Modeling, Analysis, and Characterization of Dubai Financial Market as a Social Network Ahmed El Toukhy 1, Maytham Safar 1, Khaled Mahdi 2 1 Computer Engineering Department, Kuwait University 2 Chemical Engineering Department, Kuwait University ahmadtookhy@hotmail.com, maytham.safar@ku.edu.kw, khaled.mahdi@ku.edu.kw Abstract. A social network is a structure made up of nodes, which are also called social actors, linked together with edges, which are also called social links. Social networking has been evolving during the past years. A lot of researches have been conducted in that field and a lot of applications have been arisen. In social networking applications, a social network in constructed for the specific application field and then analyzed based on some parameters to try to understand, analyze, and predict the behavior of the constructed network. In this work, we analyze two social networks constructed for the Dubai Financial Market to try to understand and predict the behavior of the stock market as a result to the financial crises and the cause of the stock market collapse. Keywords: Social Networks, Stock Market, Dubai Financial Market, Entropy, Cycles. 1 Introduction The studies and researches conducted in the social networking field have been increasing and evolving in the past few years. A lot of applications have arisen to the field where social networking and analysis would be of great benefit to analyze, understand, and predict the behavior of the social networks constructed for the specific application area [3, 1]. Social networking analysis is a method of constructing a single or multiple social networks for a specific type of application consisting of nodes, edges, and information transferred and communicated between the different nodes via the different edges connecting them [9]. The application areas varies very widely from communication networks, information networks, sharing, financial, business, people, and many other types where different information are being transferred between the nodes. One of the social networks applications is stock markets. Stock markets affect the financial status and economy of the country. A stock market is a place where stocks, shares of listed companies, bonds, and other financial securities are being traded. The amount of money traded in the stock market is an indicator of how strong is the economy of the country and how big the volume of trading in its stock market can be an indicator of investments and business growth in this country [8].
However, stock markets are prone to collapses. During the last financial crises in 2008, many stock markets have collapsed. When a stock market collapses, the amount of trading in it would decrease drastically and the listed companies shares would lose much of its value. Since stock markets and the amount of trade in it is an indicator of the economy strength of the country, when financial crises occurs and the shares values fall down, the stock market would collapse and so the economy of the country would lose its strength. This means losing many investments and business opportunities in the respective country meaning that the economy would suffer more and more. Using social networking analysis methods would be very useful because it would allow us to analyze the behavior of the stock market in terms of social networks parameters. Analyzing the stock market and identifying the main properties of it represented in a social network would enable us to understand and know the reasons behind such activities and reactions happening in the stock market as well as predicting the behavior of the market in case of collapse or even normal situation. Predicting the behavior of the stock market in different financial situations would allow the authorized people to take the suitable actions to prevent a major collapse to occur or increase the trading amount in the market and gaining more strength to the economy. Dubai Financial Market (DFM) is the stock market of Dubai city in United Arab Emirates (UAE) where different types of securities are being traded like shares of listed companies and bonds [11]. It is one of three stock markets in UAE. DFM started its operation in 2000 with most of the listed companies based in UAE and few of them only are based in the different gulf countries [13]. DFM was found to invest in different financial securities to serve the economy of UAE with maximum safety, transparency, and fairness in the trading process. In this work, two networks are constructed from DFM. One is called Personnel Network where the nodes are the listed companies and an edge between two nodes (companies) represents one or more persons being board members in the boards of both companies. The other network is called Families Network where the nodes are the listed companies and an edge between two nodes represents one or more board members from each of the boards of the two companies belong to the same family. In order to construct those networks, we had to go to the website of each listed company in DFM or search for the company s latest yearly report to get a list of all its board members with their family names to know the common board members between the companies and identifying the members with the same family name from boards of different companies to identify the edges between the nodes in the two networks. In order to analyze the two constructed networks, two methods are used. One is the cyclic analysis method where the number of cycles versus cycle degree (number of nodes in the cycle) is computed for each possible cycle degree and the Entropy of cycles is calculated for the network. For this method, two different algorithms are being used for the two networks. For the Personnel Network, an exact algorithm calculating the exact number of cycles for each cycle degree is used. In the Families Network, an approximation algorithm is being used because there are many edges between the nodes which makes the use of the exact algorithm not feasible and will take very long time. The other analysis method is non-cyclic where some parameters are computed to give a picture about some of the properties of the network and its behavior.
