Interconnectedness and systemic risk measures of Chinese financial institutions

3.1 Interconnectedness analysis

3.2 Linear Granger–Causality test

The Linear Granger-causality test shows the connectivity and directionality of the relationship between variables (Granger, 1969). Following Billio et al. (2010), the Granger causality captures the lagged propagation of institutions' return spillover effect in the financial market. The model is denoted as follows:

3.3 SII and VI

Systemic impact index (SII) and vulnerability index (VI) were proposed by Zhou (2010) as measures of systemic importance. Both indices are derived from the conditional probability of having at least one extra bank failure (PAO), which is presented as follows:

When the expected number of failures is considered, SII can be defined as:

1A is the indicator function. It equals 1 if A holds, and is 0 otherwise. Thus, the probability of a particular bank failure when the system confronts distress can be measured by VI:

Extreme Value Theory (EVT) is applied to calculate the value (Zhou, 2010). Suppose (X1,X2,…,Xd) follows the multivariate EVT setup, SII and VI can be calculated as:

Li,j is the L function characterizing the tail dependence of (Xi,Xj). L function based on the historical data. L(1,1,…,1) characterizes the tail dependence of (X1,…,Xd) and L≠i(1,1,…,1) characterizes (X1,…,Xi−1,Xi+1,…,Xd). The details about L function were explained by De Haan and Ferreira (2006). It is necessary to replace the PAO measure with low-level p. L(1,1,…,1) can be estimated as follows:

It is a practical and essential problem to choose the appropriate k among the above estimators. Zhou (2010) advises calculating the estimator of L(1,1,…,1) using different k. Then a line is plotted against the k values. We are choosing k in the first stable part of the line from low k value. In this paper, SII and VI with different types of financial institutions are calculated. It is necessary to balance the deviation and variance of k value when analyzing the data set. The problem is that k value changes with group size and we want to compare the SII and VI of different types of institutions. Therefore, we control the p level within each group identically. Thus, we choose p=3.5% for each group and compute k for them. In this paper, k=125 for banks; k=386  for Securities companies; k=69 for insurance companies; and k=364 for other institutions.

3.4 CoVaR

The VaRqi is implicitly defined as the q quantile of the return distribution. The CoVaRqj|i is used to represent the VaR of institution j when it is conditional on returns of institution i. That is, CoVaRqj|i is implicitly defined by the q-quantile of the conditional probability distribution. According to Girardi and Tolga Ergün (2013), the definition of VaR and CoVaR is transferred to:

Following Girardi and Tolga Ergün (2013), the calculation of ΔCoVaRqj|i can be divided into three steps. First, the VaR of each bank i is calculated based on a GARCH (1,1) model. Secondly, through the DCC(1,1) model, the bivariate density of each bank is estimated. After the two steps above, the CoVaR is calculated by the expectation over the q-tail (with q = 0.05). The benchmark state of institution i is defined as bi, i.e. μti−σti≤Rti≤μti+σti. The conditional probability distribution is calculated under the benchmark state bi by solving the dual integral equations:

3.5 MES

Acharya et al. (2010) presents a statistical model to measure financial institution's contribution to the systemic risk and the expected loss when the market gets depressed substantially. Referring to the definition of VaR, the expected shortfall (ES) is calculated as the expected returns when the portfolio's loss exceeds its VaR limit. It is defined as follows:

Marginal expected shortfall (MES) investigates the risk-taking behavior of financial institution i. In order to obtain this measure, R is defined as the total return of the financial system and is decomposed into the sum of each groups' return (ri). That is R=∑iyiri, where yi is the weight of bank i in the financial system. Then we have:

    MES measures the average return of any given institution during the 5% worst days for the overall market returns. It is estimated at a standard risk level of α = 5% using daily equity returns from CRSP (Acharya et al., 2010):

This method is simple, but it may produce inaccurate results when some extreme events happen in the tail of the return distribution. It assumes that the probability of observing a conditioning event to be constant, which is not always the case. Since the volatility of financial time series is typically relatively high, it is more likely to observe losses beyond a given threshold. Brownlees and Engle (2016) suggests an alternative method for calculating MES which may solve these flaws. The volatility is estimated by GARCH models, in order to obtain the conditional volatility and standardized residuals. Then, a DCC specification is calculated to obtain the conditional correlation and the standardized idiosyncratic residual. The innovation of this model is the GARCH/DCC residuals. The one-period-ahead MES can be expressed as follows:

