Co-movements in financial fluctuations are anchored to economic fundamentals: A mesoscopic mapping
Kiran Sharma, Balagopal Gopalakrishnan, Anindya S. Chakrabarti, Anirban Chakraborti
CCo-movements in financial fluctuations are anchored to economicfundamentals: A mesoscopic mapping
Kiran Sharma ∗ Balagopal Gopalakrishnan † Anindya S. Chakrabarti ‡ Anirban Chakraborti § February 23, 2018
Abstract
We demonstrate the existence of an empirical linkage between the nominal financial networksand the underlying economic fundamentals across countries. We construct the nominal returncorrelation networks from daily data to encapsulate sector-level dynamics and figure the relativeimportance of the sectors in the nominal network through a measure of centrality and clusteringalgorithms. The eigenvector centrality robustly identifies the backbone of the minimum spanningtree defined on the return networks as well as the primary cluster in the multidimensional scalingmap. We show that the sectors that are relatively large in size, defined with the metrics marketcapitalization, revenue and number of employees, constitute the core of the return networks,whereas the periphery is mostly populated by relatively smaller sectors. Therefore, sector-level nominal return dynamics is anchored to the real size effect, which ultimately shapes theoptimal portfolios for risk management. Our results are reasonably robust across 27 countriesof varying degrees of prosperity and across periods of market turbulence (2008-09) as well asrelative calmness (2015-16).
Widespread existence of bubbles in the financial markets and extreme movements of return se-ries indicate that the relationship between the macroeconomic fundamentals and the asset prices isunstable [1]. The ‘excess volatility puzzle’ in the stock markets refers precisely to this disconnect be-tween the volatility of asset returns and the movements of the underlying fundamentals [2]. Recentresearch emphasizes the roles played by wrong expectation, bounded rationality, herding behavior, ∗ School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India. Email:kiran34 [email protected] † Finance and Accounting area, Indian Institute of Management, Vastrapur, Ahmedabad-380015, India. Email:[email protected] ‡ Economics area, Indian Institute of Management, Vastrapur, Ahmedabad-380015, India. Email:[email protected]. § School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India. Email:[email protected] a r X i v : . [ q -f i n . GN ] J a n tc. as being important causal factors for the observed disconnect [3]. In this paper, we present analternate view that the co-movements in financial assets are anchored to the corresponding macroe-conomic fundamentals. Thus, nominal returns from individual assets might drift far from what canbe predicted using expected cash-flow, while the joint evolution of the co-movement of returns arestill related to aggregate size variables like market capitalization, revenue or number of employees.In the following, we consider the economy to be a multi-layered network [4] defined over nodesat different levels of granularity, each having significantly different properties. At the micro level,firm size distributions show power law decays [5] and bi-exponential growth size distributions [6]. Ascaling relationship between size of the firms and the corresponding volatiltity was also proposed [6].At the macro level, similar features are seen, for example, as has been proposed by [7]. These suggestthat there might be universal features of growth processes of economic entities (see also [8]). Ref.[7] also argued that the dispersion in relative sizes of firms contribute substantially to the aggregatevolatility of an economy, providing a link from the micro level to the macro level. A complementaryview has emerged from the network literature that the dynamics at the intermediate sectoral levelcould play an important role in shaping the aggregate macro-level dynamics [9]. We focus preciselyon the ‘mesoscopic’ level, which identifies with the production process of the economy while beinggranular enough to capture the network structure of co-movements in return fluctuations.There are two modes of connectedness across sectors. At the nominal pricing level, the fluc-tuations of returns from the sectoral indices show the degree of co-movements across sectors. Atthe production level, the flow of goods and services across sectors [10] gives rise to dispersion inrelative sizes of these sectors. Here, we show that there exists a universal mapping between theinter-sectoral return dynamics and relative sizes of the sectors defined with multiple metrics, thushighlighting an empirical link between financial networks and macroscopic variables in a granulareconomy. In particular, we show that the sectors with disproportionate shares of the economy,constitute the core of the corresponding return networks. Therefore, at the ‘mesoscopic’ level, thedispersion in size explains the dispersion in ‘centralities’ of nominal fluctuations of sectors.To study the topology of the return network, we construct return correlation matrices fromsectoral indices for 27 countries, and apply two commonly used clustering algorithms (minimumspanning tree and multi-dimensional scaling) to group sectors based on their co-movements. Theinfluence of the sectors in the whole network can be found by using the eigenvector centrality,which is able to handle both directed as well as weighted graphs [11]. In this