Dataset preparation

The dataset we analysed covers the set of banks provided by Bloomberg which were active (i.e. with traded instruments) at the end of the first quarter of 2014. Although quarterly information is available, we prefer to focus on annual balance sheets and income statements for accounting standard reasons, as different countries can have different obligations in terms of the provision of quarterly financial statements and this can lead to a mismatch and a poor variables coverage. Data are collected during the reference period from 2001 to end of 2013.

As regards financial statements data, we select a large set of variables among those available in Bloomberg and related to the current regulatory framework ([17]). We rely on the existing literature for the selection process, although providing a neutral approach. We focus the analysis on proxies for banking business models (see e.g. [18], [19]). In particular, balance sheet data provide a year-by-year picture of stock variables in terms of assets and liabilities for different instruments and maturities, while income statement data describe annual economic performances by partitioning profits and losses according to banking activities ranging for instance from interests to fees. Since national regulations allow firms to fix a different end of fiscal year, we extend the “end of year” definition and the relative financial statements according to a window in the range between three months before and after the end of the solar year. Solving overlapping issues in variables definitions, as well as the base currency choice, constitute the first step in the data pre-processing procedure. Firstly we discard total and sub-total measures (as they are redundant measures), and secondly we choose US dollars as currency base, thus facilitating banks comparisons.

Working with financial statements data often leads to limitations in data coverage and completeness. Therefore, the starting point of our analysis is represented by the selection of a stable set of banks in terms of data availability during the sample period. In particular, banks might change the composition of their financial statements or they might be excluded by the Bloomberg provider due to several reasons, such as for instance a new regulation or a change in the bank’s economic activities. This, in turn, might cause missing values for some variables or lack of financial statements for several banks in certain years. In order to limit the impact of these issues on our findings, we define a methodology to measure the coverage of available variables for each bank in the reference period. We refer to the Quality Ratios (QRs) as the proportion of available and usable variables V_OK over the maximum of all possible ones V_ALL in the sample period: QR = V_OK/V_ALL. The tuning of this indicator, combined with two more filters on the frequency of financial reporting, provides a stable set of banks identified by their QR. The two additional criteria are: a minimum number of financial statements of ten out of thirteen possible fiscal years and a maximum gap period between two consecutive annual reports equal to seven hundred days. Once selected those banks that report almost continuously their financial statements, we study them according to their respective QR.

Actually, individual QRs, as empirically computed on the entire perimeter, lie in the range between 0.3 (low accuracy/coverage) and 0.8 (high accuracy/coverage). Interestingly, many measures computed on the sets of banks obtained by fixing the QR do not seem to be significantly affected by its choice (except, as expected, for high QRs, where the size of the sample reduces significantly). With greater values of the QR parameter we have less available banks to be considered, since only few of them have a large set of variables present in many of their financial statements. As the estimates are stable in a reasonable QR range, in this work we decide to use the set arising from the case of QR = 0.5 that, even if arbitrary, still represents a good compromise between the accuracy of the estimate and the size of the sample (see Fig 1).

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Fig 1. Quality Ratio.

This picture shows the number of nodes and edges along the sample period for different QR values. It is clear to see how for small values of the Quality Ratio parameter the curves belong to a stricter range.

https://doi.org/10.1371/journal.pone.0162855.g001

Accounting networks

For every year a vector of financial statement variables is assigned to each bank and used to compute the cosine similarities between pairs of banks/nodes. Here the intuition is that the most similar banks (as from their financial statements) must stay closer in the network and form a cluster. Then, the measure “cosine similarity” is transformed into a metrics (as triangular inequality must hold, the square root is used). The definition is the following: we compute the cosine of the angle between each pair of vectors with the dot product and then we apply the simple transformation , where w_i,j ∈ [0, 1] and C_i,j is the cosine similarity between i and j. In network terms w_i,j is the weight. This transformation (see [20] for an introduction to similarity measures and relative metrics) is used to move from the cosine similarities defined in the space [-1,1] to weights in the interval [0, 1]. With this transformation the more two nodes are similar (or anti-similar) the larger is the weight, while a weight of 0 is assigned to a pair of nodes having totally dissimilar financial statements (actually, in our networks cosine similarities range mainly between 0 and +1).

