Dynamic structure of stock communities: a comparative study between stock returns and turnover rates

The detection of community structure in stock market is of theoretical and practical significance for the study of financial dynamics and portfolio risk estimation. We here study the community structures in Chinese stock markets from the aspects of both price returns and turnover rates, by using a combination of the PMFG and infomap methods based on a distance matrix. An empirical study using the overall data set shows that for both returns and turnover rates the largest communities are composed of specific industrial or conceptional sectors and the correlation inside a sector is generally larger than the correlation between different sectors. However, the community structure for turnover rates is more complex than that for returns, which indicates that the interactions between stocks revealed by turnover rates may contain more information. This conclusion is further confirmed by the analysis of the changes in the dynamics of community structures over five sub-periods. Sectors like banks, real estate, health care and New Shanghai take turns to comprise a few of the largest communities in different sub-periods, and more interestingly several specific sectors appear in the communities with different rank orders for returns and turnover rates even in the same sub-period. To better understand their differences, a comparison between the evolution of the returns and turnover rates of the stocks from these sectors is conducted. We find that stock prices only had large changes around important events while turnover rates surged after each of these events relevant to specific sectors, which shows strong evidence that the turnover rates are more susceptible to exogenous shocks than returns and its measurement for community detection may contain more useful information about market structure.     

Network formation in a multi-asset artificial stock market

A multi-asset artificial stock market is developed. In the market, stocks are assigned to a number of sectors and traded by heterogeneous investors. The mechanism of continuous double auction is employed to clear order book and form daily closed prices. Simulation results of prices at the sector level show an intra-sector similarity and inter-sector distinctiveness, and returns of individual stocks have stylized facts that are ubiquitous in the real-world stock market. We find that the market risk factor has critical impact on both network topology transition and connection formation, and that sector risk factors account for the formation of intra-sector links and sector-based local interaction. In addition, the number of community in threshold-based networks is correlated negatively and positively with the value of correlation coefficients and the ratio of intra-sector links, which are respectively determined by intensity of sector risk factors and the number of sectors.     

Deterministic factors of stock networks based on cross-correlation in financial market

The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.     

Average cross-responses in correlated financial markets

There are non-vanishing price responses across different stocks in correlated financial markets, reflecting non-Markovian features. We further study this issue by performing different averages, which identify active and passive cross-responses. The two average cross-responses show different characteristic dependences on the time lag. The passive cross-response exhibits a shorter response period with sizeable volatilities, while the corresponding period for the active cross-response is longer. The average cross-responses for a given stock are evaluated either with respect to the whole market or to different sectors. Using the response strength, the influences of individual stocks are identified and discussed. Moreover, the various cross-responses as well as the average cross-responses are compared with the self-responses. In contrast to the short-memory trade sign cross-correlations for each pair of stocks, the sign cross-correlations averaged over different pairs of stocks show long memory.     

Correlation based networks of equity returns sampled at different time horizons

We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001–2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.     

Hierarchical structure of countries based on carbon dioxide emission over the periods of 1971–2012; the relationships economic growth and energy consumption

This study uses hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)) to examine the hierarchical structures of the carbon dioxide emission from the 84 countries by three main sectors, namely electricity/heat, manufacturing/construction and transportation sectors. We obtain the topological properties among the countries based on carbon dioxide emission over the periods of 1971–2012. We also perform the bootstrap techniques to investigate a value of the statistical reliability to the links of the MSTs. The results of the topologies structural of these trees are as follows: (i) We identified different groups of countries according to their economic growth and geographical location. (ii) Our results show that the high income and low energy consuming country groups are more important within the network.     

Investigation of major international and Turkish companies via hierarchical methods and bootstrap approach

We present a study, within the scope of econophysics, of the hierarchical structure of 98 among the largest international companies including 18 among the largest Turkish companies, namely Banks, Automobile, Software-hardware, Telecommunication Services, Energy and the Oil-Gas sectors, viewed as a network of interacting companies. We analyze the daily time series data of the Boerse-Frankfurt and Istanbul Stock Exchange. We examine the topological properties among the companies over the period 2006–2010 by using the concept of hierarchical structure methods (the minimal spanning tree (MST) and the hierarchical tree (HT)). The period is divided into three subperiods, namely 2006–2007, 2008 which was the year of global economic crisis, and 2009–2010, in order to test various time-windows and observe temporal evolution. We carry out bootstrap analyses to associate the value of statistical reliability to the links of the MSTs and HTs. We also use average linkage clustering analysis (ALCA) in order to better observe the cluster structure. From these studies, we find that the interactions among the Banks/Energy sectors and the other sectors were reduced after the global economic crisis; hence the effects of the Banks and Energy sectors on the correlations of all companies were decreased. Telecommunication Services were also greatly affected by the crisis. We also observed that the Automobile and Banks sectors, including Turkish companies as well as some companies from the USA, Japan and Germany were strongly correlated with each other in all periods.     

