modeling overlapped mutual funds’ portfolios: a bipartite network...

Research ArticleModeling Overlapped Mutual Fundsrsquo PortfoliosA Bipartite Network Approach

Jaime F Lavin 1 Mauricio A Valle2 and Nicolaacutes S Magner2

1Escuela de Negocios Universidad Adolfo Ibanez Diagonal Las Torres 2640 Penalolen Santiago Postal Code 7941169 Chile2Facultad de Economia y Negocios Universidad Finis Terrae Pedro de Valdivia 1509 Providencia SantiagoPostal Code 7501015 Chile

Correspondence should be addressed to Jaime F Lavin jaimelavinuaicl

Received 12 February 2019 Accepted 3 June 2019 Published 1 July 2019

Guest Editor Benjamin M Tabak

Copyright copy 2019 Jaime F Lavin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper studies the topology of the Chilean mutual fund industry using networks methods With the physical positions ofthe local equity portfolios managed during 200301-20174 we analyze their connectivity structure in both the mutual fundsrsquobipartite network and their one-mode projection We estimate network measures to examine the potential effects on the topologyarising from changes in the industrial environment and changes in the mutual fundsrsquo investment strategies in their overlappedportfolios Our main results show that changes in the bipartite network and its one-mode projection are correlated with variablesrelated to fundsrsquo investment strategies and with industry-specific variables In consequence these elements are a new potential ofdisturbance in the financial network conformed by stocks andmutual funds We contribute to the existing literature improving theunderstanding of the aggregate behavior of a financial sector which despite its economic importance has attracted little attentionfrom a systemic risk perspective

1 Introduction

This paper studies the topology of networks in the mutualfund industry by analyzing the composition of their invest-ment portfolios Application of a network analysis makesit possible to identify and analyze the interrelation existingbetween mutual funds that share investments in similarfinancial assets using bipartite networks and its one-modeprojection This phenomenon called overlapping is a finan-cial network of assets and funds Understanding the topologyof this network is critical because the assets that each fundallocates affect its financial performance as the financialliterature indicates and impact the structure of the industryConsequently it influences the stability and propagation offinancial contagions such as firesales of assets and runs onmutual funds As a result this affects risk and industrydevelopment

During the subprime crisis investors favored liquid assets(liquidity hoarding) and those free of risk (flight to quality)at the cost of stocks and bonds significantly affecting theprice of financial assets [1] stocks and bonds suffered drops

in their prices that negatively affected the performance ofstockbrokers and fund managers such as mutual fundscommercial banks pension funds and hedge funds As aresult this behavior is recognized as a contagion for the restof the financial system [2 3]

The losses inflicted by the crisis highlighted for pol-icymakers regulators and academics the importance ofassessing the systemic risk and understanding the propaga-tion mechanisms of financial shocks The crisis made thecomplexity instability and fragility of the existing networkstructures in the capital markets a tangible reality [4 5] As aresult the financial system particularly the banking systemgarnered the attention of the networks literature to studyits structure and how changes to it affect the probability ofoccurrence and spread of financial contagions

The financial literature identifies two channels of financialcrisis contagion The first related to direct exposure betweentwo agents is produced by bilateral asset transactions orcontracts such as credit operations and credit default swaps[2]The second called portfolio overlaps is linked to indirectexposure generated between two or more investors such as

HindawiComplexityVolume 2019 Article ID 1565698 20 pageshttpsdoiorg10115520191565698

2 Complexity

pension funds hedge funds and mutual funds that haveexposures in the same financial asset [6] However despitethe size of these investors in the financial system the literaturepays little attention to the second channel1The present studyfocuses on studying the complexity of the phenomenon ofportfolio overlaps through network analysis

The study of the phenomenon of systemic risk throughoverlapping portfolios is novel [4 7] however there is alack of studies applied to the mutual fund industry despiteits importance and size2 Delpini and others [8] analyze thebipartite network of US mutual funds during the financialcrisis studying how the systemic fragility of the systemdepends on the overlap between portfoliosTheir results indi-cate that diversification and similarity in financial investmentstrategies are factors that increase distress propagation andsystemic fragility The authors confirm that diversificationincreases systemic risk when the funds use the same invest-ment strategies and diversify using similar assets

The relation between diversification and systemic risk isimportant due to the effect of both factors on investmentportfolio management Markowitz [9] argues that diversi-fication achieved by increasing the number of assets in aportfolio reduces the unsystematic riskThis definition how-ever does not consider the contribution of the overlappingof assets to systemic risk and the propagation of shocks atthe aggregate level In this sense the network methodologycan complement the study of financial risk analyzing thecomposition and diversification of portfolios from the samegroup of investors as well as of the degree of similarity ofthe assets that make up their portfolios and of the investmentstrategies used

The above reveals the tension existing within portfoliomanagement and the influence of diversification as a toolfor risk management Although diversification reduces thesystematic risk of the assets when this occurs in the presenceof high similarity in the portfolios as in the mutual fundindustry for example diversification becomes a generatorof systemic risk This occurs because by holding diversifiedportfolios but comprised of the same assets the funds returnto the system as a more vulnerable whole because theinterconnections and channels of contagion are increased[3 10]

An understanding of the risks generated by a portfoliomanager that seeks to minimize them through diversificationincreases the interdependencies on the portfolio overlapnetworks of mutual and pension fund managers This phe-nomenon acquires significance as an amplifier and generatorof financial shocks even more so in small economies withlittle diversity of assets to invest as is the case in emergingcountries

Nevertheless and contrary to expectations there is stilllittle attention paid in the literature to the study of financialrisks in this intermediary segment [8] and to our bestof knowledge even nonexistent in a context of emergingmarkets The segment of institutional investors includesmutual funds hedge funds and pension funds it is one ofthe primary investment vehicles globally They reached a sizeof USD 4617 trillion equivalent to 61 of global GDP in thefirst quarter of 2017Mutual funds reached a size of USD 4277

trillion the most important group in this industry 65 of themanaged assets correspond to stocks and debt instrumentswith 43 of total participation being equity funds Thesenumbers underscore the relevance of these investors andthe need to deepen understanding of the effects of theseintermediariesrsquo investment strategies on financial risk in thisindustry

The use of networks has made it possible to studymainly the structures of control chains in financial systemssystemic risk the evolution of commerce between nationsand interbank transactions between banks [11] These papersconsider similarity-based networks in which the weights of anetwork represent a measurement of similarity (or distance)between assets this measurement is a linear correlationbetween the returns on the assets The correlation thenbecomes a distance associated with a Euclidian distancewhich is why hierarchical clustering methods can be appliedto understand the industry-specific structure and clustersAlso using the network approach it is possible to detectthe relations between different market agents to discoverthe underlying control chains [12 13] Finally in the studyof transactions between two agents the links represent thetransactions whereas the nodes represent the agents in thefinancial market For example Boss and others [14] studythe formation of community structures and other topologicalelements of the networks that show free scale and small worldproperties However there is a gap in the literature respectto the relation between topological elements of the financialnetwork the variables of asset management and industryvariables For example in the case of mutual funds how doesthe path length of the network varywhen portfoliosmanagersbegin increasing the sale of assets to buy others or whenthey decide to increase or reduce the diversification of theirportfolios

Given the logical evolution of the literature on financialnetworks analysis and to contribute to a deeper understand-ing of the portfolio overlaps phenomenon in a mutual fundindustry context this study aims to examine how financialmanagement variables in conjunction with specific variablesfrom the mutual fund industry mold and shape financialnetworks between funds and financial assets

Accordingly in this workwe study the following hypothe-ses

(1) the topology of the mutual funds network changesdue to variations in the investment strategies selected by theindustry actors

(2) the topology of themutual funds network changes dueto variations in industry-specific variables

Our research contributes to the literature by improvingthe understanding of the phenomenon of overlapping fromthree perspectives First we analyze the topology of themutual funds network using a bipartite network method(similar to Delpini and others [8]) and we complement itwith an analysis of its bipartite one-mode network projection(for a summary see Zhou and others [15] and Straka et al[5]) Second we study the effect of economic and financialshocks that affect the equity market as a whole on thetopological properties of the funds network And third weconsider studying the impact of changes in the mutual fundrsquos

Complexity 3

investment strategies3 on the basic characteristics of thetopology of the network of funds from an emerging marketlike Chile

Additionally we add more depth to the analysis byincluding network parameters such as diversity modularitypath length and assortativity This is important becausethe financial phenomenon that involves managing mutualfund assets consists in studying the effect of changes onindustry variables understanding how these intermediariesmanage their investments in the event of fluctuations inthe financial context the degree to which they use similarinvestment strategies and how much they increase or reducethe diversification of their portfolios

We study the mutual fund industry because it is themost important financial intermediary in terms of volumeof managed assets invest in the same class of assets andmarkets and there is high similarity in their investmentstrategies and composition factors that increase the systemicrisk of the phenomenon of portfolio overlaps Finally ourstudy makes a methodological variation by using bipartitenetwork projections to analyze the extent to which assetoverlapping determines the level of interdependence betweenmutual funds in the same market in the event of changesin their investment strategies and fluctuations in industryconditions

The main results show that the structures of the bipartitemutual fund network and its one-mode projection changeover time and are affected by variables related to thefund investment strategies and industry-specific variablesBy studying the phenomenon of portfolio overlapping in asegment of investors who invest in the same asset class in thesame country we have found that their behavior affects thestructure of the financial network comprised of their fundsand the stocks where these invest This endogenous elementis derived from the financial strategies that funds use whenthey are fulfilling their role as third-party fund managersThis is an additional factor of changes in the structures of thefinancial networks which has effects on financial stability andrisk

The rest of the paper is structured as follows in Section 2we explain the bipartite network and its onemode projectionIn Section 3 we describe our data and explain our focus onthe Chilean mutual fund industry In Section 4 we char-acterize the mutual fund industry using bipartite networksand their one-mode projection In Section 5 we present themethodology econometric results and robustness analysisFinally in Section 6 we conclude and provide future researchextensions

2 Model

This section describes how to model the interdependenciesbetween mutual fund managers using a network approachThe network approach offers us the possibility of analyzingthe structure and temporal dynamics of these interdepen-dencies created as a product of decisions about investingin stocks These purchase and sale decisions are thosethat ultimately impact the topology of the mutual fundsnetwork

