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Volume 2 Number 3September 2016

The Jo

urn

al of N

etwo

rk Theo

ry in Fin

ance

Volume 2 N

umber 3 Septem

ber 2016

■ NetMES: a network based marginal expected shortfall measureShatha Qamhieh Hashem and Paolo Giudici

■ A multilayer model of order book dynamicsAlessio E. Biondo, Alessandro Pluchino and Andrea Rapisarda

■ Directors’ networks and firm valuation in a concentrated ownership structure economyRonen Barak and Oren Kapah

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The Journal of Network Theory in FinanceEDITORIAL BOARD

Editors-in-ChiefKimmo Soramäki Financial Network Analytics Ltd.Tiziana Di Matteo King’s College London

Associate EditorsFranklin Allen Brevan Howard Centre

& Imperial College Business SchoolIgnazio Angeloni European Central BankTomaso Aste University College LondonStefano Battiston University of ZurichChristian T. Brownlees Pompeu Fabra

UniversityGuido Caldarelli IMT LuccaAndrew Coburn RMS, Inc.

& University of CambridgeRama Cont Imperial College London

& CNRS (France)Ben Craig Deutsche BundesbankRodney Garratt Federal Reserve Bank

of New YorkCo-Pierre Georg Deutsche BundesbankAndrew G. Haldane Bank of England

Sergey Ivliev PrognozDror Kenett Office of Financial Research,

US TreasuryIman Van Lelyveld De Nederlandsche BankThomas Lux University of Kiel

& University Jaume IRosario Nunzio Mantegna Central

European University & Palmero UniversitySerafín Martínez Jaramillo Banco de

MéxicoCamelia Minoiu International

Monetary FundYaacov Mutnikas Markit GroupPeter Sarlin Hanken School of EconomicsDidier Sornette ETH ZurichMurat Unal SONEAN GmbH

& Funds at Work

SUBSCRIPTIONSThe Journal of Network Theory in Finance (Print ISSN 2055-7795 j Online ISSN 2055-7809) ispublished quarterly by Incisive Risk Information Limited, Haymarket House, 28–29 Haymarket,London SW1Y 4RX, UK. Subscriptions are available on an annual basis, and the rates are set outin the table below.

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The Journal of

Network Theoryin Finance

The journalFinancial institutions and markets are highly interconnected, but only recently hasliterature begun to emerge that maps these interconnections and assesses their impacton financial risks and returns. The Journal of Network Theory in Finance is an interdis-ciplinary journal publishing academically rigorous and practitioner-focused researchon the application of network theory in finance and related fields. The journal bringstogether research carried out in disparate areas within academia and other researchinstitutions by policymakers and industry practitioners.

The Journal of Network Theory in Finance publishes data-driven or theoreticalwork in – but not limited to – the following areas.

� Empirical network analysis that enables better understanding of financialflows, trade flows, input–output tables, financial exposures or market inter-dependencies.

� Modeling and simulation techniques for measuring interdependent financialrisks.

� New metrics and techniques for identifying central, vulnerable or systemicallyimportant institutions and markets in financial networks.

� Network modeling of time-series data for financial risk management, assetallocation and portfolio management.

� Social network analysis (SNA) in finance, such as using social network datafor making credit and investment decisions.

� Applied network visualization techniques that improve the communication offinancial risks and rewards.

� Analysis of counterparties and their risk exposure from interconnectivity withthe financial system and regulatory strategies for improving financial stability.




The Journal of Network Theory in Finance Volume 2/Number 3

CONTENTS

Letter from the Editors-in-Chief vii

RESEARCH PAPERSNetMES: a network based marginal expected shortfall measure 1Shatha Qamhieh Hashem and Paolo Giudici

A multilayer model of order book dynamics 37Alessio Emanuele Biondo, Alessandro Pluchino and Andrea Rapisarda

Directors’ networks and firm valuation in a concentratedownership structure economy 53Ronen Barak and Oren Kapah

Editors-in-Chief: Kimmo Soramäki, Tiziana Di Matteo Subscription Sales Manager: Aaraa JavedPublisher: Nick Carver Global Key Account Sales Director: Michelle GodwinJournals Manager: Dawn Hunter Composition and copyediting: T&T Productions LtdEditorial Assistant: Carolyn Moclair Printed in UK by Printondemand-Worldwide

©Copyright Incisive Risk Information (IP) Limited, 2016. All rights reserved. No parts of this publicationmay be reproduced, stored in or introduced into any retrieval system, or transmitted, in any form or by anymeans, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of thecopyright owners.




LETTER FROM THE EDITORS-IN-CHIEF

Kimmo Soramäki and Tiziana Di MatteoFinancial Network Analytics Ltd. and King’s College London

On September 13 and 14, 2016, the third annual conference on Network Theory andFinancial Risk, sponsored by The Journal of Network Theory in Finance, was heldat the Centre for Risk Studies at Cambridge University. The conference is uniquein bringing together academics, regulators and industry practitioners to discuss andshare knowledge about financial networks. The program contained nine keynotes andinvited talks from members of the journal’s editorial board. The thirty-three researchpapers presented over two days used methods from network theory to address systemicrisk, and discussed market risk and asset allocation strategies as well as risks stemmingfrom interbank exposures. Multilayer and multiplex networks featured heavily in thisyear’s program as a key new area of research, along with market-based methods formeasuring systemic risk. The conference was larger than the one in 2015 in termsof participants and research presented. The second day also featured an industrypanel with leading industry executives discussing “Networks and evolving analyticsdemands in large financial institutions”. The next conference will be held in September2017.

This issue contains three papers. The first, “NetMES: a network based marginalexpected shortfall measure” by Shatha Qamhieh Hashem and Paolo Giudici, developsa new measure for systemic risk based on the asset return series of financial insti-tutions. The authors apply this measure to the Gulf Cooperation Council countries’different banking sectors and find increased interconnectedness after the financialcrisis, where the most systemic nodes in the network are conventional banks withIslamic services windows. Market-based methods for systemic risk measurement arean important addition to the extensive work carried out by regulators to measuredirect links and channels of contagion through exposure and trade repository data.They provide a baseline and allow market participants to tackle systemic risk, as suchdata is not confidential.

The issues’s second paper, “A multilayer model of order book dynamics” byAlessioEmanuele Biondo, Alessandro Pluchino and Andrea Rapisarda, builds a simulationmodel for market price formation. The model, which borrows from similar modelsbuilt within the field of statistical mechanics, represents information spreading andtrading as separate layers in a multiplex network. In the model, realistic price for-mation emerges from the dynamical interaction among traders. Models such as thesehelp us to understand and explain the often overlooked aspect of how small changesin the microstructure of the market can have large effects on its macroscopic behavior.

www.risk.net/journal




Our third paper, “Directors’ networks and firm valuation in a concentrated owner-ship structure economy” by Ronen Barak and Oren Kapah, contributes to the activeliterature on overlapping directors’networks, and measures the impact of the networkposition of different types of directors on firm performance. The authors find that pro-fessional directors in a sample of 727 listed Israeli firms with high centrality promotefirm valuation, while central external directors have a negative effect. The results areof interest to investors, policy makers and regulators, whose agency problems maybe mitigated by strong independent boards.

Journal of Network Theory in Finance 2(3)




Journal of Network Theory in Finance 2(3), 1–36DOI: 10.21314/JNTF.2016.020

Research Paper

NetMES: a network based marginal expectedshortfall measure

Shatha Qamhieh Hashem and Paolo Giudici

Department of Economics and Management Sciences, University of Pavia,Via San Felice Al Monastero, 5, 27100 Pavia, PV, Italy;emails: [email protected], [email protected]

(Received July 5, 2016; revised September 5, 2016; accepted September 13, 2016)

ABSTRACT

This paper aims to build novel measures of systemic risk that take the multivariatenature of the problem into account by means of network models. To account for modeluncertainty, we also employ a Bayesian approach, which allows model averagingover different network classes. The resulting systemic risk measure, which we callNetMES, is applied to the evaluation of the financial stability of the banking system inthe Gulf Cooperation Council countries. Banks are classified as fully-fledged Islamicbanks, conventional banks or hybrids: conventional banks with an Islamic window.The empirical findings indicate the presence of a difference between the two bankingsystems in terms of systemic risk, which can be explained by different levels ofcapitalization and leverage.

Keywords: correlation networks; dynamic conditional covariances; graphical Gaussian models;partial correlations; systemic risk measures; Islamic banks.

Corresponding author: S. Q. Hashem Print ISSN 2055-7795 j Online ISSN 2055-7809Copyright © 2016 Incisive Risk Information (IP) Limited

1




2 S. Q. Hashem and P. Giudici

1 INTRODUCTION

The recent 2007–8 global financial crisis placed the financial system under distress,leading it to the edge of failure. The burden that this crisis placed on the financialsystem has emphasized the importance of systemic risk identification, measurementand management.

Systemic risk is typically measured in a financial system comprised of a networkof connected institutions, with linkages that allow the transfer and magnification offinancial distress during times of financial crisis (Billio et al 2012b). Some definitionsof systemic risk point out the correlation and direct causation that endogenously existwithin a network of financial institutions (see, for example, Bank for InternationalSettlements 1994; Kaufman 1994; Crockett 1997; George 1998; Board of Governorsof the Federal Reserve System 2001). Others point out an exogenous microeconomicevent that diffuses with a spillover effect from specific business units to others (see,for example, Kaminsky and Schmukler 1999; Aharony and Swary 1996; Kaminskyand Reinhart 2000; Kaufman 1994), or a macroeconomic event that adversely affectsmarket participants through causing simultaneous severe losses that diffuse throughthe system (Benoit et al 2015).

Our proposed methodology follows the approach of Billio et al (2012a), who intro-duces several econometric measures of connectedness based on principal componentanalysis and Granger causality networks. In a related paper, Diebold and Yılmaz(2014) propose vector autoregressive models; these are augmented with a least abso-lute shrinkage and selection operator (LASSO)-type estimation procedure, aimed atselecting the significant links in a network model. Similarly, Hautsch et al (2014) andPeltonen et al (2015) propose tail dependence network models aimed at overcomingthe bivariate nature of the available systemic risk measures. The previous models arebased on the assumption of full connectedness among all institutions, which makestheir estimation and interpretation quite difficult, especially when a large number ofthem are being considered. To tackle this issue, Ahelegbey et al (2015) and Giudiciand Spelta (2016) have recently introduced correlation network models, which canfully account for partial connectedness, expressed in terms of conditional indepen-dence constraints. A similar line of research has been followed by Barigozzi andBrownlees (2014), who have introduced multivariate Brownian processes with a cor-relation structure determined by a conditional independence graph. Our contributionfollows this latter perspective.

The main aim of this work is to evaluate and compare different banking systems interms of their systemic risk contribution. For this purpose, we use the stock marketreturn data of financial institutions, aggregated by banking sector type, for each con-sidered country. We then derive a correlation network between the different bankingsectors to investigate how risks spread. The recently introduced correlation network

Journal of Network Theory in Finance www.risk.net/journal




NetMES 3

models (Giudici and Spelta 2016) can account for partial connectedness, expressed interms of conditional independence constraints. They are based on graphical Gaussianmodels, which gives them a stochastic background, as well as on Bayesian modelaveraging, which improves their robustness.

Once a network is estimated, a natural request is to summarize it as a systemicrisk measure. This can be done, in financial network models, using network centralitymeasures. Below, we review the most important ones. In the next section, we proposean alternative measure of risk, which combines the well-known marginal expectedshortfall (MES) with a correlation network approach. Note that, in this paper, nodesin a network represent banking sectors of a country, the main object of our analysis.

We start the network centrality measures’ review with node degree centrality, asit is considered the simplest network summary. Node degree centrality measures thesignificant links that are present in the selected model, between a single node and allothers. For a node i in a network model with nodes j D 1; : : : ; n, let eij represent abinary variable that indicates whether a link between i and j is present (1) or not (0).The degree of a node i is then

Di DnX

j D1

eij :

Another important measure is betweenness centrality, which measures the inter-mediation importance of a node based on the extent to which it lies on paths betweenother nodes. It is defined as

Bi DX

jt ;jk

njt ;jk.i/

mjt ;jk

;

where njt ;jk.i/ is the number of shortest geodesic paths between nodes jt and jk

passing through node i , and mjt ;jkis the total number of shortest geodesic paths

between jt and jk , given that i ¤ jt ¤ jk for all nodes in the network.A third measure is closeness centrality, which for each node measures the average

geodesic distance to all other nodes. For a node i , it is defined as

Ci D 1Pnj D1 d.i; j /

;

in which d.i; j / is the minimum geodesic path distance between nodes i and j .A further measure that is considered pivotal in financial network models is the

eigenvector centrality (see, for example, Furfine 2003; Billio et al 2012a). It measuresthe importance of a node in a network by assigning relative scores to all nodes in thatnetwork, based on the principle that connections to few high-scoring nodes contributemore to the score of the node in question than equal connections to low-scoring nodes.

www.risk.net/journal Journal of Network Theory in Finance





More formally, for the i th node, the eigenvector centrality is proportional to the sumof the scores of all nodes which are connected to it, as in the following equation:

xi D 1

�

NXj D1

ai;j xj ;

where xj is the score of a node j , ai;j is the .i; j / element of the adjacency matrixof the network, � is a constant and N is the number of nodes of the network. Theprevious equation can be rewritten for all nodes, more compactly, as

Ax D �x;

where A is the adjacency matrix, � is the eigenvalue of the matrix A and x is theassociated eigenvector for an N -vector of scores (one for each node). Generally, therewill be many different eigenvalues � for which a solution to the previous equationexists. However, the additional requirement that all the elements of the eigenvectors bepositive (a natural request in our context) implies (by the Perron–Frobenius theorem)that only the eigenvector corresponding to the largest eigenvalue provides the desiredcentrality measures. Therefore, once an estimate of A is provided, network centralityscores can be obtained from the previous equation as elements of the eigenvectorassociated with the largest eigenvalue.

All the previously introduced measures are based on the adjacency matrix of acorrelation network and depend, therefore, only on the presence or absence of a linkbetween two nodes, and not on the actual dependence between them. To introducesuch dependence, we can extend the node degree into a partial correlation degree.This employs partial correlation between pairs of nodes as weights, as follows:

si DX

j

eij �ijV :

Once calculated, centrality measures must be interpreted. In general, for each cen-trality measure, the most important node will be the one with the highest score rank.As, in this paper, nodes are banking sectors of a country, the most systemic bankingsector will be the one with the highest rank.

Note, however, that for policy purposes it may be important to compare bankingsystems across all countries, somewhat aggregating the corresponding ranks. To thisend, we can calculate a ranking concentration (RC) ratio, as follows.

Consider a vector of ranks ki , where i D f1; : : : ; ng is the rank number such that1 is the highest and n is the lowest. Then, let wi indicate the weight of each rank,defined by

wi D n � .ki / � 1:





NetMES 5

Let is D f1; : : : ; nsg indicate the set of all indexes that correspond to a specificbanking sector s, such that is � i . The RC ratio of a banking sector s is the percentageof the aggregate weight, for each banking sector type

Pns

isD1 wis , from the total weightof all ranks’ numbers

PniD1 wi . Then, the RC ratio can be defined as

RCs DPns

isD1 wisPniD1 wi

:

The RC ratio RCs describes the risk of a banking sector, based on the ranks it has,in the different countries that have that banking sector. A higher RC ratio indicateshigher systemic risk for the specified banking sector type.

The introduction of the RC ratio will improve the achievement of the main appliedaim of this paper: the comparison of the stability, in terms of systemic risk contribution,of different banking sectors.

In pursuing this aim, we will focus on a relatively homogeneous set of coun-tries: those belonging to the Gulf Cooperation Council (GCC). Our data analysis willinclude publicly traded banks (deposit-taking institutions) within the GCC region forthe period 2005–14. The banks will be classified as one of three types: the fully-fledged Islamic banks (IB), the conventional banks (CB) and the conventional bankswith Islamic services window (CBwin).

Our application to the GCC countries contributes to the ongoing debate regardingthe ability of the Islamic banking system to support the financial system stability ofthe country or region in which it is based. This debate gained momentum as IslamicBanks maintained stronger asset growth compared with conventional banks duringthe later stages of the 2007–8 financial crisis (Hasan and Dridi 2011). The attention ofpolicy makers and researchers was thus directed toward them.According to our currentknowledge, there is no direct research comparison between Islamic and conventionalbanks from a systemic risk point of view.

For completeness, we recall the main peculiarities of the Islamic banking businessmodel. An Islamic bank is a financial institution that is engaged in all the bankingactivities of a conventional bank, but at a zero interest rate, in accordance with IslamicShariah rules (see, for example, Shafique et al 2012). The Islamic bank accounts arebased on profit and loss sharing (PLS) rather than on having an interest obligation, asis the case in a conventional bank. In addition, all its transactions are equity based orasset based; in other words, each transaction is backed by real assets or equity. Otherrules that an Islamic bank must satisfy include not being allowed to take excessiveuncertainty (called “gharar”), as in short-selling transactions, or excessive risk-taking(called “maysir”), as in gambling. Finally, Islamic banks are not allowed to financeany activity that is not halal, such as alcohol production or distribution (all ethicallyaccepted actions under Islamic Shariah principles are referred to as halal).