In the next sections, we will provide a background about stock markets in general, cycles and parameters calculation for social networks, and an explanation for the entropy of cycles and its calculation. After that, information about Dubai Financial Market, its history and properties, and the networks constructed and method of modeling them is presented. We then present the experimental work and results conducted on the two DFM networks including the entropy and parameters calculation. Finally, possible future expansion to our work as well as the conclusion of it is mentioned at the end. 2 Background & Related Work In the coming subsections, we introduce stock markets, their importance, and some of their characteristics. We also introduce cycles as the modeling method used to model the social networks constructed in this work. Finally, we give an introduction about the non-cyclic analysis and parameters calculation conducted on the social networks. 2.1 Stock Market Economy is becoming the moving force in nowadays world. It is considered a very important reason and motivation for many events and things happening in the world. Many wars have started because of economic and financial goals while many researches have been conducted only for pure economic motivations. Stock markets have always had huge effect on a country s economic status. It is actually considered the most important indicator for the status of a country s economy in terms of strength and stability. The stock market is a public market in which the shares of specific listed companies and firms are being exchanged (bought and sold) at an announced known price. The stocks exchanged are considered financial securities for those listed companies and organizations [16]. The stock market in any country is of great importance. It is a primary source of money for companies [16]. A company needing cash would sell some of its ownership shares in the stock market in order to expand its capital to get the needed amount and solve any financials issues it could face without the need to get a loan from a bank. The price of shares has a great impact on the company itself, and the economic activity in the whole market as well. High share prices tend to be related to the value of the company and the amount of business being done by it. On the other hand, stock markets are always prone to collapses. A collapse would occur to the stock market in case of a sharp sudden change in shares price of listed securities. The stock market collapse can be a result of many various financial and economic factors. However, it can be said that the general reason for any stock market collapse is the lack of confidence in the country s economy [8]. This even can be a result of any political, public, or local issues. There have been famous stock market collapses varying in size and effect on the country and the whole world. The last collapse was the stock market collapse in 2008 which has affected most of the countries all over the world and is still affecting the economy of many countries until
today. In this work, we analyze the Dubai Financial Market by constructing two networks from it and use the cyclic and non-cyclic parameters for analysis. 2.2 Cycles The first part of network analysis conducted in this work is cyclic analysis and entropy calculation. In a social network, the state of the network can be defined according to several choices. One of these choices is the degree, defined as the number of links going in or out of an actor in the network. This definition is commonly used by most of the researchers. Different non-universal forms of distribution could result when analyzing the social network using the degree. For example, random network has a Poisson distribution of the degree. Small-World network has generalized binomial distribution [1]. There is no unified form reported. A different unified distribution form that is applicable for all social networks can be generated by using a different definition of the state of the network. The state is defined as the number of cycles existing in the network. Then we find the distribution function of the cycles and calculate the Entropy of the network [1]. 2.3 Parameters Beside the previous cyclic method of social networks analysis (Entropy calculation), there are other non-cyclic parameters that can be calculated to analyze the network further more. Those parameters include Degree Centrality, Betweenness Centrality, Closeness Centrality, Eccentricity, Eigenvector Centrality, Graph Diameter, Graph Density, and Clustering-Coefficient. Degree Centrality simply means the number of edges linked to a node. In directed graphs, two measures are considered, indegree and outdegree. Indegree refers to the edges pointing to a node while outdegree refers to the edges pointing out from the node [14]. Betweenness Centrality is a measure that describes the probability a node would arise in shortest paths between other nodes in the network. Closeness Centrality calculates the average number of nodes between a specific node and all other nodes in the network. Eccentricity refers to the distance between a specific given node and the farthest node from it in the network. Eigenvector Centrality is a measure corresponding to the node s importance in the graph based on the node s connections. This is done by assigning a score for each edge linked to each node so high-score edges would contribute to a node s score more than low-score edges [14]. Graph Diameter means the farthest distance between the two farthest nodes from each other in the graph while Graph Density calculates the closeness of the network to completeness. A complete network would have all possible edges between all nodes in it and so its density is equal to 1. Finally, the clustering coefficient is a measure that indicates how close a network to small world. It indicates how nodes in the graph tend to cluster together. It is calculated for each node by itself as well as the average clustering coefficient for the whole graph which is the average of local clustering coefficient values across all nodes in the graph. A small world network has higher average clustering coefficient than a random diverse network [15].