An appropriate network to model the interdependenciesbetween funds and stocks is through a bipartite network Webeginwith this description which gives us the input to projectthis network in a one-modeThat is a network that representsonly the interdependencies between mutual funds

The bipartite networks are useful for studying situa-tions where financial institutions possess overlapping expo-sures to different asset classes The bipartite network hastwo types of nodes mutual fundsmdashentities that manageinvestmentsmdashand stocks denoted by U and V respectivelyWe denote with E the links that join the two types of nodeswhich are disjointed between them Each node is linked to aweight wij that represents the level of exposure of the mutualfund i on the asset j Then G(UVE) is a weighted bipartitenetwork since each element of E connects a vertex of U andV such that there are no edges that connect elements of Uand V between them The links that go from funds to stocksrepresent diversification whereas the weights of the bipartitenetwork are equivalent to the exposure of the funds in stocks

Figure 4(a) shows an example of a bipartite networkbetween mutual funds and stocks It shows three differentcases with different exposures (different weights) but alwayswith the same level of diversification We analyze the bipartitenetwork using three properties The first is the degree ofthe set of nodes corresponding to the mutual funds whichmeasures the level of diversification of the funds in the stocksThe second is the strength which measures the level ofexposure of the fund to the stocks Finally we calculate thediversity which measures the complexity of a mutual fundgiven by its diversification and exposure

The bipartite network tells us how mutual funds andstocks are connected between them But how do mutualfunds relate to each other The answer is given by the stockportfolios they share Thus we propose to compress thebipartite network by one-mode projection to understand howmutual funds relate to each other

There are different methods to project a bipartite networkto a one-mode projection In particular for a weighted bipar-tite network the resulting weighted adjacent matrix wkmwill always be symmetrical ie wkm = wmk Neverthelessthe dependency of a fund k on a fund m may be differentfrom the influence that m has on k because the fundshave different levels of exposure among all the differentalternatives of assets available to invest Therefore a morenatural projection alternative is the one that allows for anasymmetrical weighting method Consequently we use anetwork resource-allocation method [15]

The result of this projection is a network in which we onlyobserve links between nodes of the set U of mutual fundsand theweights represent the degree of dependenceinfluencebetween them and not a measure of investment amountsas occurs in the bipartite network These weights are theresult of the resource-allocation method determined by [15]applied on the mutual funds that comes from the fund-by-fund connection matrix which indicates the level of recip-rocal interdependence among them generated by the sharedproperty of the stocks For any mutual fund i it will have aweight 119908119894119899119896119894 that denotes the influence this fund has on fund

4 Complexity

k while at the same time it has a weight of 119908119900119906119905119894119896 that denotesthat fund i is also influenced by fund k Therefore to studythe degree of influence and dependency of mutual fundswe focus on the strength of the projected funds network[16] According to this methodology the investors (mutualfunds) act as retainers of resources that flow through thebipartite networkThe appendix shows a simple example withtwo mutual funds and three stocks with different exposuresand their respective one-mode projections In this way it ispossible to understand better the relationships of dependenceand influence between the funds changes

3 The Data

31 Main Data Source To analyze the bipartite network ofmutual funds and stocks and its projection we constructeda database with the portfolios of each mutual fund for theperiod January 2003 to April 2016 This study stands on thelevel and accuracy of the financial and industry data Forthis we obtain information from three sources the first fromthe CMF (wwwcmfcl is the Chilean equivalent of the USSecurities and Exchange Commission) the second from theSantiago Stock Exchange (wwwsebracl) and the third fromthe Bloomberg platform (wwwbloombergcom)The datasetfree of survivorship bias includes precise information aboutthe price and number of portfolio stocks the number ofparticipants share values and assets under management foreach mutual fund Additionally each stock is described bythe closing price market capitalization trading volume andbook-to-market ratio Thus we can construct variables thatrepresent the characteristics of each fund such as the averagesize of the investors of the fund return and number of stockswhere the fund invests along with variables that according tothe financial literature describe their financial strategy overtime size liquidity book-to-market market capitalizationturnover active share and others [17ndash21]

Consequently we can construct the monthly bipartitenetwork for the Chilean mutual fund industry To describeits topology we calculate the degree strength and diversityparameters and their probability distributions for the shareson the bipartite network Then to extend our analysiswe estimate the bipartite network projection and calculateparameters that help us analyze the mutual fund industry interms of its interdependencies These variables are strengthmodularity path-length and assortativity index

32 The Chilean Mutual Fund Industry The equity mutualfund network in Chile is interesting for many reasons Firsthaving accurate monthly data regarding the number of sharesin each fund portfolio allows us to study in a dynamiccontext the networks formed by a segment of institutionalinvestors that have not yet been studied in depth in theliterature on financial networks Second mutual funds haveenjoyed outstanding development obtaining managed assetsof MMUSD 53887 in 2017 and reaching a penetration of22 of GDP This performance places them as the mostdynamic investors in the Chilean delegated portfolio man-agement industry This figure equivalent to 50 of the meanpenetration of developed countries is higher than the mean

growth of developing countries [22] For example comparedto 2002 when the managed amounts represented a numberclose to 9 of GDP this penetration has grown to a meanrate of 55 annually This growth makes mutual funds thethird actor in the delegated portfolio management industryin Chile behind pension fund administrators and insurancecompanies Third according to the World Economic Forumthe country has a medium level of financial developmentsince it ranks 29th out of 62 countries Consequently theapprenticeships gained from this industry are useful for otheremerging markets on the road to more significant economicand financial development Finally equity markets in Chilehave a high size in terms of percentage ofGDP comparedwithother OECD markets or other emerging markets

4 Network Characterization of Chilean EquityMutual Funds

41 The Bipartite Network of Mutual Funds and StocksFinancial intermediaries such as mutual funds fulfill threefundamental roles in providing the delegated portfolio man-agement service First activities associated with economiesof scale and scope enable them to reduce transactioncosts second they invest in less liquid but more profitableassets and finally they engage in delegated investmentmonitoring of the investments (for a survey see Stracca[23]) Thus in this delegated portfolio management pro-cess every fund manager must choose from among awide range of financial assets (equity bonds and depositsmainly) to make up an investment portfolio The maingoal is to achieve the best risk-return combination for theirclients

411 Degree The degree distribution of the mutual fundsdescribes the typical scale-free property of the bipartitenetwork Figure 1 (left) represents the degree distributionof the mutual funds in the bipartite network (ka) in threedifferent periods before during and after the crisis of 2008Regardless of the time we observe that few funds tend to beconnected tomany stocks and the majority of the funds tendto be connected to fewer stocks In other words there are afew mutual funds that are highly diversified whereas mostfunds are less so

The evolution of this variable over time is in Figure 2(a)Note that there was a change in the degree of mutual fundsbefore and after the financial crisis Specifically after thecrisis the mutual funds adjusted their diversification strategyto the downside and as a result the degree of the funds fallsand increases the concentration of the fundsrsquo equity portfoliosas a consequence

412 Strength The strength for a mutual fund i is the sum ofall weights of the links incident to it indicating the exposureof the mutual fund The weights 119908119894119895 of a fund i on an asset jare related to the amounts of money in local currency that thefund i has on the asset j determined by the composition of itsportfolio in a particular month It is usual for these weights119908119894119895 to change from one month to the next reflecting thereassignment of positions (or exposures) in the mutual funds

Complexity 5

10minus2

10minus2

10minus25

10minus25

10minus3

10minus3

10minus4

10minus35

10minus35

Ｅ

P(K=

Ｅ)

P(S=

Ｍ)

Ｍ

102

1015

101

1005

100

102

103

1015

1025

101

1005

100

Figure 1 Degree (ka) and Strength (sa) densities for stocks in the bipartite networks Different colors for each period In blue precrisis periodfrom January to June 2008 In red crisis period from June 2008 to January 2009 In green postcrisis period from February to June 2009

portfolio carried out as part of their particular diversificationstrategy

Figure 1 (right) describes the distribution of the strengthof the mutual funds in the bipartite network (sa) Regard-less of the analysis period this distribution also follows asimilar behavior A few mutual funds seem to have veryhigh exposure in assets whereas the vast majority have lessexposure

The evolution of this variable over time is in Figure 2(a)We observe that during the crisis the drop in stock pricesnegatively affected the strength of the network Howevercontrary to expectations the exposure did not recover duringthe postcrisis period despite the improvement in stockmarketprices This evidence (added with the results of the degree)indicates that there was a change in the portfolios that couldnot be explained solely by changes in the values of thefinancial assets but also by changes in the exposure of theportfolios and fluctuations in the economic and financialconditions of the equity market

413 Diversity If at a given moment a mutual fund 119865 has alarger number of stocks than another mutual fund 1198651015840 then

fund 119865 has greater diversification than fund 1198651015840 Similarly iffund 119865 has a larger amount invested in stocks than anotherfund1198651015840 then fund119865 is more exposed than fund1198651015840 In the firstcase fund 119865 has a more diversified portfolio whereas in thesecond it is more exposed To capture the combined propertyof the level of diversification and exposure we used theShannon entropy index [24] This representation of diversityhas been used to describe quantitatively the flow of biomassbetween different species in ecology literature [25] For ourpurposes the Shannon or entropy index for mutual fund 119894would be

119867119894 = minus119873

sum119895=1

119908119894119895119908119894lowast

log2119908119894119895119908119894lowast

(1)

where 119908119894119895 represents as indicated previously the amount ofmoney that fund 119894 has in stock 119895 The value 119908119894lowast is the sum ofall themoney that fund 119894 has in its portfolio Shannon entropyis between 0 (minimum) and 1 (maximum) In consequence119867119894 is maximumwhen amutual fund invests in all the assets inits portfolio in equal proportion that is when all119908119894119895 are equalfor each fund and each stock

6 Complexity

2628

3032

3436

dicminus02 febminus07 aprminus11 junminus15

Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity

(a) Time series of bipartite networks variables

01

23

4


Average Path Length

78

91

dicminus02 aprminus11febminus07 junminus15

Assortativity

05

11

52


Modularity

1015

2025

30


Strength

(b) Time series of bipartite network projection variables

Figure 2

Complexity 7

As the index is calculated with a logarithm in base 2 wecalculate the reciprocal of119867119894 and 119899119894 where 119899119894 = 2