The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning.     

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms

In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing.Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.     

Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System

A nested structure is a structural feature that is conducive to system stability formed by the coevolution of biological species in mutualistic ecosystems The coopetition relationship and value flow between industrial sectors in the global value chain are similar to the mutualistic ecosystem in nature. That is, the global economic system is always changing to form one dynamic equilibrium after another. In this paper, a nestedness-based analytical framework is used to define the generalist and specialist sectors for the purpose of analyzing the changes in the global supply pattern. We study why the global economic system can reach a stable equilibrium, what the role of different sectors play in the steady status, and how to enhance the stability of the global economic system. In detail, the domestic trade network, export trade network and import trade network of each country are extracted. Then, an econometric model is designed to analyze how the microstructure of the production system affects a country’s macroeconomic performance.     

Spectrum,intensity and coherence in weighted networks of a financial market

We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the correlation between the nodes. The eigenvalue spectrum of the correlation matrix reflects the structure of the market, which also shows in the cluster structure of the emergent network. The stronger and more compact a cluster is, the earlier the eigenvalue representing the corresponding business sector occurs in the spectrum. On the other hand, if groups of stocks belonging to a given business sector are considered as a fully connected subgraph of the final network, their intensity and coherence can be monitored as a function of time. This approach indicates to what extent the business sector classifications are visible in market prices, which in turn enables us to gauge the extent of group-behaviour exhibited by stocks belonging to a given business sector.     

Detecting and Analyzing Politically-Themed Stocks Using Text Mining Techniques and Transfer Entropy—Focus on the Republic of Korea’s Case

Politically-themed stocks mainly refer to stocks that benefit from the policies of politicians. This study gave the empirical analysis of the politically-themed stocks in the Republic of Korea and constructed politically-themed stock networks based on the Republic of Korea’s politically-themed stocks, derived mainly from politicians. To select politically-themed stocks, we calculated the daily politician sentiment index (PSI), which means politicians’ daily reputation using politicians’ search volume data and sentiment analysis results from politician-related text data. Additionally, we selected politically-themed stock candidates from politician-related search volume data. To measure causal relationships, we adopted entropy-based measures. We determined politically-themed stocks based on causal relationships from the rates of change of the PSI to their abnormal returns. To illustrate causal relationships between politically-themed stocks, we constructed politically-themed stock networks based on causal relationships using entropy-based approaches. Moreover, we experimented using politically-themed stocks in real-world situations from the schematized networks, focusing on politically-themed stock networks’ dynamic changes. We verified that the investment strategy using the PSI and politically-themed stocks that we selected could benchmark the main stock market indices such as the KOSPI and KOSDAQ around political events.     

Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets.     

Tiling the plane without supersymmetry

We present a way of tiling the plane with a regular hexagonal network of defects. The network is stable and follows in consequence of the three-junctions that appear in a model of two real scalar fields that presents Z3 symmetry. The Z3 symmetry is effective in both the vacuum and defect sectors, and no supersymmetry is required to build the network.     

The structural role of weak and strong links in a financial market network

We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than the strong links (high correlation). We find that nodes connected through strong links form well defined communities. These communities are clustered together in more complex ways compared to the widely used classification according to the economic activity. We find that some companies, such as General Electric (GE), Coca Cola (KO), and others, can be involved in different communities. The communities are found to be quite stable over time. Similar results were obtained by investigating markets completely different in size and properties, such as the Athens Stock Exchange (ASE). The present method may be also useful for other networks generated through correlations.     

The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.     

Characteristics of the Korean stock market correlations

We establish in this study a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Based on this analysis, it is found that the Korean stock market does not form the clusters of the business sectors or of the industry categories. When the MSCI (Morgan Stanley Capital International Inc.) index is exploited, we find that the clusters of the Korean stock market is formed. This finding implicates that the Korean market, in this context, is characteristically different from the mature markets.     

Regularities and irregularities in order flow data

We identify and analyze statistical regularities and irregularities in the recent order flow of different NASDAQ stocks, focusing on the positions where orders are placed in the order book. This includes limit orders being placed outside of the spread, inside the spread and (effective) market orders. Based on the pairwise comparison of the order flow of different stocks, we perform a clustering of stocks into groups with similar behavior. This is useful to assess systemic aspects of stock price dynamics. We find that limit order placement inside the spread is strongly determined by the dynamics of the spread size. Most orders, however, arrive outside of the spread. While for some stocks order placement on or next to the quotes is dominating, deeper price levels are more important for other stocks. As market orders are usually adjusted to the quote volume, the impact of market orders depends on the order book structure, which we find to be quite diverse among the analyzed stocks as a result of the way limit order placement takes place.     

The structure and resilience of financial market networks

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.     

Correlation and volatility in an Indian stock market: A random matrix approach

We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index.