This paper is organized into four main sections. Section 2 is the methodology thatwill introduce our proposal. Section 3 includes the description of the data and ourresults. Section 4 ends the paper with a summary conclusion from the obtained results.

2 METHODOLOGY

2.1 Correlation networks

Following Billio et al (2012a), we consider a cross-sectional perspective to understandsystemic risk transmission mechanisms, fitting to the data a network structure that candescribe the mutual relationships between the different economical agents involved.

Correlation network models, introduced in Giudici and Spelta (2016), are suitableto stochastically infer a network structure, employing pairwise correlations among aset of N observed, agent-specific time series.

If we associate different time series with different nodes of a network, each pair ofnodes can be thought to be connected by an edge, with a weight that can be related tothe correlation coefficient between the two corresponding time series. Thus, a networkof N nodes can be described by its associated matrix of weights, named the adjacencymatrix: this is an N � N matrix, say A, with elements ai;j . Alternatively, if the aimof the research is to focus more on the structure of the interconnections, and less ontheir magnitude, the adjacency matrix can be made binary by setting ai;j D 1 whentwo nodes are correlated, and ai;j D 0 when they are not correlated.

It is well known that pairwise correlations measure both the direct and the indirecteffects of one variable on another. If the aim is to measure only the direct effect betweentwo variables, without the mediation of others, pairwise partial correlations, ratherthan marginal ones, should be calculated. From a statistical viewpoint, correlationscan be estimated, on the basis of N observed time series of data, assuming that obser-vations follow a multivariate Gaussian model, with an unknown variance–covariancematrix ˙ ; meanwhile, partial correlations can be estimated assuming that the sameobservations follow a graphical Gaussian model, in which the variance–covariancematrix ˙ is constrained by the conditional independence described by a graph (see, forexample, Whittaker (1990) and Lauritzen (1996), or, from an econometric viewpoint,Corander and Villani (2006) and Carvalho and West (2007)).

More formally, let x D .x1; : : : ; xN / 2 RN be an N -dimensional random vectordistributed according to a multivariate normal distribution NN .�; ˙/. We will assumethroughout that the covariance matrix ˙ is not singular. For an undirected graph, letG D .V; E/, with vertex set V D f1; : : : ; N g and edge set E D V �V ; this is a binarymatrix, with elements eij that describe whether pairs of vertexes are (symmetrically)linked to each other (eij D 1) or not (eij D 0). If the vertexes V of a graph areput in correspondence with the random variables X1; : : : ; XN , the edge set E induces





NetMES 7

conditional independence on X via the so-called Markov properties (see, for example,Lauritzen 1996). More precisely, the pairwise Markov property determined by G statesthat, for all 1 6 i < j 6 N ,

eij D 0 () Xi ? Xj j XV nfi;j gI

this indicates that the absence of an edge between vertexes i and j is equivalent toindependence between the random variables Xi and Xj conditionally on all othervariables xV nfi;j g.

In our context, all random variables are continuous and it is assumed that X �NN .0; ˙/. Let the elements of ˙�1, the inverse of the variance–covariance matrix,be indicated as f� ij g. Whittaker (1990) proved that the following equivalence alsoholds:

Xi ? Xj j XV nfi;j g () �ijV D 0;

where

�ijV D �� ij

p� i i�jj

denotes the ij th partial correlation, that is, the correlation between Xi and Xj con-ditionally on the remaining variables XV nfi;j g. It can also be shown that the partialcorrelation coefficient �ijV is equal to the correlation of the residuals from the regres-sion of Xi on all other variables (excluding Xj ) with the residuals from the regressionof Xj on all other variables (excluding Xi ), as in the following:

�ijV D ."Xi jXV nfj g ; "Xj jXV nfig/:

In other words, the partial correlation coefficient measures the additional contribu-tion of variable Xj to the variability of Xi not already explained by the others, andvice versa.

A graphical Gaussian model is a Gaussian distribution constrained by a set ofpartial correlations equal to zero, which corresponds to variables whose additionalcontribution is not statistically significant.

Mathematically, by means of the pairwise Markov property, and given an undirectedgraph G D .V; E/, a graphical Gaussian model can be defined as the family of allN -variate normal distributions NN .0; ˙/ that satisfy the constraints induced by thegraph on the partial correlations for all 1 6 i < j 6 N , as follows:

eij D 0 () �ijV D 0:

In practice, the available data will be used to test which partial correlations are dif-ferent from zero at the chosen significance level threshold ˛. This leads to the selec-tion of a graphical model on which all inferences are conditioned and, in particular,summary network measures, such as those seen in Section 1, are determined.






A drawback of all the previous measures is that they are conditional on a fixedgraphical structure. To overcome this problem and robustify the results, we assumean open model perspective and employ a Bayesian model averaging approach, inwhich the measure estimates are the averages of those coming from different graphs,each with a weight that corresponds to the Bayesian posterior probability of thecorresponding graph.

To achieve the above aim, the first task is to derive the likelihood of a graphical net-work and specify an appropriate probability distribution over all graphical networks,as follows.

For a given graph G, consider a sample X of size n from a Gaussian probabilitydistribution P D NN .0; ˙/, and let S be the observed variance–covariance matrixthat estimates ˙ .

For a subset of vertexes A � N , let ˙A denote the variance–covariance matrix of thevariables in XA, and denote by SA the corresponding observed variance–covariancesubmatrix. When the graph G is decomposable, the likelihood of the data, under thegraphical Gaussian model specified by P , nicely decomposes as follows (see, forexample, Giudici and Spelta 2016):

p.x j ˙; G/ DQ

c2C p.xC j ˙C /Qs2Sp.xS j ˙S /

;

where C and S , respectively, denote the set of cliques and separators of the graph G,and

P.xC j ˙C / D .2�/�n�jC j=2j˙C j�n=2 expŒ�1=2tr.SC .˙C /�1/�;

and similarly for P.xS j ˙S /. A convenient prior for the parameters of the abovelikelihood is the hyper-inverse Wishart distribution. This can be obtained from acollection of clique-specific marginal inverse Wisharts, as follows:

l.˙/ DQ

c2C l.˙C /Qs2S l.˙S /

;

where l.˙C / is the density of an inverse Wishart distribution, with hyperparametersTC and ˛, and similarly for l.˙S /. For the definition of the hyperparameters, wefollow Giudici and Spelta (2016) and let TC and TS be the submatrixes of a largermatrix T0 of dimension N � N , obtained in correspondence of the two complete setsof vertexes C and S . Assume also that ˛ > N . To complete the prior specification,for P.G/, we assume a uniform prior over all possible graphical structures.

Dawid and Lauritzen (1993) show that, under the previous assumptions, the poster-ior distribution of the variance–covariance matrix ˙ is a hyper Wishart distribution,with ˛ C N degrees of freedom and a scale matrix given by

Tn D T0 C Sn;





NetMES 9

where Sn is the sample variance–covariance matrix. This result can be used for quanti-tative learning on the unknown parameters for a given graphical structure. In addition,Dawid and Lauritzen (1993) show that the proposed prior distribution can be used tointegrate the likelihood with respect to the unknown random parameters, obtaining theso-called marginal likelihood of a graph, which will be the main metric for structurallearning. Such marginal likelihood is equal to

P.x j G/ DQ

c2C p.xC /Qs2Sp.xS /

;

in which

p.xC / D .2�/�n�jC j=2 k.jC j; ˛ C n/

k.jC j; ˛/

det.T0/˛=2

det.Tn/.˛Cn/=2I

here, k.�/ is the multivariate gamma function, given by

kp.a/ D �p.p�1/=4

pYj D1

�

�a C 1 � j

2

�:

Assume that we have several possible graphs, say jGj, and that they are equally likelya priori, so that the probability of jGj is

P.G/ D 1

jGj :

By Bayes’s rule, the posterior probability of a graph is given by

P.G j x/ / P.x j G/P.G/I

therefore, since we assume a uniform prior over the graph structures, maximizingthe posterior probability is equivalent to maximizing the marginal likelihood. Forgraphical model selection purposes, we shall thus search in the space of all possiblegraphs for the structure, such that

G� D arg maxG

P.G j x/ / arg maxG

P.x j G/:

A Bayesian model averaging approach does not force conditioning inferences onthe (best) model chosen. If we assume that the network structure G is random andassign a prior distribution to it, we can derive any inference on unknown parametersas model averages with respect to all possible graphical structures, with weightsthat correspond to the posterior probabilities of each network. This derives from theapplication of Bayes’s theorem, as follows:

P.˙ j X/ D P.˙ j x; G/P.G j x/:






Note that, in many real problems, the number of possible graphical structures couldbe very large, and we may need to restrict the number of models to be averaged. Thiscan be done efficiently, for example, following a simulation-based procedure formodel search, such as Markov chain Monte Carlo (MCMC) sampling. In our context,given an initial graph, the algorithm samples a new graph using a proposal distribu-tion. To guarantee irreducibility of the Markov chain, we follow Giudici and Spelta(2016) to test whether the proposed graph is decomposable. The newly sampled graphis then compared with the old graph, calculating the ratio between the two marginallikelihoods: if the ratio is greater than a predetermined threshold (acceptance prob-ability), the proposal is accepted; otherwise, it is rejected. The algorithm continuesuntil practical convergence is reached.

2.2 A network-based marginal expected shortfall

The measures of systemic risk that are most employed in the academic and regulatoryworlds include the MES, proposed by Acharya et al (2010); the systemically riskimportant financial institution measure (SRISK), proposed by Acharya et al (2012)and Brownlees and Engle (2012); and the Delta conditional value-at-risk (�CoVaR),introduced by Adrian and Brunnermeier (2011).

It is known that the MES is in favor of a too-interconnected-to-fail (TIF) logicrather than of a too-big-to-fail (TBTF) one. This makes it appropriate as a systemicrisk measure based on network models.

In our implementation of MES, we will use a dynamic conditional correlationapproach to take into account the increase in volatility during crisis times. To thisend, we will follow Brownlees and Engle (2012) and Engle (2012), who employ abivariate GARCH model for the demeaned returns process, which is based on a capitalasset pricing model (CAPM). We now briefly review their assumptions.

Consider a bivariate vector rt D .rit ; rmt /0 that contains, at each time point, the

returns of a sector and those of its reference market. Let H be its variance–covariancematrix; Brownlees and Engle (2012) and Engle (2012) propose that

rt D H1=2t �t ;

where �t D .�mt ; �it / represents a vector of independent and identically distributed(iid) zero mean innovations, and

Ht D

�2mt �mt �it �it

�mt �it �it �2it

!; (2.1)

where �mt is the standard deviation of the reference market returns, �it is the standarddeviation of the sector returns, and �it is the correlation between the sector and thereference market returns.





NetMES 11

To estimate Ht , we use the dynamic conditional correlation model of Engle (2002)and Engle and Sheppard (2001). Once Ht is estimated, we can proceed with theestimation of the MES measure, which is a function of Ht .

The MES measures the vulnerability of a banking sector i to the systemic riskoriginating from a financial market m. MES provides the one-day loss expected ifmarket returns are less than a given threshold C (in practice, it is assumed thatC D �2%). More precisely, MES is defined as a weighted function of tail expectationsfor the market residual, and tail expectations for the banking sector residual, bothcalculated at time t � 1, as follows:

MESit .C / D �mt�itEt�1

�"mt

ˇ̌ˇ̌ "mt <

C

�mt

�

C �it

q1 � �2

itEt�1

��it

ˇ̌ˇ̌ "mt <

C

�mt

�:

From an interpretational viewpoint, the higher a banking sector MES, the higherits contribution to the risk of the financial system.

We propose to modify the MES measure by building the bivariate GARCH modelon an extension of the CAPM model that takes correlations into account with moreprecision.

As previously described, the Engle (2012) model expresses returns as a functionof the correlation between the market and the sector under consideration. In highlycorrelated markets, such as financial ones, it could very well be the case that thecorrelation between the market and one sector’s returns contains other effects, forexample, the correlation of the considered sector with another sector, or the correlationof the market with another sector’s returns.

To remove “spurious” effects, which may bias the correlation between the sector andthe market returns, we replace correlations with partial correlations: the correlationsbetween the residuals from the regression of the sector returns on all other sectors,and the residuals from the regression of the market returns on all other sectors. In thisway, we obtain a “netted” estimate of H , which is not biased by spurious effects, and,consequently, a “netted” estimate of the MES.

Partial correlations can be easily calculated, conditionally on a graphical structure,within the quantitative learning framework of graphical Gaussian models describedin Section 2.1.

They can then be inserted in the Ht formula (2.1) in place of the correspondingcorrelations, giving rise to a different estimate of H and, consequently, MES. We willcall the latter NetMES, emphasizing both the fact that the new measure is “netted”from spurious correlations and also that it is conditional on a graphical network model.

To improve the stability and the robustness of the results, we can average theNetMES result from the different graphical networks, in a Bayesian model averaging






perspective, according to the paradigm introduced in Section 2.1, as follows:

E.MES j x/ DX

g

E.MES j x; g/P.g j x/;

where x represents the observed data evidence and g is a specific network model.We refer to E.MES j X/ as a Bayesian network-based MES measure (BayesianNetMES).

3 APPLICATION

3.1 Data description

In this subsection, we focus on data extraction. We work with the GCC countries,as they hold 38.19% of the total global Islamic banking assets (Islamic FinancialServices Board 2014). To construct our sample, we extract the GCC deposit-takinginstitutions present in Bureau Van Djik’s Bankscope, and we gather quarterly data onliabilities, equity and total assets from the beginning of 2005: this provides us with130 institutions. We exclude those that are not publicly traded, as our network modelsand systemic risk measure are based on equity returns: this reduces the number ofinstitutions to eighty-three. We also exclude those that disappeared before the endof our sample period in December 2014, leading to seventy-nine publicly traded,deposit-taking institutions, from six GCC countries. These are Bahrain (BH), withthirteen institutions; Kuwait (KW), with fifteen; Qatar (QA), with nine; United ArabEmirates (AE), with twenty-three; SaudiArabia (SA), with twelve; and, finally, Oman(OM), with eleven.

For the seventy-nine chosen institutions, we extract daily stock market closingprices and corresponding market capitalization from Thomson Reuters Datastream,for a total of 2608 observations, over a study period from January 2005 to December2014.

We construct stock market return time series under the stationary assumption thatthe mean � D 0. To achieve stationarity, we transform the daily stock market closingprice into returns that are expressed, as usual, in time variation. Formally, if Vit andVit�1 are the closing stock prices of bank i at times t and t � 1, the return is thevariation represented by rit D .Vit �Vit�1/=Vit�1, where Vit�1 ¤ 0 and is preparedusing log returns.

Then, for each country, we classify institutions into sectors, according to their banktype, and construct aggregate sectorial returns.We define the aggregate sectorial returnrst as the value-weighted average of the returns of all banks that belong to a countryspecific sector s: i D 1; : : : ; ns , as in the following:

rst DnsX

iD1

witrit ;





NetMES 13

in which wit D mvit=Pns

iD1 mvit;s represents the weight of the i th bank in thespecified banking sector s at time t , given by its market capitalization mvit relativeto the sector aggregate capitalization

Pns

iD1 mvit;s .The list of countries, along with the corresponding percentage of banking sector

assets, is described in Table 1.From Table 1, we note that the country with the largest banking assets is AE,

followed by SA, QA, KW, BH and OM, in descending order. Note also that theCBwin sector is usually the largest one for all GCC countries. Further, the CB sectoris larger than the IB sector in both OM and AE, but IB is larger than CB in SA, QA,KW and BH.

We also report the banking sectors, ranked in terms of their leverage (defined asthe ratio between the book value of equity and the book value of assets) in Table 2,market value (defined as the number of shares outstanding multiplied by share price)in Table 3, and quasi-leverage (defined as the ratio between the market value of assetsand the market capitalization) in Table 4. In Table 5, we report the RC ratio, RC%,which summarizes the importance of each banking sector type (CBwin, IB and CB).The first part of Table 5 shows the RC% for leverage, the second part shows the RC%for market capitalization and the third part shows the RC% for quasi-leverage.

Table 2 lists the CBwin sector in the highest leverage ranks for all periods. However,the RC% for leverage shows that the CBwin sector has its highest leverage level inthe crisis period but decreased after, while the IB sector increased its leverage in thepost-crisis period; the CB sector seems to have a stable low leverage ranking levelacross the three periods.

Table 3 also lists the CBwin sector in the highest market capitalization ranks for allperiods. The RC% for market capitalization shows that the CBwin sector increasedits capitalization in the crisis period, while the IB sector has the opposite behavior.As for the CB sector, it shows a stable low market capitalization level in all periods.

Table 4 shows results that are consistent with those in Table 2, with the addition ofaspects related to Table 3. This is expected, as quasi-leverage takes both leverage andcapitalization into account.

3.2 Correlation network models

In this subsection, we address the issue of how different banking sectors are intercon-nected with each other. For this purpose, we build a graphical Gaussian model, on thebasis of partial correlations between the aggregate returns of the banking sectors, forthe pre-crisis (2005–6), during crisis (2007–8) and post-crisis (2009–14) periods. Thebest model is selected using a backward selection procedure that starts from a fullyconnected model and subsequently tests for edge removal at the selected significance





14 S. Q. Hashem and P. GiudiciTA

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NetMES 15

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.






TABLE 2 Leverage.

