4.1. Topological Properties of the Asian Indices Network
Topological properties are characteristic of networks abstracting real-world system-level interdependencies. The interdependency structures present in the equity market networks may be classified under the category of complex networks and possess some unique topological properties identifiable by a set of quantifiable network metrics. To this end, we have calculated network-based topological metrics that give a quantifiable interpretation of the position of a node (an index) within the weighted network (the Asian equity markets linkage structure) in a relative scale. The topological measures computed in this study are centrality measures (degree, closeness and Eigen vector) and influence strength measures (overall and India-specific). Because these centrality measures are indicative of the position of the Asian indices (in order of criticality in the network), their computations and further elucidation in light of cross-market linkages are important in terms of information transmission in the network. In conceptual terms, each of these centrality measures is demonstrative of the alternative processes by which the selected markets may influence the information flow through the Asian indices network. Recognizing the most essential nodes in an interlinked system helps financial managers understand the information flow dynamics of such networked systems. The symbolic representations used in this study for referring to the Asian market indices are provided in Table 3
The average values of closeness centrality, betweenness centrality, Eigen vector centrality and the overall influence strength of each of the Asian indices are presented in Table 4
The network analysis methodology facilitates the identification of some distinctive characteristics for each of the market indices representing the nodes in the equity network. In this study, the distinctive characteristics of the nodes are elucidated using the centrality measures (degree centrality, Eigen vector centrality and closeness centrality) and the influence strength measures (overall and India-specific). These attributes symbolize the significance of market indices in terms of different metrics. On the basis of the assumption that the market indices networks have consistent structural make-ups over a temporal scale, the same consistency will be reflected in the network attributes. However, systemic shocks, internally or externally aroused, will definitely have a bearing on the network structures of these market indices, which will soon get reflected in the network attributes. Thus, tracking these network attributes on a temporal scale will basically serve three main purposes. First, it will provide us with a reflection of the changes in the interdependency structure among the Asian indices and will possibly serve as lagging indicators of structural changes in the equity networks. The structural changes may be an outcome of macroeconomic shocks affecting a part of the system or its whole, and such alterations are indirect pointers to the impact of such shocks on the system. Second, it will demonstrate the role played by each of the market indices in the information propagation process in the event of a possible shock transmission through the network. The information propagation process determined from historical empirical data may also be true in futuristic time periods also; thereby, this knowledge is of key significance for the policymakers and regulators in determining future interventional measures. Third, it will facilitate the identification of peripheral and central market indices in the equity network. This will lead to the determination of the risk premium associated with investing in each of these markets.
In the context of investment decisions, the identification of peripheral and central market indices via network attributes has a major role to play in the portfolio selection process. Empirical studies in the past have provided evidence that future returns of portfolios are considerably impacted by the present and the future level of interdependence amongst the securities constituting this portfolio. Essentially, the level of the intrinsic correlation risk is represented by the closeness for stocks [73
]. To be specific, the securities possessing the highest linkages in the equity network acquire the maximum value of expected return amongst the central nodes in the network. On the other hand, the securities that are most affected by the hub node in the network possess the highest value of risk premium amongst all the peripheral securities in the networks. Therefore, it is a reasonable expectation by the investors that securities located centrally should deliver relatively higher returns on investments, as they perceive this as a premium for the enhanced level of contagion risk associated with such securities. Hence, the security comovements as reflected in equity networks play a significant part in the determination of the mechanisms of asset pricing [73
]. Taking all this into consideration, international portfolios constituted by selected peripheral markets would possess relatively lesser risk and higher returns than portfolios constituted by selected centrally-located markets (in which the network centrality measures quantify the centrality or peripherality of the market).