119867119894 which wewill call general diversity We take the average of the diversityindices of all existing mutual fund for every periodsThis waythe higher the value of 119899119894 is the higher the level of entropy inthe industry is

Thismeasurement fitswell to calculate the global diversityof the bipartite network from the fund managersrsquo point ofview and therefore to be able to understand how the levelof industry diversification and exposure behaves in differentperiods Its evolution over time is in Figure 2(a) It is possibleto observe a permanent upward trend in general diversityfrom period April 2011 onwards In other words there seemsto be a more focused investment in resources by funds overfewer assets (or low diversification) This could be explainedby the decrease in the average degree of the system inFigure 2(a) (Degree) On the other hand investment amountsalso have a downward trend (Strength) The combined effectof these elements produces an increase in the Entropy ofthe industry which suggests an effect of less exposure anddiversification taken by fund managers

42The One-Mode Projection of the Bipartite Network Fromthe bipartite network of stocks andmutual funds it is possibleto construct a one-mode projected mutual funds networkto build a network in which the funds are related only toeach other We use the one-mode projection proposed by [15]because when choosing stocks to comprise their portfoliosthey share the property of some of them and consequentlyoverlapped portfolios are formed in themutual fund industrythus making it possible to study the interdependence amongthem

421 Strength The strength is the sum of the weights ofthe incident links to the node As the one-mode projectednetwork is directed each node may have links that enterthe node and others that leave it The sum of the weights ofthe links that enter the node the in-strength measures theinfluence that the fund has on the others The out-strengththe sum of the weights of the links leaving the nodemeasuresthe dependence that the fund has from the others In this waywe have a way to measure the degree of mutual influence anddependence between the different participants in the fundindustry

As we are dealing with averages over different periodsthe mean of the in-strength is equal to the mean of the out-strength simply because in the one-mode projection processin each period all the primary resources of the system remainintactThuswe speak of strengthwithoutmaking a differencebetween one and the other5

The results indicate that the interconnection (or degreeof influence of each fund on the others) of Chilean equitymutual funds is variable over time and increase during thecrisis Figure 3 shows a comparison between strengths for12 months (a) and 24 months (b) before and after March20096 We observe that there is variability in the strength ofthe projected network In the case of in-strength note thatbefore and after the crisis the variability stays steady becausethe median and interquartile ranges are similar However

in the crisis we observe an increase in variability althoughwith values similar to the precrisis period This is evidenceof an increase in the dispersion of the dependency of thefunds on each other ie in the crisis the dependence ofeach fund increases concerning the industry or in otherwords the topology of the network projection is variableover time Similarly the out-strength shows an increase inthe median which is not accompanied by an increase in itsvariability

422 Modularity To describe the structure of the one-mode projected network we perform a calculation of themodularity or cluster quality measure [26] considering allpossible community structures based on edge-betweennessedge removals The edge-betweenness of an edge measuresthe number of shortest paths that pass through it The ideaof using this measurement to detect communities within anetwork is that edges with a high edge-betweenness createthe bridges between different communities in the networkThus if these edges are removed it would clearly show areasof the network isolated one from the other revealing thecommunity structure

The calculation of the modularity Q is done iterativelyfinding the number of communities that maximize the valueof the modularity The modularity allows us to know thedegree to which specific modules in the network are moreor less densely or sparsely connected to other modules [27]Thus modularity values close to Q = 0 indicate a low or nulllevel of community structure by contrast values close to Q= 1 which is the maximum indicate a strong presence ofcommunity structure In the case of the projected networkhigh modularity values suggest that there are structuresor modules inside the network that tend to be influencedinternally but not mutually

In practice we observe over time that there are increasesand decreases of the level of modularity of the networkbut they are always between values of 01 and 02 (seeFigure 2(b)) indicating low level of community structureand consequently a high level of influence of ldquoall with allrdquowithout seeing structures inside the network However overtime variability is noted which suggests that certain factorsseem to influence the network structure

423 Average Path-Length The average path length lt d gt isthe average of the shortest distances between all the pairs ofnodes in the network for this we estimate the value for theprojection of the bipartite network monthly [28] As this is adirected network we have that

lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)

where N is the number of vertices in the network (number offunds in the industry)

Given that the strength of the projection indicates theinfluence-dependency level on other funds this value sym-bolizes the average degree of influence between the fundsexisting in the market at a given moment Thus for exampleif at somepoint in time119889119894119896 is low about another period then it

8 Complexity

0

1

2

3

March 2008 March 2009 March 2010Period

log1

0 of

Stre

nght

Strengthin

out

(a) Boxplots of logarithms of strengths-in and strengths-out of thebipartite network projection of mutual funds 12 months before and afterthe crisis (March 2008 2009 and 2010)

0

1

2

3


log1

0 of

Stre

nght

Strength

in

out

(b) Boxplots of logarithms of strengths-in and strengths-out of thebipartite network projection of mutual funds 24months before and afterthe crisis (March 2007 2009 and 2011)

Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3

(a) Bipartite Network

MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4

can be interpreted that the level of interdependence betweenfunds i and k are lower than at the beginning As a result asmall lt dgt value indicates little interdependence between thefunds in the industry at a specific time whereas higher valuesindicate a greater interdependence levelTheir evolution overtime is in Figure 2(b)

424 Assortativity Assortativity measures the tendency ofnodes to connect with other nodes of the same degreeThus nodes with high degrees tend to be connected to eachother and in the opposite direction a disassortative networkindicates that nodes with high degrees tend to be connectedwith low-degree nodes [29]

Complexity 9

In our case as we are dealing with weighted bipartitenetworks we wished to find the degree of assortative mixingin terms of the weights w119894119895 of a fund i on an asset j Forthis we calculated Pearsonrsquos correlation coefficient betweenthe strengths of mutual funds and the shares in the bipartitenetwork for each period [30] Thus assortativity levels closeto 1 indicate that the mutual funds with high levels of investedcapital tend to invest in stocks that are also heavily present inthe portfolios of other mutual funds Otherwise assortativityvalues close to -1 indicate thatmutual fundswith high levels ofinvestment tend to invest in stocks that are little representedin the portfolios of other funds in the industry

In practice it is observed that these values are close to09 (see Figure 2(b)) which indicates that the Chilean mutualfund industry tends to exhibit a kind of elevated preferentialattachment in which the fundsrsquo portfolios conform to thelevel of capital they have and the presence of the stocks inthe market This behavior may be the result of investmentstrategies that managers follow in a high level of portfoliooverlap These values are similar to that found in [31] in thepercentage of shares that firms share with each other and inthe Italian bank industry [32]

An explanation of the high levels of assortativity foundcould be based on the phenomena of herding in the man-agement of investments [33] and the reduced diversity andliquidity of shares available in emerging markets On theother hand compensation and career development motivatemutual fund managers to invest in shares in which everyoneinvests thus eliminating the possibility of losing moneywheneveryone wins a very negative event for their remunerationand career development A second explanation is the limitedavailability of investment options and liquidity problemsThis explains why the funds invest a large amount of moneyin a few shares as they manage liquidity risk

5 Econometric Analysis

51 Specification of the Model In this study we focus onthe dynamic analysis of the topological behavior of thebipartite network and its projection using elements specificto the mutual fund industry as well as variables related tomutual fund investment management strategies Howeverthe context in which these investors act is related to thegeneral economic and financial environment which affectsthe behavior of the stock market as a whole Eberhard andothers [34] find that the network structure of equity markettransactions changes together with variables from the localand international financial environment Specifically for thecase of the Chilean equity market the network structureof stock exchange transactions fluctuates with the SampP 500index the blue-chip Chilean index (IPSA) the ChicagoBoard Options Exchange Market Volatility Index (VIX) theexchange rate between the Chilean peso and the USD dollar(CLP) the emerging market index (MSCI) the oil price (Pe)and the copper price (Cu)

For the case of the factors of the mutual fund industrywe use variables that characterize the industry at aggregatelevel and at financial level In the first group the total numberof investors or participants in the industry the total number

of stocks in the portfolios under delegated management andthe total number of mutual funds existing in the market areincluded In the second group variables studied by the liter-ature are incorporated to measure the financial performanceand investment abilities of the mutual funds The size of thefunds is incorporated measured by the market capitalization(ln mcap) and the book-to-market ratio (ln book) [17] themomentum of the performance of the funds measured by theone-month delayed return (Lperformance) and the rotationof the portfolios measured by turnover (ln to) [18] activemanagement of the funds measured by the active share(ln as) [19 20] and the liquidity of the assets of the fundsmeasured by liquidity of the portfolios (ln liq) [21]

As previously mentioned our hypothesis studies theimpact on the topology of the mutual funds bipartite net-work and its projection of fluctuations in the economicand financial conditions of the capital market as well aschanges in the investment management decisions made bythe funds as a result of their role as third-party portfoliomanagers According to this as we indicate in Sections 31and 32 the topological variables that study the bipartitenetwork are the variation in degree (vdegfon) the variationin strength (vstrengthb) and the variation in the diversity ofthe funds (vdiversity) Likewise for the case of the projectednetwork we study the variation in strength (vstrengthp)the variation in modularity (vmodularity) the variation inpath-length (vpathlenth) and the variation in assortativity(vassortativity)

According to the above to study the effects of variationson the financial strategies deployed by the mutual funds as awhole and by changes in themutual fundsrsquo industry aggregatevariables we estimate the following econometric model forthe bipartite network and its projection

119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)

The dependent variable is 119884119905 and represents the variation inthe topological variables of the bipartite and the projectednetworks 119883119905 corresponds to the independent variables asso-ciated with the investment decisions of the whole funds andaggregate variables of the industry 119862119905 corresponds to thecontrol variables associated with the economic and financialenvironment 119898119905 are monthly fixed effects to control forseasonality All models are estimated with robust standarderrors