paper, we alsopropose a methodology to find a binary characterization of the ‘core-periphery’ structure by usinga modification of the eigenvector centrality. Such classification of the sectors according to whetherthey belong to the core or the periphery, allows one to pin down exactly which sectors are drivingthe market correlations. We show that these sectors identified as core by the centrality measure,also constitute the backbone of the minimum spanning tree (MST) and cluster very closely in multi-dimensional scaling (MDS) maps, thereby confirming the robustness of our method of extractionof the core-periphery structure.To study the connection between the financial network with the underlying production process,2e regress the eigenvector centrality measure on sector sizes defined with three different metrics,viz., market capitalization, revenue and employment, all aggregated at the sectoral level. The resultsacross 27 countries clearly indicate that the dispersion in the economic size explains the variationin the dispersion of sectoral centralities in the correlation matrix. This is the primary finding of ourpaper, as it establishes the the linkage between the economic fundamentals and the fluctuations ofthe return series. Finally, we study the risk diversification of a portfolio comprising sectoral indices,based on the eigenvector centralities. For the sake of simplicity, we use a rudimentary Markowitzportfolio allocation problem and show that the core sectors, i.e., the ones with sufficiently highcentralities, do not usually appear in a minimum variance portfolio. Intuitively, very large sectorscontribute significantly to the movement of the return correlations and they constitute the ‘marketfactor’ of correlations. Hence, for reduction of the volatility of the portfolio, the weights assignedto such sectors contributing to the aggregate risk, are necessarily minimized.We perform statistical tests on a comprehensive list of 27 countries that includes developed aswell as developing countries across five continents, totaling 72 sectors in the financial economies.We base most of our studies on a recent and relatively calm period (2015-16), and then compareand contrast with a volatile period (2008-09), in order to check robustness of our findings acrosstime. We show that the 2015-16 period gives very consistent results (25 out of 27 countries are inexpected direction), whereas 2008-09 period is largely consistent (22 out of 26), although there aresome aberrations as the number of statistically insignificant relationships increases. A consistentpathogenic case is Greece, which has been known to possess weak economic fundamentals alongwith severe crises in the financial markets in the recent times. We have used the sectoral price indices from the Thomson Reuters Eikon database [12], within thetime frames January 2008- December 2009, and October 2014- September 2016. We have analyzedthe data for a total of 72 sectors (see table 1), for the following countries: (1)
AUS - Australia(2)
BEL - Belgium (3)
CAN - Canada (4)
CHE - Switzerland (5)
DEU - Germany (6)
DNK -Denmark (7)
ESP - Spain (8)
FIN - Finland (9)
FRA - France (10)
GBR - United Kingdom (11)
GRC - Greece (12)
HKG - Hong Kong (13)
IDN - Indonesia (14)
IND - India (15)
JPN - Japan (16)
LKA - Sri Lanka (17)
MYS - Malaysia (18)
NLD - the Netherlands (19)
NOR - Norway (20)
PHL -Philippines (21)
PRT - Portugal (22)
QAT - Qatar (23)
SAU - Saudi Arabia (24)
SWE - Sweden(25)
THA - Thailand (26)
USA - United States of America and (27)
ZAF - South Africa, spreadacross the continents of the Americas, Europe, Africa, Asia and Australia. The time series data onthe real variables, such as market capitalization, revenue and the number of employees within eachsector, are also available in the same database although at the company level rather than at thesectoral level. Hence, for our purposes of constructing sector-level macro aggregate variables, wecollected the companies listed within each sector for one particular country, and then aggregated3he relevant company-specific variables across all such companies within the corresponding sector.We find that the USA economy is a good representative of the empirical results and hence, inthe main text, we present the results for the USA economy in details. For the other 26 countries,the detailed results are presented in the Supplementary material. Note that data for Finland (FIN)was not available for the period 2008-09.Table 1: Abbreviations of the 72 sectors analyzed.
Label Sector Label SectorAF
Agro & Food Industry MD Media AG Agriculture MF Manufacturing AM Automobiles MG Mining BC Building & Construction MI Multi Investments BF Banks & Finance
MID
Miscellaneous Industries
BFT
Beverage, Food & Tobacco MM Metals & Mining BK Bank MO Mining & Oil BM Basic Materials
MOT
Motors BR Basic Resources MP Metal Products CC Consumer & Cyclical
MP1
Media & Publishing CD Consumer Discretionary MT Media & Telecomm
CD1
Consumer Durables OC Oil & Coal Products CE Cement OG Oil and Gas CG Consumer Goods PC Property & Construction
CG1
Capital Goods PE Power & Energy IT Information Technology PG Personal Goods CH Chemicals PH PetroChemicals CM Consturction & Materials PL Plantation CN Construction PR Property CP Consumer Products
PSU
Public Sector Undertaking CS Consumer Staples RB Rubber
CSR