Next, we elaborate upon the findings obtained from the analysis of each of the network centrality measures. The first centrality measure considered in this study is degree centrality. This centrality measure indicates the number of links a given market index possesses. The market indices possessing higher values on this measure will have a quick transmission of information directed to the networked system. The market indices possessing a high degree centrality are more likely to possess higher levels of linkages to other market indices; hence, they would be less dependent on other market indices for the information flow. These centrally-located market indices, since they possess a greater number of linkages, would have more opportunities to exchange information targeted at them and would, therefore, be a more central character in the information flow system. In Table 2
, we can notice that Hong Kong (AS_SEHK) and Singapore (AS_SGX) have the highest average degree centrality for all 151 observations. This is followed by the market index of South Korea. In the temporally-varying plot of degree centrality (Figure 3
), we can notice that during January 2002–May 2004, the Korean stock market index (AS_KRX) has the highest degree centrality. From May 2004 to October 2006, the market indices of Singapore (AS_SGX) and Hong Kong (AS_SEHK) are competing for the highest values of degree centrality. After that period; the Hong Kong market index (AS_SEHK) has the highest level of degree centrality throughout the remaining time frames.
The second centrality measure considered in this study is closeness centrality. Closeness centrality in the context of equity networks is the measure of how swiftly the spread of information may happen from a given Asian index to other indices in the network. In the temporally-varying plot of closeness centrality (Figure 4
), we can notice that Hong Kong (AS_SEHK), Singapore (AS_SGX) and South Korea (AS_KRX) have the highest average closeness centrality values. As a result of being situated close to others in the Asian indices network, indices high in closeness measures (i.e., the market indices of Hong Kong, Singapore and South Korea) can perform an information-transmission process better and in an efficient manner. They also have much higher degrees of autonomy as they do not have to look for information from other indices located peripherally. Basically, closeness centrality is a measure of how close a given index is to all other market indices in the network. The higher the scores of a particular market index, the faster the index spreads the information to all others in the network.
In Figure 4
, we can observe that the Singapore stock market index (AS_SGX) has the highest values of closeness centrality in the initial periods of 2002 and 2003. After that period, till the end of 2005, the highest position is well contested by four indices together, i.e., Korea (AS_KRX), Taiwan (AS_TWSE), Singapore (AS_SGX) and Hong Kong (AS_SEHK). Succeeding this time-frame, the Singapore stock market index has dominated the rankings till 2016, except during a few periods when the Hong Kong stock market index has had relatively higher values.
The third centrality measure considered in this study is Eigen vector centrality. Eigen vector centrality in the context of equity networks gives high scores to market indices according to the centrality of the neighbours of that market index. The temporal plot of Eigen vector centrality is provided as Supplementary Figure S1
. The temporal plot indicates that most of the market indices have their values lying in the range of 0.8–1 in all 151 temporally-varying observations, which reflects that the majority of them are connected to highly central nodes in the equity network.
The temporally-varying plot (Figure 5
) of the average centrality captures the properties of all three different centrality measures in an equally weighted proportion. In this plot, we can notice that the market indices of Hong Kong (AS_SEHK) have the highest value of average centrality during the initial periods of January 2002–October 2002, after which the market index South Korea (AS_KRX) has gained the top position for the period between October 2002 and May 2004. The period May 2004–July 2007 is dominated by the Singapore market index (AS_SGX). From July 2007 till the end of the study period, the market index of Hong Kong (AS_SEHK) possessed the highest values in the average centrality measure.
The mean value of the average centrality measures for the top four and bottom four market indices are presented in Table 5
. In this study, the top four market indices with the highest average centrality measures are referred to as ‘central nodes’, and the bottom four market indices with the lowest average centrality measures are referred to as ‘peripheral nodes’.
Next, we elaborate on the findings obtained from the analysis of each of the influence strength measures. In the temporally-varying plot of the overall influence strength (Figure 6
), it can be observed that from the initial phases of 2002 till the early months of 2005, the Korean stock market index (AS_KRX) has had the highest influence on the remaining Asian indices in the network. After this period until the final phase of 2006, we can observe that the Singapore market index (AS_SGX) has the highest influence. From the initial phases of 2007 till the end of 2016, the Hong Kong stock market index (AS_SEHK) has had a strong influence on the other members of the Asian indices network.