52 Main Results To test our hypotheses the econometricstudy that is reported next is based on the analysis of thestatistical significance between restricted and unrestrictedmodels in order to evaluate whether the changes in the topo-logical variables of the bipartite networks and the projectedone are explained by changes in variables related to thefinancial management of the funds andor by changes in thevariables specific to the mutual fund industry

521 Econometric Models of the Bipartite Network

(1) Degree Table 1 column (1) shows that changes in theaverage diversification of the industry (vdegfon) are jointlyassociated by changes related to industry-specific variables

10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast

X t+120574 lowastC t

+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto

00198lowastlowastlowast

000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast

-00323lowastlowastlowast

-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values

inparentheseslowastplt01lowastlowastplt005andlowastlowastlowastplt001

12 Complexity

and changes in the mutual fundsrsquo investment strategiesWithin the first group of variables with statistical significancehighlighted by the magnitude of its effect is the variableaverage number of stocks within the funds (ln stocks) a onestandard deviation increase in ln stocks would yield a 79standard deviation increase in the predicted vdegfon (120573 =079 normalized coefficient) It is also observed that when thepast return of the industry increases (Lperfomance) diversifi-cation also does soThe intuition of these results indicates thatwhen the return of the previousmonth increases the industrytends to increase the diversification within the funds thisbeing consistent with an increase in the number of stocksbought by each fund

Nevertheless an inverse effect is noted between thenumber of investors in the industry (ln investors) and thediversification of the funds (vdegfon) In order of magnitudea one standard deviation increase in ln investorswould yield a53 standard deviation decrease in the predicted vdegfon (120573 =-053 normalized coefficient)This result indicates that in theevent of an increase in investors and probably also an increasein the amounts of money managed mutual funds tend toconcentrate the investment in popular or glamour stocks [35]causing the diversification to decrease

As far as the variables related to the financialmanagementof the funds is concerned a positive relation can be seenwith turnover (ln to) and a negative one with liquidity(ln liq) with the former being the one that presents thegreatest magnitude of impact on the diversification of theindustry Indeed an increase in a one standard deviationin the turnover causes an increase of 04 times in thestandard deviation of the diversification (120573 = 04 normalizedcoefficient) The intuition of this phenomenon is based on arelevant objective of investment management materializedthrough the rotation of its assets [21] which consists ofmanaging the diversification of the mutual funds On theother hand by increasing the liquidity of the assets bought bythe funds these reduce the diversification of their portfoliosconcentrating their investments on fewer assets (120573 = -025normalized coefficient)

(2) Strength In relation to the level of exposure of the mutualfunds (vstrengthb) column (6) shows that the changes inthe fundsrsquo exposure depend exclusively on changes related toinvestment management variables Indeed when the signif-icance test is applied it is demonstrated that the industry-specific variables do not affect the exposure of the mutualfunds (pvalue = 024) Also it is observed that when theyincrease the liquidity (ln liq) book-to-market ratio (ln book)and turnover (ln to) the exposure of the funds decreasesWhen the liquidity of the portfolio assets increases thefunds respond by investing less in these assets because theirexpected return is lower [36] On the other hand whenthe book-to-market ratio of the portfolio stocks increasesthe funds reduce their exposure because the prices of theassets are falling discouraging their appeal [17] Finally byincreasing the rotation of the portfolios of the funds theexposure decreases because the funds reduce the averageexposure in each asset This means by rotating the portfoliotheir investments reassign among a greater number of assets

These three variables have similar magnitudes with thebook-to-market ratio being the most relevant (120573 = -028normalized coefficient)

(3) Diversity The complexity of the mutual funds networkmeasured by the diversity index (vdiversity) as in the caseof diversification is dependent on industry-specific variablesand the fundsrsquo investment management variables Column(7) shows that there is a positive relation between diversitythe book-to-market ratio (ln book) turnover (ln to) andthe active share (ln as) of the mutual funds Of these threevariables related to the financial management of the fundsthe one that has the greatest impact is the book-to-marketratio (120573 = 051 normalized coefficient)

In relation to the effect of the industry-specific variablesit is observed that the numbers of stocks per fund (ln stocks)and past performance (Lperformance) are significant Theimportance of the first is highlighted as its coefficient issimilar to the one of the book-to-market ratio (120573 = 053normalized coefficient) We see that as the number of stocksand past performance increase the diversity also does whichmakes sense because the greater the availability of stocks toinvest the greater the diversity in terms of portfolio diversifi-cation and exposureOn the other hand a better performanceattracts a larger number of participants to the funds [37]causing the funds to invest more [38] and as a result theexposure also increases increasing the diversity Interestinglyas the number of funds in the industry increases the diversityfalls This could be explained because having more funds thestock of money invested in the industry is distributed amongmore agents and therefore the weights 119908119894119895 tend to decrease

522 Econometric Models of the One-Mode Projection Re-membering that the purpose of the projected network isthe analysis of the mutual dependency between funds inthe industry the links in this network indicate the degreeof dependency that exists between one fund manager andanother unlike the bipartite network whose links andweights show levels of asset diversification and exposurerespectively In general terms the results in Table 2 indicatethat changes in the strength modularity and assortativityof the projected network depend on both variations inindustry variables as well as changes in the fundsrsquo financialmanagement variables However these variables do not affectthe case of path length

(1) Strength Table 2 column (1) directly studies the aver-age interdependence level that exists in the industry in acertain period The significant variables are book-to-market(ln book) and number of funds (ln funds) both are negativemagnitudes (120573 = -056 and 120573 = -055 respectively normalizedcoefficients)Thiswould imply that by increasing the numberof funds in the industry the interdependence decreaseswhich could be explained by the fact that by keeping theexposure constant by increasing the number of participantsin the industry the average exposure level between themfalls negatively affecting the mutual interdependence Inthe case of the book-to-market ratio the results show thatwhen this falls it increases the interdependence between

Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control

forseasonalityAllmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund

s-0256lowastlowastlowast

-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ

ity-0225lowastlowast

-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15

the funds because the assets are increasing in value withwhich the exposure increases and as a result the mutualinterdependence increases

(2) Modularity In relation to the modularity of the projectednetwork column (4) shows that the investment manage-ment variables of market cap (ln mcap) and active share(ln as) negatively affect this network characteristic (120573 = -044 and 120573 = -040 respectively normalized coefficients) Theinverse relation between market cap and modularity couldbe understood by the fact that when the funds begin to buystocks with low market capitalization (uncommon assets)inevitably their investment portfolios tend to be differentfrom the rest of the industry and consequently groups offunds appear in the network that have greater similarityto one another In the first group are those that invest inassets with low market-cap and in the second those thatorient their portfolios to assets with high market-cap withthe mutual interdependence between these groups being low

The inverse relation between active share (ln as) andmodularity can be understood similarly to the previous caseAs the active share increases there are fundswhose portfoliosbegin to be different from those of other investors becausethey move away from the benchmark when allocating assetsinto their portfolios thereby generating a grouping of fundsof greater modularity

The positive relation between number of funds (ln funds)and modularity (120573 = 068 normalized coefficients) has theopposite effect indicating that when new funds enter theindustry these tend to invest in assets unlike those that fundsin the industry already have Thus it is observed that theintroduction of new funds increases the level ofmodularity ofthe projected network because there are funds with differentassets making it so that mutual fundsrsquo clusters that withinhave the same kind of assets but between them do not

(3) Assortativity A high level of assortativity implies thatfunds with high dependency (high level of strength) are alsoconnectedwith other funds of high influence (and vice versa)A negative or low assortativity indicates that funds with highdependency are connected with funds of low influence (lowlevel of strength)

Table 2-Column (10) shows that changes in assortativityin the network is negatively affected by changes in theliquidity level (ln liq) and positively by past performance(Lperformance) (120573 = -037 and 120573 = 025 respectively nor-malized coefficients) This implies that in months where theindustry increases the liquidity of its mutual funds they tendto do so by choosing similar stocks (the most liquid) whereasin periods where the industry uses lower liquidity levelsthey tend to spread their investments across a larger numberof stocks This aggregate behavior is related to the herdingphenomenon that mutual funds exhibit [37 39] a situationwhere they buy and they sell the same stocks

On the other hand when the past performance is positive(Lperformance) we observe that assortativity increases Thisis due to a good performance being associated with a gooddecision as a result the investment increase in the betterstocks amplifies the assortativity between those funds that

employ the same investment strategies By contrast whenthe performance is negative it is natural to observe that thefunds change their investment strategies and consequentlyreduce their interdependence on those funds that had similarstrategies

53 Robustness We provide additional econometrics anal-yses to provide further insights and to test the robustnessof our main results According to the literature during thefinancial crisis of 2008 investorsrsquo behavior changed in boththe developing and developed financialmarkets For examplewe observed the liquidity hoarding effect with its resultingimpact on prices returns and assets valuation and the flight-to-quality effectwith its direct impact on risky assets and theirvaluations [1] Emerging markets were not immune to thisphenomenon and suffered more than developed markets

Accordingly Table 3 shows models that evaluate the con-sistency of the previous results controlling for the possibleeffects of the financial crisis of 2008 All models include adummy variable (dum crisis) that takes the value of 1 foreach month in the period from Oct-07 to Oct-09 and zerootherwise7 The idea is to corroborate that our results arenot the result of the financial turmoil that occurred duringthat time As we can see in Table 3 the main results holdwhen we control for the possible effects of the financial crisisIn other words the changes in the bipartite network and itsprojection are driven by variations in the financial decisionsof the mutual fundsrsquo portfolio managers and changes in thestructural characteristics of the mutual fund industry

6 Conclusions

The network literature states that in context of financialstress the interconnectedness among financial institutionsplay a key role in terms of the systemic risk of the marketIn these situations a shock on a node of the system couldtrigger a collapse of the entire financial network [40] Usuallythese shocks have an exogenous origin For example acurrency devaluation a sudden hike in interest rates asudden fall in the stock markets or even an unexpectedcentral bank intervention could turn on the alarms of theentire financialmarket and in consequence generate changesin the structure of the financial network Depending on thetopology of the network is how the propagation of the shocksalter the stability and resiliency of the system [41]