Consumer Services RE Real Estate EC Energy & Chemical RT Retail EG Energy RY Realty EM Electrical Machinery SC Semiconductor EU Energy & Utilities ST Steel FB Food & Beverages SU Securities FN Finance TC Telecom GD Gold TD Trade HC Health Care TE Transport & Equipment HG Household Goods TP Transport HT Hotel & Tourism TS Trade & Services ID Industries TT Travel & Tourism IF Infrastructure TX Textiles IP Industrial Production UT Utilities IS Insurance WS Wholesale If r ...N represents the return of N sectors, which is calculated as r i ( τ ) = ln P i ( τ ) − ln P i ( τ − P i ( τ ) is the adjusted closure price of sector i in day τ , then the equal time Pearson correlationcoefficients between sectors i and j is defined as ρ ij = (cid:104) r i r j (cid:105) − (cid:104) r i (cid:105)(cid:104) r j (cid:105) (cid:113) [ (cid:104) r i (cid:105) − (cid:104) r i (cid:105) ][ (cid:104) r j (cid:105) − (cid:104) r j (cid:105) ] , (1)where (cid:104) ... (cid:105) represents the expectation. We use ρ to denote the return correlation matrix.Following a standard procedure in the literature, we construct the distance metrix from thecorrelation coefficients using the following transformation, d ij = (cid:112) − ρ ij ), where 2 ≥ d ij ≥ d ij are “ultrametric” [13, 14, 15]). To analyze the influence of a sector in the whole network, the ranking of the sectors is measuredby the eigenvector centrality. It is not necessary that a sector with high eigenvector centrality ishighly linked but the sector might have few but important links. Given an N × N matrix A , theeigenvector centrality is defined as an N × x , which solves Ax = λ m x , (2)where λ m is the dominant eigenvalue of A .In general, almost all pair-wise correlations are positive. However, in rare cases (e.g., Goldsector in Canada), certain sectors show mild negative correlations with other sectors. We considerthe absolute value of the correlation matrix | ρ | for computing the eigenvector centrality, sinceaccording to the Perron-Frobenius theorem, a real square matrix with positive entries has a uniquelargest real eigenvalue and the corresponding eigenvector has strictly positive components. Finally,we normalize the centrality vector x such that (cid:80) i x i = 1.We consider a further modification of the centrality measure to identify the core-peripherystructure in a binary fashion. Instead of the level values of the correlation coefficients, we consider ρ c , where c is a sufficiently large even number, since this transformation would make the manyweak correlations have asymptotically zero weights while maintaining positive signs. We foundthat c = 2 = 32 is the lowest value, which gives reasonably good estimates of the backbone of theminimum spanning tree. Hence, we present results for c = 32 although, in principle, one can usehigher values as well. To determine the core sectors of a country, we then construct a thresholdvalue θ e , as a fixed percentage of the coefficient of variation (standard deviation/mean) for theeigenvector centralities. If the sectoral centrality is above the threshold value θ e , then the sector isconsidered as core, otherwise not. To analyze the similarity among different sectors in terms of distances ( d ij ), geometrical maps aregenerated using MDS for each of 27 countries, where each sector corresponds to a set of coordinatesin a multi-dimensional space. The concept behind MDS is to represent two similar sectors as twosets of coordinates that are close to each other, and two sectors behaving differently are placed farapart in the space [16]. Given d ij , the aim of MDS is to generate N vectors y , ..., y N ∈ (cid:60) q , suchthat (cid:107) y i − y j (cid:107) ≈ d ij ∀ i, j ∈ N, (3)5here (cid:107) . (cid:107) represents vector norm. To plot the vectors y i in the form of a map, the embeddingdimension q is chosen as 2. Generally, MDS can be obtained through an optimization problem,where ( y , ..., y N ) is the solution of the problem of minimization of a cost function, such asmin y ,...,y N (cid:88) i Given the return correlation ρ , we computed the modified eigenvector centralities to find the coresectors of the countries, and to visualize the co-movements and clusters of sectors based on return6orrelations, we applied two clustering algorithms, viz., MDS and MST. Fig. 1 ( Upper ) shows theMST. Fig. 1 ( Upper Left Inset ) shows that using the eigenvector centrality, we can identify thatout of 10 sectors of the USA, 5 sectors constitute the core of the economy, viz., Finance (FN),Information Technology (IT), Industries (ID), Basic Materials (BM) and Consumer Discretionaries(CD) (see table 1 in Sec. 2.1 for names of the sectors). Fig. 1 ( Lower Right Inset ) shows theMDS. The MST generates a core-periphery structure based on minimizing the distance betweencorrelated sectors, and since it is a hierarchical clustering method, similar sectors can be foundclose to each other (or in one branch). Similarly, closer the sectors are placed on the MDS map,more correlated (similar) they are; farther they are placed on the map, less correlated they are.There are two major observations: First, the MST shows that all core sectors form a chainor the “backbone” in the tree (see Fig. 1 ( Upper )). Similarly, the MDS also reiterates the sameinformation: the core sectors, as identified by the modified eigenvectors centrality, belong to onecluster in the MDS (see Fig. 1 ( Lower Right Inset )); all sectors with negligible centrality are spacedin the periphery – far away from the core – in the MDS. Thus, our method of the modified centralityto extract the core sectors is reinforced by the clustering algorithms, indicating