From the temporally-varying plot of the overall influence strength (Figure 6
), it is clear that the market indices of Hong Kong (AS_SEHK), Singapore (AS_SGX) and South Korea (AS_KRX) have had the highest influence on the Asian indices network. This indicates that any sort of shocks (external or internal) arising in the domestic, regional or global economy having an impact on these markets will subsequently spread the effects to other capital markets in Asia in a substantial way.
The market indices of Pakistan (AS_KSE), Jordan (AS_JSE) and Sri Lanka (AS_CSE) have the lowest levels of average influence over the entire Asian indices network. This indicates that any sort of shocks (external or internal) arising in the domestic, regional or global economy having an impact on these markets will not get efficiently transmitted to other markets in Asia. Even if the transmission happens from these markets, the overall impact of this transmission on other markets would be minimal.
Based on the number of times the Asian index is ranked in the top four positions in overall influence strength scores in the ranking list across 151 observations, we observe that the four top Asian indices are Hong Kong, Singapore, Korea and Taiwan.
Next, the India-specific influence strength of the Asian market indices is discussed. The average influence of each of the Asian indices on the Indian equity market (AS_BSE) is depicted in Figure 7
. To compare the relative influence of Asian indices on the Indian market index (AS_BSE), we have summed up the weights in absolute terms for computing node strength. From this averaged plot (Figure 7
), it is clear that the market indices of Singapore (AS_SGX) and Hong Kong (AS_SEHK) have had the highest influence on the Indian market index. This is followed by the market indices of Indonesia (AS_IDX), South Korea (AS_KRX) and Taiwan (AS_TWSE). The least influential Asian stock market indices in terms of India-specific influence are those of Pakistan (AS_KSE), Sri Lanka (AS_CSE) and Jordan (AS_JSE).
In the temporally-varying plot of the India-specific influence strength of the Asian market indices (Figure 8
), we can notice that during the initial months of 2002, the South Korean and Singaporean market indices have had the highest influence on the Indian market index (AS_BSE). From October 2002–August 2003, the Singaporean market index had had the highest influence on the Indian market index (AS_BSE). Later, for the period from August 2003–July 2007, both the market indices of Singapore and Hong Kong have had a relatively equivalent amount of influence on the Indian market index (AS_BSE). From July 2007 till the end of the study period, the Singaporean market index had had the highest influence throughout, which is closely followed by the Hong Kong market index. We can notice that Singapore and Hong Kong have a positive weight of the edge, which reflects their directionality.
On the other hand, on observing the market indices bearing lower India-specific influence strengths, we observe that at initial periods, the Shanghai market index (AS_SSE) has negative weights of edges. This reflects that the direction of influence is opposite. In addition to this, we can note that for short periods of time. The market indices of Sri Lanka (AS_CSE) and Jordan (AS_JSE) have had negative weights of the edges. This reflects that the direction of influence is opposite.
4.2. Reduced Network Visualization
In cases where the weighted correlations over a moving time window are used for computing threshold filtered networks, the topological structures of these filtered networks can be altered in a dynamic fashion with the transformations in the window position, mirroring the progressions happening in the market structure amid such a timeframe. Here, we employed filtered graphs to quantitatively evaluate the relevance and centrality of these Asian indices in the context of an integrated regional Asian block.
