Group dynamics of the Japanese market

Preprint submitted to Elsevier correlated with each other, has received attention as a typical complex system [1,2]. A popular method is the minimum spanning tree (MST) which constructs the asset tree using correlations between stock prices [3,4,5,6,7,8,9,10]. It gives us the characteristic feature of the market in the simple way. In a MST of N nodes, each node represents a company and N -1 links with the most important correlations are selected. The MST is a loop-less network, and every node at least has a link. Also, the grouping of companies in the MST can be identified and extended to portfolio optimization and the companies of the US market are clearly grouped with the industry category or business sector [11].

Several papers show that the characteristics of the mature market cannot be simply extended to the emerging market [12,13] and change dynamically due to the globalization [14]. Especially, the Korean market is synchronized to external markets due to the globalization, and the tendency of grouping by industry categories disappeared [15]. In addition, the Korean market forms clusters according to the MSCI index after 2000 and the tendency of synchronization to the US market is stronger and stronger [16].

The Japanese market attracts many econophysicists since its unique character [17,18]. It is not an emerging one but it has a strong connection with the Asian emerging markets. For instance, the Korean market has many common features with the Japanese market. Korea and Japan have developed close interdependence of their economic systems for a long time. Two countries experienced very high rate of economic growth. Their economies were commonly driven by the government-directed investment model and the protective trade policy at first. In addition, the integration into the global economy has much developed in the recent days, especially in the Asia. Such violent changes make the studies of the Asian financial markets very interesting.

We investigated characteristics of the Japanese stock market with the history of the market. First, we compared the analysis of the Japanese market with that of the Korean market and found common features of these two markets such as decreasing of grouping by industry categories. Second, we used S&P500 index as the international market to reduce external influences due to the globalization. This study showed that the international market obviously influences the Japanese market.

There are several stock exchange markets in Japan, and we selected the Tokyo Stock Exchange (TSE), the largest Japanese market. We used the daily closing stock price from 1980 to 2004, and a total of 624 companies remained for the full 25 year-period were selected for our analysis. To demonstrate the trend of the Japanese market, we plot the index which averages over the 624 companies in Fig. 1.

The logarithmic return is defined as S i (t) ≡ ln J i (t + ∆t) -ln J i (t), where J i (t) is the closing price of a given Japanese company i. And, the cross-correlation coefficient between stock i and j is defined as:

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To explore the evolution of the market, we construct the MSTs with time windows of width T corresponding to daily data for 3 years, sliding the window with 20 trading day, approximately 1 month. Each node of the MST corresponds to a company, and each link has a weight ρ ij (= ρ ji ), which is simply the value of the cross-correlation coefficient.

To investigate the group dynamics of the financial market more detail, we define a quantity, grouping coefficient, to measure how well groups with the industry categories, where n( i ) represents the number of whole links in the network, and n( i∈C ) is the number of links between companies in the same industry category.

In our previous study [15], we found the grouping coefficient of the recent Korean market decreases with elapsing time. In other words, the recent Korean market does not make the groups by industry categories even though the recent US market’s MST is grouped well by industry categories [11]. As expected, we observe the similar trend in the Japanese market (Fig. 2). Before the mid-1980s, the coefficient G of the Japanese market shows no special movement. However, the coefficient tends to decrease after the mid-1980s, and this tendency is strengthened more and more by burst of the bubble in 1990’s. It is natural to form groups of industry categories, because companies included in the same category are highly related to each other in comparison to companies in other categories. However, the groups of industry categories are breaking down in recent, and it is related to the globalization of Asian markets. We will explain more in the following section. (d) S&P500 (c) Japan Fig. 3. The indexes and log returns of the Japanese

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