A social network approach to examine the role of influential stocks in shaping interdependence structure in global stock markets

Ram Babu Roy1, Uttam Kumar Sarkar2*Indian Institute of Management Calcutta, Kolkata, India, 700 104

* Corresponding Author: 2Contact: uttam@iimcal.ac.in (U K Sarkar), Tel +91-9433018562, Fax +91 33 2467-8307 1Contact: rbroy07@iimcal.ac.in (R B Roy), Tel +91-9903883394

Abstract— This paper investigates the role of influential stocks in shaping the emergent system-level interdependence in global stock markets using a large set of stocks selected from major stock market indices from across the globe. We have proposed a method to identify influential stocks using various centrality measures used in social network analysis literature. Our study shows how these influential stocks provide key linkages in integrating the global stock markets as an interconnected system. We have also shown that the regional influence dominates over the economic sector influence in shaping the topological structure of stock market network. The study also captures the change in the topology of this network following the collapse of Lehman Brothers.

Keywords-Network Approach, Minimum Spanning Tree, Centrality, Stock Market, Correlation, Financial Crisis

I. INTRODUCTION

Representation of stock market data using network and the properties of the network topology of US stock market have been studied extensively in [1]. It has been shown in [2] that the US stock market netwok obtained from price returns constitute small world and has scale-free degree distribution and this property has been exploited to propose a degree-based index as an indicator of market performance. As per power law, the network is characterized by the presence of few dominant nodes having large number of linkages and bulk of nodes with smaller number of linkages. These dominant nodes may have connections with far away nodes which is crucial in integrating the various components of a network into a system as a whole. The concept of networks has been applied to study the behaviour of Chinese [3], Indian [4], and Brazilian [5] stock markets. The evolution of interdependence between stock markets have been reported in [6, 7] that have studied the regional behaviour of stock markets with relatively small sample of indices. The interdependence in the world equity market with large sample of indices reveals increasing integration of global equity market over the period 1997-2006 [8]. Minimum Spanning Tree (MST) is used to reduce the full

network into a simpler network that helps in getting better visual insights about the network [9].

Centralization is an important concept in social network analysis and there are mainly four types of node centrality measures namely degree, betweenness, closeness, and eigenvector centrality are established in the literature [10,11]. Investors often make their decisions based on the behaviour of other stocks of their interest. Hence some of the key stocks may influence investor’s decision. The importance of a stock is normally represented by the market capitalization of the firm corresponding to the stock but the comovement of stocks in the social network of stocks is not taken into account in judging their importance. As per the Efficient Market Hypothesis (EMH), stock prices reflect all the available information in the market. Though EMH is debated in the literature, to a reasonably good approximation the stock price represents all the information available in the market. To the best of our knowledge, no work has been reported on identifying influential stocks using the social network approach and the impact of recent financial crisis during 2008 on the evolutionary behaviour of the global stock market network. This paper attempts to contribute towards bridging this research gap in the literature. Our objective in this paper is to look for the answers regarding the way stocks cluster together under regional influence. Another aim is to identify influential stocks in the global market using various centrality measures and examine change in their ranks following some critical event e.g. the collapse of Lehman Brothers in the USA.

II. DATA DESCRIPTION AND METHODOLOGY

The closing prices for 3566 stocks selected from 20 stock indices from major economies from across the world for 13 years from January 1998 to January 2011 obtained from Bloomberg have been used. We have chosen this period to study the behaviour of the stock market network before and after the collapse of Lehman Brothers in the USA. The correlation network and associated Minimum Spanning Tree (MST) are constructed using the weekly returns and the method described in [1] and [9]. The nodes of the network and

2011 International Conference on Advances in Social Networks Analysis and Mining

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DOI 10.1109/ASONAM.2011.87

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the MST represent the stocks and the edges between any pair of stocks represent the interrelationship between them. We have set the threshold of the correlation in our study at 0.5 for constructing the correlation network. In order to study the dynamics of the network structure, the data set is partitioned into 118 periods of length 3600 weekly returns each with each consecutive period obtained by sliding the sampling window by 10 data points (corresponding to 2 weeks approximately). Period 119 corresponds to the entire data set of thirteen years from 1/1/1998 to 1/29/2011 and gives the long-run behaviour of the network. The start and end dates for periods 31 and 34 in (MM/DD/YYYY) format are 11/4/1998 to 9/11/2008 and 12/4/1998 to 10/11/2008 respectively. The evolutionary behaviour of the metrics of the derived networks are investigated to get more insight into the evolution of the network structure during the recent financial crisis.

A. Identifying influential stocks using centrality measure

We propose a method to identify influential stocks using all the four the centrality measures widely used in the social network literature. Nodes are arranged in descending order of their centrality value and assigned ranks in ascending order with rank one being assigned to the node with the highest centrality. These ranks are normalized by dividing with the respective maximum rank. The final rank of each of the stocks is computed based on the average of these four normalized ranks for all the indices.