In addition, before the computation of the metrics, we need to take care of the size distribution of banks, as it spans over several orders of magnitude. To avoid a bias toward large institutions, for each bank we divide all variables in its vector by the respective total assets in such a way that the attributes of the vector refer to economic and financial ratios. This operation ensures that clusters will be formed by banks with similar business activities regardless their sizes.

An important methodological choice of our study is the “neutral” approach used for the selection of the variables within the financial statements. Apart from removing related and redundant measures (total and subtotals), we used all the available information applying the same weight to each variable in the vectors. This agnostic approach is in line with the goal of the paper, i.e. introducing the concept of Accounting Network, although we are aware that practitioners can give a different importance to each variable of the financial statement. In our perspective we expect that the relevant information will emerge in a bottom up process, as a spontaneous feature selection carried by our methodology. Finally, we introduce a confidence level (95%) during the link formation. By using a Montecarlo sampling test, if the cosine similarity is statistically significant with 95% of confidence we retain the link otherwise we discard it. As a result of this filtering procedure, we observe that the networks tend to be very dense and almost complete. The most of the information is carried by the weights of the links and less by the simple topology (degrees and other structural features).

Community detection

A classical method to investigate the structure of a network is the search of communities, i.e. regions of the network with larger internal links density. Intuitively, these regions are formed by clusters of nodes with higher degrees or, for weighted networks, with larger strengths. Several methods were proposed to find network communities without imposing a priori the number of communities but letting them emerging from the network itself. Among others we cite the optimization of the modularity that is a measure of how much the link structure differs from the random network where links are assigned with uniform probability and internal communities are not present (apart from fluctuation). For weighted networks, the modularity is defined by the following formula: (1) where s_i = ∑_j w_ij and s_j = ∑_i w_ij are the strengths (sum of weights) of the nodes i and j respectively, W = ∑_ij w_ij is the total sum of the weights and the function δ(c_i, c_j) is equal to 1 if (i, j) belong to the same community or 0 if they are members of different communities. The maximum modularity value is 1 (an ideal case for which the communities are isolated) and can also take negative values. The 0 value coincides with a single partition that will correspond to the whole graph. A negative value means that there is no particular advantage in separating the nodes in that particular clusters and so there is not community structure whatsoever.

To study the presence of communities it is often necessary to prune the network cutting the links if their weight is below a certain threshold. In our case we intend to consider only the links formed by nodes having a large similarity/weight w of their financial statement vectors. The procedure of pruning can be guided by the use of the tools related to the community detection methodology ([21]). In particular, working with the modularity optimization function ([22]), with the Louvain technique ([23]), it is possible to look at the significance associated to the threshold (as in [24]), where the modularity is introduced as a parameter to check for the best resolved community structure. We use this parameter to help finding a reasonable pruning threshold range of values for the networks. A rule of thumb in this process is indeed avoiding network fragmentation, i.e. keeping the graph connected while removing not significant links. We made extensive tests computing quality/significance of the partitions (looking at the modularity parameter) using different pruning thresholds (i.e. removing the links having a low weight), determining a range of weights thresholds (0.35 < w_i,j < 0.5) that helps to prune the original networks to an optimal level. In this interval, communities are stable and the interpretation of each region can be seen as a result of the financial statement similarities across banks in different countries.

Network measures vs. economic indicators

Comparisons among network measures and economic indicators are provided to describe the correlation between nodes’ network topology and economic behavior. We study these features by means of extensive linear correlation tests (Pearson correlation) for the overall set of banks for each year and we verify the significance of the estimates by means of parametric tests. These estimates are based on the filtered networks, which are themselves based on the significance and the quality of the community detection algorithm. This analysis shows how nodes’ network properties (e.g. Strength or Clustering Coefficient) are associated to basic economic indicators (e.g. Return on Assets, Total Assets and Total Debts to Total Assets), thus showing whether nodes’ topological properties are positively or negatively related to certain economic features and how these relationships have weakened or reinforced during the crisis.

