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Structure and causality relations in a global network of financial companies

Leonidas Sandoval Junior

arXiv:1310.5388v1q-fin.GN

TL;DR

The paper addresses the need for empirical mapping of financial networks and their links. It builds correlation and Transfer Entropy networks from major financial stocks and studies connections to companies in crisis-hit European countries. The stocks cluster mainly by country, then industry and subindustry, with insurance companies and banks among the most central.

  • Problem

    The paper responds to the need to map financial networks and understand how institutions’ connections shape network structure.

    Source: §1 · p. 1

  • Method

    The study builds correlation and Transfer Entropy networks from daily returns of 197 major financial companies and adds liquid stocks from crisis-hit European countries.

    Source: §1 · p. 2

  • Results

    Stocks cluster mainly by country, then industry and subindustry; insurance-company stocks and bank stocks are among the most central, and the analysis identifies large financial companies affected by stocks from crisis-hit countries.

    Source: §6 · pp. 19–20

  • Takeaways & Limitations

    The resulting real-network map identifies companies central to crisis propagation and companies more dependent on failing economies, and may inform policies to avoid financial-crisis spread.

    Source: §6 · p. 20

    Transfer Entropy assumes that only the previous day matters for influence on a given day.

    Source: §4.2 · p. 10

Abstract

from arXiv · show

This work uses the stocks of the 197 largest companies in the world, in terms of market capitalization, in the financial area in the study of causal relationships between them using Transfer Entropy, which is calculated using the stocks of those companies and their counterparts lagged by one day. With this, we can assess which companies influence others according to sub-areas of the financial sector, which are banks, diversified financial services, savings and loans, insurance, private equity funds, real estate investment companies, and real estate trust funds. We also analyzed the causality relations between those stocks and the network formed by them based on this measure, verifying that they cluster mainly according to countries of origin, and then by industry and sub-industry. Then we collected data on the stocks of companies in the financial sector of some countries that are suffering the most with the current credit crisis: Greece, Cyprus, Ireland, Spain, Portugal, and Italy, and assess, also using transfer entropy, which companies from the largest 197 are most affected by the stocks of these countries in crisis. The intention is to map a network of influences that may be used in the study of possible contagions originating in those countries in financial crisis.

1 Introduction

The paper addresses calls to map the financial network amid concerns that complexity and reduced diversity may contribute to crises. It studies stock-based relationships across major financial companies using correlation and Transfer Entropy networks, including links to stocks from crisis-hit European countries.

1 Introduction

  • Haldane (2009) warned that financial networks had become more complex and less diverse, which may have contributed to the 2008 crisis.Connected networks can dampen shocks by sharing them, but may also spread crises faster and farther; highly connected nodes and opaque counterparties add vulnerabilities.Source: §1 · p. 1
  • The article studies daily returns for 197 large financial companies using correlation networks for common movements and Transfer Entropy networks for directed causal relations.It also examines centrality and adds liquid stocks from European crisis-hit countries to identify major companies affected by their price movements.Source: §1 · p. 2
  • Prior empirical work largely derived financial-network structure from interbank borrowing and lending, while theoretical and empirical studies examined how network structures relate to cascades.Upper (2011) surveyed simulation methods using varied financial data; the paper notes that describing all published work is beyond its scope.Source: §1 · pp. 2–3
  • Allen and Gale (2000) showed that contagion depends on network topology, while Allen and Babus (2009) called for empirical mapping that also examines link quality.Allen and Gale considered overlapping claims, while identifying incomplete information and currency markets as other possible contagion channels.Source: §1 · pp. 2–3

2 Data and methodology

The study selects liquid financial-sector stocks from the S&P 1200 Global Index and prepares daily closing-price series for comparison. It converts prices to log-returns and includes both original and lagged series to address differing market operating times.

2 Data and methodology

  • The sample comprises 197 sufficiently liquid financial stocks selected from the 200 financial-sector stocks in the S&P 1200 Global Index.The index covers stocks from 31 countries and approximately 70 percent of world stock-market capitalization.Source: §2 · p. 3
  • Daily closing prices were aligned to NYSE trading days by deleting observations on NYSE-closed days and carrying forward the previous close when a stock observation was missing.The authors note this approach would be particularly poor for markets with weekends differing from Western countries, which were not represented in their sample.Source: §2 · p. 3
  • The 197 stocks span eight financial industry categories, classified by country and then by Bloomberg industry and subindustry.Categories include banks, diversified financial services, insurance companies, real estate companies, and REITs.Source: §2 · p. 3
  • Log-returns of closing prices are used to reduce non-stationarity in the price series.The log-return compares a stock’s closing price on day t with its close on day t − 1.Source: §2 · p. 3
  • Because global markets operate at different times, the analysis treats each stock’s original and one-day-lagged log-return series as distinct, yielding 394 time series.The authors follow a procedure that uses original and lagged series in the same framework.Source: §2 · pp. 3–4

3 Correlations

Correlation matrices and asset graphs reveal geographic, industry, and temporal clustering among financial stocks; centrality rankings highlight different prominent nodes across measures.