4.1 Interconnections in the financial network

Granger causality test investigates the interconnections among financial institutions from the perspective of interaction of stock prices. The volatility of market value is one of the important manifestations of systemic risks. This method builds the granger causality network by measuring the number of interconnected institutions under certain confidence levels. Figure 2 depicts the network structure of the interbank market in 2014 and 2017 based on the interbank lending matrix. The bilateral exposure matrix X is illustrated in a directed graph as shown in Figure 2. The upper and lower panels demonstrate the interconnections among all financial institutions in 2014 and 2017, respectively. The width of an edge denotes the inter-bank exposure size at the end of the year, and the color shows the mixing of its source node and target node. The size of the node denotes the number of connections of individual financial institution (Kanno, 2015). Big banks are more interconnected and have the most extensive inter-bank transaction scales in the financial network. In 2017, the number of interbank connections among financial institutions rose dramatically as compared to 2014. It is apparent from the graph that the range of intense connections in 2017 is larger than that in 2014, indicating that more financial institutions have shown higher interconnection levels in 2017. In 2014, China Development Bank (CDB), Bank of China (BOC), Industrial and Commercial Bank of China (ICBC) and Agricultural Bank of China (ABC) had bigger inter-bank transaction scales than other institutions. Meanwhile, Industrial Bank, Minsheng Bank, Bank of Communications and Postal Savings Bank play significant roles in the interbank market. In 2017, CDB and ICBC became more significant while other commercial banks, including BOC, ABC and China Construction Bank (CCB) became relatively less interconnected in the interbank network. More banks have expanded their inter-bank lending and connections among financial institutions.

4.2 Results of degree centralities

The centralities of more than 200 financial institutions have been determined, as illustrated in Figure 3- (a)–(d). The x-axis represents the financial institutions in the network [3]. Overall, there is no discernible difference between Degree centrality, Betweenness, and PageRank. Each year, the degree of centrality of each financial institution varies widely. For example, the degree centrality of China Huarong Asset Management Co., Ltd. was 39 in 2014, but it reached as high as 200 in 2017. The degree value at China Guangfa Bank fell from 157 in 2014 to 69 in 2017. This result is in line with Huang et al. (2017) . Degree, Betweenness and PageRank centrality have shown similar power-law distribution tendencies, with degree k being proportional to k−γ (indicates a power exponent). It also suggests that the interconnection network has a scale-free network structure (Kanno, 2015; Hausenblas et al., 2015). There is, however, a minor variation in closeness centrality, and the value climbed dramatically from 2016 to 2017. It indicates that different financial institutions have the same level of farness to borrow funds, and it was easier to access fund in 2017. The top 100 institutions' degree centrality accounted for 81.9 % of all institutions. The top 20 institutions' PageRank centrality accounted for 66.5 % value, showing that the top 20 big financial institutions had significant effects on other institutions in the network.

4.3 Results for Linear Granger-causality tests

Unlike network analysis, which studies the interconnection of financial institutions from the perspective of interbank lending, granger causality test examines the connection among financial institutions from the perspective of stock price volatilities. Figure 4 depicts the granger causality network of financial institutions graphically. The circles indicate 58 financial institutions in China. The straight lines show the Granger-causal connections among institutions. In order to eliminate heteroskedasticity in series, Generalized Autoregressive Conditional Heteroskedasticity (GARCH (1,1)) is applied (Billio et al., 2010; Mensah and Premaratne, 2017; Gao and Ren, 2013).

The result indicates that the top five institutions include three commercial banks, one security business, and an insurance firm. The financial industry is still dominated by large state-owned banks like ICBC, CCB, ABC, and BOC. The Financial Stability Board (FSB) has designated ICBC and CCB as global systemically significant banks (G-SIBs). In order to mitigate possible risk exposure, both banks will need an additional 1.5 % capital ratio cushion. Non-state-owned institutions like joint-stock banks, city commercial banks, and insurance companies play a more significant role in the Chinese financial system. Huaxia Bank and Bank of Nanjing have 41 and 40 connections with other institutions, respectively. They are the second and third most interconnected banks in the financial network. Southwest Securities and China Life Insurance have 32 and 31 causality connections, respectively.

Some of the smaller, less well-known institutions have also demonstrated strong ties with others. After 2010, China saw a marketization and deregulation trend. The economic expansion and risk-taking activities make non-state-owned institutions tend to be more active in the interbank market for fund raising. Therefore, the financial stability of non-state-owned institutions merits greater attention [4]. Table 1 displays the descriptive information on financial institution interconnections.