Clustering coefficient is a measure of the local tendency of the nodes to form small regions of fully connected nodes, it is an average measure of the local clustering coefficient (actual number of triangles centered in each node over the total). Return on assets (ROA) is the net income over total assets and is a measure of the bank performance. Total debts to total assets is an indicator of the leverage of the bank and it is computed as the ratio between debts and its size (measured by total assets).

Principal Component Analysis

Once communities are identified, we attempt to describe which financial statement variables are more likely to characterise these clusters. In order to facilitate comparability, we focus on those indicators more popular within the set of variables utilised to compute the cosine similarities (i.e. those indicators appearing with larger frequency in the entire dataset). In fact the inclusion of very poorly represented measures across different banks would have made the comparisons less effective with potential biases related to e.g. different regulations frameworks or geographical memberships. Hence, since we are interested in disentangling potential similarities/peculiarities across different communities, we prefer to rely on common and well-diffused measures of banking activities among those present in banks’ financial statements. In addition, we enrich this set by means of indicators such as ratios (e.g. Return on cap and Total debts to total assets) and aggregated measures (e.g. Total assets). Community detection identifies four main clusters, whose constituents are more numerous and stable in time. For the sake of conciseness, the Result section will focus mainly on these communities. In particular, for each year we describe by means of Principal Component Analysis (PCA) which economic features are more (less) able to contribute to the explained variability of communities’ members.

PCA is a multivariate technique that analyses observations described by several inter-correlated variables. PCA extracts the important information from the data and expresses it as a set of new orthogonal variables (principal components). In our exercise, since measures present different ranges of dispersion (e.g. by construction some ratios are bounded) we rely on a scaled version of PCA; finally, we consider only principal components with eigenvalues greater than 1 (in almost all cases they correspond to the first 3 components). Then, we compute the proportion of the variance of each original economic measure that can be explained by the selected principal components. This, in turn, leads to a ranking of the original economic measures in terms of their ability to describe a certain community’s variability. In particular, since we are interested in how the onset of financial crisis has affected the banking system, we split this analysis in three periods: from 2001 to 2006 (before the crisis), from 2007 to 2009 (the onset of the crisis), and from 2010 to 2013 (after the breakdown of the markets). For each period we decided to characterise each community by the top and the bottom three measures, thus analysing how these ranks have evolved over time and across communities.

Community Detection Results

In this sub-section we focus our attention on the bottom up clusterization of the network from the application of the community detection algorithm and on the presence of geographical structures arising when we label each bank with its country. Therefore, we describe whether banks belonging to different countries (as a proxy for different regulations and/or level playing fields) have shown the tendency to be part of separate or, alternatively, common clusters and we verify, by analysing communities’ evolution over time, whether the crisis influenced these configurations. In particular, our community detection analysis on Accounting Networks shows these main results.

It exhibits the presence over time of a clear community representing US banks and another one composed by Japanese banks, although for both regions there is also an additional smaller second group quite persistent in time. By contrast, it is not possible to identify a single and an unambiguous European community, since banks belonging to European countries seem to be likely to form national or sub-regional communities or to be included in a vast and geographically heterogeneous cluster (hereinafter the Mixed community). In addition, Asian banks are fragmented in several sub-regions where, in particular, the Arab and the Indian-Pakistan groups emerge. Therefore, the detection of communities within Accounting Networks reveals the presence of two homogeneous clusters corresponding to US and Japanese banks surrounded by a more diversified cloud of banks belonging to different countries; remarkably, European banks are not able to clusterise together in a single community, while it persists over time a certain level of separation based also on national borders. Hence, an interesting contribution of the paper points to the presence of a large and geographically heterogeneous community, which can be related to the fact that the globally established regulatory framework might have indeed accelerated the tendency of banking activities of different countries to converge into more uniform banking practices. This is shown for instance in Fig 2 where we also observe that the outbreak of financial markets contributed to make the Mixed community more cohesive; furthermore, although still representing separate communities, both US and JP clusters result topologically closer to the Mixed community after the breakdown of 2007-08, thus supporting the interpretation of a gradual convergence of different areas into more similar patterns. In addition, the application of the community detection on Accounting Networks allows to identify even small communities, such as those related to African or Scandinavian banks. This represents a quite promising aspect of the methodology, since it ensures the detection of local reliable communities although the approach taken so far is eminently agnostic.