3 Entropy and Cycles Entropy is one of the most important analysis methods and indicator of social network behavior. One definition of Entropy is the degree of robustness of the network [4]. Giving this definition, it is assumed that the network is fully dynamic, meaning that the links can change without any constraint on their behavior. Therefore, Entropy can be defined as the level of disorder of a defined system. It can be understood from the definition that a dynamic changing network is of low entropy while a static rigid strongly connected network would have high Entropy. From a statistical point of view, Entropy means the probability P(k) that the system is in a specific state k. it can be represented by the following equation: (1) The definition of the state of the system differs depending on the system itself. In biological systems, the state means the positions of the molecules while edges mean the interaction between them [1]. In social networks, the state of the system can be interpreted by several ways. One way is the degree, which is the number of links associated with each social actor (node) in the social network. This interpretation is commonly used by almost all the researchers. It is very easy to calculate; however, not accurate because it would result in different forms of distribution and so different analysis of the social networks [1]. Another interpretation of the state of a social network is cycles. Cycles are considered one of the major concerns and analysis methods in social networks. It results to a universal form of distribution even for different types of social networks. Using cycles to analyze the networks means in statistical mechanisms to find the probability that a social actor in the network would receive the information he sent again from one of the social actors linked to it [1]. In other words, if a network is noncyclic, the entropy would be infinity because the network is very static and there is no way a social actor would receive the information it sent again. In this work, we use the concept of entropy of cycles to analyze the social network of a stock market exchange and try to understand the behavior of such network and the relation between the performance of different listed companies in the stock market and the performance of the exchange market in total. 4 Dubai Financial Market The Dubai Financial Market (DFM) is the stock exchange market based in the Trade Centre Building in Dubai city and started operations on 26 March 2000. It was founded to provide trading shares of Dubai, UAE, and some regional companies or Public Join Stock Companies (PJSC) [13]. It is one of three stock exchange markets in United Arab Emirates (UAE) which are Dubai Financial Market (DFM), Dubai International Financial Exchange (DIFX), and Abu Dhabi Securities Exchange
(ADX) [13]. DFM has currently 79 listed companies most of them based in UAE and categorized into 10 categories: Banks, Investments and Financial Services, Insurance, Real estate and Construction, Transportation, Materials, Consumer Staples, Telecommunication, Utilities, and NASDAQ Dubai. NASDAQ Dubai is formally called Dubai International Financial Market and it is a stock exchange market founded in Dubai in 2005 aiming to be the main gateway of opportunities and stock exchange in the Gulf region, Middle East, South Africa, Turkey, as well as Central and South Asia [12]. DFM is considered the secondary market (primary market is DIFX) for trading of different types of securities. These types include public joint stock companies shares, bonds issued by the federal government, or any of the local governments or public institutions of UAE, investment funds, or other types of financial instruments approved by the DFM [11]. Each stock exchange has a regularity authority. Dubai Financial Market s regulatory authority is Emirates Securities and Commodities Authority (ESCA). It is also the regulator for Abu Dhabi stock market exchange (ADX). However, a separate authority is responsible for the regulatory of DIFX which is Dubai Financial Services Authority (DFSA) [13]. DFM s mission is to create a fair, efficient, liquid and transparent marketplace that provides choices through the best utilization of available resources in order to serve all stakeholders [11]. As part of this mission, it was decided by an Executive Council Decree