The results indicate that banks have the greatest number of interconnections, followed by insurance companies, securities companies and other institutions. Larger institutions tend to have more interconnections with others. Banks have demonstrated more connections than other institutions. The government provides policy leaning to state-owned banks, which function as wholesale banks in China's credit-driven economy. The credit line is regarded as a key factor in influencing the behavior of customers and the asset prices, such as housing price (Qi et al., 2016; Dospinescu et al., 2019; Su et al., 2021). Because of the large volume of money transactions, state-owned banks play the most crucial role in the financial system. On the other hand, insurance companies are taking a more active part in the market than securities. Dynamic Causality Index (DCI) is used to calculate the level of interconnectedness in a system and makes it possible to compare systems with a different number of institutions. According to Mensah and Premaratne (2017), DCI can be defined as follows:

The average DCI value is 0.141 between 2012 and 2018, which is less than the value between 2008 and 2011.The findings indicate that the DCI value of all listed financial institutions between 2012 and 2018 is 0.14, which is significantly lower than the value between 2008 and 2011 by Gao and Ren (2013). It indicates that the Granger causality among Chinese financial institutions shows a downward trend after the financial crisis and the weak connection of asset prices. This result can be attributed to the fact that. First; The impact of the financial crisis in China and globally becomes weak, which made the systemic risk faced by financial institutions decrease. The reduction in the pressure coming from the whole system caused the interconnection of the asset price decrease. Second,more non-bank financial institutions are widely involved in the system after 2012. They provide more transaction choices for individual institutions. Since the interbank lending channel is not restricted to banks any more, more non-bank institutions began to provide liquidity to the system. The expansion of the system scale promotes the reduction of DCI. The increased market size dilutes the systemic risk caused by the interconnection of asset prices.

Mensah and Premaratne (2017) argued that Asia's (excluded China mainland) financial system becomes more densely connected during a financial crisis. Our findings corroborate this result and reveals a downward trend in interconnectedness among Chinese financial institutions after the financial crisis. The lower level of interconnectedness compared to other Asian areas can be linked to the fact that more non-bank financial institutions are broadly integrated into the system, allowing more transaction options for individual institutions. Since the interbank lending channel is not restricted in banks, more non-bank institutions began to provide liquidity to the system which reduced the DCI value. Because the interbank lending channel is open to non-bank institutions, more non-bank institutions begin to provide liquidities to the system. Compared with other regions, the DCI is about 0.21 and 0.12 in Southeast Asia and Asia, respectively, from 2012 to 2014 (Hamilton, 2015; Mensah and Premaratne, 2017). On the other hand, the DCI for the worldwide financial system, comprising banks, hedge funds, and insurance institutions, was roughly 0.13 in 2018 (Billio et al., 2012). It shows that the Chinese financial system is marginally more integrated than the rest of the globe and Asia, but much less than Southeast Asia over the same period.

4.4 Results for SII and VI

The interconnectedness can evaluate the possibility of an institution to be affected when the systemic risk arises, but cannot measure the consequence of the risk quantitatively. The potential loss of an institution is an important measure when the risk is spreading. The tail risk, which measures the risk of individual institution and the whole system, is useful to evaluate the intensity of risk contagion. The results of four types of institutions are listed in Table 2. All banks are expected to have an SII of approximately 10. It means that if one bank fails, nearly ten more institutions will fail as a result. The VI values vary from 0.2565 to 0.2771. It suggests that another institution will be affected with the probability ranging from 25.65 % to 27.71 % when a bank fails. The similar VI and SII statistics show that all banks in China have comparable market business practices. However, China Everbright Bank, Bank of Communications, and Huaxia Bank, all of which are not typical large state-owned banks, rank the first, second and fifth in terms of SII and VI. China Everbright Bank, in particular, becomes the most systemically significant bank in terms of the SII and VI indexes. This can be attributed to joint-stock banks' aggressive business approach, given they have fewer assets than large state-owned banks. A proactive company strategy generally entails more market linkages and interactions. The most susceptible banks include China Everbright Bank, China Construction Bank, Agricultural Bank of China, and Bank of Communications. Three of them are state-owned banks, indicating that the bank size has a considerable influence in determining the vulnerability. One factor might be that state-owned banks are increasingly involved in sophisticated financial transactions.

Huang (2017) examines the tail risk measures of Chinese listed banks between 2007 and 2014, and argues that the SII values are between 8.56 and 9.48. However, the SII values in our analysis range between 9.33 and 10.46, which are higher than that of Huang (2017) [5]. It reveals that the systemic risk in China's financial sector keeps a downward trend. On the other hand, Zhou (2010) investigates 28 listed banks in the US between 1987 and 2008, and finds that the SII values range between 6.53 and 12.44, which is lower than the value of Chinese banks. It can be attribute to the fact that the Chinese banking industry is more concentrated than the United States and other industrialized countries. As a result, the impact of systemic risk is greater than the findings of Huang (2017). This observation is consistent with the Granger Causality result.