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Fig 2. Communities.

In the upper panels it is shown the Community Structure for the three periods. The impact of the financial down-turn of 2007-08 seems to be reflected more heavily after the crisis, with the emergence of many sub-region communities as a response against the deteriorated market conditions. In the lower panel the most important financial statements components by the PCA analysis.

https://doi.org/10.1371/journal.pone.0162855.g002

It is not simple to explain the reasons behind the emergence and evolution of these communities, however it is possible to advance some intuitions based on the impact of globally recognized accounting standards ([25]), the establishment of supranational supervisory and regulatory authorities, and on the role of the harmonization process of banking practices which have been implemented through e.g. the various Basel regulations ([17]). These contributions point to a common level playing field, which might have facilitated the emergence of a large and geographically heterogeneous community and its increasing topological proximity to both US and JP clusters. However, latter communities highlight the persistence of regional peculiarities. In Japan a deregulation process, known as the ‘Japanese Big Bang’, was formulated during the 1990s to transform the traditional bank-centered system into a market-centered financial system characterised by more transparent and liberalised financial markets ([26]). In fact, peculiar features of Japanese banking sector were the over-reliance on intermediated bank lending, the absence of a sufficient corporate bond market and a marginal role for non-bank financial institutions, whose main consequences were an abundance of non-performing loans, excess in liquidity, scarce investments and low banks profitability (see e.g. [27]). Although this program was intended to cover the period 1996–2001, the goals have not yet been achieved and policy makers’ continuing reform efforts to remove past practices by market participants confirm the slowing convergence of the Japanese regulatory framework to a capital-market based financial system ([28]). Thus, the presence of the JP community which gradually tends to the Mixed cluster is in line with evidences from the Japanese financial sector reforms aimed to change its reliance on indirect finance into a system of direct finance related to capital markets. Furthermore, it is remarkable the presence of a US community quite stable over time, which seems to be progressively attracted by the Mixed cluster. The US financial system presents peculiar features compared to other geographical areas. It is characterised by a relatively greater role of capital market-based intermediation, a higher importance of the ‘shadow banking system’, and differences in the accounting standards ([7]). The impact of non-bank financial intermediation relates to the use of originate-to-distribute lending models, which determine the direct issuance of asset-backed securities and the transfers of loans to government-sponsored enterprises (GSEs, e.g. Fannie Mae and Freddie Mac). Financial innovation played a key role and the increasing use of securitisation explains the low percentage of loans to households on banks’ balance sheets ([7]). In addition, the US ‘shadow banking system’ is highly dependent on the presence of finance companies, money market funds, hedge funds and investment funds, which influenced the growth of total assets in the US financial sector during the last decades ([29], [30]). The presence of a distinct community is probably also due to differences in accounting standards which mainly involve the treatment of derivatives positions between the US Generally Accepted Accounting Principles (US GAAP) and the International Financial Reporting Standards (IFRSs). In particular, US GAAP allows to report the net value of derivative positions with the same counterparty under the presence of a single master agreement, thus impacting on the size representation of balance sheets items. However, in Fig 2 we observe that the US community (similarly to the JP community) is gradually approaching the Mixed community, and the consequences of the breakdown of 2007-08 seem to have enhanced this behaviour. Among the possible several reasons, it is worthwhile to consider the impacts of the reform on the OTC derivatives market (embedded in the Dodd-Frank Act) and the Basel III new banking regulation, which may have facilitated similarities among US institutions and their peers in the Mixed cluster.