that DFM itself is a public join stock company in the UAE with a capital of AED 8 Billion allocated over 8 Billion shares with value of AED 1 per share and 20% of the DFM shares are offered for public subscription. The main objective of DFM is to invest in securities to serve the national economy of UAE and regulate the trading process in order to ensure maximum protection and safety achieved [11]. DFM helps creating and providing liquidity in the market by the fair trading practices between the investors as well as arranging the change and transfer of securities ownership through settlement and clearing mechanisms managed by an electronic system to guarantee maximum efficiency achieved during this process. Brokers present a very remarkable part and play a very important role in any stock exchange market and so handling them and the interaction between them and the stock market and the investors is one of the most important roles of a stock market. DFM implements certain rules and regulations for professional communication between the brokers and DFM staff to guarantee a high level of integrity. Reports are also a key factor because they show the status of the market and the securities listed in it which in turn helps the decision makers take better decisions on time. This can be achieved by collecting data and statistics and issuing reports on time and so the forecasting process can be done on time as well which is being achieved in DFM. [11]. 5 Network Modeling and Characterization In order to construct a social network for Dubai Financial Market, all the board members of all the listed companies have been gathered in one list by visiting all the
websites of those companies. Then, two social networks are constructed for Dubai Financial Market. In the first one, named Personnel Network, the companies are nodes (social actors), while an edge represents a person being a board member in the two companies connected by that edge. In other words, if a person is a board member in 4 companies, this means there is a link between each company and the other 3 companies. Fig. 1. Personnel Network of Dubai Financial Market In the second network, named Families Network, the companies are nodes, same as the first one, while a link between two companies means that there are two board members from the same family in those two companies.
Fig. 2. Families Network of Dubai Financial Market Logically, this network would be much more connected than the first one. This has led us to use the exact algorithm in order to calculate the Entropy of Cycles for the first network (Personnel Network), while use the approximation algorithm to calculate the probability of cycles in the second network (Families Network). The exact algorithm of computing cycles of a graph is NP-complete [2, 5]. Hence, applying it to highly connected large networks is not practical. Both networks were constructed with undirected links. That is, if two companies have the same board member (or two board members with the same family), an edge is placed between the two networks, with no direction (the edge is considered to be in both directions). On the other hand, edges weight (cost) was not considered. If two companies have more than one board member in common between them, a link of regular cost (no additional weight is assigned) would be placed between them. Pajek 2.0 network analysis software was used to draw the constructed networks while Gephi 0.7 network analysis software was used to calculate the non-cyclic parameters. The cyclic analysis (Entropy of cycles) was computed using both exact algorithm [3] for Personnel Network and approximation algorithm [5] for Families Network. 6 Experimental Work & Results The purpose of this work is to apply the social networking analysis methods (Entropy of Cycles as well as calculation of non-cyclic parameters) to analyze and understand the behavior of Stock Markets, applied on Dubai Financial Market in this work, and to find any relation between this behavior and the market collapse occurred to it