3 Correlations

  • The study uses Pearson correlations between log-return series for the 197 largest-cap stocks and their lagged counterparts, then forms asset graphs by retaining edges whose correlation-based distances fall below selected thresholds.The distance ranges from 0 for totally correlated stocks to 2 for completely anticorrelated stocks.Source: §3 · p. 4, §3.1 · pp. 5–6
  • Stocks cluster geographically, with stronger same-day links among major regions and cross-day correlations connecting Australasian stocks with earlier American and European stocks.The matrix pattern repeats for original and lagged returns; thresholded views also show clusters by industry and national market.Source: §3 · pp. 4–5

3.1 Asset graphs

  • The two-dimensional map separates original from lagged stocks and shows geographic groupings, with present Australasian stocks near lagged American and present European stocks.The two dimensions are a compromise between fidelity to distances and ease of visualization.Source: §3.1 · p. 6
  • At threshold 0.6, a large REIT cluster coexists with smaller country- and industry-based groups; at 0.4, only three stock pairs connect.The Brazilian bank pair and Spanish bank pair remain isolated from other nodes in the reported threshold-0.6 graph.Source: §3.1 · p. 6
  • At distance threshold 0.8, asset graphs show separate US, Canadian, UK, European, Japanese, Hong Kong, Singaporean, and Australian clusters.As the threshold rises, clusters merge, including North America with Europe and original with lagged stocks.Source: §3.1 · p. 6

3.2 Centrality

  • Centrality rankings favor lagged stocks except for betweenness; Japan ranks prominently in betweenness, while European stocks dominate node strength.The authors attribute Japan's betweenness role to connecting lagged US and European stocks with next-day stocks from both continents; European stocks have higher average correlations among themselves.Source: §3.2 · p. 7

4 Transfer Entropy

This section defines and applies Transfer Entropy to financial-stock time series with one-day lags to examine directed influence and network structure. It describes entropy-based network measures and reports node-strength rankings alongside threshold-based asset-graph results.

4 Transfer Entropy

  • Unlike correlation, which cannot establish causal influence, Transfer Entropy is dynamic and non-symmetric and is applied here to 197 financial-company stocks and their lagged counterparts.The analysis uses it to examine influence among financial subsectors and to characterize the network formed by the stocks.Source: §4 · pp. 7–8

4.1 Shannon Entropy

  • Shannon entropy estimates a log-return series’ uncertainty from the probabilities of values assigned to bins, and its result depends on the number of bins.For J.P. Morgan, the reported entropy is 2.55 with bin size 0.02 and 0.59 with bin size 0.1; across stocks, the two binning choices yield correlated entropies of 0.97.Source: §4.1 · p. 9

4.2 Transfer Entropy

  • Transfer Entropy measures information from a source series about a destination’s next state that is not already in its past, and this study uses one-day lags and bin size 0.1.For Deutsche Bank to J.P. Morgan, the reported Transfer Entropy is 0.0155; bin size 0.1 was retained because it provided clearer results with less computation time than bin size 0.02.Source: §4.2 · pp. 9–11

4.3 Effective Transfer Entropy

  • Effective Transfer Entropy is non-symmetric, with its largest transfers from lagged stocks to original stocks; these transfers show geographic structure and cross-region influences.The analysis subtracts randomized Transfer Entropy from the original matrix; 25 shuffled-data simulations preserve individual distributions while breaking causal relations. Regional patterns include U.S.-to-Canada and Europe-to-U.S./Canada transfers, while same-day transfers are much smaller.Source: §4.3 · p. 11

4.4 Normalized Transfer Entropy and Asset Graphs

  • To construct asset-graph distances, the study normalizes Transfer Entropy, sets diagonal distances to zero, and symmetrizes each pair using the smaller of its two directed values.The resulting distances place original and lagged stocks close together; the graph analysis reports Australasia closer to America than to Europe.Source: §4.4 · p. 12
  • Asset graphs show integration beginning within countries and then extending across continents; at threshold 0.4, clusters include U.S. REITs, European and Japanese banks, and other same-country groups.Most relations in the threshold-0.4 graph are reciprocal, although transfer strengths between stocks are rarely similar.Source: §4.4 · p. 13