Pre-crisis Crisis Post-crisis

SA.CBwin SA.CBwin AE.CBwinAE.CBwin AE.CBwin SA.CBwinBH.CBwin BH.CBwin QA.CBwinKW.CBwin QA.CBwin SA.IBSA.IB KW.CBwin KW.IBQA.CBwin AE.IB AE.IBAE.IB KW.IB BH.CBwinKW.IB SA.IB KW.CBwinBH.IB BH.IB QA.IBOM.CBwin OM.CBwin OM.CBwinKW.CB QA.IB BH.IBQA.IB KW.CB KW.CBOM.CB OM.CB OM.CBAE.CB AE.CB AE.CBBH.CB BH.CB BH.CBOM.IB OM.IB OM.IB

TABLE 3 Market capitalization.


SA.CBwin SA.CBwin SA.CBwinSA.IB AE.CBwin AE.CBwinAE.CBwin SA.IB QA.CBwinQA.CBwin KW.IB SA.IBKW.IB QA.CBwin KW.IBAE.IB KW.CBwin QA.IBQA.IB AE.IB KW.CBwinKW.CBwin QA.IB AE.IBBH.CBwin BH.CBwin BH.CBwinBH.IB OM.CBwin OM.CBwinOM.CBwin BH.IB KW.CBKW.CB KW.CB BH.IBAE.CB AE.CB AE.CBOM.CB OM.CB OM.CBOM.IB OM.IB OM.IBBH.CB BH.CB BH.CB





NetMES 19

TABLE 4 Quasi-leverage.


BH.CBwin BH.CBwin BH.IBKW.CB AE.IB BH.CBwinOM.CB AE.CBwin AE.IBKW.CBwin BH.IB AE.CBwinBH.IB SA.CBwin SA.CBwinOM.CBwin OM.CBwin KW.CBwinAE.CBwin KW.CBwin OM.CBwinAE.IB OM.CB AE.CBSA.CBwin KW.CB OM.CBBH.CB QA.CBwin KW.IBAE.CB AE.CB KW.CBQA.CBwin KW.IB QA.CBwinKW.IB BH.CB QA.IBQA.IB QA.IB SA.IBSA.IB SA.IB BH.CBOM.IB OM.IB OM.IB

level of ˛ D 0:05. The selected graphical model for the pre-crisis period is describedin Figure 1; the crisis period model is described in Figure 2; and the post-crisis periodmodel is described in Figure 3.

In Figures 1–3, we can read the capacity of the corresponding banking sectorsas agents of systematic risk through the indication of their contagion channels. Thegraphs that correspond to the above figures can be employed to derive the centralitymeasures introduced in Section 1, in order to rank sectors from the most to the leastcontagious.

Table 6 for the pre-crisis period, Table 7 for the crisis period and Table 8 for thepost-crisis period show the centrality measure rankings that are calculated on the basisof the graphical models in Figures 1, 2 and 3, respectively. In addition, Table 9 showsthe RC ratio, RC%, for each of the centrality measure tables.

Tables 6–8 display the change in network centrality ranks before, during and afterthe crisis. If we focus on the sector that appears in the top rank within the differentcentrality measures, we find that both the CB and CBwin sectors have higher risks inthe pre-crisis period. The CBwin sector dominates the crisis period except when thenode partial correlation measure is considered, which selects the IB sector instead.As for the post-crisis period, we note that all three banking sectors appear in the topranks: both of the CBwin and IB sectors have two top ranks, while the CB sector hasone top rank, in terms of closeness centrality.






TABLE 5 RC% for leverage, market capitalization and quasi-leverage.

(a) RC% for leverage


CBwin 0.56 0.57 0.52IB 0.33 0.33 0.38CB 0.11 0.10 0.10

(b) RC% for market capitalization


CBwin 0.49 0.51 0.51IB 0.42 0.40 0.38CB 0.10 0.10 0.10

(c) RC% for quasi-leverage


CBwin 0.46 0.51 0.49IB 0.23 0.29 0.33CB 0.31 0.20 0.18

In summary, the RC% table shows that the CBwin sector almost always has the high-est systemic risk concentration in the pre-crisis period, and that it fully dominates thecrisis period. The IB sector increases its systemic importance in the post-crisis period,in which its systemic importance becomes equivalent to that of the CBwin sector.

To improve the robustness of our conclusions with respect to model selection,we have repeated the analysis with different significance thresholds (in particular, at˛ D 0:01). The results described above did not substantially change.

To further check our conclusions’ robustness, we have considered model averagingfor all the results, using a Bayesian approach, and have thus provided inferences thatfully take model uncertainty into account. In order to match the time periods with thoseof the correlation network models, all centrality measures have been calculated on atwo-year time window. Tables 10–14 provide the resulting Bayesian model centralitymeasure rankings. In addition, Table 15 shows the RC% for the centrality measuresof the Bayesian averaging model in the subsequent time periods.

From the previous tables, note that the rankings of the centrality measures obtainedvia Bayesian model averaging are mostly consistent with those conditional on the





NetMES 21

FIGURE 1 Pre-crisis network.

AE.w

AE.c

AE.i

BH.wBH.c

BH.i

KW.w

KW.c

KW.i

OM.w

OM.c

OM.iQA.w

QA.i

SA.w

SA.i

FIGURE 2 During-crisis network.

AE.w

AE.c

AE.i

BH.wBH.c

BH.i

KW.w

KW.c

KW.i

OM.w

OM.c

OM.iQA.w

QA.i

SA.w

SA.i






FIGURE 3 Post-crisis network.

AE.w

AE.c

AE.i

BH.w

BH.c

BH.i

KW.w

KW.c

KW.i

OM.w

OM.c

OM.i

QA.wQA.i

SA.w

SA.i

TABLE 6 Correlation model centrality rankings: pre-crisis (2005–6).

Node Node partial Eigenvectordegree Betweenness Closeness corr. degree centrality

AE.CB AE.CB AE.CBwin AE.CBwin AE.CBwinAE.CBwin KW.CB AE.CB KW.IB AE.CBKW.CB BH.IB AE.IB QA.IB AE.IBAE.IB BH.CBwin KW.CB KW.CBwin KW.CBBH.CBwin KW.CBwin BH.IB QA.CBwin OM.CBwinKW.CBwin AE.CBwin OM.CBwin AE.IB KW.CBwinBH.IB AE.IB BH.CBwin BH.IB KW.IBKW.IB SA.CBwin KW.CBwin OM.CB BH.IBOM.CBwin QA.IB KW.IB SA.IB SA.CBwinQA.IB OM.CB QA.IB SA.CBwin BH.CBwinSA.CBwin OM.IB SA.CBwin BH.CBwin SA.IBBH.CB KW.IB BH.CB OM.IB QA.IBOM.CB SA.IB QA.CBwin AE.CB BH.CBOM.IB BH.CB SA.IB KW.CB QA.CBwinQA.CBwin QA.CBwin OM.CB BH.CB OM.CBSA.IB OM.CBwin OM.IB OM.CBwin OM.IB





NetMES 23

TABLE 7 Correlation model centrality rankings: crisis (2007–8).


QA.CBwin QA.CBwin QA.CBwin KW.IB QA.CBwinAE.CBwin OM.CBwin AE.CBwin AE.IB AE.IBAE.IB AE.CBwin OM.CBwin AE.CBwin AE.CBwinOM.CBwin SA.CBwin OM.CB QA.CBwin OM.CBOM.CB KW.IB AE.IB OM.CB QA.IBAE.CB OM.CB BH.IB OM.CBwin OM.CBwinBH.IB BH.IB KW.IB SA.CBwin AE.CBKW.IB KW.CB AE.CB SA.IB BH.IBQA.IB AE.CB QA.IB KW.CBwin KW.IBKW.CBwin AE.IB KW.CB QA.IB BH.CBwinKW.CB KW.CBwin BH.CBwin BH.IB KW.CBSA.CBwin QA.IB KW.CBwin KW.CB OM.IBBH.CBwin SA.IB SA.CBwin BH.CBwin SA.CBwinOM.IB OM.IB OM.IB AE.CB KW.CBwinSA.IB BH.CBwin SA.IB BH.CB SA.IBBH.CB BH.CB BH.CB OM.IB BH.CB

TABLE 8 Correlation model centrality rankings: post-crisis (2009–14).


OM.CBwin BH.IB BH.CB AE.IB OM.CBwinAE.CBwin OM.CBwin OM.CBwin OM.CBwin AE.CBwinAE.IB KW.IB AE.IB AE.CBwin AE.IBSA.IB AE.IB BH.IB KW.IB SA.IBAE.CB AE.CBwin AE.CBwin QA.IB QA.IBBH.CBwin BH.CBwin BH.CBwin SA.IB AE.CBBH.IB SA.IB SA.IB QA.CBwin BH.CBwinQA.IB AE.CB AE.CB SA.CBwin QA.CBwinKW.IB OM.CB QA.IB KW.CBwin BH.IBOM.CB QA.IB OM.CB OM.CB OM.CBQA.CBwin SA.CBwin QA.CBwin OM.IB SA.CBwinSA.CBwin QA.CBwin SA.CBwin AE.CB OM.IBKW.CBwin KW.CBwin KW.IB BH.IB KW.IBKW.CB KW.CB OM.IB BH.CBwin KW.CBwinOM.IB OM.IB KW.CBwin KW.CB KW.CBBH.CB BH.CB KW.CB BH.CB BH.CB






TABLE 9 RC% for correlation network model.

(a) Pre-crisis (2005–6)


CBwin 0.40 0.35 0.41 0.40 0.42IB 0.32 0.35 0.33 0.46 0.33CB 0.29 0.30 0.26 0.13 0.25

(b) During crisis (2007–8)


CBwin 0.44 0.49 0.44 0.44 0.40IB 0.34 0.30 0.34 0.40 0.38CB 0.22 0.21 0.22 0.16 0.22

(c) Post-crisis (2009–14)


CBwin 0.42 0.39 0.38 0.43 0.43IB 0.41 0.46 0.38 0.46 0.41CB 0.17 0.15 0.24 0.11 0.15

selected models, commented on beforehand, thus emphasizing the robustness of theresults.

In more detail, the pre-crisis and crisis periods list the CBwin banking sector in thetop rank across all centrality measures. For interpretational purposes, the post-crisisperiod of this model does not extend over the whole 2009–14 period; instead, it issplit into three parts. The first post-crisis period of 2009–10 lists the CB sector in thetop rank, except for node partial correlation, in which the IB sector has higher risk.The second post-crisis period of 2011–12 lists only the CBwin banking sector in thetop rank, while the third post-crisis period is also in favor of the CBwin sector, exceptfor node partial correlation, which is repeatedly in favor of the IB sector.

The RC% table gives a summary perspective for the higher systemic risk sectors.The pre-crisis period indicates that the CBwin sector has the highest systemic risk.The crisis period shows that the systemic risk of the IB sector increases at the expenseof the CBwin sector, and this increase continues in the first post-crisis period, with





NetMES 25

TABLE 10 Bayesian model centrality rankings: pre-crisis (2005–6).


OM.CBwin OM.CBwin OM.CBwin AE.CBwin OM.CBwinAE.CBwin AE.CBwin AE.CBwin QA.IB SA.CBwinAE.CB AE.CB AE.CB AE.IB AE.CBwinAE.IB AE.IB AE.IB QA.CBwin BH.CBwinBH.CBwin BH.CBwin BH.CBwin BH.IB BH.CBBH.CB BH.CB BH.CB SA.CBwin BH.IBBH.IB BH.IB BH.IB SA.IB KW.CBwinKW.CBwin KW.CBwin KW.CBwin OM.CB KW.CBKW.CB KW.CB KW.CB OM.IB OM.CBOM.CB KW.IB OM.CB BH.CBwin OM.IBOM.IB OM.CB OM.IB KW.CBwin QA.CBwinQA.CBwin OM.IB QA.CBwin AE.CB QA.IBQA.IB QA.CBwin QA.IB BH.CB SA.IBSA.CBwin QA.IB SA.CBwin KW.IB AE.CBSA.IB SA.CBwin SA.IB OM.CBwin AE.IBKW.IB SA.IB KW.IB KW.CB KW.IB

TABLE 11 Bayesian model centrality rankings: crisis (2007–8).


OM.CBwin OM.CBwin OM.CBwin OM.CBwin OM.CBwinQA.IB QA.IB QA.IB SA.CBwin BH.CBwinSA.IB SA.CBwin SA.IB SA.IB BH.CBBH.CBwin OM.IB OM.IB QA.CBwin BH.IBBH.CB SA.IB SA.CBwin OM.CB KW.CBwinBH.IB KW.IB BH.CBwin QA.IB OM.CBKW.CBwin QA.CBwin BH.CB KW.IB SA.IBOM.CB OM.CB BH.IB BH.IB QA.IBOM.IB BH.CBwin KW.CBwin AE.CBwin OM.IBSA.CBwin BH.CB KW.IB AE.IB SA.CBwinKW.IB BH.IB QA.CBwin AE.CB KW.IBQA.CBwin KW.CBwin OM.CB BH.CBwin QA.CBwinAE.CBwin AE.CBwin AE.CBwin KW.CB AE.CBwinAE.CB AE.CB AE.CB KW.CBwin AE.CBAE.IB AE.IB AE.IB BH.CB AE.IBKW.CB KW.CB KW.CB OM.IB KW.CB






TABLE 12 Bayesian model centrality rankings: post-crisis, part 1 (2009–10).


KW.CB KW.CB KW.CB KW.IB OM.CBOM.CB OM.CB OM.CB QA.IB SA.CBwinKW.IB QA.IB KW.IB AE.IB KW.IBQA.IB KW.IB QA.IB OM.CBwin KW.CBSA.CBwin SA.CBwin SA.CBwin QA.CBwin SA.IBOM.CBwin OM.CBwin OM.CBwin SA.IB OM.CBwinOM.IB OM.IB OM.IB KW.CBwin OM.IBSA.IB SA.IB SA.IB AE.CBwin QA.IBAE.CB KW.CBwin AE.CB SA.CBwin AE.CBBH.CBwin AE.CB BH.CBwin OM.CB BH.CBwinQA.CBwin BH.CBwin QA.CBwin KW.CB QA.CBwinKW.CBwin QA.CBwin KW.CBwin BH.IB KW.CBwinAE.CBwin BH.CB AE.CBwin AE.CB AE.CBwinAE.IB AE.CBwin AE.IB BH.CB AE.IBBH.CB AE.IB BH.CB BH.CBwin BH.IBBH.IB BH.IB BH.IB OM.IB BH.CB



SA.CBwin SA.CBwin SA.CBwin SA.CBwin SA.CBwinKW.CBwin KW.CBwin KW.CBwin KW.IB KW.CBKW.CB KW.CB KW.CB KW.CBwin QA.CBwinQA.CBwin KW.IB QA.CBwin QA.CBwin KW.CBwinBH.IB OM.CB BH.IB SA.IB OM.IBKW.IB QA.CBwin KW.IB OM.CBwin BH.IBOM.CB SA.IB OM.CB AE.CBwin SA.IBOM.IB BH.IB OM.IB QA.IB OM.CBSA.IB QA.IB SA.IB AE.IB AE.IBAE.IB OM.IB AE.IB OM.CB OM.CBwinBH.CBwin BH.CBwin BH.CBwin AE.CB BH.CBBH.CB BH.CB BH.CB BH.IB BH.CBwinOM.CBwin AE.IB OM.CBwin BH.CBwin KW.IBQA.IB OM.CBwin QA.IB OM.IB QA.IBAE.CBwin AE.CBwin AE.CBwin BH.CB AE.CBAE.CB AE.CB AE.CB KW.CB AE.CBwin





NetMES 27



OM.CBwin OM.CBwin OM.CBwin AE.IB OM.CBwinSA.CBwin SA.CBwin SA.CBwin OM.CBwin SA.IBSA.IB SA.IB SA.IB SA.IB BH.IBBH.IB BH.IB BH.IB AE.CBwin KW.CBwinKW.CBwin KW.CBwin KW.CBwin SA.CBwin AE.CBwinAE.CBwin OM.IB AE.CBwin KW.IB AE.IBAE.IB AE.CBwin AE.IB QA.IB BH.CBwinBH.CBwin AE.CB BH.CBwin QA.CBwin BH.CBBH.CB AE.IB BH.CB OM.CB KW.CBKW.CB BH.CBwin KW.CB KW.CBwin KW.IBKW.IB BH.CB KW.IB OM.IB QA.CBwinOM.CB KW.CB OM.CB BH.IB QA.IBQA.CBwin KW.IB QA.CBwin BH.CBwin SA.CBwinQA.IB OM.CB QA.IB KW.CB OM.CBOM.IB QA.CBwin OM.IB AE.CB OM.IBAE.CB QA.IB AE.CB BH.CB AE.CB

the IB sector becoming the highest systemic risk sector. More specifically, the firstpost-crisis period shows that the differences between the three sectors’ RC% becomevery small. In the second post-crisis period, the CBwin sector retrieves its highestsystemic risk level. Finally, in the third post-crisis period, the IB sector again startsto increase its risk level, but to a lesser magnitude.

Overall, Bayesian model averaging confirms the presence of a difference in thesystemic risk level of the three banking sectors. The CBwin sector has the highestrank and highest RC% in most time periods and is indeed the main driver of conta-gion in GCC countries. However, the systemic risk originating in the IB sector gainsimportance in the crisis period, and in the first part of the post-crisis period.