the robustness ofour findings. Second, the MST built from the return correlation matrix, contains information aboutthe actual production structure of the economy. For example, Energy (EG) is most closely relatedto Basic Materials (BM), which in turn is related to Industries (ID), and so on. On the otherend of the MST, Consumer Staples (CS) is connected to Telecom (TC) sector, Utilities (UT) andConsumer Discretionary (CD). Again, this qualitative feature is quite robust, as observed in almostall the countries analyzed.More importantly, we show that the core-periphery structure based on the return correlationmatrix, ρ , has an intriguing relationship with the relative sizes of the sectors. In order to demon-strate and establish the relationship, we study the variations in the eigenvector centralities of thereturn correlation matrix, and exploit the variations in three major variables, viz., aggregate marketcapitalization, aggregate revenue and the aggregate employment. We have described in Sec. 2.1how we constructed the sector-level data by aggregating the company-level data. In Fig. 1 ( Lower ),we plot the linear regressions of scaled eigenvector centrality with the (scaled) market cap, rev-enue and employees for the USA. We have performed similar analyses for the other countries, andtabulated the results in the Supplementary material. Detailed analyses and tables suggest thatgenerally, such a mapping exists for almost all countries.Fig. 2 shows the core-periphery structure for all countries. As can be seen, there are at least twosectors in the core for all countries, but the core-periphery structure often changes with time (whencompared for the periods 2008-09 and 2015-16). Thus, the relative importance of the sectors doeschange with time, and the sectoral dynamics and co-movements may convey deeper insight aboutthe aggregate macro-level dynamics. In Fig. 3, we present similar MSTs (with the core/backbonecolored in red) for 20 other countries, elucidating the core-periphery structures.Fig. 4 shows the results of regressing the sectoral eigenvector centralities on the sector-levelaggregate market capitalization, revenue, and employees, for the years 2008-09 and 2015-16. As7igure 1: (Color online) Results for USA: ( Upper ) Identification of the sectors that are in thecore (red) and periphery (pale green) of the minimum spanning tree, where the nodes representdifferent sectors; sectoral abbreviations given in the table 1. Top Left Inset : Eigenvector centralitiesof ρ . Lower Right Inset : Multidimensional scaling, where the different sectors are plotted ascoordinates in a map. ( Lower ): Linear regressions of scaled eigenvector centrality with scaledmarket capitalization (orange filled circles), scaled revenue (cyan filled squares), and scaled numberof employees (magenta filled up-triangles). The best fits (linear regressions) are plotted as linesfor market capitalization (orange solid), revenue (cyan long dashed) and employees (magenta shortdashed). The variables have been scaled so that they can be plotted and compared in the samefigure. 8igure 2: (Color online) Sectoral dynamics and core-periphery structure: Chart of the 72 sectors(horizontal axis) in the 27 countries (vertical axis), showing the core (red) and periphery (pale-green) structures for the years 2008-09 (diamonds) and 2015-16 (squares), and their changes overtime. The sector abbreviations can be found in the table 1 in Sec. 2.1. Visual inspection revealsthat sectors FN and ID are frequently occurring in the core/backbone, across almost all countries.Figure 3: (Color online) Minimum spanning trees for 20 countries out of the 27 countries (shownin peach) that are being studied across the globe. The core sectors are colored red (darker shade),while the sectors in the periphery are in pale green (lighter shade). The sector abbreviations canbe found in the table 1 in Sec. 2.1. 9igure 4: (Color online) Comparison of the regression results (estimates of β using Eq. 5) toexplain variation in the sectoral eigenvector centralities ( y ) by the variation in sector-level macrodata ( x ). Upper : market capitalization, Middle : Revenue, Lower : Employees, for the years 2008-09and 2015-16. Detailed estimation results are given in the tables in Supplementary material.10e see in Fig. 4 ( Upper ), for 2015-16, the coefficient β for market capitalization 25 out of 27countries are positive, and 11 out of those 27 countries have statistically significant relationships.The two countries which have very mildly negative relationships, are Greece (significant) and SouthAfrica (insignificant). For 2008-09, the coefficient β for 22 out of 26 countries are positive, and 3out of those 26 countries have statistically significant relationships. Also, the countries Belgium,Switzerland, South Africa and Sri Lanka have negative relationships. In Fig. 4 ( Middle ), for2015-16, the coefficient β for revenue, 23 out of 26 countries are positive, and 9 out of those 26countries have statistically significant relationships. The three countries which have negative (andstatistically insignificant) relationships, are Greece, Qatar and United Kingdom. For 2008-09, thecoefficient β for 22 out of 26 countries are positive, and 9 out of those 24 countries have statisticallysignificant relationships. Finally, in Fig. 4 ( Lower ), for 2015-16, the coefficient β for employees,23 out of 24 countries are positive, and 9 out of those 24 countries have statistically significantrelationships. The