during the last financial crises. We are trying to relate between the board members of the listed companies and how they were affected by the financial crises. In this work, we are finding the relation between the market collapses resulted from the financial crises in 2008, and persons being board members in multiple listed companies. Looking at the constructed networks (Figure1 and Figure2), we can see that the nodes (companies) in the networks are very connected and related to each other by many links. This would prove and explains the massive market collapse that happened in Dubai Financial Market as a result to the financial crises of 2008. Simply, because if a company s value is getting lower in the stock market, it would in turn affect many other companies since it is connected to multiple companies by having common board members as shown and illustrated in the constructed networks, which will result in the collapse of many other companies as well as the collapse of the entire market. 6.1 Cycles and Entropy Calculation We started the experiment by collecting data about the board members of each listed company in DFM. Most of the board members we found easily in the About us page of the company s website. Some of them we could find the board members in the yearly report uploaded on the company s website. After constructing the two networks; Personnel and Families Networks, we used the exact algorithm to calculate the number of cycles versus the cycle length for the Personnel Network while the approximation algorithm was used to calculate the probability of having cycles versus the different cycle lengths. This is because the first network is much simpler and has less number of edges between its nodes than the second one which makes the exact algorithm run in a finite amount of time for the first network but not applicable for the second one. The Families network showed entropy of 2.65. The maximum cycle length along with the total number of cycles cannot be calculated for the Families Network because the approximation algorithm was used, not the exact. The Personnel network showed a maximum cycle length of 23 nodes, 146655 as total number of cycles of all lengths in the network, and entropy of 2.19. Based on previous works by the authors [7], one technique to characterize the studied social networks is to evaluate the cyclic probability distributions and the corresponding cyclic entropy. Such a distribution has a universal class in the form of a Gaussian distribution p i aexp (x b) 2 / c 2. It fits all types of social network. Each social network type has a reasonably difference range of values of the distribution constants a, b and c. Furthermore, the value of the network cyclic entropy is another property that can be used to identify the type of social network. In this study, we this method of social network characterization on the personnel and families networks. Based on the values of distribution constants and the cyclic entropy, the personnel network is a form of a Small-World network and the families network is almost certain is a Scale-Free network. The results are summarized in Table 1. In other words, Dubai Financial Market on 2009 was families controlled and biased stock market as the types of social network indicate. A fair and unbiased market is expected to have a random social network structure. As suggested by [17],
the lack of corporate governance in most Arab stock markets lead to a biased market prone to failure and collapse or on the other side well-protected but inflexible. Table 1. Network parameters calculation and comparison between the two networks. Social Network a b c Cyclic Entropy Network Type Personnel 0.195 17.297 2.847 2.186 Small-World Families 0.119 109.928 7.071 2.645 Scale-Free Fig3. Personnel Network cycles distribution vs. cycle length
Fig4. Families Network cycles probabilities distribution vs. cycle length 6.2 Degree-based Parameters Calculation Confirming the findings in section 6.1, further analyses to calculate known social network parameters in the literature for each network were done beside such parameters will provide another point of view of the social network behaviors. Some of the parameters are calculated for each node (company) in the network as a local value and then a network value is calculated based on the average. Some other parameters are calculated for the entire network directly. Some other parameters are related to edges in the network. All the parameters are calculated using Gephi 0.7 Beta software and the setup of the two constructed networks is undirected with no edge weight included. Table 2 compares the degree-based parameters of personnel and families networks.