From the visualization of these threshold filtered networks belonging to the 151 temporally-synchronous observations, the following key findings emerge: (i) The country-specific stock market indices of Singapore, South Korea, Hong Kong and Taiwan are interconnected throughout the 151 observations. (ii) From Observation Number 57 (beginning in June 2006), the Chinese stock market index (AS_SSE) started becoming linked to the Hong Kong stock market index (AS_SEHK), and after that period, the Chinese stock market index (AS_SSE) has been rarely connected to any index other than the Hong Kong stock market index (AS_SEHK). This connectivity pattern is exhibited in Figure 9
. (iii) Over the past 14 years, there has been a progressive increase in the number of connections between the major Asian indices. In the initial time periods (Figure 10
), the developed markets of Singapore, South Korea, Hong Kong and Taiwan were the only ones that had connectivity with one another, and they formed an interconnected mesh structure. After a particular period of time, the remaining Asian indices became connected one after the other to this large block of developed markets (Singapore, South Korea, Hong Kong and Taiwan). (iv) A segmented set of Asian indices having no linkages with any peers (and the large block) is also evident in this study. These indices belong to the stock exchanges of Jordan (Amman Stock Exchange), Pakistan (Karachi Stock Exchange) and Sri Lanka (Colombo Stock Exchange). These kind of disjointed indices are evident in recent time frames of the study period also (Figure 11
). They form the biggest group of distanced indices (vertices) throughout all the observations. These disconnected indices depict the state of segmentation existent in the Asian markets. These disconnected groups of indices are a clear opportunity for regional portfolio diversification, supported by a proper market liquidity ratio and growing market capitalization of these markets.
From among the disconnected indices, the stock market of Jordan deserves special attention. In past studies on the Amman Stock Exchange, it has been demonstrated that there is a steady rise of average market capitalization as a percentage of GDP (average market capitalization figures have also increased from 0.49 in 2000 to 3.6 in the year 2005) measures [74
]. This makes the Jordan stock market an attractive investment destination and a suitable destination for Asian portfolio diversification. The paper by Saadi-Sedik and Petri [75
] also stresses the same point of disconnection of Asian markets with Jordan as is evident in our study. It employs the cointegration approach to demonstrate that there is no cointegration relationship between the Amman Stock Exchange and other emerging and developed stock markets in Asia.
We computed the FDR for the detected edge connections obtained from the threshold filtering approach. The FDR values are computed for all 151 filtered weighted networks, and then, they are further averaged. The averaged value of the FDR was obtained to be 0.00357. The low value of FDR for the detected edge-list signifies that the connectivity structures obtained from the threshold filtering approach are statistically significant and reliable.
4.3. Pre-Crisis, Crisis and Post-Crisis Period Analysis
1. Pre-crisis period analysis
In the threshold filtered network belonging to the pre-crisis period (Figure 12
), we can observe that the stock market indices of Israel (AS_TASE), Pakistan (AS_KSE), Jordan (AS_JSE), Sri Lanka (AS_CSE) and Malaysia (AS_MYX) are not connected to the major interconnected block of the markets of Singapore (AS_SGX), India (AS_BSE), Taiwan (AS_TWSE), China (AS_SSE), Hong Kong (AS_SEHK), The Philippines (AS_PSE), Indonesia (AS_IDX) and South Korea (AS_KRX). These indices do not have any existing linkage with any other member of the Asian indices network. In this period, the Indian market index (AS_BSE) is connected to those of South Korea (AS_KRX), Hong Kong (AS_SEHK), Singapore (AS_SGX), Taiwan (AS_TWSE) and Indonesia (AS_IDX). The disjointed indices that had no connectivity with major hub nodes in the network are ideal candidates for portfolio diversification as shocks directed at the hub nodes will not get transmitted to those segregated indices easily. The close connectivity structure of Hong Kong, Korea, Singapore and Taiwan with the Indian market index reflects that there exists a strong nature of the influence of these markets on the stock movements in the Indian capital market. Besides, any shocks originating or directed at these markets would be swiftly transmitted to the Indian markets, and this would affect the pricing of securities traded in the Indian capital market.