only country which has negative (and statistically significant) relationship, isGreece. For 2008-09, the coefficient β for 21 out of 24 countries are positive, and 5 out of those24 countries have statistically significant relationships. For detailed statistical values of regressionsperformed on the sector-level aggregate data, please refer to the text in Supplementary material.There is already an existing finding that centralities in input-output networks are closely relatedto the relative sizes of the corresponding nodes (see Ref. [9]). However, here we further show thatthe centralities based on nominal return fluctuations are related to relative size, i.e., the returnnetwork is also very closely related to the underlying size effects. An immediate corollary is thatthe core sectors of the return correlation network are also economically big, and hence, the marketeffect of the correlations are driven by the sectors, which have very high market capitalization (orother indicators like revenue and employment). We studied the dynamics of a total of 72 sectors across 27 countries, covering both developed anddeveloping economies. Using methods of modified eigenvector centrality, MDS and MST, we canfind the core-periphery structure of all the economies. Fig. 2 showed the core-periphery structureof all the countries, and indicated that most of the sectors do not change much in the core-peripherystructure during the periods of market turbulence, as well as relative calmness. There are of course,some sectors who were core in a volatile period, became the peripheral ones in the calm period, andvice versa. Fig. 5 shows the comparison among the modified eigenvector centralities for the years2008-09 and 2015-16, for the four countries: United Kingdom, India, Japan, and United States ofAmerica, as examples. The relative importance of each sector can be compared for the volatile andcalm period. Certainly the sectoral dynamics are interesting to note in the different countries, andmay help in taking important policy decisions in economic growth and development.11igure 5: (Color online) Sectoral dynamics and robustness: The comparison of the eigenvectorcentralities for the years 2008-09 (light orange) and 2015-16 (dark green) for four countries. UpperLeft : United Kingdom (GBR), Upper Right : India (IND), Lower Left : Japan (JPN), Lower Right :United States of America (USA). 12igure 6: (Color online) Upper Left : Relationship between the bit-strings of sectoral centralities(EVC) and their corresponding inclusion in the portfolio (PWT) for the different sectors of theUSA. The threshold values θ e and θ p (as 2% of the coefficient of variations of EVC and PWT,respectively) would determine, whether the sector is central or not (EVC is 0 or 1), or whether thecorresponding sector would appear in the optimal portfolio or not (PWT is 0 or 1). The labels forthe different sectors are given in table 1. Upper Right : The Hamming distance D computed fromthe bit-strings EVC and PWT, against the different values of n (percentage) of the coefficient ofvariations of EVC and PWT, respectively, which determine the threshold values θ e and θ p . Lower :The Hamming distance D computed from the bit-strings EVC and PWT, against the differentvalues of n , for the different countries, plotted as a 3D-bar.13 .3 Constructing the minimum risk portfolio In this part, we study how the sectoral centralities influence the aggregate risk of a portfolio. For thepurpose of simple exposition, we compute the benchmark model of Markowitz portfolio selectionwith the sectoral return data. Assuming rational investors with risk-aversion, the investors willminimize w (cid:48) Σ w − Θ R (cid:48) w, (6)with respect to the weight vector w , where Σ is the covariance matrix of the sectoral returns, R (cid:48) isthe expected return vector and Θ is a parameter which denotes the risk appetite of the investor.We set a short-selling constraint ( w i ≥ 0) and Θ equals to zero for finding the minimal risk portfoliowhich will entail a convex combination of sectoral returns (the other extreme would lead to a cornersolution).Our main observation in this part is that the optimal weight vector, w ∗ , is negatively related tothe eigenvector centralities, i.e., if a sector is very “central” in the return correlation network ρ , thenit is less likely to appear in the optimal portfolio with the minimum risk (and no short selling). Wedemonstrate this in a naive way: we construct threshold values θ e and θ p , as a fixed percentage (say n % of the coefficient of variation (standard deviation/mean) for both the eigenvector centralities,as well as the minimum risk portfolio weights, respectively. These threshold values θ e and θ p would determine, respectively, whether the sector is central or not (i.e., 0 or 1), or whether thecorresponding sector would appear in your optimal portfolio or not (i.e., 0 or 1). So, for the vectorof sectors, we would have two strings of 0’s or 1’s corresponding to the centrality vector (EVC)and the optimal weight vector (PWT), respectively. The Hamming distance D between any twobit-strings of equal length, is the number of positions at which the corresponding bits are different.So, the Hamming distance between the two strings EVC and PWT would tell how significant theobservation is for a particular country; higher the value of D , better the conformity. The sectorwhich is central (i.e., 1) would not appear in your portfolio (i.e., 0), and so for