Although the above is a first-order reaction of the marketto external conditions an external shock generates a second-order reaction from the entities that conform the financialnetwork Depending on the nature magnitude and durationof the financial shock financial institutions react to maintaintheir financial viability preserve clients minimize exposuretake advantage of price selloffs or simply hedge financialrisks This reaction modifies their investment strategies andin consequence provokes a change in their financial behaviorIn turn this response generate a certain kind of chain reactionamong the actors of the market that modify the structure ofthe whole network

In the above context the phenomenon of overlappingportfolios among institutional investors takes relevance In

16 Complexity

Table 3 Robustness ModelsThis table summarizes the results of the following model Yt= 120572 + 120573lowastXt+ 120574lowastCt +mt+ 120576t The dependent variableis Yt and represent the variation in the topological variables of the bipartite networks Xt corresponds to the independent variables Ctcorresponds to the control variables mt are monthly fixed effects to control for seasonality All models are estimated with robust standarderrors

Bipartite Networks Projected Bipartite Networks(1) (2) (3) (4) (5) (6)

vdegfon vstrengthb vdiversity vstrenghtp vmodularity vassortativityln mcap 00127 -00202 000989 00565 -00917lowastlowastlowast 0000292

(0181) (0557) (0344) (0175) (0007) (0984)ln liq -00119lowast -00544lowastlowast -000409 000225 -00240 -00260lowastlowastlowast

(0091) (0037) (0602) (0925) (0235) (0003)ln book 00239 -0141lowastlowastlowast 00568lowastlowast -0209lowastlowast -00188 -00216

(0323) (0005) (0039) (0048) (0829) (0493)ln to 00207lowastlowastlowast -00750lowastlowast 00215lowastlowast -00159 00127 00102

(0002) (0033) (0010) (0590) (0491) (0236)ln as 00204 00180 00494lowastlowast 00918 -0129lowastlowast -00135

(0273) (0756) (0013) (0189) (0031) (0487)ln stocks 0165lowastlowastlowast 0126lowastlowast -0231 0154 00620

(0000) (0019) (0121) (0191) (0262)ln funds -00372 -00475lowast -0255lowastlowastlowast 0243lowastlowastlowast -00208

(0106) (0051) (0007) (0002) (0501)ln investor -00336lowastlowast -000801 -00312 -00394 -000273

(0016) (0593) (0602) (0499) (0881)Lperformance 0159lowastlowastlowast 0162lowastlowastlowast -00609 -0154 0146lowastlowast

(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152

(0195) (0899) (0602) (0947) (0355) (0833)ipsa ret 00793 1196lowastlowastlowast 00618 -0401lowast 00979 -000789

(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast

(0448) (0482) (0190) (0895) (0292) (0051)varmsci 00148 0182 0111lowastlowast -00421 00244 00901

(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast

(0062)Lvstrengthb 0100

(0406)Lvdiversity -00492

(0551)Lvstrenghtp -0275lowastlowastlowast

(0004)Lvmodularity -00589

(0594)Lvassortativity -0227lowastlowast

(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued


vdegfon vstrengthb vdiversity vstrenghtp vmodularity vassortativityN 158 158 158 158 158 158R2 0369 0504 0255 0299 0240 0271adj R2 0226 0410 0086 0140 0068 0106P-value 000 000 001 000 001 001F 3520 9374 1938 3443 1877 1840Nonstandardized coefficients p-values in parentheses lowastp lt 01 lowastlowastp lt 005 and lowastlowastlowastp lt 001

these circumstances when two or more investors share thesame financial assets and allocate their investments applyingsimilar financial strategies and invest in the same market thesecond-order effect of an external shock as described earliercould be a source of disturbance that affects the stability of afinancial network

Following the aforementioned this study dynamicallyanalyzes the phenomenon of overlapped portfolios by study-ing the aggregate behavior of the equity mutual fundsindustry in an emerging market context These markets arecharacterized for having well-developed physical financialinfrastructure such as central banks commercial banksand stock exchanges but at the same time compared todeveloped markets for having less well-developed processesand systems of accounting governance and regulationand mainly less efficient markets with less liquidity [42]Additionally they possess a high level of property and controlconcentration of the firms [43] that becomes them sensibleto this phenomenon and their economic effects especiallyduring economic and financial downturns

The main conclusion of this work is that in a developingeconomies context the structure of the mutual fund networkchanges as consequence of external financial and economicfactors and as result of changes in the investment behaviorof the entities of the network Specifically the topology ofthe bipartite network of funds and its one-mode projectionis dynamic over time and is correlated with variations inthe investment strategies of mutual funds (hypothesis 1)and with industry-specific variables (hypothesis 2) Fromthis perspective changes in macroeconomic and financialconditions in conjunction with changes in the mutual fundrsquosindustry context promote changes in the fundsrsquo investmentstrategies that trigger modifications in the fundrsquos networkstructure

On the other hand we believe that there is an interestingvein of study that consists of studying the richness of theinformation contained in the directed network from theresulting one-mode projection An analysis of the structuraldiversity of the network of interdependencies between fundsusing the assortative or dissasortative nature of the edgesthat compose it [44] would reveal interesting information onchanges in dependence and influence between components ofthe industry

Our results evidence new factors that alter the stabilityand the systemic risk of financial systems that have not yetbeen studied by the literature in this segment of institutional

investors in an emerging marketThese results are interestingbecause the equity portfolios we analyzed in this study fallwithin the characteristic of overlapped portfolios confirmingthe existence of a channel of contagion generated by theaggregate investment behavior of the entities belonging tothe network Similar results are showed by the networkliterature that study the effects of the interconnectedness offinancial institutions and the propagation of shocks over thesystemic risk of the financial market [40 41 45] From apolicy and regulator point of view this evidence highlightsthat improving the knowledge of overlapping portfolios inemerging markets is a fundamental element to a betterunderstanding of the risks and magnitudes of financial andeconomic contagions with respect to the likelihood of theiroccurrence and extension and their relation to the numberand density of the connections within the financial system

From a financial perspective our research is related to thestudy of herding among investors As this literature statesthis phenomenon can exacerbate the volatility levels in themarket destabilizing it increase the fragility of the financialsystem and eventually generate assets bubbles [46]This lineof research indicates that under certain financial and marketconditions investors exhibit herd behavior in which theydo not only apply the same investment strategies of theirpeers but they also copy their same buy and sell decisionsof financial assets [33 47 48] To our best understandingthe channel evidenced in this study has not yet been linkedto the herd behavior literature despite having similaritiesFor example the level of herd behavior among mutualfunds increases during high periods of volatility and pricedownturns [39] precisely when financial shocks disturb themarkets An alternative to study the problem of herdingcould consider a more detailed analysis of the assortativity ofthe bipartite network of funds and stocks when consideringhigher order assortativity measures that could describe newtopological characteristics of the network [49]

Gaining a deeper knowledge of how herding could influ-ence the structure of the mutual funds networks will facilitatea better comprehension of the channels for transmissionof the systemic risk associate with this financial behaviorHowever the financial literature has studied mutual fundsextensively for both their size and importance in the delegatedportfolio management industry we believe that this venueof research in conjunction with the perspective of networkanalysis has much to contribute to the preservation of thefinancial stability especially in developing markets

18 Complexity

Appendix

Relationship between the BipartiteNetwork and Its Projection in the MutualFunds Domain

This appendix shows the relationship between a bipartitenetwork of mutual funds and stocks and their correspondingprojection using the Zhou et al [15]method For this we takeas an example three simple bipartite networks in which thereare two mutual funds MF1 and MF2 which invest in threepossible stocks namely S1 S2 and S3

Figure 4(a) shows the three bipartite networks andtheir respective projections in the mutual funds domain inFigure 4(b) For clarity of notation we will distinguish 119908119894119895 asthe weight of the bipartite network between the mutual fund119894 and stock119895 while 119908119901

119894119896is the weight of the directed network

resulting from the projection of the bipartite network indi-cating the influence that the mutual fund 119896 has on the mutualfund 119894 (or that it is the same the mutual fund 119894 dependence ofthe mutual fund 119896)

In case 1 we have that mutual funds are equally exposedsince they invest the same amount of money on all the threestocks In this case there is a symmetrical weighted bipartitenetwork Thus the weights 119908119894119895 = 1 of the bipartite networkfor funds 119894 = 1 2 and for stocks 119895 = 1 2 3 It is not surprisingthat the corresponding projection indicates that 11990811990112 = 119908

11990121

That is the influence that the MF1 fund has on the MF2 fund(given by 11990811990121) is the same as the influence that MF2 has onMF1 (given by 11990811990112)

In case 2 MF1 invests an equal sum of money in thethree stocks so that 119908119894119895 = 10 for 119895 = 1 2 3 However MF2also invests in the three stocks equitably but one tenth ofwhat MF1 does so 1199082119895 = 1 for 119895 = 1 2 3 In this casemutual funds invest their money in the same assets but inasymmetrical way The result of the projection is such that11990811990121 = 10 while 119908

11990112 = 01 In other words the influence

that MF1 has on MF2 is 100 times greater than the influencethat MF2 has on MF1 This indicates that a highly exposedmutual fund with a high investment and diversification inassets in relation to another well diversified mutual fund butnot so exposed in terms ofmoney in the same assets producesin the projection a high value of strength indicating thestrong effect of the influence of the first mutual fund over therest

Case 3 is different MF1 is more diversified than MF2 butless exposed in their allocations That is to say the weightsof the bipartite network are asymmetrical as well as theconnections because the degree of MF2 is different from thedegree of MF1 Thus in this case 1199081119895 = 1 for all 119895 = 1 2 3and 11990823 = 10 while 11990821 = 11990822 = 0 MF1 is less exposed butit is well diversified while MF2 is highly exposed but poorlydiversified The projection result indicates that 11990811990121 = 01 and11990811990112 = 043 In this case the influence that MF2 has on MF1is 43 times stronger than the influence that MF1 has onMF2This is because even whenMF2 is not very diversified it has ahigh amount of investment in S3 As we increase the exposurevalues of MF1 but keeping its diversification the influence

of MF2 in relation to MF1 will decrease until MF1 becomesmore influential than MF2

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors would like to thank CONICYT-Chile undergrant Fondecyt 11160072 (Mauricio A Valle) for financiallysupporting this research