4.5 Centralities

  • At threshold 0.05, Americas and European stocks are more central on all measures except directed betweenness; out-degree leaders are mainly insurers, while in-degree leaders are mainly banks.Because the strong edges run from lagged to original stocks, the results indicate a tendency for entropy to transfer from insurers to banks. At threshold 0.1, insurance companies occupy the first positions across all centrality measures.Source: §4.5 · p. 14
  • At threshold 0.2, US insurance companies and banks predominate, while banks and REITs occupy the first positions at thresholds 0.3 and 0.4.At the latter thresholds, these are among the only nodes present in the asset graphs.Source: §4.5 · p. 14
  • Node Strength measures connection strength through incoming or outgoing connections, and the reported calculations use ETE, which the authors say gives the same results as TE.In Node Strength sums incoming connections; Out Node Strength sums outgoing connections.Source: §4.5 · p. 14
  • Insurance companies dominate the five highest In Node Strength and Out Node Strength rankings, acting as information-receiving authorities and information-sending hubs.The results use ETE; Table 4 identifies the top five stocks for each measure, but the supplied passage does not provide their names or values.Source: §4.5 · p. 14, Table 4 · p. 16

5 Relations with economies in crisis

The section adds liquid financial stocks from six crisis-country markets to the 197-company network and uses ETE to map measured influences. European companies, particularly banks, are prominent among both recipients and crisis-country senders.

5 Relations with economies in crisis

  • For each analysis, the authors remove the crisis country's stocks from the original network and add its liquid Bloomberg-listed financial stocks; the six countries are Greece, Cyprus, Ireland, Spain, Portugal, and Italy.Available stock counts and the liquidity filter constrain each country's sample.Source: §5 · p. 17
  • In the distance embedding, Greek and Cypriot stocks lie near Australasia, possibly because of time zones, while Spanish, Portuguese, Italian, and Irish stocks scatter through Europe's main cluster.Source: §5 · p. 17
  • ETE maps show Greek, Spanish, and Italian stocks influencing European companies; Cyprus's transfers are generally weak, while some Portuguese stocks strongly influence Spanish stocks.Irish stocks have mild influences on European stocks.Source: §5 · pp. 17–18
  • Nearly all leading recipient stocks are banks; ING Groep is most affected by Greek stocks, while National Bank of Greece leads for Cypriot stocks.Deutsche Bank appears in five recipient lists, and ING Groep and KBC Groep appear in four.Source: §5 · p. 18, Table 5 · p. 18
  • Country influence is measured by summing ETE received by a company, so the number of relevant financial firms in a country contributes to its measured influence.Source: §5 · p. 18
  • Leading crisis-country senders are mainly banks, with insurance and investment-company stocks also represented; origins and concentration vary across the six countries.Spanish and Portuguese influence is concentrated in commercial-bank stocks, while Irish influence is mainly distributed among two banks and one insurer.Source: §5 · p. 19, Table 6 · p. 19
  • European companies, especially particular banks, are most influenced by crisis-country stocks; crisis-country bank stocks, particularly foreign banks traded there, are the strongest measured senders.Source: §5 · p. 19

6 Conclusions

The stock networks cluster first by country, then by industry and sub-industry, while Transfer Entropy captures directed influences and prior-day relationships. Insurance companies and banks are among the most central stocks, and the crisis-country analysis identifies firms potentially exposed to defaults or falling stock prices in those economies.

6 Conclusions

  • The stock networks cluster primarily by country, then by industry and sub-industry, and correlation and Transfer Entropy produce different network structures.Transfer Entropy represents directed causal influences, including influences from previous-day stocks to following-day stocks.Source: §6 · p. 19
  • Insurance companies in Europe and the USA, followed by banks in the USA and Europe, are the most central stocks; CDS trading may partly explain this pattern.Insurance and reinsurance companies are major CDS sellers, while banks are major buyers and sellers.Source: §6 · pp. 19–20
  • The crisis-country analysis identifies which largest financial stocks are most affected by stocks in Greece, Cyprus, Spain, Portugal, Italy, and Ireland.The findings call attention to potential liabilities to defaults or falling stock prices in those countries.Source: §6 · p. 20
  • The work maps central companies and firms more dependent on failing economies as a basis for studying contagion on a real financial network.The authors suggest the mapping may inform policies aimed at avoiding the spread of financial crises.Source: §6 · p. 20

A List of stocks used

The stock roster is presented by country, industry, and sub-industry, excluding stocks from the particular countries in crisis. It includes financial companies across the countries and sectors listed in the tables.

A List of stocks used

  • The roster is organized by country, industry, and sub-industry and excludes stocks from particular countries in crisis.The list identifies each company alongside its country, industry, and sector.Source: A List of stocks used · p. 20
  • The listed entries include US, Canadian, and UK banks, insurers, diversified financial services firms, and real-estate companies.Examples include US insurers and REITs, Canadian banks, and UK investment-management firms and REITs.Source: A List of stocks used · p. 21
  • The roster also includes European and Asian financial companies, spanning banks, insurers, diversified financial services, and real estate.The listed countries include France, Germany, Switzerland, Italy, Spain, Japan, Hong Kong, and Singapore.Source: A List of stocks used · p. 22
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