any country theideal finding would be that D is unity. The choice of the threshold(s), θ e and θ p , equaled by thepercentage(s) ( n ) of the coefficient of variation(s) in the vectors EVC and PWT, would be importantfor determining the Hamming distance D between the strings for any country (see Fig. 6 ( Upper ))for the USA. We can optimize the value of D against the percentage n , for all the countries, asshown in Fig. 6 ( Lower ). We found that n = 2, i.e. 2% was an optimal threshold value θ e for mostcountries, which we then used to distinguish between the core and periphery sectors. Combinedwith the finding that core sectors in the return correlation network are bigger in size, the abovefinding implies that peripheral sectors contribute to lower risk of a diversified portfolio. In this paper, we have analyzed financial and economic data for 27 countries at the sector level.We show that the variation in the centrality in the return correlation matrix across sectoral indices,14an be explained by the size dispersion across the sectors. This finding indicates that financialfluctuations are mapped to the macroeconomic fundamentals. From the perspective of portfoliooptimization, we show that the very big sectors that are also highly central in the return network,rarely appear in a risk-minimizing portfolio. Essentially, such sectors constitute the main driversof the market-wide fluctuations. In summary, our study sheds light on: (a) the mapping betweenthe joint evolution of the financial variables and the underlying macroeconomic fundamentals,and (b) extracting information about the individual influences on aggregate risk from sector-level,disaggregated time-series data.Methodologically, we provide a way to extract the core-periphery structure of the correlationnetworks in a binary fashion. As a result, the generic rule of thumb we come up with is that size is animportant causal factor even behind financial fluctuations. We attribute significant importance tothis finding as it provides a way to exactly pin down the sectors, which are main drivers of financialfluctuations through the size effect. The way return series are constructed, the size differential ofthe prices across the sectoral indices, should disappear due to the normalization. The fact that theco-movements are still tied to the fundamentals is therefore intriguing. As our results suggest, thefinding is considerably robust across countries. An illuminating exception is Greece showing anexact opposite relationship, which has been known to possess weak economic fundamentals alongwith severe crises in the financial markets in the recent times. In both periods, economically large(either in terms of market capitalization or revenue or employment) sectors in Greece are at theperiphery of the return correlation networks, which constitute an inverted relationship between theeconomy and the financial networks.We have also shown that the relative importance of the sectors may change significantly overtime although some sectors like finance and industry are at the core of a significant fraction of coun-tries. In general, our results indicate that the core may not be very stable. Possible reasons could besectoral competition in terms of productivity and innovation and the resultant evolution [17]. Theemergence of the core-periphery structure changes the complexity of the financial markets and hasimplications of the pricing of risk in the economy [18]. Our work indicates the potentials of usinga binary characterization to reduce the computational burden by introducing proper identificationof the country-specific core sectors, as opposed to considering the full network.To conclude, we note that the recent applications of network theory in the macroeconomicsliterature has focused mostly on studying the dynamics of real economic quantities [19], whereasthe relevant finance literature has focused on the dynamics of nominal quantities [20]. The presentwork may provide a linkage between the two. In other words, we make the point that the oft-quotedquips ‘too-big-to-fail’ and ‘too-interconnected-to-fail’ may not be as different as is currently thoughtof [21]. 15 cknowledgment ASC acknowledges the support by the institute grant (R&P), IIM Ahmedabad. BG acknowledgesFPM fellowship provided by IIM Ahmedabad. AC and KS acknowledge the support by grantnumber BT/BI/03/004/2003(C) of Govt. of India, Ministry of Science and Technology, Departmentof Biotechnology, Bioinformatics division, and University of Potential Excellence-II grant (ProjectID-47) of the Jawaharlal Nehru University, New Delhi. KS acknowledges the University GrantsCommission (Ministry of Human Research Development, Govt. of India) for her senior researchfellowship. References [1] R. Shiller, “Do stock prices move too much to be justified by subsequent changes in dividends?,” American Economic Review , pp. 421–436, 1981.[2] X. Gabaix, “Variable rare disasters: an exactly solved framework for ten puzzles in macro-finance,” The Quarterly Journal of Economics , vol. 127, pp. 645–700, 2012.[3] D. Sornette, Why stock markets crash: critical events in complex financial systems . PrincetonUniveristy Press, 2004.[4] M. Newman, Networks: an introduction . 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Stiglitz, “The price of complexityin financial networks,” Proceedings of the National Academy of Sciences , vol. 113, no. 36,pp. 10031–10036, 2016.[19] “Crises and complexity,” Special issue in Journal of Economic Dynamics and Control , vol. 50,pp. 1–202, 2015.