We investigated the grouping coefficients of industrial sectors in the stock network based on stock data for the U.S. and Korean stock markets. These complex networks were modeled using the minimal spanning tree (MST) method. We propose a novel approach based on the shortest path length (SPL) between stocks to quantify the grouping characteristics of the industrial sectors. We find that the grouping coefficients for the industrial sector in the U.S. are larger than those of the Korean stock market. In particular, for the Korean stock market the conglomerates, comprised of a diverse of industrial companies, have a significant grouping coefficient.
Recently, the complex systems of financial markets have been increasingly studied by both physicists and economists [1] and [2]. The stock market has evolved due to non-trivial interactions between heterogeneous agents such as noise and fundamental traders [3] and due to events generated by the internal and external market forces. Therefore, stock price properties cannot be explained by the traditional pricing model based on the efficient market hypothesis (EMH) [4] and [5] and so-called “stylized facts” [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] and [20]; prices of individual stocks in financial markets are determined by interactions between traders who use various investment strategies and by unpredictable external shocks. Moreover, the stock market shows a complex connection structure among the formation of various stock groups according to the characteristics of specific industries [21], [22] and [23].
Previous studies have found that interactions among stocks in financial markets deviate from the random interactions given by random matrix theory [24], [25] and [26] and are closely related to common factors existing in the financial market [23]. In addition, Mantegna et al. [21] found that an individual stock is clustered based on the characteristics of the industrial sectors to which it belongs. Until now, most studies have focused on qualitative analyses of this clustering behavior based on industry sector, so we cannot directly compare previous results to the clustering phenomena of a minimal spanning tree (MST) structure created by diverse financial markets (foreign exchange and stock markets).
We propose a novel method for quantifying the grouping behavior of a MST structure and measure the grouping coefficient of each industrial sector for the United States and Korean stock markets. We used the daily closing price of individual stocks traded on the U.S. and Korean stock markets from 1993.01.03 to 2006.12.31. We find that the grouping coefficient of the U.S. stock markets (S&P500) are larger than those of the Korean stock market (KOSPI). In addition, for the Korean stock market we observe higher grouping coefficients in the insurance, health care, and construction sectors, while no grouping characteristics are observed in the remaining sectors. In particular, Korean conglomerates such as Samsung, LG, Hyundai, SK, Hanwha, Kumho, and Dongbu exhibited large grouping coefficients.
In the next section, we describe the data sets and methodology used in this paper. In the 3 sector, we present our results of this study. Finally, conclusions are given in Section 4.
In this paper, we investigated the grouping properties of individual industrial sectors in a MST structure estimated from a correlation matrix describing individual stocks listed on the Korean and U. S. stock markets KOSPI and S&P500. We utilized a surrogate method to determine which factors influence the degree of grouping of industrial sectors. We found that the degree distribution of the MST structure for both stock markets followed a power-law relation with an exponent of γ∼2.31γ∼2.31. In addition, we showed that the grouping coefficients of the U.S. stock market (S&P500) are larger than those of the KOSPI stock market. However, the construction & materials, financial services, and the health care sectors in the Korean stock market showed a large grouping coefficient. To determine the cause of the grouping characteristics in the stock network, we used an artificial time series in which the nonlinear properties were removed using a surrogate method. We found that the grouping coefficient of the surrogate time series is approximately zero. In other words, the degrees of grouping in the MST structure for both stock markets were closely related to the nonlinear properties of the original time series. Finally, conglomerates such as Samsung, LG, Hyundai, SK, Hanwha, Kumho, and Dongbu have high grouping coefficients. In other words, the grouping coefficient of an industrial sector may increase as the grouping coefficient of the conglomerate increases. The above findings imply that conglomerates play an important role determining the grouping mechanism of an industrial sector. Further research should study the relationship between the grouping property of industry sector and the market efficiency using international stock markets.
This work has been supported in part by Korea Research Foundation Grant funded by the Korean Government (Grant No. 2013-0355), in part by a research fund from Chosun University 2012.