Endnotes

1 The impact of financial assets on the propagation ofshocks is a significant subject in risk analysis Althoughmost of the literature on financial networks concentrateson the analysis of interbank loans networks and itsresponse to shocks at assets level for example fire-sales the propagation of shocks through more denselyconnected networks such as the networks establishedthrough financial assets is greater Delpini and others[8] indicated that as a consequence of a more diversifiedpattern of investment ndash like in pension funds andmutualfunds ndash a more densely connected network servesas a mechanism of propagation of shocks increasingsystemic risk as a result

2 ICI Fact Book 2017 (wwwicifactbookorg)

3 For example by analyzing the degree distribution andstrength of the stocks in a portfolio itmay be determinedwhether the classic characteristic of free scale property isfulfilled in which most of the stocks are in the hands ofa few funds and where many funds have a few stocks

4 Using exact positions of each stock over time allows usto avoid their inference from the financial reports ofeachmutual fund thereby avoiding unrealistically densenetworks and biased underestimation of systemic risk[5]

5 For any period of time of the bipartite network the sumof all the strengths of the fundsmust be equal to the sumof the strengths of the stocksThat is equivalent to sayingthat the amount of money invested by the funds mustbe the same as the amount of money that is invested inthe stocks For the projection of the bipartite network inmutual funds the mean of the in-strength is the sameas the mean of the out-strength since the direction inwhich an edge enters a node is equivalent to the directionin which another node exits which is why the all theresources are retained in the system

Complexity 19

6 We useMarch 2009 as a reference point because the SampP500 Index reached 66679 points being this value theminimum during the financial crisis

7 During this period the stocks markets experienced theworst performance in terms of return and volatility

References

[1] A G Haldane ldquoRethinking the financial networkrdquo in FragileStabilitat ndash stabile Fragilitat pp 243ndash278 2013

[2] R Greenwood A Landier andDThesmar ldquoVulnerable banksrdquoJournal of Financial Economics vol 115 no 3 pp 471ndash485 2015

[3] P Glasserman and H P Young ldquoContagion in financial net-worksrdquo Journal of Economic Literature vol 54 no 3 pp 779ndash831 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 ArticleID 9895632 16 pages 2017

[5] M J Straka G Caldarelli T Squartini and F Saracco ldquoFromecology to finance (and back) recent advancements in theanalysis of bipartite networksrdquo Journal of Statistical Physics vol173 no 3-4 pp 1252ndash1285 2018

[6] M Elliott B Golub and M O Jackson ldquoFinancial networksand contagionrdquoAmerican Economic Review vol 104 no 10 pp3115ndash3153 2014

[7] F Caccioli P Barucca and T Kobayashi ldquoNetwork modelsof financial systemic risk a reviewrdquo Journal of ComputationalSocial Science vol 1 no 1 pp 81ndash114 2017

[8] D Delpini S Battiston G Caldarelli and M Riccaboni ldquoTheNetwork of US Mutual Fund Investments DiversificationSimilarity and Fragility throughout the Global Financial Crisisrdquo2018 httpsarxivorgabs180102205

[9] H Markowitz ldquoPortfolio selectionrdquoThe Journal of Finance vol7 no 1 pp 77ndash91 1952

[10] P Glasserman and H P Young ldquoHow likely is contagion infinancial networksrdquo Journal of Banking amp Finance vol 50 pp383ndash399 2015

[11] S Battiston J B Glattfelder D Garlaschelli F Lillo and GCaldarelli ldquoThe structure of financial networksrdquo in NetworkScience pp 131ndash163 Springer London UK 2010

[12] S Battiston and M Catanzaro ldquoStatistical properties of cor-porate board and director networksrdquo The European PhysicalJournal B vol 38 no 2 pp 345ndash352 2004

[13] S Battiston J F Rodrigues and H Zeytinoglu ldquoThe net-work of inter-regional direct investment stocks across EuroperdquoAdvances in Complex Systems (ACS) vol 10 no 1 pp 29ndash512007

[14] M Boss H Elsinger M Summer and S Thurner ldquoNetworktopology of the interbank marketrdquo Quantitative Finance vol 4no 6 pp 677ndash684 2004

[15] T Zhou J Ren M Medo and Y C Zhang ldquoBipartite networkprojection and personal recommendationrdquo Physical Review EStatistical Nonlinear and Soft Matter Physics vol 76 no 4Article ID 046115 2007

[16] A BarratMBarthelemyR Pastor-Satorras andAVespignanildquoThe architecture of complex weighted networksrdquo Proceedingsof the National Acadamy of Sciences of the United States ofAmerica vol 101 no 11 pp 3747ndash3752 2004

[17] E F Fama and K R French ldquoThe cross-section of expectedstock returnsrdquoThe Journal of Finance vol 47 no 2 pp 427ndash4651992

[18] M M Carhart ldquoOn persistence in mutual fund performancerdquoJournal of Finance vol 52 no 1 pp 57ndash82 1997

[19] K J M Cremers and A Petajisto ldquoHow active is your fundmanager a new measure that predicts performancerdquo Review ofFinancial Studies vol 22 no 9 pp 3329ndash3365 2009

[20] A Petajisto ldquoActive share and mutual fund performancerdquoFinancial Analysts Journal vol 69 no 4 pp 73ndash93 2013

[21] J Lavin and N Magner ldquoReversing the question on what doesthe turnover of mutual funds depend evidence from equitymutual funds in Chilerdquo Emerging Markets Finance amp Trade vol50 no 5 pp 110ndash129 2014

[22] A Khorana H Servaes and P Tufano ldquoExplaining the sizeof the mutual fund industry around the worldrdquo Journal ofFinancial Economics vol 78 no 1 pp 145ndash185 2005

[23] L Stracca ldquoDelegated portfolio management A survey of thetheoretical literaturerdquo Journal of Economic Surveys vol 20 no5 pp 823ndash848 2006

[24] C E Shannon ldquoAmathematical theory of communicationrdquoBellLabs Technical Journal vol 27 pp 379ndash423 1948

[25] L-F Bersier C Banasek-Richter and M-F Cattin ldquoQuantita-tive descriptors of food-webmatricesrdquoEcology vol 83 no 9 pp2394ndash2407 2002

[26] M Newman and M Girvan ldquoFinding and evaluating commu-nity structure in networksrdquo Physical Review E vol 69 no 2 pp1ndash16 2004

[27] M E Newman ldquoMixing patterns in networksrdquo Physical ReviewE Statistical Nonlinear and Soft Matter Physics vol 67 no 2Article ID 026126 2003

[28] R Albert and A Barabasi ldquoStatistical mechanics of complexnetworksrdquo Reviews of Modern Physics vol 74 no 1 pp 47ndash972002

[29] E Estrada and P Knight A First Course in Network TheoryOxford University Press USA 2015

[30] M Newman ldquoAssortative mixing in networksrdquo Physical ReviewLetters vol 89 no 20 Article ID 208701 2002

[31] G Rotundo and A M DrsquoArcangelis ldquoOwnership and controlin shareholding networksrdquo Journal of Economic Interaction andCoordination vol 5 no 2 pp 191ndash219 2010

[32] G De Masi G Iori and G Caldarelli ldquoFitness model for theItalian interbank money marketrdquo Physical Review E StatisticalNonlinear and Soft Matter Physics vol 74 no 6 Article ID066112 2006

[33] M Grinblatt S Titman and R Wermers ldquoMomentum invest-ment strategies portfolio performance and herding A studyof mutual fund behaviorrdquo The American Economic Review pp1088ndash1105 1995

[34] J Eberhard J F Lavin and A Montecinos-Pearce ldquoA network-based dynamic analysis in an equity stock marketrdquo Complexityvol 2017 Article ID 3979836 16 pages 2017

[35] J Y Campbell C Polk and T Vuolteenaho ldquoGrowth orglamour Fundamentals and systematic risk in stock returnsrdquoReview of Financial Studies vol 23 no 1 pp 305ndash344 2010

[36] Lrsquo Pastor and R F Stambaugh ldquoLiquidity risk and expectedstock returnsrdquo Journal of Political Economy vol 111 no 3 pp642ndash685 2003

[37] V A Warther ldquoAggregate mutual fund flows and securityreturnsrdquo Journal of Financial Economics vol 39 no 2-3 pp209ndash235 1995

[38] M Grinblatt S Titman and R Wermers ldquoMomentum invest-ment strategies portfolio performance and herding a study of

20 Complexity

mutual fund behaviorrdquo American Economic Review vol 85 no5 pp 1088ndash1105 1995

[39] J F Lavin andN SMagner ldquoHerding in themutual fund indus-try evidence from Chilerdquo Academia Revista Latinoamericanade Administracion vol 27 no 1 pp 10ndash29 2014

[40] R Cerqueti G P Clemente and R Grassi ldquoSystemic riskassessment through high order clustering coefficientrdquo 2018httpsarxivorgabs181013250

[41] M DrsquoErrico D Felletti and R Grassi ldquoShock propagation andthe topology of complex networksrdquo Tech Rep DipartimentodiMetodi Quantitativi per le Scienze Economiche ed AziendaliUniversita degli studi di Milano Bicocca Working Papers 2010

[42] C Kearney ldquoEmerging markets research Trends issues andfuture directionsrdquo Emerging Markets Review vol 13 no 2 pp159ndash183 2012

[43] M P Abreu R Grassi and R R Del-Vecchio ldquoStructure of con-trol in financial networks An application to the Brazilian stockmarketrdquo Physica A Statistical Mechanics and Its Applicationsvol 522 pp 302ndash314 2019

[44] J G Foster D V Foster P Grassberger and M Paczuski ldquoEdgedirection and the structure of networksrdquo Proceedings of theNational Acadamy of Sciences of the United States of Americavol 107 no 24 pp 10815ndash10820 2010

[45] G P Clemente R Grassi and C Pederzoli ldquoNetworks andmarket-based measures of systemic risk the European bankingsystem in the aftermath of the financial crisisrdquo Journal ofEconomic Interaction and Coordination pp 1ndash23 2019

[46] S Bikhchandani and S Sharma ldquoHerd behavior in financialmarketsrdquo IMF Staff Papers vol 47 no 3 pp 279ndash310 2000