[20] R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: correlations and complexityin finance . Cambridge University Press, 2007.[21] D. Acemoglu, A. Ozdaglar, and A. Tahbaz-Salehi, “Systemic risk and stability in financialnetworks,” American Economic Review , vol. 105 (2), pp. 564–608, 2015.17 upplementary material All detailed regression tables are provided below.18able 2: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled market capitalization (2015-16). *** : significant at 1%, **: at 5%, *: at 10%. Countries β Tstat Pvalue β Tstat Pvalue Rsquare Australia 0.0000(0.3481) 0.0000 0.9999 0.2131(0.3692) 0.5773 0.5817 0.0454Belgium 0.0000(0.3695) 0.0000 0.9999 0.2517(0.3951) 0.6371 0.5475 0.0633Canada 0.0000(0.3018) 0.0000 0.9999 0.0758(0.3153) 0.2404 0.8148 0.0057Denmark 0.0000(0.2703) 0.0000 0.9999 0.5918(0.2849) 2.0767 0.0714* 0.3502Finland 0.0000(0.2246) 0.0000 0.9999 0.7425(0.2368) 3.1353 0.0139** 0.5513France 0.0000(0.2523) 0.0000 0.9999 0.7003(0.2394) 2.7751 0.0241** 0.4904Germany 0.0000(0.2544) 0.0000 0.9999 0.6516(0.2681) 2.4299 0.0412** 0.4246Greece 0.0000(0.1617) 0.0000 0.9999 -0.8759(0.1705) -5.1368 0.0008*** 0.7673Hong Kong 0.0000(0.3042) 0.0000 0.9999 0.4208(0.3207) 1.3123 0.2257 0.1771India 0.0000(0.3329) 0.0000 0.9999 0.1219(0.3509) 0.3474 0.7373 0.0149Indonesia 0.0000(0.232) 0.0000 0.9999 0.7221(0.2445) 2.9524 0.0183** 0.5214Japan 0.0000(0.3239) 0.0000 0.9999 0.2588(0.3415) 0.7579 0.4702 0.0670Malaysia 0.0000(0.2719) 0.0000 0.9999 0.5853(0.2866) 2.0421 0.0754* 0.3426Netherlands 0.0000(0.3292) 0.0000 0.9999 0.3821(0.3492) 1.0941 0.3100 0.1460Norway 0.0000(0.2992) 0.0000 0.9999 0.4516(0.3154) 1.4316 0.1901 0.2039Philippines 0.0000(0.1552) 0.0000 0.9999 0.9537(0.1736) 5.4929 0.0118** 0.9095Portugal 0.0000(0.3133) 0.0000 0.9999 0.5715(0.3349) 1.7061 0.1388 0.326619atar 0.0000(0.3742) 0.0000 0.9999 0.5723(0.41) 1.3959 0.2352 0.3275Saudi Arabia 0.0000(0.2669) 0.0000 0.9999 0.2807(0.277) 1.0133 0.3309 0.0788South Africa 0.0000(0.3739) 0.0000 0.9999 -0.2033(0.3997) -0.5086 0.6291 0.0413Spain 0.0000(0.2684) 0.0000 0.9999 0.1531(0.5705) 0.8057 0.1577 0.0234Sri Lanka 0.0000(0.267) 0.0000 0.9999 0.5423(0.28) 1.9363 0.0848* 0.2940Sweden 0.0000(0.2852) 0.0000 0.9999 0.5995(0.3025) 1.9818 0.0879* 0.3594Switzerland 0.0000(0.2831) 0.0000 0.9999 0.4543(0.2969) 1.5302 0.1603 0.2064Thailand 0.0000(0.3152) 0.0000 0.9999 0.5643(0.337) 1.6743 0.1450 0.3184UK 0.0000(0.3132) 0.0000 0.9999 0.3575(0.3301) 1.0830 0.3103 0.1278USA 0.0000(0.2728) 0.0000 0.9999 0.5817(0.2875) 2.0228 0.0777* 0.338420able 3: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled revenue (2015-16). *** : significant at 1%, **: at 5%, *: at 10%. Countries β Tstat Pvalue β Tstat Pvalue Rsquare Australia 0.0000(0.3144) 0.0000 0.9999 0.4704(0.3335) 1.4106 0.2012 0.2213Belgium 0.0000(0.2247) 0.0000 0.9999 0.8084(0.2402) 3.3644 0.0151** 0.6535Canada 0.0000(0.2916) 0.0000 0.9999 0.2689(0.3045) 0.8830 0.3979 0.0723Denmark 0.0000(0.2837) 0.0000 0.9999 0.5333(0.299) 1.7834 0.1123 0.2844Finland 0.0000(0.2988) 0.0000 0.9999 0.4542(0.3149) 1.4422 0.1872 0.2063France 0.0000(0.236) 0.0000 0.9999 0.7104(0.2487) 2.8557 0.0212** 0.5048Germany 0.0000(0.3203) 0.0000 0.9999 0.2964(0.3376) 0.8778 0.4056 0.0878Greece 0.0000(0.3069) 0.0000 0.9999 -0.4029(0.3235) -1.2453 0.2482 0.1623Hong Kong 0.0000(0.2877) 0.0000 0.9999 0.5140(0.3032) 1.6948 0.1285 0.2642India 0.0000(0.3158) 0.0000 0.9999 0.3368(0.3329) 1.0117 0.3413 0.1134Indonesia 0.0000(0.233) 0.0000 0.9999 0.7193(0.2456) 2.9286 0.0190** 0.5173Japan 0.0000(0.3137) 0.0000 0.9999 0.3531(0.3307) 1.0678 0.3167 0.1247Malaysia 0.0000(0.2746) 0.0000 0.9999 0.5739(0.2895) 1.9824 0.0827* 0.3294Netherlands 0.0000(0.3411) 0.0000 0.9999 0.2886(0.3618) 0.7976 0.4512 0.0833Norway 0.0000(0.222) 0.0000 0.9999 0.7495(0.234) 3.2031 0.0125** 0.5618Philippines 0.0000(0.4578) 0.0000 0.9999 0.4625(0.5118) 0.9035 0.4328 0.2139Portugal 0.0000(0.2655) 0.0000 0.9999 0.7187(0.2838) 2.5320 0.0445** 0.516521atar 0.0000(0.4536) 0.0000 0.9999 -0.1102(0.4969) -0.2219 0.8352 0.0121Saudi Arabia --South Africa 0.0000(0.3129) 0.0000 0.9999 0.5729(0.3346) 1.7121 0.1377 0.3282Spain 0.0000(0.5099) 0.0000 0.9999 0.1577(0.5701) 0.2767 0.7999 0.0248Sri Lanka 0.0000(0.243) 0.0000 0.9999 0.6442(0.2549) 2.5267 0.0324** 0.4150Sweden 0.0000(0.2945) 0.0000 0.9999 0.5626(0.3124) 1.8006 0.1147 0.3165Switzerland 0.0000(0.2646) 0.0000 0.9999 0.5537(0.2775) 1.9952 0.0771* 0.3066Thailand 0.0000(0.3558) 0.0000 0.9999 0.3628(0.3804) 0.9538 0.3770 0.1316UK 0.0000(0.3346) 0.0000 0.9999 -0.0688(0.3527) -0.1952 0.8500 0.0047USA 0.0000(0.2667) 0.0000 0.9999 0.6063(0.2811) 2.1566 0.0631* 0.367622able 4: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled number of employees (2015-16). *** : significant at 1%, **: at 5%, *: at 10%. Countries β Tstat Pvalue β Tstat Pvalue Rsquare Australia 0.0000(0.3038) 0.0000 0.9999 0.5225(0.3222) 1.6213 0.1489 0.2730Belgium 0.0000(0.2631) 0.0000 0.9999 0.7247(0.2812) 2.5766 0.0419** 0.5252Canada 0.0000(0.2919) 0.0000 0.9999 0.2652(0.3049) 0.8698 0.4048 0.0703Denmark 0.0000(0.3164) 0.0000 0.9999 0.3316(0.3335) 0.9942 0.3492 0.1099Finland 0.0000(0.2762) 0.0000 0.9999 0.5671(0.2912) 1.9474 0.0873* 0.3216France 0.0000(0.1525) 0.0000 0.9999 0.8905(0.1608) 5.5374 0.0005*** 0.7930Germany 0.0000(0.2836) 0.0000 0.9999 0.5336(0.299) 1.7845 0.1121 0.2847Greece 0.0000(0.1481) 0.0000 0.9999 -0.8971(0.1561) -5.7451 0.0004*** 0.8049Hong Kong 0.0000(0.2471) 0.0000 0.9999 0.6759(0.2605) 2.5943 