §5.3 · p. 9
5.4. Based on key people
- A co-occurrence network of people in 21,578 mostly economics-focused Reuters articles from 1987 has small-world and power-law features, and its rankings correlate moderately with Wikipedia-based importance in 2007 [100].Source: §5.4 · p. 9
5.5. Based on investors
- Investor networks relate social proximity to trade correlations [101], while central Istanbul traders earned higher returns and traded earlier around information events [102]; investor clusters across IPO stocks were stable between new and mature stocks [103].The persistent institutional investor cluster is presented as evidence about institutional herding [103].Source: §5.5 · p. 10
- Multilayer investor networks place households in Finland's capital at high centrality [67], while a reconstructed FX trader network identifies five-minute order-flow leaders and a herding measure causally linked to inter-dealer liquidity [104].Source: §5.5 · p. 10
5.6. Based on several corporate networks
- Combining ownership, board ties, research collaborations, and stock correlations into a multiplex network yields initial evidence of a relation between company performance and multiplex centrality [68].Source: §5.6 · p. 10
6. Financial applications
The review describes applications of clusters and networks in portfolio design, trading, risk management, and financial policy, while noting that risk-system proposals remain limited.
6.1. Portfolio Design
- Hierarchical clustering is used to build diversified portfolios, but HRP's relative performance depends on covariance estimation and rebalancing frequency; the cited comparison used portfolios of only 10 assets [38, 114, 115, 116, 117, 118, 119].With crude covariance estimates, inverse-volatility portfolios outperform other methods; HRP is intermediate between that approach and optimization-based methods, and minimizes out-of-sample variance with longer rebalancing horizons [119].Source: §6.1 · p. 11
6.2. Trading Strategies
- Clustering supports portfolio and trading applications including cluster-based index tracking, mean-reversion strategies, earnings forecasts, and alternative peer classifications [110, 50, 120, 94, 125].Text-based peer classifications can enhance industry momentum returns and outperform traditional industry peers in explaining firm valuations and peer comovement [94, 125].Source: §6.2 · pp. 11–12, §6.1 · p. 11
6.3. Risk Management
- Clustering hierarchies can filter correlation [106, 129] or tail-dependence [37] matrices to measure risk in normal and stressed conditions, while early-warning systems may compare similar states or monitor rapid correlation-structure changes.Networks are relevant to studying chains of defaults.Source: §6.3 · pp. 12–13
- Studies report changing correlation regimes, less-separated asset classes after 2008, evolving cluster persistence, and associations between network centrality measures and systemic-risk contributions [48, 134, 135].Shipping-market correlations also increased, with the analysis using an MST, Granger causality, and Brownian distance; structural entropy was proposed as an early-warning indicator and was highly linearly correlated with asset-price volatility [33, 138].Source: §6.3 · p. 13
- The review characterizes correlation-network and cluster risk research as mainly descriptive, with too few proposals to build effective network- or cluster-based risk systems.Source: §6.3 · p. 14
6.4. Financial Policy Making
- A study of the Glass–Steagall Act repeal argues that cross-sector investment increased links among otherwise weakly coupled economic sectors, increasing rather than decreasing risk [130].Source: §6.4 · p. 14
- Widely adopted VaR requirements may amplify aggregate fluctuations when simultaneous asset sales create unintended positive feedback, with empirical results suggesting effects on institutional returns and systemic risk [23].Source: §6.4 · p. 14
- Bayesian networks and probabilistic graphical models are presented as tools for modeling firm debt dependencies and reasoning about default and bailout counterfactuals [69].Source: §6.4 · p. 15
7. Practical Fruits of Clusters, Networks, and Hierarchies1
The review collects recurring empirical patterns in financial correlation networks and hierarchies, while noting that several conclusions remain disputed across studies.
7.1. Stylized facts
- Energy and Financial firms are strongly connected within their sectors, while several other sectors are less connected; the MST taxonomy aligns with external sector classifications [2, 72].General Electric is central in US stock networks under several centrality criteria [1, 74, 72, 39], while classic Markowitz portfolio assets lie on tree peripheries [72, 105, 108].Source: §7.1 · p. 15
- During market crashes, the correlation matrix’s maximum eigenvalue rises as mean correlation increases, while the MST shrinks and contains fewer clusters [147, 72, 86].The post-subprime correlation matrix also shows markedly higher absolute correlations, with less asset-class separation [48].Source: §7.1 · pp. 15–16
- Market structure varies across time scales and regimes: indices show fast and slow correlation dynamics, and MSTs are star-like in low volatility but chain-like in high volatility [9, 82, 76].Volatility shocks are reported to start at the fringe and propagate inward [76].Source: §7.1 · p. 15
- Studies report further network patterns, including a market-wide largest-eigenvector component [20], small-world effects across time horizons [151], and weaker sector identity in emerging markets [153, 154].Among the largest NYSE stocks, auto and lagged intraday correlations became more prominent in 2011–2013 than in 2001–2003, with end-of-day connectivity surges [70].Source: §7.1 · p. 16
7.2. Moot points and controversies
- Reported disagreements include whether to invest in central or peripheral stocks, how crises propagate, which clustering method is more stable, and whether network portfolios relate to minimum-variance portfolios.Most papers report declining cluster stability during crises, while one using the p-median method reports an increase [131, 134, 22].Source: §7.2 · p. 16
8. Conclusion
Correlation networks offer quantitative tools for several financial tasks, including systemic-risk monitoring and portfolio construction. The review also identifies reproducibility, comparison, benchmark, and data-sharing challenges, and recommends sharing code and data or synthetic alternatives.
8. Conclusion
- Correlation networks can support systemic-risk monitoring, portfolio diversification, statistical arbitrage, hierarchical risk-factor removal, and searches for less crowded cross-sectional risk premia.The review also describes acting preemptively on a few institutions to prevent cascading effects as a potential use.Source: §8 · pp. 16–17
- The field faces limited reproducibility, reimplementation bias and lack of open code, no widely accepted common benchmarks, and mostly confidential data.The authors identify these challenges as obstacles to making the techniques part of practitioners’ standard toolbox.Source: §8 · p. 17
- The authors recommend sharing code and data, or synthetic data when the originals are confidential, to establish common tasks and benchmark results.They suggest generative models such as GANs as one way to produce anonymized synthetic data with properties similar to the original.Source: §8 · p. 17