[47] J Lakonishok A Shleifer and R W Vishny ldquoThe impactof institutional trading on stock pricesrdquo Journal of FinancialEconomics vol 32 no 1 pp 23ndash43 1992

[48] R Wermers ldquoMutual fund herding and the impact on stockpricesrdquoThe Journal of Finance vol 54 no 2 pp 581ndash622 1999

[49] A Arcagni R Grassi S Stefani and A Torriero ldquoHigherorder assortativity in complex networksrdquo European Journal ofOperational Research vol 262 no 2 pp 708ndash719 2017

Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

2 Complexity

pension funds hedge funds and mutual funds that haveexposures in the same financial asset [6] However despitethe size of these investors in the financial system the literaturepays little attention to the second channel1The present studyfocuses on studying the complexity of the phenomenon ofportfolio overlaps through network analysis

The study of the phenomenon of systemic risk throughoverlapping portfolios is novel [4 7] however there is alack of studies applied to the mutual fund industry despiteits importance and size2 Delpini and others [8] analyze thebipartite network of US mutual funds during the financialcrisis studying how the systemic fragility of the systemdepends on the overlap between portfoliosTheir results indi-cate that diversification and similarity in financial investmentstrategies are factors that increase distress propagation andsystemic fragility The authors confirm that diversificationincreases systemic risk when the funds use the same invest-ment strategies and diversify using similar assets

The relation between diversification and systemic risk isimportant due to the effect of both factors on investmentportfolio management Markowitz [9] argues that diversi-fication achieved by increasing the number of assets in aportfolio reduces the unsystematic riskThis definition how-ever does not consider the contribution of the overlappingof assets to systemic risk and the propagation of shocks atthe aggregate level In this sense the network methodologycan complement the study of financial risk analyzing thecomposition and diversification of portfolios from the samegroup of investors as well as of the degree of similarity ofthe assets that make up their portfolios and of the investmentstrategies used

The above reveals the tension existing within portfoliomanagement and the influence of diversification as a toolfor risk management Although diversification reduces thesystematic risk of the assets when this occurs in the presenceof high similarity in the portfolios as in the mutual fundindustry for example diversification becomes a generatorof systemic risk This occurs because by holding diversifiedportfolios but comprised of the same assets the funds returnto the system as a more vulnerable whole because theinterconnections and channels of contagion are increased[3 10]

An understanding of the risks generated by a portfoliomanager that seeks to minimize them through diversificationincreases the interdependencies on the portfolio overlapnetworks of mutual and pension fund managers This phe-nomenon acquires significance as an amplifier and generatorof financial shocks even more so in small economies withlittle diversity of assets to invest as is the case in emergingcountries

Nevertheless and contrary to expectations there is stilllittle attention paid in the literature to the study of financialrisks in this intermediary segment [8] and to our bestof knowledge even nonexistent in a context of emergingmarkets The segment of institutional investors includesmutual funds hedge funds and pension funds it is one ofthe primary investment vehicles globally They reached a sizeof USD 4617 trillion equivalent to 61 of global GDP in thefirst quarter of 2017Mutual funds reached a size of USD 4277

trillion the most important group in this industry 65 of themanaged assets correspond to stocks and debt instrumentswith 43 of total participation being equity funds Thesenumbers underscore the relevance of these investors andthe need to deepen understanding of the effects of theseintermediariesrsquo investment strategies on financial risk in thisindustry

The use of networks has made it possible to studymainly the structures of control chains in financial systemssystemic risk the evolution of commerce between nationsand interbank transactions between banks [11] These papersconsider similarity-based networks in which the weights of anetwork represent a measurement of similarity (or distance)between assets this measurement is a linear correlationbetween the returns on the assets The correlation thenbecomes a distance associated with a Euclidian distancewhich is why hierarchical clustering methods can be appliedto understand the industry-specific structure and clustersAlso using the network approach it is possible to detectthe relations between different market agents to discoverthe underlying control chains [12 13] Finally in the studyof transactions between two agents the links represent thetransactions whereas the nodes represent the agents in thefinancial market For example Boss and others [14] studythe formation of community structures and other topologicalelements of the networks that show free scale and small worldproperties However there is a gap in the literature respectto the relation between topological elements of the financialnetwork the variables of asset management and industryvariables For example in the case of mutual funds how doesthe path length of the network varywhen portfoliosmanagersbegin increasing the sale of assets to buy others or whenthey decide to increase or reduce the diversification of theirportfolios

Given the logical evolution of the literature on financialnetworks analysis and to contribute to a deeper understand-ing of the portfolio overlaps phenomenon in a mutual fundindustry context this study aims to examine how financialmanagement variables in conjunction with specific variablesfrom the mutual fund industry mold and shape financialnetworks between funds and financial assets

Accordingly in this workwe study the following hypothe-ses

(1) the topology of the mutual funds network changesdue to variations in the investment strategies selected by theindustry actors

(2) the topology of themutual funds network changes dueto variations in industry-specific variables

Our research contributes to the literature by improvingthe understanding of the phenomenon of overlapping fromthree perspectives First we analyze the topology of themutual funds network using a bipartite network method(similar to Delpini and others [8]) and we complement itwith an analysis of its bipartite one-mode network projection(for a summary see Zhou and others [15] and Straka et al[5]) Second we study the effect of economic and financialshocks that affect the equity market as a whole on thetopological properties of the funds network And third weconsider studying the impact of changes in the mutual fundrsquos

Complexity 3






2 Model








4 Complexity


3 The Data










Complexity 5

10minus2

10minus2

10minus25

10minus25

10minus3

10minus3

10minus4

10minus35

10minus35

Ｅ

P(K=

Ｅ)

P(S=

Ｍ)

Ｍ

102

1015

101

1005

100

102

103

1015

1025

101

1005

100







119867119894 = minus119873

sum119895=1

119908119894119895119908119894lowast

log2119908119894119895119908119894lowast

(1)


6 Complexity

2628

3032

3436


Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity


01

23

4


Average Path Length

78

91


Assortativity

05

11

52


Modularity

1015

2025

30


Strength


Figure 2

Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3






2 Model








4 Complexity


3 The Data










Complexity 5

10minus2

10minus2

10minus25

10minus25

10minus3

10minus3

10minus4

10minus35

10minus35

Ｅ

P(K=

Ｅ)

P(S=

Ｍ)

Ｍ

102

1015

101

1005

100

102

103

1015

1025

101

1005

100







119867119894 = minus119873

sum119895=1

119908119894119895119908119894lowast

log2119908119894119895119908119894lowast

(1)


6 Complexity

2628

3032

3436


Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity


01

23

4


Average Path Length

78

91


Assortativity

05

11

52


Modularity

1015

2025

30


Strength


Figure 2

Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity


3 The Data










Complexity 5

10minus2

10minus2

10minus25

10minus25

10minus3

10minus3

10minus4

10minus35

10minus35

Ｅ

P(K=

Ｅ)

P(S=

Ｍ)

Ｍ

102

1015

101

1005

100

102

103

1015

1025

101

1005

100







119867119894 = minus119873

sum119895=1

119908119894119895119908119894lowast

log2119908119894119895119908119894lowast

(1)


6 Complexity

2628

3032

3436


Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity


01

23

4


Average Path Length

78

91


Assortativity

05

11

52


Modularity

1015

2025

30


Strength


Figure 2

Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5

10minus2

10minus2

10minus25

10minus25

10minus3

10minus3

10minus4

10minus35

10minus35

Ｅ

P(K=

Ｅ)

P(S=

Ｍ)

Ｍ

102

1015

101

1005

100

102

103

1015

1025

101

1005

100







119867119894 = minus119873

sum119895=1

119908119894119895119908119894lowast

log2119908119894119895119908119894lowast

(1)


6 Complexity

2628

3032

3436


Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity


01

23

4


Average Path Length

78

91


Assortativity

05

11

52


Modularity

1015

2025

30


Strength


Figure 2

Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity

2628

3032

3436


Degree

100

200

300

400

500


Strength

04

045

05

055


Diversity


01

23

4


Average Path Length

78

91


Assortativity

05

11

52


Modularity

1015

2025

30


Strength


Figure 2

Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7













lt 119889 gt= 1119873 (119873 minus 1)

sum119894119895=1119873119894 =119895

119889119894119895 (2)



8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity

0

1

2

3


log1

0 of

Stre

nght

Strengthin

out


0

1

2

3


log1

0 of

Stre

nght

Strength

in

out


Figure 3

Case 1

MF1 MF1 MF1

S1 S1 S1

S1

S1

S2 S2

S3 S3

10

10

1

11

10

101

11

11

1

1

1

1

MF2 MF2 MF2

Case 2 Case 3


MF1 MF1MF1

101

1 01 043

01

MF2 MF2 MF2

(b) Zhou Projection

Figure 4



Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9










119884119905 = 120572 + 120573 lowast 119883119905 + 120574 lowast 119862119905 + 119898119905 + 120576119905 (3)





10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








10 ComplexityTa

ble1Bipartite

Netwo

rkMod

elsTh

istablesummarizes

ther

esultsof

thefollowingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thed

ependent

varia

bleisY t

andrepresentthe

varia

tionin

the

topo

logicalvariables

ofthebipartite

networksX

tcorrespo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

taremon

thlyfixed

effectsto

controlfor

season

ality

Allmod

elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

lnmcap

00104

-0000299

-00372

-00217

000

857

-000878

(0248)

(0964

)(0356)

(0444

)(037

8)(0266

)ln

liq-00127lowast

-000336

-00573lowastlowast

-00559lowastlowast

-0004

55000

477

(0072)

(0616)

(0033)

(0023)

(0561)

(0496)

lnbo

ok00212

000

632

-0249lowastlowast

-014

4lowastlowastlowast

005

51lowastlowast

00134

(0382)

(0641)

(0019)

(0002

)(0041)

(0369)

lnto


000

509

-00583

-00752lowastlowast

002

10lowastlowast

000

636

(0003)

(0488)

(014

4)(0033)

(0012)

(0412)

lnas

00185

-00158

00159

00186

004

83lowastlowast

000

522

(032

7)(0293)

(0813)

(074

5)(0015)