We finally remark that the ranks obtained with correlation networks, in both theconditional and model-averaged versions, closely resemble those obtained with thequasi-leverage measure, which means that they capture a mixed effect from bothleverage and market capitalization.

3.3 NetMES and Bayesian NetMES

In this section, we compare the systemic risk contribution of the three banking sec-tors in the GCC countries using the standard MES, the proposed NetMES measureand the Bayesian NetMES measure. Table 16 describes the banking sectors’ systemic






TABLE 15 RC% for Bayesian model averaging.

(a) Pre-crisis (2005–6)


CBwin 0.44 0.43 0.44 0.40 0.54IB 0.26 0.29 0.26 0.46 0.22CB 0.29 0.29 0.29 0.14 0.24

(b) Crisis (2007–8)


CBwin 0.40 0.42 0.42 0.44 0.43IB 0.41 0.43 0.44 0.38 0.35CB 0.18 0.15 0.14 0.18 0.21

(c) Post-crisis, part 1 (2009–10)


CBwin 0.33 0.33 0.33 0.40 0.35IB 0.37 0.36 0.37 0.46 0.37CB 0.30 0.31 0.30 0.15 0.28

(d) Post-crisis, part 2 (2011–12)


CBwin 0.41 0.39 0.41 0.50 0.41IB 0.37 0.38 0.37 0.38 0.35CB 0.22 0.24 0.22 0.12 0.24

(e) Post-crisis, part 3 (2013–14)


CBwin 0.49 0.46 0.49 0.44 0.45IB 0.35 0.38 0.35 0.46 0.40CB 0.15 0.17 0.15 0.10 0.15





NetMES 29

TABLE 16 MES rankings.


SA.IB SA.IB KW.CBwinAE.IB SA.CBwin SA.IBSA.CBwin KW.CBwin OM.CBwinQA.IB OM.CBwin SA.CBwinQA.CBwin AE.IB QA.CBwinKW.CBwin QA.IB AE.IBAE.CBwin OM.CB OM.CBAE.CB QA.CBwin QA.IBOM.CB AE.CBwin AE.CBwinBH.IB BH.IB BH.IBKW.IB KW.IB KW.IBKW.CB AE.CB AE.CBOM.CBwin KW.CB KW.CBBH.CBwin BH.CBwin BH.CBwinOM.IB OM.IB OM.IBBH.CB BH.CB BH.CB

risk rankings using the standard MES. Table 17 describes the same rankings using theproposed NetMES, in which we consider a multivariate perspective, as we replace thecorrelations in MES estimation with partial correlations. Table 18 describes the rank-ings using the proposed Bayesian NetMES measure, which averages the previouslyestimated NetMES; finally, Table 19 shows the RC% for the risk measures rankings.

Table 16 for MES and Table 17 for NetMES both show that the IB banking sectordominates the top rank in the pre-crisis and crisis periods, while the CBwin sectordominates the top ranks in the post-crisis period. In other words, within the GCCbanking systems case, it seems that MES ranks capture the size effect, represented bymarket capitalization, which is also captured by node partial correlation degree, butnot by the other centrality measures that seem to be more dependent on leverage.

In terms of the RC% for the systemic risk measures, the first part of Table 19indicates for the MES measure a higher risk for the IB sector in the pre-crisis period,followed by the dominance of the CBwin sector in both the crisis and post-crisisperiods. The same risk hierarchy applies to the NetMES measure. The BayesianNetMES RC% instead indicates that CBwin is the higher risk sector throughout allperiods.

To better understand the difference between the MES, NetMES and BayesianNetMES measures, we further examine their evolution in a time dynamic manner.For this purpose, we follow the component expected shortfall (CES) measure prin-






TABLE 17 NetMES rankings.


SA.IB SA.IB OM.CBwinQA.IB OM.CBwin SA.IBAE.CBwin BH.IB KW.CBwinOM.CB OM.CB BH.IBKW.CBwin SA.CBwin QA.IBBH.CBwin KW.CBwin OM.CBKW.IB AE.CBwin AE.CBwinAE.CB AE.CB QA.CBwinAE.IB QA.CBwin SA.CBwinSA.CBwin BH.CBwin AE.CBOM.IB KW.IB KW.IBBH.IB QA.IB AE.IBOM.CBwin OM.IB BH.CBwinQA.CBwin AE.IB OM.IBKW.CB KW.CB KW.CBBH.CB BH.CB BH.CB

TABLE 18 Bayesian NetMES rankings.


SA.IB SA.IB KW.CBwinKW.CBwin SA.CBwin SA.IBSA.CBwin KW.CBwin OM.CBwinAE.IB QA.IB KW.IBQA.CBwin OM.CBwin SA.CBwinOM.CBwin OM.CB QA.CBwinQA.IB AE.IB OM.CBKW.IB QA.CBwin AE.IBAE.CBwin KW.IB QA.IBBH.IB AE.CBwin AE.CBwinOM.CB BH.IB BH.IBAE.CB AE.CB AE.CBKW.CB KW.CB KW.CBBH.CBwin BH.CBwin BH.CBwinOM.IB OM.IB OM.IBBH.CB BH.CB BH.CB





NetMES 31

TABLE 19 RC% for MES, NetMES and Bayesian NetMES.

(a) RC% for MES


CBwin 0.40 0.46 0.49IB 0.43 0.40 0.37CB 0.17 0.15 0.15

(b) RC% for NetMES


CBwin 0.38 0.46 0.45IB 0.44 0.35 0.40CB 0.18 0.18 0.15

(c) RC% for Bayesian NetMES


CBwin 0.46 0.44 0.46IB 0.42 0.40 0.39CB 0.12 0.15 0.15

ciple that is provided by Banulescu and Dumitrescu (2015). We prepare a weightedaggregate for MES, NetMES and Bayesian NetMES, per banking sector type and atthe overall GCC region level, using market capitalization as a weighting scheme.

More formally, the timely aggregate systemic risk measure RMs;t for each bankingsector type is

RMs;t DnjX

j D1

wjs;t rmjs;t ;

where rmjs;t is the risk measure for the specific banking sector type s in country j

at each time point t , and wjs;t D mvjs;t=Pnj

j D1 mvjs;t represents the weight of thebanking sector s in country j at time t , given by its market capitalization mvjs;t ,relative to the aggregate capitalization of that sector

Pnj

j D1 mvjs;t across all countriesin the GCC region that have that banking sector, j D f1; : : : ; nj g. We repeat a similarweighting scheme process on the resulting RMs;t in order to have the aggregate GCClevel measure, RMGCC;t .

Figure 4 describes the resulting aggregated GCC measure, using the weighted MES,the weighted NetMES and, finally, the weighted Bayesian NetMES.






FIGURE 4 MES, NetMES and Bayesian NetMES at the GCC banking sectors’ level.

(a)

(b)

(c)

0.078

0.058

0.038

0.018

–0.002

–0.022

0.018

0.013

0.008

0.003

–0.002

–0.007

–0.012

0.00016

0.00012

0.00010

0.00008

0.00006

0.00004

Jan2005

Jan2006

Jan2007

Jan2013

Jan2014

Jan2009

Jan2010

Jan2011

Jan2012

MES.CB MES.CBwin MES.IB MES.GCC

NetMES.CB NetMES.CBwin NetMES.IB NetMES.GCC

NetMES.CB NetMES.CBwin NetMES.IB NetMES.GCC

Jan2008

Jan2005

Jan2006

Jan2007

Jan2013

Jan2014

Jan2009

Jan2010

Jan2011

Jan2012

Jan2008

Jan2005

Jan2006

Jan2007

Jan2013

Jan2014

Jan2009

Jan2010

Jan2011

Jan2012

Jan2008

0

(i)

(iv)

(ii) (iii)

(v)(vi)

(a) MES weighted by market capitalization per sector; (i) 0.23: March 2005, IB. (b) NetMES weighted by marketcapitalization per sector; (ii) �0.03: March 2006, CB; (iii) �0.02: April 2008, CB; (iv) 0.02: September 2008, CB.(c) Bayesian NetMES weighted by market capitalization per sector; (v) 0.028%: January 2005, IB; (vi) 0.055%:March 2005, IB.





NetMES 33

From Figure 4, note that the CB sector has a lower magnitude than the CBwin andIB sectors: this is due to its lower market capitalization weight in the GCC countries.We also note that all graphs depict the presence of high volatility during 2005, andthat the effect of the global crisis started prior to 2007 and increased in 2009, withthe alignment of crisis effect on three sectors’ aggregates.

Comparing the graphs of MES and NetMES, we note that the latter takes lessaccount of the size effect, resulting in a lower magnitude scale. This is expected, asNetMES is based on partial rather than marginal correlations. The Bayesian NetMESis, as expected, more consistent in terms of its results than the previous two measures.Even though the changes in the sectors’ aggregates have similarities with the MESgraph, they have a lower magnitude, as in NetMES. Moreover, the Bayesian NetMESclearly can better distinguish the differences between the banking sectors comparedwith MES, but in a more smooth manner than NetMES.

We can conclude that, in spite of the high systemic risk effect that the IB sectorhad on the region before 2007, the main systemic risk driver in the GCC countries,during both the crisis period and going forward, is the CBwin sector. In addition, theCB banking sector shows high volatility, especially in terms of the weighted NetMESmeasure; however, this volatility does not much affect the system, as its market sizeis much lower than that of the other two sectors.

4 CONCLUSIONS

The aim of this research was twofold: to develop a novel measure of systemic risk,which takes its multivariate nature into account, and to determine if there are differ-ences between the Islamic and the conventional banking sectors in terms of systemicrisk, especially in the wake of the recent financial crisis.

The results indicate that the proposed NetMES and Bayesian NetMES measuresare, indeed, valid systemic risk measures that can detect crisis signals and differ-ences between different banking systems. The Bayesian NetMES is more robust thanNetMES, as it takes model uncertainty into account.

From an applied viewpoint, our findings confirm a difference in the systemic riskmeasurement of the different banking sectors. Interconnectedness, measured by net-work centrality measures, mostly depends on leverage. In this sense, the CBwin sectoris the most systemic, followed by the IB sector in the post-crisis period. Loss impact,measured by the MES, mostly depends on market capitalization. In this sense, theCBwin sector is gaining more and more relevance as its relative market size grows.Finally, conventional banks exhibit a high level of volatility that is not, however,carried onto the system due to their small market size.






From a policy-making viewpoint, the most systemic sectors are found to be thosewith a large asset size and a relatively high leverage, such as SA.CBwin, SA.IB andAE.CBwin.

DECLARATION OF INTEREST

The authors report no conflicts of interest. The authors alone are responsible for thecontent and writing of the paper.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support from the PhD program inEconomics and Management of Technology at Pavia University. The authors alsoacknowledge Pejman Abedifar of the University of St Andrews for the data.

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Research Paper

A multilayer model of order book dynamics

Alessio Emanuele Biondo,1 Alessandro Pluchino2 andAndrea Rapisarda2

1Department of Economics and Business, University of Catania, Corso Italia 55,95129 Catania, Italy; email: [email protected] Sezione di Catania and Department of Physics and Astronomy, University of Catania,Via S. Sofia 64, 95123 Catania, Italy; emails: [email protected],[email protected]

(Received August 16, 2016; revised September 8, 2016; accepted September 14, 2016)

ABSTRACT

Multilayer networks give us the chance to represent the multiplicity of relations amongfinancial operators. In particular, such a framework provides the natural environmentfor depicting both the informative diffusion and the transactions phase in separate,though interacting, network levels. In this paper, we present a two-layer order bookmodel; this implements information spreading on the first layer, which exhibits self-organized criticality (SOC) to describe herding behavior among traders, and financialtrading on the second one. Like its single-layer version (see, for example, Biondo et al2015), this model is also based on the relevant role played by individual imitationin determining trading decisions; but the introduction of the order book layer nowmakes the price-formation mechanism much more realistic. Despite the simplifyingassumptions in the trading dynamics, the results of numerical simulations show fat-tailed distributions of financial returns and other interesting features typical of realfinancial markets.

Keywords: financial markets; econophysics; self-organized criticality; herding; agent-basedmodels.

Corresponding author: A. E. Biondo Print ISSN 2055-7795 j Online ISSN 2055-7809Copyright © 2016 Incisive Risk Information (IP) Limited

37




38 A. E. Biondo et al

1 INTRODUCTION

In the last two decades, many studies have shown the characterization of social systemsas complex entities, suggesting the fruitful adoption of tools from statistical physics(Helbing 1995, 2012; Mantegna and Stanley 1999). Several papers have lately dis-cussed that new approaches to financial markets may reveal unexpected improvementsin the aggregate behavior of the entire system (Biondo et al 2013a,b,c, 2014, 2015,2016). The description of financial markets can be based on the individual behav-ioral attributes of agents, on the one hand, and on the rules and configuration of theirinteractions, on the other (Hommes 2001). The existence of emergent phenomenathat influence the macro scenario of markets every day can be explained in order toset appropriate strategies for investors, banks and policy makers, who interact in avery unstable environment while pursuing different goals (Delli Gatti 2011). Networktheory and agent-based models have revealed themselves as powerful in describingeconomic and financial systems (Boccaletti et al 2006; LeBaron 2006). New researchtools and more detailed analyses of financial systems may contribute toward buildinga more efficient and less dangerous market mechanism.

In this paper, we propose a reproduction of financial market dynamics in orderto represent the occurrence of known stylized facts by means of two main roots ofinvestor interactions, ie, information and trading. To this end, we decided to adopt amultilayer network framework, which has recently been introduced as more appro-priate than the single-layer one for the description of several different kinds of socialnetworks (Battiston et al 2014; Boccaletti et al 2014; De Domenico et al 2013).

In particular, a two-layer order book model is presented, where the informationspreading happens on the first layer, while the financial trading is developed on thesecond one. Such a characterization allows us to replicate relevant features of actualmarkets, namely self-organization and imitation among market participants. Actually,the addition of a trading layer for the order book dynamics, separated by the infor-mative one, makes the price-formation process much more realistic and detailed withrespect to the previous single-layer version (Biondo et al 2015), where the globalmarket price was simply expressed by a weighted average of the individual prices.

The order book design is the mechanism that enables the everyday life of financialmarkets to develop: the way orders are placed and influence the current price, theway the bid–ask spread is canceled trade after trade, the size and the timing of theexecution of orders and so on. There exists a very well-established branch of literaturedealing with the characteristics and the dynamics of order books (see, for example,Bouchaud et al 2002; Challet and Stinchcombe 2001; Gopikrishnan 2000; Maslovand Mills 2001). Different mechanisms dealing with the market microstructure havealso been studied (such as in Garman (1976), Kyle (1985), Glosten (1994), Biais et al(1987), O’Hara (1997) and Hasbrouck (2007), among others).





A multilayer model of order book dynamics 39

The model presented here is based on the following simplified assumptions withregard to the order book dynamics. First, in the market there exists just one asset. Sec-ond, orders are just limit orders. Third, orders are of quantity one. Dividends dynam-ics is introduced as the main determinant of the fundamental value of the asset (that,therefore, ends up being variable). By considering information and trading, ideallyseparately, this model combines the influence of herding dynamics and the matchingof orders within a framework that counts on the expressive potential of multilayernetworks (Boccaletti et al 2014; Musmeci et al 2014). In summary, this paper aimsto provide a realistic description of the following aspects of real financial markets:

(a) separation and interaction between the formation of the informative set oftraders and the trading execution of their orders;

(b) an endogenously formed price series resulting from a truly operating orderbook mechanism for orders placement;

(c) individual imitation and herding among agents due to informational cascades.

The paper is organized as follows. Section 2 contains the model description.Section 3 reports simulation results and their discussion. Section 4 presents someconclusions.

2 THE MULTILAYER–CONTAGION-FINANCIAL-PRICING MODEL

In order to simulate the operation of a financial market, the model here presentedmainly extends the basic network framework contained in Biondo et al (2015), whichis called the contagion-financial-pricing (CFP) model, by augmenting it with a secondlayer, devoted to the order book mechanism. Thus, the order-book-driven multilayer–contagion-financial-pricing model (ML–CFP) is obtained (see Figure 1). Technically,this kind of multilayer network is called “multiplex”, since the nodes (traders) are thesame in both the layers, changing only the meaning of the edges (see Boccaletti et al(2014) for details).

In the next subsections, the role of each of the two layers will be described in detail.Here, we summarize the info-trading dynamics, which proceeds at each simulationtime step t following this two-phase evolution:

(I) in the informative layer, according to the link configuration given by the networktopology, agents collect and share information, therefore deciding their status(bidder, asker or holder) as well as the (ask or bid) price of their possible order,depending on the global price at time t and the herding effect;

(II) in the trading layer, investors put their orders in the order book, which providesa sort of compensation room to execute them, and the next global price.






FIGURE 1 The two-layer configuration of the multilayer–contagion-financial-pricing (ML–CFP) model.

The upper (or informative) layer is a two-dimensional small world square lattice with N traders, connected by meansof short- and long-range links. The lower (or trading) layer is a fully connected network, in which each trader isconnected to all the others. In both layers, different colors represent different levels of information: the brighter atrader is, the more informed he or she is. Initial levels of information are distributed randomly.