III. EMPIRICAL FINDINGS

A sharp change in the cross correlation between stocks and various network metrics following the event of collapse of Lehman Brothers in the USA corresponding to period 32 has been observed. Similar evolutionary behaviour of stock market network has been observed in our recent study on the dynamics of stock returns in various individual stock markets [12] at the onset of recent crisis. The impact of the failure of Lehman Brothers and various other events on the stock market network is captured by significant decrease in the length of the MST impling a significant increase in the correlation between stocks following that event. Fig. 1 depicts the MST with the stocks from various indices being shown with different colors and the geographical proximity of the stocks being depicted using the shapes of the nodes. The stocks belonging to different continents have been shown by different geometrical shapes as shown in Table I. We observe that the geographical proximity dominates the proximity based on the stock indices i.e. the stocks from different indices but from same geographical regions tend to cluster together. We have also investigated the sector-level influence on the clustering behaviour of stocks. Fig. 2 depicts the MST with all the stocks from various economic sectors as classified by Global Industry Classification Standard (GICS) represented by different colors as given in table II. The geographical

proximity of the stocks is again depicted using the shapes of the nodes as given in Table I.

Figure 1. MST showing dominance of geographical proximity over Indices

TABLE I. NODE SHAPES USED IN FIGURES 1 AND 2

Continent Node Shape Continent

Node Shape

Australia Diamond Europe EllipseAsia Triangle North America Box

Figure 2. MST showing dominance of geographical proximity over sectors

TABLE II. COLOR CODE USED IN FIGURE 2

GICS Sector Color GICS Sector Color

Materials Brown Information Technology Blue

Industrials Pink Consumer Staples Black

Health Care Orange Telecommunication

Services Green Energy Red Utilities Purple

Consumer Discretionary Yellow Unknown sector Grey

Financials Magenta

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CONCLUSIONSThe clustering pattern reveals that the geographical proximity dominates the economic sector based proximity in determining clusters of stocks in the global stock market. Subsequently, fifty influential stocks are selected from the set of all stocks based on their degree centrality corresponding to the period no. 119 that captures the direct linkages bwtween stocks based on the long-run behaviour of stock markets. The network of the countries based on the interconnectivity of stocks from these countries is shown in Fig. 3. The network clearly shows a dense linkage between the countries having either geographical proximity or economic ties, hence a small set of dominant stocks provides linkages between global stock markets making them the parts of an integrated system.

We have given a novel method to identify influential stocks using centrality measures of social network analysis literature. Our findings indicate dominance of geographical proximity over economic sectors in forming stock clusters. WTAN LN and SCIN LN from UK emerge as the most influential stocks from the social network of the global stocks and the stock market behaviour is dominated by European stocks as all the top 10 stocks ranked as per centrality measures are from this region. We have also shown that even a small set of fifty dominant stocks provides a linkage between all the stock indices across the globe making it an integrated system.

Japan India Mexico

NewZealand

UK

US

Brazil France

China Korea

Singapore

Hong Kong

Germany

Australia

Canada

Taiwan

Thailand

REFERENCES

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[5] Tabak, B.M., Takami, M.Y., Cajueiro, D.O., and Petiting, A. Quantifying price fluctuations in the Brazilian stock market. Physica A, 388 (2009), 59-62.

Figure 3. Network of countries based on the long-run similarity in evolutionary behaviour of stocks for period 119

[6] Ravichandran, K., and Maloain, A.M. The Global Financial Crisis and Stock Market Linkages: Further Evidence on GCC Market. Journal of Money, Investment and Banking, 16, ISSN 1450-288X (2010).

The ranks of all the stocks are computed for periods 31 and 34 to investigate the time evolution of the rankings. The ranks of top ten influential stocks for the periods corresponding to pre-crisis and post-crisis scenario marked by the collapse of Lehman Brothers are shown in Table III. WTAN LN and SCIN LN from UK emerge as the most influential stock index from the social network of the global stocks for pre and post Lehman Brothers collapse respectively. We observe that the ranks of the stocks do not remain constant across times but keep changing. The change in ranks of top three influential stocks are relatively low compared to those ranked lower.

[7] Morana, C., and Beltratti, A. Comovements in International Stock Markets. Journal of International Financial Markets Institutions and Money, 18 (2008 ), 31-45.

[8] Coelho, R., Gilmore, C.G., Lucey, B., Richmond, P., and Hutzler, S. The evolution of interdependence in world equity markets—Evidence from minimum spanning trees. Physica A: Statistical Mechanics and its Applications,376, 15 (2007), 455-466.

[9] Garas, A., and Argyrakis, P. Correlation study of the Athens Stock Exchange. Physics A, 380 (2007), 399-410.TABLE III. TOP TEN INFLUENTIAL STOCKS

[10] Freeman, L.C. Centrality in social networks: Conceptual clarification. Social Networks, 1, 3 (1979), 215-239.

[11] Bonacich, P. Power and Centrality: A Family of Measures. The American Journal of Sociology, 92, 5 (1987).Rank

Period 31 Pre-crisis

Country (P-31)

Period 34 Post-crisis

Country (P- 34)

1 WTAN LN UK SCIN LN UK2 SCIN LN UK SMT LN UK3 SMT LN UK WTAN LN UK4 EDIN LN UK EDIN LN UK5 SDP LN UK ATST LN UK6 EFM LN UK FRCL LN UK7 MNKS LN UK BNKR LN UK8 FRCL LN UK EFM LN UK9 BNKR LN UK SDP LN UK10 ATST LN UK BSET LN UK

[12] Roy, R.B., and Sarkar, U.K. Capturing Early Warning Signal for Financial Crisis from the Dynamics of Stock Market Networks: Evidence from North American and Asian Stock Markets. Society for Computational Economics 16th International Conference on Computing in Economics and Finance, City University London, UK, 2010.

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