2. Crisis period analysis
In the threshold filtered network belonging to the crisis-period (Figure 12
), we can observe that the stock market indices of Israel (AS_TASE), Pakistan (AS_KSE), Jordan (AS_JSE), Sri Lanka (AS_CSE) and Malaysia (AS_MYX) do not possess any linkage to the major block of Asian indices. Even though there has been a substantial increase in correlation among all the market indices of Asia during the crisis period, segmentation still exists. In this period, the Indian market index (AS_BSE) is connected to South Korea (AS_KRX), Hong Kong (AS_SEHK), Singapore (AS_SGX), Taiwan (AS_TWSE) and Indonesia (AS_IDX). In several past empirical studies [76
], it is well documented that there has been a noticeable incline in correlation structures during the times of market stress. The same is noted in the case of the Asian market network. This issue of rising correlations is of particular significance in cases of portfolio constructions wherein the constituting securities belong to international asset classes, and such constructed portfolios should ideally possess the capability to withstand shocks during the times of market stress. A peculiar pattern is observed here that even though there is a rise in correlations amongst the market indices of Asia, disjointed indices, which were present in the pre-crisis period, still exist. Thus, investing in these peripheral markets during the pre-crisis period would have reduced the systemic risk spread to the investable portfolios in the crisis period.
3. Post-crisis period analysis
In the threshold filtered network belonging to the post-crisis period (Figure 12
), we can observe that indices of Israel (AS_TASE), Pakistan (AS_KSE), Jordan (AS_JSE), Sri Lanka (AS_CSE) and Malaysia (AS_MYX) do not possess any linkage to the major block of Asian indices. In this period, the Indian market index (AS_BSE) is connected to the market indices of Hong Kong (AS_SEHK), Singapore (AS_SGX), Taiwan (AS_TWSE) and Indonesia (AS_IDX). In the post-crisis period, there is some amount of resemblance to the connectivity structure of pre-crisis periods. However, an observable transformation in the connectivity structure amongst indices in the form of realignment is evident. This realignment in the linkage structures is an outcome of shocks received during the 2008 financial crisis. Though there is a realignment of the linkage structures, the major Asian markets indices of Hong Kong (AS_SEHK) and Singapore (AS_SGX) are still the hub nodes, and the majority of the disjointed indices observed in pre-crisis and post-crisis time frames are still visible.
From the comparative analysis of the three plots, we can infer that the cross-market linkage structure in the post-crisis phase almost resembles that of the pre-crisis period. This resilience of the linkage structure is in line with the fact that Asia’s markets were quick to rebound from the 2008 financial crisis. This rebounding was because of three major reasons [77
]. The first reason was that, Asia’s largest economy, China, at that point in time exhibited the fastest recovery rate, and its indicator for growth had a rate much higher than its own domestic long-term trend rate. The second reason for rebounding is that there was a quick rebounding of external factors impacting the Asian countries to the point of the pre-crisis stage. This happened much before the stabilization of overall economic activities had occurred in the Western economies. A steady recovery was observed in Asian countries since February 2009, and subsequently, a normalization of trading and financial activities was also visible. The third reason for the rebounding of the economy to the pre-crisis level was the aggressive level of the countercyclical responsive actions that were initiated by policymakers and regulatory authorities of Asian countries. This pushed the economic activities in those countries to a higher level [78
]. Another factor that was also noticeable in the case of the 2008 financial crisis was that in comparison to the delayed rebounding during the Asian crisis, in this crisis, the rebounding was swifter. This was because of the gradual strengthening of the regional linkages among Asian countries in the past decades, which has subsequently resulted in a limited external dependence among the countries in the Asian region. Many past studies using different methodological approaches (econometrics techniques) have also agreed upon the point that the scale of market integration within the economies in the Asian region had inclined either during or after the crisis period. Any form of financial crisis hitting a country, region or globe significantly transforms the stock market relationships with the global markets and the regional markets. All these factors established that whatever events are occurring in the real economy, their subsequent impacts are automatically reflected in the cross-market linkage structures of the capital markets of the respective countries.
However, from the visual comprehension of the plots, we can still observe that pockets of segregated markets that were isolated prior to the crisis and were still in the state of isolation during and after the crisis. Accordingly, these sets of identified disjointed markets in Asia are open avenues for the materialization of international portfolio diversification objectives. Thus, making portfolio investments in these disjointed sets of markets can be a viable approach for protecting the overall portfolio from the systemic shocks of such crisis-like events.