In phase I, all market participants are devoted to gaining information about the mar-ket and the unique asset. As will be described below, information enters the modelas a twofold phenomenon in order to replicate a realistic market setting: from a first(global) point of view, it is a generalized (exogenous) signal that reaches all agents,even if with different (random) weights; from a second (individual) point of view,it comes from known people in the social network, whether this is by means ofprofessional competence or by simple word-of-mouth transmission. Such a configu-ration may, for example, represent real markets, where all agents can receive general(and maybe low-quality) informative signals, while the personal contacts, opinionsand persuasive behaviors of trusted people may suggest a personal component ofinformation. Under the influence of both the informative sources, and following theprescription of their group (fundamentalists or chartists), agents attempt to form theirindividual (heterogeneous) expectation for the future price. Then, according to this,they select their trading status (whether to set an order and negotiate, or not) and,






just in case, the ask or bid price of the order. It is worth noting that, when tradershave to decide their status and price, the contagion mechanism comes into play, inorder to take into account the chance that the euphoric or pessimistic expectations cangenerate information cascades of purchases and sales. In this respect, as explained inSection 2.1, one can imagine that each trader is endowed with a sort of confidence tankthat is filled by the accumulation of information coming from the general informativesource. When, at a given time t , an agent, who we shall call the “trigger agent”, over-comes their threshold, ie, when they reach the level of knowledge that they considersatisfying, they transmit (individual) information about their status and price to theirneighbors in the network. In turn, the neighbors can overcome their threshold too: inthis case, they imitate both the status and price of the first agent and transmit the sameinformation to their neighbors, and so on. In such a way, the herding avalanche candevelop. At the end of each avalanche, all the traders involved in the herding processoperate in the same way, while the others act independently.

At this point, phase II can start, and all the orders are organized in the order book,which operates the matching for the transactions to be actually done. Then, the newasset price will be determined as explained in Section 2.2.

2.1 The informative layer

Let a community of traders Ai (with i D 1; : : : ; N ) be connected among themselvesin a small world (SW) network (Biondo et al 2013c). This topology, first introducedin Watts and Strogatz (1998), is usually adopted in order to describe realistic commu-nities in social or economical contexts. In particular, the SW network considered here(see top layer in Figure 1) has been obtained from a square two-dimensional (2D)regular lattice, with open boundary conditions, by randomly rewiring its short-rangelinks with a probability p D 0:02. This creates a given number of long-range links.In this way, we still have an average degree hki D 4 (see Biondo et al (2013c) formore details).

As above explained, each trader is exposed to two flows of information (Biondoet al 2013c, 2014, 2015): a global one (a) and an individual one (b).

(a) The global informative pressure reaches all investors uniformly, at every timestep, from external sources. Each trader is endowed with a real variable Ii .t/

.i D 1; 2; : : : ; N / that represents their information at time t . Initially, at t D 0,the informative level of each trader is set randomly, in such a way that Ii .t/ 2Œ0; Ith�, where Ith D 1:0 is a threshold assumed to be the same for all agents.Then, at any time step t > 0, the information accumulated by each trader intheir awareness tank is increased by a quantity ıIi ; this is different for eachagent and randomly extracted within the interval Œ0; .Ith � Imax.t//�. Such anaccumulation process may lead a given trader Ak , before the other, to exceed






FIGURE 2 Informative pressure and contagion cascade.

Global informative pressure coming from external sources

Individual information transfer

Contagion cascade

Level ofinformation

A1 Ak

Sk

Sk

Ith = 1

Ith = 1

Ith = 1

Sk

AN

(a)

(b)

(c)

their personal threshold value at a given time t D tav (where the subscript “av”stands for “avalanche”; see later). In this case, that trader becomes “active” andtransmits their opinion, as an informative signal, to their neighbors.

(b) Such an opinion spreading represents the second (individual) flow of informa-tion, since every trader may receive signals from their neighbors (who havepossibly passed their threshold). If this happens, it may cause other agents toexceed their thresholds in turn, because of this supplementary amount of infor-mation, which is additive with regard to the global one (a). Such a processexplains how the informative cascades may generate herding in the market.

The information transfer happens in the information network, according to thefollowing simple mechanism (Biondo et al 2013c). This is analogous to the energytransmission in earthquake dynamics modeled in networks of terrestrial crust pieces,which can be found in Olami et al (1992):

Ik > Ith )

8<:

Ik ! 0;

Inn ! Inn C ˛

NnnIk;

(2.1)






where “nn” denotes the set of nearest neighbors of the active agent Ak . Nnn is thenumber of direct neighbors, and the parameter ˛ controls the level of dissipation ofthe information during the dynamics (˛ D 1 if there is no dissipation). It is realisticto presume that part of the information content is lost in transmission, and therefore,in our simulations, we always adopt ˛ < 1. As a consequence of the received amountof information, it has been said that other traders may be activated and they may,possibly, pass the threshold level as well. This process is shown in the three stepsdepicted in Figure 2: from step .a/ to step .c/, all the newly active traders will imitatethe status Sk of the first agent and will transmit, in turn, their own signal to theirneighbors, following (2.1), and so on. In such a way, an informative avalanche willtake place at time tav, producing a contagion cascade of traders who will share thesame behavior and choice.

2.2 The trading layer

In our model, we consider an ideal financial market, where only one asset exists andmoney has an ancillary function just for transactions regulation. Let us imagine, first,that the trading layer is not influenced by the herding avalanches of the informativelayer. In this case, we could consider the process of status setting and price formationfor an individual agent as independent from the behavior of the other agents. Thetraders Ai (with i D 1; : : : ; N ) are endowed, at the beginning of each simulation,with an equally valued portfolio, composed of the same initial quantity of moneyMi D M for all i and the same initial quantity of the unique asset Qi D Q for alli . The total wealth Wi of each trader is then defined as Wi D Mi C Qipt , wherept is the global price of the asset at time t . As we know, two groups of tradersexist: fundamentalists and chartists. At each time step, traders will behave differently,according to their “character”.

(F) Fundamentalists presume the existence of a “fundamental value”, FVt , andbelieve that the market price of the asset will always tend to it. The fundamentalvalue changes every tf time steps following the rule

FVtCtf D FVt C Dt ; (2.2)

where FV0 D 0 and Dt is a random variable extracted from a normal dis-tribution with zero mean and standard deviation �f . This corresponds to theassumption that dividends follow a random walk. The fundamental value isthen used by each fundamentalist in order to form a personal opinion about the“correct” price for the asset, known as the “fundamental price”, pF

t , which iscomputed as

pFt D p0 C FVt C �; (2.3)






where p0 is the initial global asset price and � is randomly chosen in theinterval .��; �/ in order to account for the heterogeneity of investors. Thus,fundamentalists form their expected price for the asset according to

EŒptC1� D pt C �.pFt � pt / C �; (2.4)

where the parameter � is a sensitivity parameter that describes the expectedspeed of convergence to the fundamental price, and � is a stochastic noiseterm, randomly chosen in the interval .��; �/. In order to limit the numberof parameters, we let the value of � be fixed even if, in principle, it could bedifferent for each trader of this group.

(C) Chartists decide on their behavior according to their inspection of past prices.Therefore, before defining their expectation for the future, they will analyzethe past dynamics of the asset price series. In particular, they consider theinformation coming from such an inspection as a “past reference value”, PRVt ,computed at any t by averaging the previous prices over a time window oflength T , which is different for each chartist and randomly chosen in the interval.2; Tmax/:

PRVt D 1

T

tXj Dt�T

pj : (2.5)

Then, the expected price for the next time step is determined by each chartistas

EŒptC1� D pt C �

T.pt � PRVt / C �; (2.6)

where � (a constant) is the sensitivity parameter and � is, again, a stochasticnoise term defined as in (2.4).

In order to choose the status of the traders, a sensitivity threshold � has beenintroduced in the model. This has been done in such a way that, if the expectationsare not “sufficiently” strong, the trader will decide to hold without setting any order.In particular, only if EŒptC1� > pt C � will traders expect a rise in the market priceand decide to buy the asset, setting their status Si on “bidder”. However, only ifEŒptC1� < pt � � will traders expect a fall in the market price and decide to sell theasset, setting their status on “asker”. Finally, if pt � � < EŒptC1� < pt C � , traderswill decide to hold on without doing anything. Of course, traders who decide to buymust have a positive amount of money (Mi > 0), and, similarly, those who decide tosell must have a positive amount of the asset (Qi > 0).

Once the individual status has been decided, each trader sets their order in the bookby choosing the preferred price for the transaction. Both in case of sales and purchases,the price chosen by each trader for the transcription in the order book (personal bid






price for bidders and personal ask price for askers) is a function of the expectationthat inspired the status of the same trader. Since orders are always of quantity 1, bid(ask) prices are decided by traders by means of simple price setting rules that describetheir willingness to pay (to accept) according to their expectations, instead of beingdefined by means of function optimization procedures. The heterogeneity of tradersis embedded in the model by defining feasible intervals from which each investor canextract their bid–ask price.

(I) If the status is “bidder”, the chosen bid price will be extracted (with uniformprobability) from a range whose minimum and maximum are defined as follows:

(min) since it is not convenient for any buyer to set a bid price too low, becauseno seller would accept selling, the lower bound for the bid price settingat time t C 1 is equal to the best ask price (ie, the lowest one) observed attime t ;

(max) since the reason the investor is bidding is that their expected price ishigher than the current one, the upper bound for the bid price setting isexactly that expected price (but, of course, in case the trader does not haveenough money, the maximum value that they can bid is limited to theirowned money).

(II) If the status is “asker”, the chosen ask price will be extracted (with uni-form probability) from a range, whose minimum and maximum are definedas follows:

(min) since the reason the trader is selling is that their expected price is lowerthan the current one, the lower bound for the ask price setting is the worstscenario that they infer, ie, the expected price;

(max) since it is not convenient for any seller to set an ask price too high, becauseno buyer would accept buying, the upper bound for the ask price settingin t C1 is the expected price plus twice the difference between the currentprice and the expected one.

After status and price setting activities, orders for a “C1” or “�1” quantity areposted in the book. This is exactly the point at which the interaction between thetrading layer and the informative one becomes crucial. Actually, as anticipated inSection 2.1, in the presence of herding avalanches all the traders involved in theavalanche, regardless of their character (fundamentalist or chartist), will imitate boththe status and the price of the agent who started the avalanche itself. And this, ofcourse, strongly influences the order book aspect.

Once posted, all the orders in the book, on both sides (buy and sell orders), areranked according to their associated prices. Bid prices are ranked in decreasing order






of willingness to pay: in such a way, the trader who has set the highest bid price(namely the “best-bid”) will be the top of the list and will have priority in transactions.Conversely, ask prices are ranked in increasing order of willingness to accept: thetrader with the lowest willingness to accept (who sets the so-called “best-ask”) will bethe top of the list and will have the priority in transaction execution. Then, the matchingis done by comparing the best ask and the best bid. The number of transactions NT thatactually does occur between askers (whose total number is Na) and bidders (whosetotal number is Nb) strictly depends on such a comparison.Actually, only if best-bid >

best-ask do we have NT > 0, ie, a given number of transactions do occur, dependingon the matching among ask and bid prices present in the order book. After the firsttransaction, which occurs among traders who post their own order at the best price,from both the demand and supply sides, transactions continue following the order inthe book (ascending for the ask list and descending for the bid list) until the bid priceis greater than the ask price and all the transactions are regulated at the ask price.Finally, the new global asset price will be ptC1 D pL, where pL is the ask price ofthe last transaction that occurred.

3 SIMULATIONS RESULTS

In this section, we present the simulation results of a typical run of the ML–CFPmodel, analyzing both its macroscopic and microscopic details and plotting the finaldistributions of its main quantities.

We consider a network of N D 900 traders, equally divided into 450 funda-mentalists and 450 chartists. The (typical) initial setup for the values of the controlparameters of the model is the following: p0 D 500 (initial price), ˛ D 0:95 (level ofconservation of information), �f D 2 (standard deviation of the normal distributionfor the fundamental value FVt ), tf D 10 (time increment for FVt ), � D 30 (rangeof variation for the fundamentalists’ heterogeneity), � D 0:5 (sensitivity parameterfor fundamentalists), Tmax (maximum extension of the window for chartists), � D 2

(sensitivity parameter for chartists), � D 30 (maximum intensity of the stochasticnoise for the expectation values), � D 15 (sensitivity threshold for the status setting),M D 40 000 (initial quantity of money) and Q D 200 (initial quantity of the asset).

In Figure 3(a), we show a typical time evolution of the global asset price.After 5000time steps have passed without trading (not visible), and due to a need for the system toenter into the SOC regime (where power-law-distributed avalanches can be observedin the informative layer), agents start to trade and the values of the asset price areplotted for the next 10 000 time steps, starting from the initial price p0 D 500. In theinset, a more detailed version of the same series is reported. Sometimes, very strongfluctuations are visible in the price series, due to the effect of herding avalanches.These fluctuations, of course, affect the volatility of the price, as can be seen in the






FIGURE 3 A typical simulation run of the ML–CFP model.G

loba

l ass

et p

rice

460

470

480

490

500

510

520

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0 2000 4000 6000 8000 10 000

0 2000 4000 6000 8000 10 000

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–10

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ret

urns

Time steps

–5 50

10–3

10–2

10–1

PD

F(b) (c)

Gaussian

(a) Typical time series for the global asset price; in the inset, a more detailed image of the series. (b) Normalizedreturns of the price series. (c) Probability density function of the normalized returns compared with a Gaussiandistribution of unitary variance.

normalized returns time series reported in Figure 3(b). Normalized returns are definedas

rnormt D .rt � rav/=rstdev;

where rt D log.ptC1/ � log.pt / are the logarithmic returns, while rav and rstdev

are, respectively, their mean and standard deviation calculated over the whole series.Consequently, the probability density function of normalized returns, plotted in Fig-ure 3(c), shows the asymmetric fat tails characteristic of financial markets, a symptomof the presence of extreme events.

On the other hand, the central part of the distribution is not peaked but follows anormal shape, as is visible from the comparison with a Gaussian curve with zero meanand unitary variance. This is probably a consequence of the strong approximation






FIGURE 4 Final distributions of some quantities of interest. (Figure continues on nextpage.)

0

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of tr

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s

0 400300100 200

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0 20 000 40 000 60 000 80 000 100 000Final money

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135 000 137 500 140 000 142 500Final wealth

From top to bottom, final distributions of the asset quantity, money and wealth of all traders.

adopted in the ML–CFP model, in which only one asset is considered and the ordersare limited to one. Under these conditions, the system is evidently able to self-organize,maintaining a dynamical balance between purchase orders and sales. The latter feature






FIGURE 4 Continued.

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0 20 000 40 000 60 000 80 000 100 000 0 20 000 40 000 60 000 80 000 100 000Final money Final money

Initial money Initial money

Initial wealth Initial wealth

135 000 137 500 140 000 142 500Final wealth

135 000 137 500 140 000 142 500Final wealth

The same distributions as in Figure 4(a) are plotted separately for (b) fundamentalists and (c) chartists.

clearly appears if we look at the details of the transactions in the trading layer.Actually,the average numbers of askers and bidders calculated during the whole time periodwere, respectively, Na D 229:61 and Nb D 220:42. Further, over an average numberof transactions equal to NT D 88:65, the average numbers of buyers and sellers were,respectively, 52:02 and 52:49 for fundamentalists, and 51:2 and 50:75 for chartists,indicating a strong average equilibrium among the competing forces in the market.

Such an equilibrium can also be revealed by plotting, as in Figure 4, the finaldistributions of the asset quantity, money and wealth for all the traders (part (a)) and,separately, for the fundamentalists (part (b)) and chartists (part (c)). The initial valuesof the three quantities, equal for all the traders, are also reported as dashed verticallines.As one might expect, the final distributions appear to be widespread around theirinitial values, but, for what concerns money and asset quantity, the trading dynamicsseems to be well balanced between gains and losses. The only source of asymmetry isthe small difference between the average number of buyers and sellers, which changes






its sign for fundamentalists and chartists, leading the former group to slightly favorpurchases and the latter to slightly favor sales. This, in turn, induces fundamentaliststo sell their assets, thus increasing their money, and chartists to buy new assets, thusdecreasing their money. But these two variables, together with the fluctuations inthe asset price, evidently provide compensation in producing a similar final wealthdistribution for the two groups.

The features observed for this typical run are quite robust and remain almostunchanged if one varies the total number of agents, the relative proportion of funda-mentalists and chartists, the initial value of the asset price or the initial asset quantityand money. However, they are quite sensitive with respect to variations in some controlparameters, such as the sensitivity parameters for the expectation prices, the sensitiv-ity threshold for the status setting or the maximum intensity of the stochastic noise.In this case, the observed equilibrium between bidders and askers becomes unstableand, typically, one of the two trading groups, fundamentalists or chartists, starts tobuy the asset much more than the other one, thus generating a spiral effect that leadsfundamentalists or chartists to spend all their money, and in fact pushes them out ofthe market.