Relationships between Economic Indicators and Network Properties

In this Section we provide a preliminary investigation of the relationships between banks’ economic indicators and their network properties. In order to characterise banks, we consider three common proxies for their classification: Return on Assets (for the Performance), Total Assets (for the Size) and Total Debts to Total Assets (for the Leverage). Then, comparisons are presented against two basic network measures: the Strength and the Clustering Coefficient. For each year from 2001 to 2013, we provide some insights for these relationships by estimating for the overall sample the correlations between banks’ economic indicators and network measures. As explained in the Method, in this exercise we consider the network filtered according to the quality/significance of the Louvain community detection algorithm. This helps us in the assessment of the significance of our results. Below, we show some examples to discuss how these relationships have evolved over time.

In particular, we investigate whether once the effects of the crisis have spread throughout the financial sector, the capacity of traditional economic indicators (e.g. leverage, size, performance) to group banks could result undermined. For instance, the onset of the financial crisis clearly affects the relationships between Total Debts to Total Assets and network properties. Although the correlation between Strength and Total Debts to Total Assets remains negative during the entire sample period, the breakdown of financial markets seems to further enhance this effect for subsequent years (Fig 3, plot on the left). Thus, this relationship suggests that, after the onset of the crisis, the use of leverage became on average more anti-correlated to the Strength. This implies that banks that are more dissimilar in terms of their financial statements (i.e. with lower values of Strength) are those that turned out to be less capitalised (i.e. with higher values of Total Debts to Total Assets). Furthermore, one might be interested in understanding the role played by the Size which represents a typical indicator utilised to classify banks. The correlation between Strength and Total Assets is almost flat and negative even after the collapse of 2007-08, but it shows an increasing trend in the recent period (Fig 3, plot on the center). Hence, it seems that after the outbreak of the crisis the Size became less correlated to the similarity among banks, as estimates pointing sharply to zero seem to suggest. We finally analyse the relationship between Performance and network properties (Fig 3, plot on the right). In particular, in order to mimic how the presence/absence of more connected groups of banks is related to economic results we consider the Clustering Coefficient for determining the level of structure in the system. Although poorly statistically significant in the early 2000s, correlations with Return on Assets exhibit a decreasing pattern before the onset of the crisis and then remain negative although slightly erratic. The negative relationship between Clustering Coefficient and Return on Assets seems to suggest that the presence of well connected areas in the network (nodes with higher clustering coefficients) do not foster economic performance.

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Fig 3. Correlations.

In these plots we present the correlations between banks’ Strength versus the Total Debts to Total Assets (Leverage) (plot on the top-left), Strength versus Total Assets (Size) (plot on the top-right) and Clustering Coefficient versus Return on Assets (Performance) (plot on the bottom part). The correlation is computed across the years 2001-13. It is clear the effect of the financial crisis across the outbreak of 2007-08. Red points stand for no-significant estimates at 5% level.

https://doi.org/10.1371/journal.pone.0162855.g003

These basic examples suggest that a clear investigation on the relationships between economic indicators and network properties might be not always conclusive. Moreover, once we consider the entire set of banks, there might be some cases where estimates are poorly significant. Still, some remarkable effects arise from this investigation strategy and preliminary results point to a turning point in the correlations across the outbreak of the financial crisis. In particular, diagrams confirm that leverage is an useful indicator for differentiating banks, hence deviations to a lower capitalization are associated to increasing dissimilarity with the rest of the system and the impact of the crisis suggests a reinforcement in this relationship. By contrast, it seems that size does not contribute too much on the similarity between banks after the breakdown of 2007-08, while it played a greater role before and during the crisis. Finally, the relationship between performance and the structure of the system is less clear and prevents straightforward conclusions.

The identification of economic features potentially able to characterise specific portions of the system is addressed in the next sub-section.