0.0318** 0.4569India 0.0000(0.3354) 0.0000 0.9999 0.0189(0.3535) 0.0534 0.9588 0.0003Indonesia 0.0000(0.2816) 0.0000 0.9999 0.5428(0.2969) 1.8283 0.1049 0.2947Japan 0.0000(0.292) 0.0000 0.9999 0.4919(0.3078) 1.5982 0.1486 0.2420Malaysia 0.0000(0.2975) 0.0000 0.9999 0.4615(0.3136) 1.4717 0.1792 0.2130Netherlands 0.0000(0.2279) 0.0000 0.9999 0.7686(0.2417) 3.1794 0.0155 0.5908Norway 0.0000(0.2736) 0.0000 0.9999 0.5784(0.2884) 2.0054 0.0798* 0.3345Philippines 0.0000(0.4688) 0.0000 0.9999 0.4191(0.5241) 0.7996 0.4823 0.1756Portugal 0.0000(0.3207) 0.0000 0.9999 0.5425(0.3429) 1.5820 0.1647 0.294323atar --Saudi Arabia --South Africa 0.0000(0.3768) 0.0000 0.9999 0.1614(0.4028) 0.4008 0.7024 0.0260Spain 0.0000(0.483) 0.0000 0.9999 0.3537(0.5400) 0.6550 0.5591 0.1251Sri Lanka 0.0000(0.1924) 0.0000 0.9999 0.7958(0.2018) 3.9435 0.0033*** 0.6334Sweden 0.0000(0.315) 0.0000 0.9999 0.4673(0.3341) 1.3986 0.2046 0.2184Switzerland 0.0000(0.2719) 0.0000 0.9999 0.5177(0.2851) 1.8154 0.1028 0.2680Thailand --UK 0.0000(0.255) 0.0000 0.9999 0.6495(0.2688) 2.4165 0.0420** 0.4219USA 0.0000(0.2529) 0.0000 0.9999 0.6566(0.2666) 2.4628 0.0391** 0.431224able 5: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled market capitalization (2008-09). *** : significant at 1%, **: at 5%, *: at 10%. Countries β Tstat Pvalue β Tstat Pvalue Rsquare Australia 0.0000(0.3507) 0.0000 0.9999 0.1770(0.3719) 0.4759 0.6485 0.0313Belgium 0.0000(0.3791) 0.0000 0.9999 -0.1193(0.4053) -0.2943 0.7783 0.0142Canada 0.0000(0.3027) 0.0000 0.9999 0.0000(0.3162) 0.0001 0.9998 0.0000Denmark 0.0000(0.3058) 0.0000 0.9999 0.4103(0.3224) 1.2727 0.2388 0.1683Finland --France 0.0000(0.3074) 0.0000 0.9999 0.3995(0.3241) 1.2329 0.2526 0.1596Germany 0.0000(0.2716) 0.0000 0.9999 0.5865(0.2863) 2.0484 0.0746* 0.3440Greece 0.0000(0.3327) 0.0000 0.9999 0.1258(0.3507) 0.3587 0.7290 0.0158Hong Kong 0.0000(0.3173) 0.0000 0.9999 0.3239(0.3344) 0.9684 0.3611 0.1049India 0.0000(0.2756) 0.0000 0.9999 0.5696(0.2905) 1.9605 0.0855* 0.3245Indonesia 0.0000(0.2925) 0.0000 0.9999 0.4891(0.3083) 1.5861 0.1513 0.2392Japan 0.0000(0.334) 0.0000 0.9999 0.0915(0.352) 0.2600 0.8013 0.0083Malaysia 0.0000(0.273) 0.0000 0.9999 0.5809(0.2877) 2.0188 0.0782* 0.3375Netherlands 0.0000(0.3165) 0.0000 0.9999 0.4594(0.3357) 1.3686 0.2134 0.2110Norway 0.0000(0.3016) 0.0000 0.9999 0.4369(0.318) 1.3739 0.2067 0.1909Philippines 0.0000(0.4176) 0.0000 0.9999 0.5880(0.4669) 1.2592 0.2970 0.3457Portugal 0.0000(0.3116) 0.0000 0.9999 0.5779(0.3331) 1.7346 0.1334 0.334025atar 0.0000(0.3914) 0.0000 0.9999 0.5140(0.4288) 1.1987 0.2967 0.2642Saudi Arabia 0.0000(0.2714) 0.0000 0.9999 0.2179(0.2817) 0.7734 0.4542 0.0474South Africa 0.0000(0.3802) 0.0000 0.9999 -0.0932(0.4064) -0.2293 0.8262 0.0086Spain 0.0000(0.4885) 0.0000 0.9999 0.3238(0.5462) 0.5928 0.5950 0.1048Sri Lanka 0.0000(0.301) 0.0000 0.9999 -0.2309(0.3243) -0.7120 0.4945 0.0533Sweden 0.0000(0.3435) 0.0000 0.9999 0.3643(0.2658) 0.7297 0.4892 0.0706Switzerland 0.0000(0.3173) 0.0000 0.9999 -0.0532(0.3328) -0.1599 0.8764 0.0028Thailand 0.0000(0.3677) 0.0000 0.9999 0.2691(0.3931) 0.6845 0.5191 0.0724UK 0.0000(0.3346) 0.0000 0.9999 0.0691(0.3527) 0.1959 0.8495 0.0047USA 0.0000(0.3315) 0.0000 0.9999 0.1508(0.3495) 0.4315 0.6774 0.022726able 6: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled revenue (2008-09). *** : significant at 1%, **: at 5%, *: at 10%. Countries β Tstat Pvalue β Tstat Pvalue Rsquare Australia 0.0000(0.335) 0.0000 0.9999 0.3408(0.3553) 0.9592 0.3694 0.1161Belgium 0.0000(0.3676) 0.0000 0.9999 -0.2708(0.3929) -0.6891 0.5164 0.0733Canada 0.0000(0.2869) 0.0000 0.9999 0.3194(0.2996) 1.0658 0.3115 0.1020Denmark 0.0000(0.2908) 0.0000 0.9999 0.4982(0.3065) 1.6254 0.1427 0.2482Finland --France 0.0000(0.2457) 0.0000 0.9999 0.6805(0.259) 2.6273 0.0303** 0.4631Germany 0.0000(0.2792) 0.0000 0.9999 0.5538(0.2943) 1.8814 0.0966* 0.3067Greece 0.0000(0.3071) 0.0000 0.9999 -0.4015(0.3237) -1.2401 0.2500 0.1612Hong Kong 0.0000(0.2956) 0.0000 0.9999 0.4719(0.3116) 1.5142 0.1684 0.2227India 0.0000(0.3022) 0.0000 0.9999 0.4333(0.3186) 1.3601 0.2108 0.1878Indonesia 0.0000(0.2747) 0.0000 0.9999 0.5734(0.2896) 1.9798 0.0830* 0.3288Japan 0.0000(0.3226) 0.0000 0.9999 0.2727(0.3401) 0.8018 0.4458 0.0743Malaysia 0.0000(0.2758) 0.0000 0.9999 0.5687(0.2908) 1.9555 0.0862* 0.3234Netherlands 0.0000(0.3406) 0.0000 0.9999 0.2934(0.3613) 0.8122 0.4433 0.0861Norway 0.0000(0.2482) 0.0000 0.9999 0.6723(0.2617) 2.5688 0.0331** 0.4520Philippines 0.0000(0.4791) 0.0000 0.9999 0.3728(0.5357) 0.6959 0.5365 0.1389Portugal 0.0000(0.2975) 0.0000 0.9999 0.6268(0.318) 1.9705 0.0962* 0.392827atar 0.0000(0.3915) 0.0000 0.9999 -0.5138(0.4289) -1.1979 0.2970 0.2640Saudi Arabia 0.0000(0.274) 0.0000 0.9999 0.1724(0.2843) 0.6064 0.5555 0.0297South Africa 0.0000(0.3191) 0.0000 0.9999 0.5492(0.3411) 1.6100 0.1585 0.3017Spain 0.0000(0.367) 0.0000 0.9999 0.7033(0.4103) 1.7139 0.1850 0.4947Sri Lanka 0.0000(0.3167) 0.0000 0.9999 -0.0857(0.3321) -0.2579 0.8022 0.0073Sweden 0.0000(0.3071) 0.0000 0.9999 0.5071(0.3257) 1.5566 0.1634 0.2571Switzerland 0.0000(0.3153) 0.0000 0.9999 0.1245(0.3307) 0.3765 0.7152 0.0155Thailand 0.0000(0.3748) 0.0000 0.9999 0.1908(0.4007) 0.4761 0.6507 0.0364UK 0.0000(0.3293) 0.0000 0.9999 0.1884(0.3472) 0.5427 0.6020 0.0355USA 0.0000(0.3319) 0.0000 0.9999 0.1431(0.3499) 0.4091 0.6931 0.020528able 7: Regression table: Dependent variable is the scaled centrality and the independent variableis the scaled number of employees (2008-09). *** : significant at 1%, **: at 5%, *: at 10%.