4 CONCLUSIONS

In this paper, we have presented a simple multilayer order book model of the financialmarket, namely the ML–CFP model, with heterogeneous agents. This model gener-alizes the previous CFP one, in which only a single informative layer existed. Theaddition of the trading layer makes the price-formation dynamics much more real-istic; this is mainly due to the fact that the global market price is no more a simpleaverage of the individual prices (such as in the CFP model) but emerges from thedynamic interaction among traders, still subject to the contagion mechanism that isnow extended to the imitation of both status and price entering in the order book. Sucha new, realistic framework is fruitfully coupled with interesting numerical results,which, despite the simplifying assumptions about assets and orders, adhere to sometypical features of real financial markets. Even if, at this stage, these results do notsubstantially improve the findings of the single-layer CFP model in terms of whatconcerns the stylized facts, the more realistic price-formation dynamics based on theorder book mechanism does allow us to observe the evolution of both the asset andmoney distributions in the trading community. The obvious generalization of thismodel, achievable by introducing more than one asset or variable order quantities, isin progress and will be the subject of further studies, together with a deeper analysisof stylized facts and the exploration of different topologies for both the informativeand trading layers.








ACKNOWLEDGEMENTS

This study was partially supported by the FIR Research Project 2014 N.ABDD94 ofthe University of Catania.

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Research Paper

Directors’ networks and firm valuation ina concentrated ownership structure economy

Ronen Barak1 and Oren Kapah2

1Department of Economics and Business Administration, Ariel University, Ariel 40700, Israel;email: [email protected] School of Business Administration, Bar-Ilan University, Ramat Gan 5290002, Israel;email: [email protected]

(Received July 31, 2016; revised August 30, 2016; accepted September 13, 2016)

ABSTRACT

We explore the implications of directors’ networks for company valuation in a con-centrated ownership environment and in pyramidal control structures. Using commoncentrality indexes on a sample of 727 directors serving in 105 Israeli listed firms, weshow that the effect is very dependent on the type of director. Directors who areneither external nor ultimate owners, and therefore presumably experts, tend to pro-mote firm valuation and mitigate the negative impact of a pyramidal control structure.Conversely, central external directors have a tendency to harm firm performance andeven magnify the negative effect of the vote–ownership wedge, due to the pyramidalownership structure. Our findings support the claim that shareholders with control-ling interests are, in fact, shadow directors, who utilize their excessive influence onexternal directors to carry out tunneling (ie, the diversion of value from the companyfor their own personal gain).

Keywords: directors’ networks; tunneling; concentrated ownership; pyramids; external directors.

Corresponding author: R. Barak Print ISSN 2055-7795 j Online ISSN 2055-7809Copyright © 2016 Incisive Risk Information (IP) Limited

53




54 R. Barak and O. Kapah

1 INTRODUCTION

Social networking is defined as a social structure composed of individuals or orga-nizations connected by (one or more) types of interdependency, such as friendship,common interests, knowledge or beliefs. Technological developments over the lastdecade have emphasized the growing importance of social networking. In the financialeconomics literature, the question of the economic impact of social networks has beenaddressed from several perspectives: venture capital (Hochberg et al 2007), mutualfunds (Kuhnen 2009; Cohen et al 2010), employment (Ioannides and Loury 2004),investment decisions (Duflo and Saez 2003) and executive compensation (Barnea andGuedj 2009). The aim of this research is to explore the effect of directors’ centralityon firm value in a concentrated ownership structure economy. Concentrated owner-ship creates a conflict between insiders with controlling interests and other stake-holders, as controlling shareholders may be tempted to expropriate firm resourcesand reap the private benefits of control, thereby damaging the firm’s value (see, forexample, Barclay and Holderness 1989; Dyck and Zingales 2004). We examine theimpact of directors’ centrality on firm value in the Israeli economy, which is known tohave a highly concentrated ownership structure and many pyramidal business groups(La Porta et al 2000, 2002; Dyck and Zingales 2004; Barak and Lauterbach 2011).1

The paper is organized as follows: Section 2 provides a brief literature review andsome background on centrality indexes; Section 3 presents the theory and hypothe-ses; Section 4 explains the methodology; Section 5 describes the sample; Section 6presents the empirical results; and Section 7 concludes.

2 SCIENTIFIC BACKGROUND

2.1 Literature review

The financial literature provides supporting evidence about the economic significanceof positioning within networks, from the perspective of both performance and cor-porate governance variables and implications. Hochberg et al (2007) and Barnea andGuedj (2009) are prominent examples of this literature. Hochberg et al (2007) inves-tigate the performance of US venture capital funds over the period 1980–2003, andshow a significantly better rate of successful exits within venture capital funds whoseparent company is more influential in the venture capital market, ie, presents highercentrality measure scores.2

1 Dyck and Zingales (2004) and Barak and Lauterbach (2011) estimate private benefits of controlin Israeli firms to be about one-third of its equity market value, which is relatively high and abovethe world median.2 Hochberg et al (2007) expose another aspect of the networking effect by identifying networkdensity as a major factor in the magnitude of barriers to entering local venture capital markets.





Directors’ networks and firm valuation in a concentrated ownership structure economy 55

Barnea and Guedj (2009) investigate the effect of directors’ centrality on chiefexecutive officer (CEO) compensation schemes, and examine two opposing hypothe-ses:

(a) the reputation hypothesis, which argues that connected directors do not needto exert an effort, since their centrality serves them well enough (relative tononconnected directors, who promote themselves by performing useful butcostly monitoring);

(b) the bargaining power hypothesis, which argues that connected directors havemore bargaining power than the CEO (since they are less concerned aboutthe management and the impact of monitoring on their reputation) and henceperform better monitoring, relative to nonconnected directors.

They find that firms with more connected boards grant higher pay to CEOs: a resultthat supports the reputation hypothesis over the bargaining power hypothesis.

In addition, there is ample evidence of significant links between directorates’ traitsand firm performance. Yermack (1996), using a sample of 452 large US firms, findsa negative correlation between board size and firm value (Tobin’s Q), supporting theclaim that small boards are more effective at carrying out their necessary functionswithin the corporation.

Similarly, but concerning a different class of firms, Eisenberg et al (1998) discoversignificant negative correlations between board size and profitability in small andmid-sized Finnish firms. Fich and Shivdasani (2006) show that firms are also lessprofitable when most of their external/independent directors are (too) busy, ie, holdthree or more directorships. By showing that CEO turnover is less sensitive to firmperformance, Fich and Shivdasani also find that busy boards monitor CEO behaviorless effectively. Bebchuk and Cohen (2005) document a significant negative relationbetween firm value (Tobin’s Q) and entrenched (staggered) US boards.3 Menozzi et al(2012) investigate Italian state-owned firms and discover that directors with politicalconnections tend to have a negative influence on firm performance, probably becausetheir commitment to company profitability is lower than that of the political party orstate authority to which they are linked.

The financial literature presents the economic and financial implications of a con-centrated ownership structure economy. Such capital markets are characterized bymany closely held publicly traded firms. Concentrated ownership creates a conflictbetween insiders with controlling interests and other stakeholders, since controlling

Significant barriers presumably help incumbent capitalists to improve their bargaining power overentrepreneurs and present excess yields.3 On these boards, directors are grouped into classes; only one of these classes can be removed ateach election, making board removal much more difficult.






shareholders may be tempted to expropriate firm resources and consume private bene-fits of control, thereby damaging firm value (see, for example, Barclay and Holderness1989; Dyck and Zingales 2004). Moreover, concentrated ownership structure usuallyyields unique formations, such as pyramidal business groups. These business groupspossess the potential of creating serious externalities, due to the potential to distortarm’s length markets by their excessive size and dominance.

In addition, a pyramidal ownership structure imposes a morally hazardous situa-tion, resulting from the wedge created between ultimate owners’ voting power andtheir share in firm equity.4 Higher voting power provides the ability to control afirm’s actions, while a lower equity share shields against the negative consequencesof improper and value-destroying proceedings. Thus, pyramid controllers might behighly tempted to expropriate firm resources for their own benefit, and divert fundsfrom low-equity-share firms to higher-equity-share firms in the pyramid: a practicereferred to as tunneling.

Bertrand et al (2002) find evidence of tunneling among Indian pyramidal owner-ship structures. It appears that controlling shareholders use related party transactionmechanisms in order to divert resources from low cashflow rights to higher ones inthe pyramid. Volpin (2002) investigates pyramidal groups in Italy during the period1986–97 (in which Italy was considered to be a highly centralized economy) and doc-uments a significant deterioration of a firm’s Q-value for companies that are locatedat the bottom of the pyramidal structure.5 Volpin (2002) also reports higher executiveturnover in these firms than in upper pyramid (parent) companies, suggesting they areused by the ultimate owners as a means to test and select the best managers, wherebythe highest-performing executives are promoted to the higher levels of the pyramid.The negative implication of the pyramidal structure is also documented by Barak andLauterbach (2012), who report a significant positive relation between the intensity ofprivate benefits of control (the level of firm expropriation by its controller) and themagnitude of the control–ownership wedge in Israeli pyramidal group firms.

In this concentrated environment, and especially in the presence of pyramidal own-ership structures, directors’networking and centrality have the potential to play impor-tant roles in shaping firm performance. The correlation between directors’ centralityin a concentrated ownership economy and the effect of pyramids has, to the best ofour knowledge, never previously been tested.

4 The “owner” is the person, family or business associates who sit at the top of the pyramidalownership structure and practically control the firm.5 However, during the past two decades, major legal reforms have forced many Italian firms to altertheir juridical form and thereby improve some essential aspects of corporate governance (Bertoniand Randone 2006), a move that apparently also reduced the concentration of ownership (Rotundoand D’Arcangelis 2010, 2014), although many of the established corporations maintain their highcentrality through directors’ networks (Bellenzier and Grassi 2014; Drago et al 2015).






2.2 Analysis of networks

The term “centrality” is defined as the importance (or relative importance) of a personin the network. In this study, we focus on three common centrality measures usedin the social science literature that discusses networks: degree, eigenvector centrality(or closeness) and betweenness.

The degree of an agent in a network is simply the number of connections the agenthas. In mathematical terms, a degree ki of agent i is expressed by

ki DnX

j D1

Aij ; (2.1)

where Aij equals 1 if agent i is connected to agent j , and 0 otherwise.As shown in Figure 1, agents 5 and 6 get the highest degree scores, as each is

connected to four other agents.Eigenvector centrality, suggested by Bonacich (1972, 1987), evaluates the impor-

tance of the links that each agent has, acknowledging the fact that not all connectionsbetween two agents in the network are equivalent.6 In general, connecting to an agentwith more connections makes the original agent more influential. The eigenvectorcentrality is defined as

�y D Ay; (2.2)

where the eigenvector yi denotes the centrality of agent i with the matchingeigenvalue �.

Since we usually want centralities to be nonnegative, � must be the largest eigen-value of the connections matrix A, with y its corresponding eigenvector.7 In summary,the eigenvector centrality of an economic agent depends on both the number and qual-ity of its connections. Figure 2 illustrates this feature of the eigenvector centrality.Although agents 5 and 6 have an equal number of connections to the other agents,agent 5 possesses higher-quality (more connected) ties.

6 In the financial literature, eigenvalue centrality is sometimes defined as closeness centrality (see,for example, Barnea and Guedj 2009). However, in the theory of networks, the term “closenesscentrality” focuses on the distance through paths. Paths are used for the definition of other centralitymeasures, such as “betweenness centrality”, although they measure different properties of networknodes (agents).7 According to the Perron–Frobenius theorem, a real square matrix with positive entries has aunique largest real eigenvalue, and the corresponding eigenvector has strictly positive components.The centrality of agent i is expressed as

yi D 1

�

nXj D1

Aij yj :






FIGURE 1 The degree centrality measure.

432

1

5 69

87

3

2

31

1

44

11

FIGURE 2 The eigenvector centrality measure.

432

1

5 69

87

0.130.370.44

0.35

0.51

0.190.16

0.43

0.16

Betweenness centrality is based on the concept of network paths. A path in anetwork is the sequence of links from agent i to agent j across the network. As aresult, there are several ways to define the links between two agents in the network. Inour study, we define the betweenness centrality of an agent using the geodesic path.A geodesic path is the shortest path between agents i and j in the network. Geodesicpaths are not unique, as there may be several shortest paths between two agents.

Thus, the betweenness centrality of agent z is a summation of the fractions ofthe geodesic paths between agents i and j that z falls on (Newman 2008), which isusually normalized by dividing it by the total number of shortest paths in the network.Figure 3 shows that agent 6 has the highest betweenness centrality score. The sum ofthe fractions of shortest paths between all pairs of other agents that pass through it is15, which is 53.6% of all geodesic paths in the network. In the context of this study, the






FIGURE 3 The betweenness centrality measure.

4

32

1

5 69

87

0(0%)8.5(30.4%)4(14.3%)

0(0%)

11.5(41.1%)

0(0%)

15(53.6%)

0(0%)

0(0%)

betweenness index provides an advantage for those directors simultaneously servingmore than one large business group.

3 THEORY AND HYPOTHESES

An improved location of the director’s network has the potential to enhance firm valuein various ways. First, better network positioning raises the availability, as well asthe quality, of information and reduces the cost of searching for such (Wilson 1968;Sah and Stiglitz 1986). Second, influential directors have the privilege to access otherrelevant, key personnel more easily (Hochberg et al 2007). Third, well-connected andpowerful individuals can use their higher bargaining power to impose better terms inmore promising collaborations with other business entities (Lerner 1994; Hochberget al 2007). In total, higher directorial centrality should be correlated with the abilityto reduce frictions and improve efficiency, and usually indicates a higher businessreputation.

However, from a governance perspective, the reputation effect can have two con-trasting and mutually exclusive implications: on the one hand, the well-connecteddirector will be motivated to justify and preserve their reputation, harnessing theircapabilities to promote the firm’s value and supervise the ethical conduct within.On the other hand, higher reputation and important business ties might lead to over-confidence, insufficient monitoring (Barnea and Guedj 2009) and even using theirreputation to cross barriers8 in exploiting firm resources.

8 Such as obtaining approval for a resolution that requires special majority.






Thus, we base our research on two basic competing hypotheses.

Hypothesis 3.1 In closely held firms, directors who are more central in thedirectors’ network (ie, have a better reputation) tend to promote firm value.

Hypothesis 3.2 In closely held firms, directors who are more central in thedirectors’ network (ie, have a better reputation) tend to harm firm value.

A pyramidal ownership structure sharpens the agency problem aspect of directors’centrality, especially within companies at the bottom of the pyramid (Volpin 2002).In these firms, the wedge between ultimate owners’ voting power and their equityholdings amplifies the temptation to “tunnel” funds to parent companies. FollowingVolpin (2002) and Bertrand et al (2002), we reaffirm that in our sample the control–ownership wedge also usually harms firm value.

Proposition 3.3 The wedge between ultimate owners’ voting power and equityshare tends to decrease firm value.

Hypotheses 3.1 and 3.2, in conjunction with Proposition 3.3, yield the followingtwo competing hypotheses.

Hypothesis 3.4 The negative value impact of the control–ownership wedge ismoderated proportionally to the centrality of the directorate.

Hypothesis 3.5 The negative value impact of the control–ownership wedgeworsens proportionally to the centrality of the directorate.

Board size, ie, the number of directors, is also one of the directorate-related traitsthat may have possible value implications. The literature documents the negative valueimpact of disproportionately large boards of directors, characterized by cumbersomedecision-making processes and insufficient monitoring, due to increased commu-nication and coordination problems (Yermack 1996; Jensen 1993). A concentratedownership environment like Israel yields another problematic aspect of directoratesize. In closely held firms, directors are frequently nominated by large shareholders(controllers), who often prefer to hire their own relatives. In fact, prestigious nomina-tions granting high salaries are part of controllers’ private benefits of control (Barakand Lauterbach 2011; Amzaleg and Barak 2013). Israeli firms are known for theirrelatively high consumption of private benefits of control, which are above the worldmedian (see Dyck and Zingales 2004; Barak and Lauterbach 2011, 2012). Hence,unjustified directorate size may serve as a means to loot firm resources (through






tunneling) and may be negatively correlated with firm value. Concluding the above,we expect bigger boards to have a negative value impact.

Hypothesis 3.6 There is a negative relation between directorate size (number ofdirectors) and firm value.

3.1 External (independent) directors and the “shadow director”problem

Another important related issue is the presence on the board of external (or inde-pendent) directors, ie, directors without any family (or business) ties with control-ling shareholders (or management). External directors in a concentrated ownershipstructure economy may be strongly influenced by the reputation effect, as they areconsidered to be another monitoring device that should moderate controllers’ tunnel-ing acts. Pacces (2011) designates independent directors a crucial role in protectingshareholders against expropriation by insiders. The importance of independent boardsis manifested in several empirical studies, most of them related to US listed firms.Chhaochharia and Grinstein (2007) demonstrate how a higher proportion of externaldirectors mitigates CEO agency problems; Knyazeva et al (2013) present a significantpositive relation between board independency and firm value; likewise, Fogel et al(2014) find that companies with powerful independent directors (ie, those belongingto the top quintile of centrality measure scores) feature a higher Tobin’s Q, bettermergers-and-acquisitions decisions and higher CEO turnover under conditions ofpoor performance.