PCA results

Community detection shows the presence of three large clusters (Mixed, US, and JP) and an additional quite stable and persistent but smaller community (mostly US+EU banks). In this Section we provide a way to describe how these communities can be represented in terms of economic features (see Fig 2). Given the multi-dimensionality of the set of measures utilised to build the networks, we adopt a Principal Component Analysis approach to identify those measures which contribute more (less) to the explained variance within each community. For the sake of simplicity, we propose the ranking of the top (bottom) three measures for each community during the following intervals: pre-crisis (2001–2006), crisis (2007–2009), and post-crisis (2010–2013). In particular, for each year we compute the contribution of the original measures to explained variance; then, we average within each sub-period and we determine the rankings based on the mean period values. Below, we name the community with a mixed geographical composition as C0, while we refer to the communities with a prevalence of US, JP and European plus US banks as C1, C2 and C3, respectively.

This representation allows us to compare communities’ features over time and across different groups. For instance, in Table 1 we observe that Total Assets and Interest Income are quite frequent among top measures contributors, while Total Debts to Total Assets is recurrent among measures in the bottom rankings. This is not surprising given banks heterogeneity in terms of the size (Total Assets) and the economic results (Interest Income) distributions, in contrast with the tight constraints on leverage (Total Debts to Total Assets) due to regulatory requirements. By focusing on the top rankings we notice that C0 and C1 have fairly stable top contributors, while communities C2 and C3 are more affected by the wave of financial turmoil. Furthermore, bottom rankings seem to be on average only slightly influenced by the choice of different sub-periods. In addition, differences between mean values among the set of top three and the set of bottom three contributors are quite stable over time with only few exceptions, while the middle part of the distribution of measures’ contributions (not reported, available from authors upon request) is in general quite sparse. For these reasons, we prefer to focus on the top and the bottom rankings to describe communities’ features.

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Table 1. First Table shows the sets of top three contributors for each community, while the second Table shows the bottom three contributors.

Values represent the contributions of original measures to the explained variances. Rankings refer to averaged values along each sub-period: 2001-06, 2007-09 and 2010-13. Community C0 refers to the Mixed community, while C1, C2 and C3 stand for US, JP, and EU+US clusters, respectively.

https://doi.org/10.1371/journal.pone.0162855.t001

One might be interested in how the outbreak of financial crisis have influenced these rankings. Top composition of C1 is unaffected by the 2007-08 financial breakdown, while C0 is only partially modified by the onset of the crisis (Interest Income is replaced by Net Interest Income). Conversely, C2 presents a quite different configuration during the crisis sub-period when it exhibits a relevant role for expenses measures (i.e. Non Interest Expenses and Operating Expenses). Similarly, income statement measures become more relevant among top contributors also within the C3 community. Interestingly, community C0, which is characterised by a mixed geographical composition, and the US community (C1) reach identical top contributors after the outbreak of 2007-08, while the JP community (C2), which shows the same top contributors as community C0 in the first sub-period, seems to react differently during the crisis, although in the third sub-period it shows again top contributors similar to C0 (and to C1). By contrast, community C3 seems to present a peculiar pattern over time.

Therefore, the crisis sub-period coincides with remarkable differences in the top contributors, while the recent sub-period points to a renewed tendency to get similar contributors for a wider set of banks (C0 and C1, and partially C2). This seems to be in line with the above discussion on community detection results, where we highlighted a gradual proximity between clusters over time. Hence, these results suggest that heterogeneity within clusters is driven by similar economic measures after the crisis, although specific differences persist. This is the case for instance of loans, which are not present among top contributors in the US community while they are in the top ranking of both the Mixed and the JP community (as expected according to the above discussion). We also notice that the crisis seems to suggest an increasing importance of income statement measures in terms of contribution to the explained variance within communities.

The breakdown of financial markets affected banks’ results and this justifies the high level of heterogeneity expressed by income statements indicators. This can also be related to the impact of the crisis on financial statement measures and on the different ways banks update their balance sheet structures compared to the recognition of economic results as reported in the income statements items. Similar comparisons can involve also the bottom three measures, but for conciseness we omit this part.