Table 2. Network parameters calculation and comparison between the two networks. Parameter Personnel Families Network Network Highest value 8 28 Degree Lowest value 0 0 Avg. Degree 2.125 7.2 Diameter 11 6 Graph Avg. Path Length 4.5402 2.6012 Distance No. of shortest paths 2088 4694 Highest value 436.92 392.1 Betweenness Lowest value 0 0 Average value 46.2 46.975 Highest value 7.2 4.75 Centrality Closeness Lowest value 0 0 Average value 2.83 2.269 Highest value 11 6 Eccentricity Lowest value 0 0 Average value 4.91 4.2875 Density 0.0269 0.0911 Clustering Avg. Clustering Coefficient 0.2574 0.4017 Coefficient Total Triangles 44 515 Highest value 1 1 Eigenvector Lowest value 0 0 Centralities Average value 0.161 0.231 7 Conclusion In this work, we studied the relationship between the different listed companies in Dubai Financial Market (DFM) and constructed two networks out of it, the first one we called the Personnel Network while the other one we called the Families Network. In both networks, we assumed the companies are social actors while board members would form social links between nodes. We calculated exact number of cycles in the first network and approximated the probability of cycles in the second one. Then we computed the entropy of cycles for both networks. The entropy of the Families Network was larger than the entropy of the Personnel Network which means that the Families Network is more rigid. On the other hand, we calculated some non-cyclic parameters to understand the behavior and nature of the networks. From the figures showing the networks constructed, it is very obvious that the companies in DFM are very connected and linked to each other having common members in their boards or many members from the same family. Note that the links associated in the constructed networks have no weight. Some companies had more than one common member in their boards or more than two members from the same family. Another expansion for
this work would be to give weight to the edges and reconstruct the networks to recalculate the entropy with more precise results. The analysis conducted in this work proved the huge market collapse occurred during the last financial crises in 2008 for Dubai Financial Market, the stock market of Dubai city has a reason that is the lack of corporate governance due to the Small-World structure of the personnel network and the Scale-Free structure of the families network in the market. 8 Future Work This work can be extended in the future by collecting the data regarding the listed companies and the board members of all those companies in Dubai Financial Market for the past 5 years and then construct the same two networks of listed companies as social actors and board members as social links. In this case, we would be able to determine the effect of the social network and relation between boards of listed companies on the market in Dubai and then would know how such relation between the boards has resulted in the bad stock market collapse in DFM by comparing the constructed networks and the change occurring in the stock market over time through the past 5 years. References 1. Mahdi K., Jammal L., Safar M.: Characterizing Collaborative Social Networks Using Cyclic Entropy, Case Study: Wikipedia. In: IADIS International Conference on Web Based Communities, pp. 125 130. Inderscience Publishers. Algarve, Portugal (2009) 2. Safar M., Farahat H., Mahdi K., Analysis of Dynamic Social Network: E-mail Messages Exchange Network. In: 11th International Conference on Information Integration and Webbased Applications & Services (iiwas), pp. 41 48. ACM, Kuala Lumpur Malaysia (2009) 3. Mahdi K., Safar M., Farahat H.: Analysis of Temporal Evolution of Social Networks. J. Mobile Multimedia, Vol. 5, No. 4, 333 350 (2009) 4. Mahdi K., Safar M., Sorkhoh I.: Entropy of Robust Social Networks. In: IADIS International e-society Conference. iadis, Algarve, Portugal (2008) 5. Safar M., Farahat H., Kassem A., Approximate Cycles Count in Undirected Graphs. J. DIM. 6. Mahdi K., Safar M., Sorkhoh I., Kassem A., Cycle-Based versus Degree-based Classification of Social Networks. J. DIM, Vol. 7, No. 6, 383 389 (2009) 7. Safar M., Mahdi K., Kassem A.: Universal Cycles Distribution Function of Social Networks. In: first international conference on Networked Digital Technologies, pp. 354 359. IEEE Xplore, Ostrava, The Czech Republic (2009) 8. Stock Market, http://en.wikipedia.org/wiki/stock_market 9. INSNA What is Social Network Analysis, http://www.insna.org/sna/what.html 10. Dubai Financial Market, http://en.wikipedia.org/wiki/dubai_financial_market 11. About DFM, Overview, http://www.dfm.ae/pages/default.aspx?c=801 12. NASDAQ Dubai, http://en.wikipedia.org/wiki/nasdaq_dubai 13. Dubai Financial Market (DFM), http://www.sharewadi.com/dubai-financial-market.php 14. Centrality, http://en.wikipedia.org/wiki/centrality 15. Clustering Coefficient, http://en.wikipedia.org/wiki/clustering_coefficient 16. Online Stock Trading Info, http://www.onlinestocktradinginfo.com/
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