Israeli corporate law also delegates a major responsibility to independent directors:the protection of minority (and other) shareholders against the value-destroying actsof controlling shareholders. Besides their deterrent presence in board meetings, exter-nal directors also have mandatory seats in smaller forums (where they possess greaterproportional voting power) such as audit committees, in which they have the abilityto object to disadvantageous related-party transactions (self-dealing events), whichmust obtain committee approval before being carried out. However, the cumulativeevidence suggests that the impact of external independent directors in closely heldfirms, where most directors belong to the control group, may be much less effectivethan in the United States (see Barak and Lauterbach 2012; Menozzi et al 2012; Fer-rarini and Filippelli 2014). Moreover, it is important to consider the decisive impactof the mechanism for nominating external directors in Israel (and other concentratedownership economies). In concentrated ownership structures, the excessive power ofmajor shareholders becomes an exclusive channel for nominating candidates, as wellas for ensuring the approval of their appointments in the shareholders’assembly. Sucha mechanism creates a situation in which almost all external directors are personalappointees of the controlling shareholders, who also control the appointed directors’






future employment.9 These conditions raise the possibility of a shadow director. Ashadow director (in the context of our study) is a controlling, dominant shareholderwho appoints an external director that is fully devoted to them and essentially rep-resents their “long arm”, for all practical purposes serving as the firm controller’s“marionette” within the directorate. Thus, the presence of a shadow director(s) on theboard might bias the classical interpretation of centrality by awarding high central-ity scores to external directors who gained a (negative) reputation for collaboratingwith the controlling shareholders, instead of a real (positive) reputation or bargainingpower abilities. Therefore, in order to address this different centrality view towardexternal directors, we create the following separate hypothesis.

Hypothesis 3.7 In closely held firms, when a controlling shareholder has a greatinfluence on appointments to the board, external directors with higher centralityscores (ie, that have gained a more negative reputation) tend to harm firm value.

Hypothesis 3.7, in conjunction with Proposition 3.3, leads to our last hypothesis.

Hypothesis 3.8 The negative value impact of the control–ownership wedgeworsens proportionally with the centrality of external directors.

4 METHODOLOGY

Our methodology differentiates between three groups of directors. The first refersto those who are controllers’ family members, which is common in a concentratedownership environment. Clearly, this group of directors is not suitable for examiningresearch hypotheses, as its members are aligned with the interests of the controllinggroup, making the monitoring effect attached to our assumptions irrelevant.

The second group is the cluster of external (independent) directors. In the sampleyear (2010), the Israeli law obliged each publicly traded firm to appoint at leasttwo external directors, and most Israeli firms had exactly two such directors on theirboard.10 In Section 3 we discussed the unique aspects of these directors. Justifying theneed to treat them as a separate group deserves special hypotheses (Hypotheses 3.7and 3.8).

The third, and apparently most important, group is the directors who are neitherfamily members of controlling shareholders (or employees) nor external directors.

9 This was the case during the sample years. However, in 2011 the Israeli Parliament enacted theCorporate Law 16th Amendment Act, which restrained the influence of controlling shareholders onexternal directors by demanding the approval of the appointment by a majority of noncontrollingshareholders, prohibiting dismissal of external directors and also obviating the consent of controllingshareholders for the extension of the term.10 The Corporate Law 16thAmendmentAct (2011) corrected this defect and stated that the proportionof external directors on the board should not be less than one-third.






We assume that members of this group tend to be more professional or “expertdirectors”, who received their nomination mostly because of their expertise. Hence,we believe this group deserves major attention in the analysis, as it appears tobe the most appropriate for testing our main research hypotheses regarding thereputation-overconfidence effect (Hypotheses 3.1–3.5).

The main aim of this study is to reveal the effect of a director’s importance inthe network of directors, as reflected by the centrality measures with regard to firmperformance. Our proxy for firm value is the customary Tobin’s Q, defined as

Q D market value of equity C book value of debt

book value of total assets:

Consistent with the literature on Tobin’s Q (Himmelberg et al 1999; Volpin 2002;Barak et al 2011), we employ control variables that refer to firm size, financialleverage, growth rate and ownership structure.

We detect the effect of directorates’ centrality on firm performance, ie, Tobin’s Q,in two ways. First, for each company we calculate the average board centrality index.According to this approach, each director’s contribution to the firm’s value is linearlyproportional to their centrality tally.

However, measuring the centrality effect in this manner, especially in relation tolarger boards, might underestimate the influence of high-scoring individual directorswhose reputation and eminence lend them a special status within the board. It isplausible that the presence of these dominant directors could induce a monitoringeffect on a scale that is higher than their relative share in the company’s directorate.Therefore, taking this possible bias into consideration, we additionally quantify boardcentrality by using the highest score found among the firm’s directors.

As a final yet very important methodological point, we should not ignore the poten-tial endogeneity problem embedded in our main research question. It is sensible thatdirectors’ centrality is endogenous, since influential and reputable directors will tendto sit on boards of higher-valued firms, in order to effortlessly protect and/or promotetheir status.

Prior corporate governance studies relating to board composition were indeed awareof the potential pitfall of ignoring this endogeneity. A recent example is the study byFogel et al (2014), which shows a positive relation between board independency andperformance in a time series sample of Standard and Poor’s (S&P) 1500 companies.The study uses two methods, both appropriate for time series analysis, to work aroundthe endogeneity problem: one is to use the value effect (negative cumulative abnormalreturns), which occurs when the sudden death of an important independent directorhas been announced; the other employs Granger’s causality test. Another contempo-rary and prominent example is that of Knyazeva et al (2013), who report a similarrelation between board independency and firm value among S&P 500 companies.






To handle the endogeneity issue, Knyazeva et al apply the two-stage least squares(2SLS) method (in accordance with Theil (1958)); a feature of the local labor mar-ket for directors (ie, the availability of worthy and reliable candidates for a directorposition) serves as an instrument. Other examples of coping with endogeneity wheninvestigating the effect of boards are found in Hermalin and Weisbach (1991, 1998),Bhagat and Black (2000) and Drakos and Bekiris (2010). All of these studies usestructural simultaneous systems and apply 2SLS/3SLS methods intermittently. Thus,aligned with the literature cited above, we also handle endogeneity by basing ourmultivariate analysis on a structural simultaneous equations model.

5 DATA AND SAMPLE CONSTRUCTION

Our study focuses on the 150 largest cap companies traded on the Tel Aviv StockExchange (TASE) at the beginning of 2010. Data regarding the ownership structure istaken fromArticle 24 of each company’s annual financial report for the 2009 fiscal year(available electronically from the official website of the Israeli Securities Authority(ISA): www.isa.gov.il). Article 24 specifies the exact holdings of every member in thecontrol group and identifies the person (ultimate owner) behind each business entityin the control group.

Using Article 24, we compute the vote percentage and equity percentage of theultimate owners, taking into account pyramids and cross-holdings. Article 26 of eachcompany’s annual financial reports presents personal data on all company directorsand is used to collect each director’s attributes as well as to construct a networkof directors, according to which we calculated centrality indexes. The market valueof stocks, obtained from PREDICTA (a commercial database), and other companyattributes and financial data taken from the annual reports are available from the ISAwebsite.

Firms were omitted from the sample for two reasons. First, we excluded the dual-listed firms, as we believe these belong to and represent a different corporate gover-nance regime. This notion is supported by their typical dispersed ownership structure(unlike almost all other non-dual-listed Israeli firms) and the lower detail level ofownership reporting. Moreover, board centrality in relation to the local directors’ net-work may be underestimated, as most of the directors in these corporations are lessactive in the local economy, and their business connections tend to be foreign. Thesecond reason is negative equity, which is typical of firms going through a restructur-ing process, facing deletion from trading and usually not representing the appropriatedefinition of a going concern. The final sample was composed of 105 companies andtheir 727 directors.






6 EMPIRICAL RESULTS

6.1 Descriptive statistics

In Table 1(a), we present descriptive statistics describing some major characteristicsof the 105 firms in the sample. The total assets’ mean is over NIS3 billion (aboutUS$850 million) but the median is just over NIS1 billion. The average debt-to-equityratio is above 5, while the median is about 2. The results indicate an upward shiftin the mean leverage in Israeli corporations compared with prior findings (see, forexample, Barak and Lauterbach 2012). This phenomenon may reflect the tendency ofsome Israeli firms to increase their financial leverage in response to the low interestrate set by the Bank of Israel (the central bank) in reaction to the 2008 global financialcrisis.11

The average five-year annual growth rate of total assets is 17.5% (with a median of10.5%).12 This solid growth is correlated with the steady growth of the Israeli economy(despite the global crisis) in the second half of the last decade.13 However, as can beseen, the impressive growth does not reflect the performance of all companies in thesample, as some of them even present a significant percentage of negative expansion.A similar pattern can be found with respect to the Q ratio, indicating a higher marketvalue than book value of assets for most of the firms, despite the significantly lowerratio of others.

Notable diversity is also detected with respect to size and financial leverage, asdescribed above, as well as the number of directors on the board, which is naturallycorrelated with firm size.

Average vote per ownership (VPO) is about 1.42 and the median is above 1, indicat-ing that most of the firms in the sample belong to pyramidal business groups, creatinga gap between the ultimate owners’ voting power and their percentage of equity.This gap, which is a major factor in our analysis, intensifies the conflict betweencontrolling shareholders and other stakeholders, and is typical of concentrated own-ership economies. Summarizing Table 1(a), our sample represents a diversity of firmattributes in a rapidly growing economy with a concentrated and complex ownershipstructure environment.

Table 1(b) focuses on board centrality. It presents the means of the firms’ centralityscores measured according to the two approaches offered in the methodology: theaverage score and the highest result on the board of directors. Both approaches employ

11 Although the Israeli economy was not significantly damaged by the global crisis, the central banktook all the necessary precautions and joined the global trend of reducing interest rates. Thus, itlooks like companies with relatively unharmed equity took advantage of the opportunity to increasetheir debt under fairly convenient terms.12 Measured as ln.TA2009=TA2004/=5.13 According to the central bank, the per capita GDP grew by about 30% during this period.






TABLE 1 Descriptive statistics of samples: 105 firms and 727 directors.

(a) Firm characteristics

Variable Obs. Mean Median SD Max Min

Size (NIS mn) 105 3 085 1101 7277 64 411 146LEV 105 5.48 2.20 7.48 38.93 0.01Growth (%) 105 17.5 10.5 3.59 231 �44VPO 105 1.42 1.09 0.704 5.45 1.00Dir-size 105 8.58 8.00 3.01 16.00 3.00Q ratio 105 1.42 1.07 0.96 6.87 0.77

(b) Means of firm directorates’ centrality measures by type of director

p-value p-valueObs. Professional External (t test) (Wilcoxon)

Average degree 105 10.295 9.602 0.160 0.071Maximum degree 105 17.771 12.419 <0.001 <0.001

Average eignvector 105 0.0116 0.0106 0.699 0.008Maximum eignvector 105 0.0444 0.0217 0.001 <0.001

Average betweenness 105 0.224 0.228 0.947 0.005Maximum betweenness 105 0.985 0.525 0.023 <0.001

Part (a) presents the simple statistics of some important characteristics concerning sample firms according to thefinancial reports of the 2009 fiscal year. “SD” denotes standard deviation. “Size” is the total assets in millions of newIsraeli shekels.“LEV” is a firm’s debt-to-equity ratio. “Growth” is the annual growth rate of a firm’s total assets over theyears 2004–9, calculated as ln.TA2009=TA2004/=5. “VPO” is the ratio of aggregate ultimate owners’ vote percentageto equity percentage. “Dir-size” is the number of directors on the board of directors. “Q ratio” is the firm’s Tobin’s Q,calculated at the end of 2009 (the beginning of 2010) as the market-to-book value of assets. Part (b) presents thefirms’ board average and maximum score centrality measures (degree, eigenvector and betweenness), classifiedby the type of directors (professional versus external/independent) along with the t test and Wilcoxon test values forcentrality scores’ differences among these types of directors.

all three conventional indexes: degree, eigenvector and betweenness. Further, and alsoin accordance with the methodology, means are calculated separately for the groupof external directors and for the group of (expert) “professionals”.14

Clearly, the experts group presents superior centrality scores in almost all cat-egories. Their advantage seems more noticeable when using the maximum scoreapproach, for which their centrality is significantly higher for all centrality indexes(ie, degree, eigenvector and betweenness), according to both parametric and non-parametric tests. This result may be an outcome of the regulatory restrictions that

14 In Section 4, we claimed that directors who are neither external nor major shareholders’ familymembers (or employees) are more likely to be highly professional and apparently experts in thecompany’s operations.






prevent external directors from serving in more than one company within the samebusiness group. However, the larger centrality range of the experts group emphasizesthe credence of the maximum score approach. If, as suggested, the monitoring effectis mainly a direct result of directors’ reputation and status (regardless of board size),then looking at average centrality scores would be misleading.

6.2 The impact of directors’ centrality on firm performance

In order to test the effect of directors’ centrality, all other things being equal, wenow turn to multivariate analysis. As stated in Section 4, and in accordance with theexisting literature, our investigation should address the endogeneity embedded in theresearch question. Directors’ centrality is likely to be endogenous, since the a priori(rational) preference of well-connected, highly regarded directors is expected to becompanies with superior performance. Such companies’ environments make the taskof preserving and consolidating the director’s status much easier.

To deal with this matter, we use a structural model composed of two simulta-neous equations. The first uses firm performance (ln Q) as a dependent variable,explained by traditional control variables, ownership structure specifications and cen-trality score(s). The second equation tests the reversal effect of firm performance overboard centrality, and therefore uses centrality score(s) as a dependent variable andln Q as an explanatory variable.

Nevertheless, choosing the instrumental (exogenous) variables for this simultane-ous system is not an easy task and should be done very cautiously. The reason for thisis the very likely possibility that other important factors, such as firm size and growth(along with other variables that appear to be highly correlated with them), may alsobe “contaminated” by some of these endogeneity complications, for the reasons givenabove.15

Therefore, in order to avoid a possible bias of the estimates, we look for purely pre-determined instruments and eventually choose industry attributes and the ownershipstructure feature, which is the difference between an ultimate owner’s voting powerand their equity share.16 Using these instruments, we then employ the three-stageleast squares (3SLS) method.17

Table 2 presents the explicit equations and estimation results. Equation (1) thereinis our basic model and, as mentioned above, its dependent variable is ln Q, which is

15 For example, a firm’s leverage is significantly correlated with its size.16 Companies were classified into eight sectors, forming seven dummy variables.17 3SLS takes into account any correlation between system error terms and is thus considered moreefficient than 2SLS (see, for example, Dhrymes 1969; Belsley 1988).






TABLE 2 The impact of director centrality on firm performance. [Table continues on nextpage.]

(a) Professional directors

I II III IV V VIAvDeg MxDeg AvEign MxEign AvBet MxBet

Q equationLnSize 0.175�� 0.160�� 0.146�� 0.138�� 0.165�� 0.164��

(3.70) (3.47) (3.01) (3.03) (3.34) (3.30)

LEV �0.0001 0.0006 �0.0008 0.001 �0.004 �0.004(�0.02) (0.08) (�0.11) (0.20) (�0.62) (�0.58)

Growth �1.122�� 1.14�� 0.972�� 0.987�� 1.088�� 1.09��(�7.04) (�7.21) (�6.08) (�6.58) (�6.64) (�6.76)

H_VPO �0.438�� 0.381�� 0.261�� 0.250�� 0.266�� 0.274��(�3.54) (�3.24) (�2.32) (�2.31) (�2.28) (�2.37)

Dsize �0.064�� 0.065�� 0.058�� 0.058�� 0.067�� 0.074��(�3.39) (�3.42) (�3.02) (�3.12) (�3.43) (�3.69)

Centrality 0.050 0.020 3.415 4.419�� 0.275 0.069(0.96) (1.52) (1.41) (2.04) (0.67) (0.73)

Centrality 0.032�� 0.016�� 13.828�� 4.220�� 0.371�� 0.110��VPO (4.98) (5.75) (5.66) (6.34) (5.54) (5.39)

Centrality equationln Q 1.418 6.930� 0.014�� 0.062�� 0.210 0.926

(1.15) (1.82) (2.05) (2.62) (1.18) (1.32)

R2 0.273 0.299 0.297 0.353 0.274 0.272

p-value 0.04 0.03 <0.01 0.04 <0.01 <0.01

the natural logarithm of a firm’s Tobin’s Q. The explanatory variables in this equationare as follows.

(i) “LnSize” is the natural logarithm of the equity market value.

(ii) “LEV” is the firm’s financial leverage, measured as the debt-to-equity ratio.

(iii) “Growth” is the average yearly growth in firm size (total assets) over 2004–9(as of December each year), calculated as .LnSize2009 � LnSize2004/=5.

(iv) “H_VPO” is a dummy variable equal to 1 if the ratio of the ultimate owners’vote percentage to their equity percentage is above the sample median.

(v) “Dsize” is the number of directors on the board of directors.






TABLE 2 Continued.