(0737)

lnsto

cks



0172

0169

0120lowastlowast

00380

(0000

)(0000

)(032

0)(017

6)(0021)

(0314)

lnfund

s-00344

00102

-00199

-00289

-0045

9lowast000

0722

(013

5)(033

3)(0837)

(0583)

(0058

)(0958)

lninvesto

r-00314lowastlowast


-010

9lowastlowast

-00457

-0006

78-00153

(0019)

(0001)

(0045

)(019

3)(0648)

(015

4)Lperfo

rmance



0129

0210



(0000

)(0000

)(0571)

(037

0)(0000

)(0006

)ipsa

ret

008

29lowast

00327

008

93lowast




00638

-00175

00367

(0095)

(0425)

(0065

)(0000

)(0000

)(0000

)(0306

)(0735)

(0567)

varvix

00139

00144

00173

000385

-0000

578

000

691

-000301

-000342

-000150

(0235)

(016

4)(015

6)(0908)

(0987)

(0841)

(0847)

(0811)

(0923)

varcu

00132

000

151

-00131

-00239

00148

-00426

00232

000314

000393

(0544

)(0946

)(0623)

(0818)

(0895)

(0680)

(0438)

(0912)

(0893)

varclp

00394

00326

-00255

0292

0297

0287

00813

00586

00291

(039

5)(0478)

(0640

)(0409)

(0404

)(0404

)(017

5)(0286)

(0611)

varm

sci

00155

00255

000213

0179

00846

0183

0111lowastlowast

0113lowastlowast

0101lowastlowast

(0690)

(0500

)(0962)

(037

3)(0687)

(0363)

(0021)

(0022)

(0043

)varpe

000272

000

612

00195

00549

00811

00716

-00224

-00129

-00111

(0883)

(0719)

(032

9)(0549)

(0403)

(0439)

(031

8)(053

1)(0612)

spxret

00931

0104lowast

00917

006

610200

00194

-00317

-00124

-00254

(013

4)(0096

)(0249)

(0841)

(053

9)(0952)

(0708)

(0886)

(0781)

Lvdegfon

-013

3lowast-012

000435

(0071)

(013

3)(0609)

Lvstre

ngthb

004

4700524

0105

(074

2)(0712)

(031

3)Lvh

erfin

dahl

Lventropy

-00483

-00207

004

11(0556)

(0800

)(0627)

cons

-0293

-014

1lowastlowast

-0004

700159

-017

9-0286

-0212

-00221

0160

(013

9)(0049

)(0957)

(0837)

(0622)

(0443)

(037

8)(0814)

(015

6)

Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11

Table1Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

vdegfon

vstre

ngthb

vdiversity

N158

158

158

158

158

158

158

158

158

R2036

4028

90142

0521

046

6050

4025

40160

0122

adjR2

0226

0167

-0013

0417

0374

0415

009

20016

-0037

P-value

000

000

058

000

000

000

005

034

077

F3522

3172

1394

950

0663

0958

119

3518

1310

99LR

-Chi2

1777

4738

1713

545

1873

2573

ProbgtC

hi2

000

000

000

024

000

000

Non

stand

ardizedcoeffi

cients

p-values


12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity










Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 13Ta

ble2

ProjectedBipartite

Netwo

rkMod

elsTh

istablesummarizes

theresults

ofthefollo

wingmod

elY

t=120572+120573 lowast


+m

t+120576 t

Thedepend

entv

ariableisY t

andrepresentthe

varia

tionin

thetop

ologicalvaria

bles

oftheb

ipartiten

etwo

rksX t

correspo

ndstotheind

ependent

varia

blesC

tcorrespo

ndstothec

ontro

lvariablesm

tarem

onthlyfixed

effectsto

control


elsa

reestim

ated

with

robu

ststa

ndarderrors

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityln

mcap

00571

-0000

637

-00855lowastlowast

-00132

00522

004

20000

0921

-000711

(014

0)(0981)

(0014)

(0495)

(0862)

(0792)

(0950)

(0490)

lnliq

000252

-0006

07-00221

-00225

00199

00550


-0020

2lowastlowastlowast

(0914)

(0778)

(0269)

(0216)

(0896)

(0720)

(0002

)(0009

)ln

book

-0209lowastlowast

-00937lowastlowast

-00119

00139

-0405

0128

-00208

-0044

8lowastlowastlowast

(0046

)(0039

)(0894)

(0663)

(0618)

(0640

)(0512)

(0004

)ln

to-00156

-00295

00148

00313lowast

0213

00320

00105

000

0331

(0586)

(0239)

(0417)

(0098

)(039

8)(0876)

(0211)

(0965)

lnas

00923

00367

-012

3lowastlowast

-00333

0527

0413

-00130

-0034

7lowastlowast

(017

9)(0433)

(0041)

(0415)

(0358)

(0343)

(0498)

(0017)

lnsto

cks

-0228

-00991

0177

0103

0708

0374

006

4700272

(010

6)(0408)

(012

8)(031

6)(053

2)(0509)

(0225)

(0565)

lnfund


-00294


00537

-0447

0480

-00215

-0004

62(0005

)(0473)

(0003)

(013

3)(0426)

(0218)

(0482)

(074

3)ln

investo

r-00319

00564

-0044

1-00484

-0558

-0211

-000331

000

136

(0579)

(010

6)(0432)

(0117)

(0227)

(0307)

(0852)

(0916)

Lperfo

rmance

-00632

006

83-017

1-0202lowastlowast

1990

1940lowast

0144lowastlowast

0124lowastlowast

(0717)

(0623)

(0117)

(0043

)(012

5)(0072)

(0020

)(0021)

ipsa

ret

-0402lowast

-019

7-0282lowast

00888

000

502

00927

-017

7-013

30650

-000888

-00356

-00188

(0051)

(0219)

(0097

)(0616)

(0973)

(0509)

(0897)

(0904

)(0670)

(0905)

(0591)

(0785)

varvix

-0056

8lowast-00591

-0056

8lowast-00348

-00357

-0040

5lowast-014

7-013

3-00512

-0006

62-000717

-000220

(0077

)(010

3)(0097

)(016

2)(015

0)(0083)

(0380)

(0428)

(0771)

(0560

)(053

8)(0853)

varcu

-013

4-015

7-016

400546

00855

00949

1014

0671

064

100125

00177

-000388

(0219)

(016

2)(014

5)(0419)

(015

8)(012

9)(0254)

(037

4)(0456)

(0732)

(0603)

(0916)

varclp

-00335

-00213

-00199

0184

0185

0218

1292

1108

0653

0180lowast

0188lowast

0138

(0887)

(0928)

(0933)

(033

5)(033

5)(0234)

(0355)

(0401)

(0566

)(0054

)(0054

)(014

0)varm

sci

-00423

-00263

00207

00226

000263

-000847

-0225

-0202

-0404

00899

00928

00790

(0806

)(0885)

(0908)

(0872)

(0985)

(0953)

(0829)

(0849)

(0693)

(0210)

(0212)

(0277)

varpe

-00436

-00497

-00626

-00682

-00490

-00573

-013

900226

00186

000

614

000

710

00154

(0589)

(0543)

(0450)

(019

7)(0304

)(0274)

(0800

)(0963)

(0971)

(0834)

(0804

)(0619)

spxret

0417

0393

0377

-0284

-0258

-0327lowast

-216

2-1906

-1753

-017

0-015

2-014

5(010

2)(012

9)(013

9)(0119)

(012

8)(0058

)(0231)

(0259)

(033

1)(010

6)(016

4)(019

3)Lvstre

nghtp


-0226lowastlowast


(0003)

(0011)

(0008

)Lvm

odularity

-00472

000

823

00123

(0663)

(0940

)(0914)

Lvpathlength

-018

6lowastlowastlowast

-017

9lowastlowastlowast

-019

2lowastlowastlowast

(0000

)(0000

)(0000

)Lvassortativ


-0209lowastlowast

-0239lowastlowast

(0028

)(0049

)(0022)

cons

0952

000

0335

-015

1-00679

-016

10147

3411

-1035

0339

-0252

-00969

-00615

(019

6)(0999)

(0679)

(0921)

(052

2)(0578)

(0503)

(0580)

(0889)

(032

6)(0409)

(0659)

14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








14 Complexity

Table2Con

tinued

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

vstre

nghtp

vmod

ularity

vpathlength

vassortativ

ityN

158

158

158

158

158

158

158

158

158

158

158

158

R2029

90233

0251

0237

0174

0158

0195

0169

0149

027

10215

0216

adjR2

0147

0101

0115

007

10032

000

6002

0002

6-0004

0113

008

10074

P-value

000

000

002

009

023

042

033

027

051

002

005

007

F3612

2229

2320

1766

1603

1684

1672

227

1262

519

3016

1017

34LR

-Chi

21428

1055

1249

1554

503

872

1164

1158

ProbgtC

hi2

001

003

003

000

041

007

004

002

Non

stand

ardizedcoeffi

cients

p-values


1

Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 15











6 Conclusions




16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








16 Complexity












(0000) (0001) (0728) (0180) (0022)dum crisis -000531 -000630 -000314 000171 00130 000152


(0115) (0000) (0324) (0053) (0587) (0915)varvix 00122 000476 -000406 -00562lowast -00306 -000607

(0307) (0858) (0799) (0083) (0232) (0607)varcu 00126 -00449 00227 -0134 00566 00127

(0564) (0672) (0447) (0220) (0400) (0726)varclp 00348 0278 00783 -00319 0197 0181lowast


(0704) (0377) (0022) (0808) (0860) (0210)varpe 000451 00742 -00213 -00441 -00738 000561

(0807) (0409) (0347) (0583) (0163) (0850)spx ret 00742 -000386 -00431 0424 -0235 -0164

(0245) (0990) (0620) (0114) (0206) (0122)Lvdegfon -0140lowast






(0027)cons -0322 -0297 -0228 0961 000294 -0244

(0110) (0475) (0353) (0197) (0996) (0338)

Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 17

Table 3 Continued











18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








18 Complexity

Appendix







11990121







Data Availability




Acknowledgments


Endnotes






Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








Complexity 19



References







































20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018








20 Complexity




















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








modeling overlapped mutual funds’ portfolios: a bipartite network...

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