(b) External directors

I II III IV V VIAvDeg MxDeg AvEign MxEign AvBet MxBet

Q equationLnSize 0.151�� 0.144�� 0.142�� 0.138�� 0.156�� 0.150��

(4.31) (3.36) (3.24) (3.32) (2.68) (2.62)

LEV �0.006 �0.007 �0.006 �0.005 �0.004 �0.003(�1.25) (�1.08) (�0.94) (�0.83) (�0.56) (�0.42)

Growth �0.980�� 0.938�� 0.923�� 0.923�� 0.876�� 0.885��(�8.66) (�6.85) (�6.74) (�7.08) (�5.08) (�5.12)

H_VPO �0.140 �0.056 �0.009 0.009 �0.077 �0.008(�1.43) (�0.49) (0.09) (0.1) (�0.59) (�0.69)

DSIZE �0.053�� 0.058�� 0.046�� 0.041�� 0.065�� 0.065��(�3.63) (�3.19) (�2.56) (�2.39) (�2.94) (�2.94)

Centrality �0.054�� 0.017 �13.588 �7.196 0.427 0.244(�2.30) (�1.01) (�1.09) (�1.23) (1.02) (1.36)

Centrality �0.008 �0.010�� 0.046�� 11.461�� 0.137 0.094��VPO (�1.46) (�2.22) (�2.56) (�12.30) (1.56) (2.95)

Centrality equationln Q �10.230�� 13.591�� 0.020�� 0.044�� 0.067 0.51

(�5.01) (�3.19) (�3.11) (�3.48) (0.28) (0.88)R2 0.399 0.337 0.459 0.512 0.155 0.179

p-value 0.06 0.06 0.09 0.02 0.14 0.06

We present 3SLS results of the following system of simultaneous equations:

ln Qi D ˇ0 C ˇ1LnSizei C ˇ2LEVi C ˇ3Growthi C ˇ4HVPO

C ˇ5Centralityi C ˇ6Centrality�VPO C ˇ7Dsize C ei ; (1)

Centralityi D ˇ0 C ˇ1 ln Qi C ei : (2)

ln Q is the natural logarithm of a firm’s Tobin’s Q. LnSize is the natural logarithm of the equity market value. LEV isthe firm’s financial leverage measured as the ratio of debt to equity. Growth is the average yearly growth in firm size(total assets) over the end of 2004–9, computed as .LnSize2009 � LnSize2004/=5. H_VPO is a dummy variableequal to 1 if the ratio of ultimate owners’ vote percentage to equity percentage is above the median. Centrality isthe directorate’s average/maximum centrality measure (degree, eigenvector or betweenness). Centrality�VPO isthe multiplication of the directorate’s centrality measure, chosen by the control group’s vote-per-owner ratio (theratio of ultimate owners’ vote percentage to equity percentage). Dsize is the number of directors on the board. p-value denotes the Hausman–Wu test p-value. Part (a) presents estimates for centrality measures of professional(experts) directors, while estimates referring to external directors are shown in part (b); in all models, the instruments(predetermined factors) are industry attributes’ dummy variables and the gap between voting power and ownershippercentage (due to the pyramidal ownership structure). To avoid multicollinearity problems, LEV is “cleaned” fromsize effects, ie, in the regressions of this table, we use the residuals of LEV (over LnSize) regressions instead of theraw variable itself. Columns I and II present regression results when the level of centrality is measured accordingto average and maximum degree, respectively. Columns III and IV (respectively, V and VI) follow the same patternfor the eigenvector (respectively, betweenness) centrality measure. t -statistics are presented in parentheses belowthe coefficients. �, �� and �� indicate that the coefficient is significantly different from zero at the 10%, 5% and 1%significance levels, respectively.






(vi) “Centrality” is the directorate’s average/maximum centrality measure (eigen-vector, degree or betweenness).

(vii) “Centrality�VPO” is the multiplication of the selected directorate centralitymeasure by the control group’s voting (power)-per-ownership ratio (the ratioof the ultimate owners’ vote percentage to equity percentage).

The above definitions also apply to (2), which examines the reversal effects of per-formance (ln Q) over centrality scores. The system is estimated separately for eachcentrality index, as well as for each of the two measurement approaches (ie, the board’saverage and maximum scores): a total of six versions. Columns I and II present regres-sion results, when the level of centrality is measured by average and maximum degree(AvDeg and MxDeg). Similarly, columns III and IV show the results of average andmaximum eigenvectors (AvEign and MxEign), while columns V and VI present theestimation outcomes of average and maximum betweenness (AvBet and MxBet).

One further note is necessary before we proceed. In a preliminary test, we checkedand found that firm leverage (LEV) is significantly correlated with firm size (LnSize).Thus, to avoid multicollinearity problems, we “cleaned” the LEV variable from firmsize effect by regressing firm leverage on LnSize and using the residuals as the leverageexplanatory variable.18

Part (a) presents system estimates that refer to the cluster of professional (“experts”)directors. Our main interest is the results concerning the effect of board centrality onperformance. However, it would be appropriate to begin inspection of the Q equationwith the intriguing significant estimates regarding the control explanatory variables.

Similarly to previous findings about Tobin’s Q, the coefficient of firm size (LnSize)is positive and different from zero at the 1% significance level. Conversely, and incon-sistently with most prior Q literature, we find the effect of the firms’ assets growth tobe significantly negative (1% significance level).

We further investigate this unexpected result and find the bivariate ln Q–growthPearson correlation to be significantly negative (�0:43). A possible explanation ofthis puzzling anomaly could be the recent change in the way in which listed com-panies in Israel report their financial statements. Since 2006, the ISA has directedlisted companies to switch to reporting in accordance with the International Financ-ing Reporting Standards (IFRS). This directive allowed them to update the book valueof their fixed assets (most of which are real estate) to their “fair” market value, insteadof their depreciated historic value (which fits the previous reporting rule). As a result,the equity of many firms has substantially “grown” without any change in their realeconomic indicators. Moreover, in many cases this artificial growth in equity provides

18 By doing so, we also “clean” the LEV variable from any endogeneity that is likely to be embeddedin firm size, since (as stated in the previous section) central directors tend to sit in larger companies.






an excuse for dividend distribution and even some extra bonuses that did not receivethe sympathy of the stock market.19 As a result, stock prices did not reflect the “posi-tive” change in equity, creating a negative relation between Tobin’s Q and total assetgrowth.20

In an attempt to neutralize the unwanted IFRS effect, for each company in thesample we obtain the five-year average annual sales growth (instead of total assetgrowth). Very surprisingly, although the reassessment of the fixed assets should notinfluence this item in the income statement, we find the relation between annual salesgrowth and Tobin’s Q to be even more significantly negative than the parallel total-asset-growth–Q relation. Further, we find the correlation between sales growth andtotal asset growth to be significantly positive (0.6). The only plausible explanation forthese exceptional results argues that insiders in companies with higher sales growthfelt more comfortable using IFRS features more aggressively, ie, relying on excessiveestimates of fixed asset value, while the (efficient) market continues to rely mainly onreal and reasonable economic indicators. The phenomenon described above empha-sizes the need to further investigate the effect of major regulatory changes, particularlyin closely held firms and concentrated ownership economies. Such an investigation,however, is beyond the scope of the current study.

We continue the inspection of (1) in Table 2(a) with the explanatory variableH_VPO representing the effect of the separation between control and ownership,which emerges from the pyramidal ownership structure. As expected, similarly toprevious studies, the disparity between voting rights and equity percentage tendsto harm firm performance. Companies with an above-median vote-per-owner ratiohave, all other things being equal, a lower Tobin’s Q, as the coefficient of this ratiois significantly negative.

The Dsize coefficient, representing the effect of board size, is also significantlynegative. This result supports Hypothesis 3.6, which assumes that, in a concentratedownership structure, larger boards are a counterproductive burden, probably sincesome appointments are not driven by economic considerations, but are part of thecontrollers’ private benefits.

We now get to our main interest in the Q equation, which is the effect of boardcentrality on firm valuation. All centrality measures and their presentation modes(as shown in regressions I–VI) yield positive coefficients. However, the most signifi-cant, positive estimate obtained for the eigenvector centrality index in its maximum

19 The case with the most media coverage was the unjustified dividends and bonuses paid in IDBGroup (one of the largest and most influential conglomerates in Israel), while relying greatly onIFRS, during 2008–10.20 It is important to remember that the estimator of Tobin’s Q has total book assets in the denominatorand stock prices in the numerator.






board score version. Apparently, the presence of well-connected and highly respectedexpert directors on the board positively contributes to firm valuation. The result sup-ports Hypothesis 3.1, which postulates that in order to preserve their reputation, theprofessional expert director will use their capabilities and business ties in order topromote firm value, while imposing an adequate monitoring effect in order to makesure that some of the surplus performance (ie, value) will eventually be conserved.

The significant result of the maximum score approach (and the higher t -values ofthe maximum score version in comparison to the average score) gives credence to thisapproach. The central directors’ monitoring effect seems to be independent of theirshare in the board.

With regard to the indexes, it seems that the eigenvector centrality measure is morebeneficial in describing centrality differences between expert directors. However,while the superiority over the degree index is crystal clear at the definition level,21

dominance with respect to the betweenness index can be explained by the relativelysmall number of completely separate business groups in the concentrated Israeli econ-omy. In this environment, it is most likely that real expert directors would be homoge-neously dispersed among these few groups, leaving insufficient betweenness diversityto measure.

The last explanatory variable in the Q equation, Centrality�VPO, captures thecombined effect of board centrality and the divergence of the vote from the owner-ship, due to a pyramidal ownership structure. The very significant positive estimatesregarding all definitions of board centrality clearly confirm Hypothesis 3.4. The neg-ative impact of the control–ownership wedge is moderated proportionally to boardcentrality. In order to preserve their status, central expert directors will invest moreeffort in firms that are more exposed to exploitation. This morally hazardous situationprobably makes both the public and media more alert, giving the director a greaterincentive to act more decisively, in order to protect their reputation.

To illustrate the potential magnitude of this combined effect, we use regression IVwith the higher explanatory power and take, for example, a firm with an averageQ, centrality score and vote-per-owner ratio (1.42, 0.0444 and 1.42, respectively).The negative impact of the excessive voting power (according to the coefficient ofH_VPO) is a deprecation in Q of about 22%.22 However, an increase of 1% in theboard centrality score is equivalent to a 4.8% rise in Q; a similar increase in VPOwill moderate its negative impact by a 0.3% rise in Tobin’s Q.

The estimation of (2.2) in Table 2(a) supports the two-way causality relationshipbetween directors’ centrality and firm value. The significant positive coefficient ofln Q indicates that expert central directors prefer to sit on boards of companies with

21 The degree index only counts the ties, while the eigenvector also considers each tie’s quality.22 Taking into consideration that our dependent variable is the natural logarithm of Q.






better market performance. Such companies will make the task of preserving andpromoting directors’ reputation and professional status much easier.

We conclude the inspection of Table 2(a) with the results of the Hausman–Wuendogeneity test, provided with each version of the structural equations. All testsconfirm the endogeneity effect embedded in expert directors’ centrality indicators.Apparently, the use of a simultaneous system was not redundant.

We now turn to Table 2(b), devoted to external directors. Evidently, the resultspoint toward a different pattern of external directors as regards the centrality–firmperformance relation. Most centrality scores yield negative coefficients, and the aver-age degree index is even significantly negative (at the 5% significance level). Thesefindings give credence to the shadow director phenomenon. This, in turn, supportsHypothesis 3.7, representing the view that overly powerful controlling shareholdersuse external directors as a rubber stamp for approving suboptimal business maneuvers,which serves tunneling activities, ie, the consumption of private benefits of control.23

Thus, the source of external directors’ centrality is probably a negative reputation forbeing easy collaborators with controlling shareholders. This view is also supportedby the highly significant negative coefficients of ln Q in the second structural equa-tion (the centrality equation in Table 2(b)). According to this line of thought, externaldirectors get higher centrality scores in firms with inferior performance. A plausibleexplanation for this would be that most collaborators’ external directors (those whogained the most negative reputation) are chosen by the major shareholders of firmswith inferior performance, due to intensive tunneling procedures.

We continue our analysis of external directors’ centrality consequences by examin-ing the combined effect of centrality and the divergence of voting power from equitypercentages (Centrality�VPO). The coefficients in most regressions are negative, andthree of them are significantly negative, supporting Hypothesis 3.8. It turns out thatthe trend described above intensifies as the company is located lower in the pyramidalownership structure. The better the (negative) reputation of the external director as acollaborator, the greater the controlling shareholders’ desire to recruit such a directorto firms in which they possess higher incentives to consume private benefits. Thisnegative, combined effect regarding external directors appears to be strong, and sig-nificant enough to contain all the explanatory power (diversity) of the pyramid effect,rendering the H_VPO coefficient insignificant.

However, according to Table 2(b), the dynamic above has one exceptional central-ity effect. It appears that external directors with higher betweenness scores tend toimprove firm performance and even eliminate the effect of negative excessive votingpower in pyramids. It also seems that those external directors who serve in several

23 According to Dyck and Zingales (2004) and Barak and Lauterbach (2011), the level of privatebenefit consumption in Israel is above the global median.






important business groups are similar in character to professional (expert) directors.It is plausible to assume that they are, in fact, experts who were specially chosen forexternal director positions in order to gain market sympathy, and thus much less (ornot at all) subject to the improper damaging influence of controlling shareholders.

Finally, the Hausman–Wu endogeneity test results, although less pronounced thanin the previous case, justify the use of appropriate means to address the problem ofendogeneity.

7 CONCLUSIONS

In this study, we explored the implications of directors’ networks for listed compa-nies’ performance in a concentrated ownership environment and pyramidal controlstructures. Our results provide interesting insights for practitioners as well as forpolicy makers.

Using common centrality indexes on a sample of 727 directors serving in 105listed Israeli companies, we showed that director type is a crucial argument whenassessing the effect of board centrality on valuation. According to our findings,well-connected (central) directors, who are neither ultimate owners’ family members(including employees) nor independent/external directors, promote firm valuation.These professional directors, who probably received their position as a result of theirexpertise and business connections, preserve their reputation through the constructiveuse of skills and status, while monitoring and restraining the controlling shareholders’tunneling activities.

Further, the constructive efforts and their value effect are on a larger scale than thoseof ultimate owners, as the company is closer to the bottom of a pyramid ownershipstructure and the wedge between the controllers’vote and equity percentage increases.It appears that well-connected, highly respected directors are concerned about thisgap’s potential to draw public attention for being an incentive to exploit the company.Such public awareness, accompanied by intensive media coverage, may result incriticism and a damaged reputation in the case of underperformance. The intensifiedefforts made in this situation by central expert directors mitigate the negative impactof the pyramidal control structure.

A similar analysis of external directors yields opposite conclusions to those statedabove. Central and well-connected external directors seem to harm firm performance,and even to magnify the negative effect of the vote–ownership wedge due to the pyra-midal ownership structure. The results support the claim that a centralized ownershipstructure encourages the shadow director phenomenon. When the surplus power ofcontrolling shareholders is not moderated properly, most external directors becomethe long arm of dominant shareholders and their tunneling (value-destroying) acts.These findings support Hypothesis 3.7 (and thus Hypothesis 3.8), which claims that






an external director’s higher centrality score is not an indication of skills and profes-sional reputation but, in most cases, simply the result of a “bad” reputation for beingsubmissive and obedient toward the dominant shareholders. The more cooperativethe director is, the more popular they are among the controlling shareholders, whoare pleased to appoint them to the board and thereby enhance the director’s networkcentrality. Moreover, from the perspective of ultimate owners in pyramids, it is mostefficient to appoint the external directors with the worst reputations to serve in com-panies located at the bottom of the pyramidal structure. In these companies, due tothe vote–ownership wedge, the incentive to exploit firm resources is higher, tunnel-ing activity is more intensive and the presence of a “convenient”, concurrent externaldirector is more essential.

The only exceptional external directors are those who serve simultaneously in majorbusiness groups (those with higher betweenness centrality scores). It appears that theseunique directors possess characteristics similar to those of the expert professionaldirector group, and were probably appointed due to intensive public attention towardmajor business groups. Thus, a higher betweenness centrality score in this case indeedreflects a reputation for proficiency that the director would like to preserve.

The conclusions of this study can serve as an additional tool for professionalinvestors and portfolio managers that operate in a complex concentrated ownershipstructure environment with overly powerful/unbalanced controlling interests. In suchcapital markets, value maximizing for noncontrolling stakeholders strongly dependson the proper functioning of a board that adequately monitors controlling shareholdersand moderates tunneling activities.

Our findings should also be of interest to policy makers and regulators in concen-trated ownership economies. The agency problem, which emerges from the separationbetween ownership and control in these economies, may be mitigated by a strong,independent board. This study recommends that a mechanism should be established inorder to restrain the influence of shareholders with controlling interests on the appoint-ing and dismissing of directors, especially external ones. Moreover, it is important toapply a mandatory appointment of at least one highly respected expert director to theboard. Such mechanisms will ensure the minimum consumption of private benefitsof control that, according to the financial literature, are negatively correlated withquality of capital markets and economic growth (see La Porta et al 2002).

Note that our study is based on a sample of Israeli firms from the beginning of2010. The Israeli economy and capital markets have undergone major regulationand structural reforms in recent years. One of these reforms, the Corporate Law16th Amendment, was first enacted in 2011 and relates directly to the subjects andconclusions of this study. Thus, there is a need for further research in order to examinethe effectiveness of the evolving regulation, which, in this case, has become moreimportant, going beyond the regular practice of calling for future validation.








ACKNOWLEDGEMENTS

The authors appreciate the helpful comments of an anonymous referee. The authorsthank the Raymond Ackerman Family Chair in Israeli Corporate Governance for itsfinancial support.

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