The peak VI value for all banks between 2012 and 2018 is 27.71 %, substantially lower than the amount between 2007 and 2014 [6]. One possible cause is that the financial crisis in 2008 heightened the systemic risks of financial institutions as a whole. Banking sector was highly concerned by regulator after the crisis due to its vulnerability. Risks began to be decreased as a result of stricter controls imposed by supervisors. In general, bank VI varies year to year, but the risk resistance capacity of Chinese banking sector continues to improve. Some relatively small banks are showing better performance in risk mitigation. For example, China Merchants Bank (CMB), a joint-stock bank, hit the highest VI value of 36.29% within all banks during 2007 and 2014 (Huang, 2017). However, between 2012 and 2018, the value fell to 25.83 %, ranking the 13th among all banks. China Construction Bank (CCB), a giant state-owned bank, had the highest VI value constantly. This finding suggests that big state-owned banks are still more vulnerable to financial market shocks compared with other banks. It validates existing domestic policies that impose stricter control on major banks, such as more significant reserve requirements or other macroprudential oversight [7]. Meanwhile, big state-owned banks, i.e. China Construction Bank, Bank of China, Agricultural Bank of China, and Industrial and Commercial Bank of China, have been classified as Global Systemically Important Banks (G-SIBs) from 2019. Additional 1% or 1.5% surcharge capital buffer will be applied to these banks. Future requirement such as Total Lost Absorb Capability (TLAC) is imposed. This indicates that the potential high systemic risks of big state-owned banks have received concern by both domestic and international regulators.

Another notable characteristic is that security companies have considerably higher SSI values than other financial institutions, indicating that they have a high systemic risk exposure in the financial system. Theoretically, the higher the level of interconnectedness, the larger the expected loss of financial institutions. Security companies have fewer interconnections in the market due to their modest size. Their potential losses, however, are expected to be greater than those of banks. This finding is consistent with Hsu et al. (2014) which suggested that security firms face higher systemic risks than banks and insurance businesses in China. It can be attributed to the fact that security companies have witnessed fast growth due to bank-security collaboration, which offers a channel for banks to transfer funds outside of the balance sheet through various asset management programs. As a result, in 2012, it became the primary component of China's shadow banking businesses (Gao and Wang, 2014).

Therefore, security companies are more involved in financial innovation, while banks, especially giant banks, are strictly supervised by the regulator. As shown in Table 2, Soochow securities hits the highest SII and VI values in the security sector. It is a small security company based in the Yangtze River Delta, the most developed area in China.

The intensive capital flow in this region makes Soochow securities act more aggressive than other institutions. CNPC Capital and Polaris Bay Group, on the other hand, have the lowest systemic risks among security firms. The CNPC Capital, which is invested by a stated-owned enterprise, provides financial services to the parent company. As a result, it has relatively fewer connections in financial system than other financial institutions. Polaris Bay Group, a local security firm, is headquartered in Hebei Province, where economic development is not as fast as than in other Chinese regions. The geographical factor has significantly limited the interconnections with other institutions.

Finally, the group of insurances companies has the lowest impact on other financial institutions, since all insurance companies have lower VI values than other institutions. One possible explanation is the relative abundance of fund makes insurance companies bear lower systemic risks. Considering the lower level of interconnection, other financial institutions have higher VI values than insurance companies, but still lower than banks and security companies.

4.5 Results of statistical measures

It is distinct to observe the trend of statistical measures, i.e. Value of Risk (VaR), CoVaR, and DCVaR, of different types of financial institutions from 2012 to 2018, as shown in Table 3. The results indicate that banks have the lowest VAR among all types of financial institutions. Security and insurance companies have greater VAR values than banks. The group of other financial institutions suffers the highest VAR value, indicating that under-regulated financial institutions may suffer even greater losses when a risk happens [8]. Considering the contagion of potential risks in the financial system, other institutions with low levels of regulations may bring about higher extreme loss and suffer the whole system. Therefore, these institutions deserve more attention from regulators. On the other hand, there is slight difference in CVaRs among different types of financial institutions. Security companies suffer higher DCVaR values than all other kinds of institutions. This is because they are more involved in the financial innovation and shadow banking business, which provide more funds to large and state-owned enterprises. However, the quick large-scale spread of financial innovation may mismatch between the virtual and real economies, increasing systemic risk and undermining the financial system's stability (Feng, 2015; Tan, 2017). Due to the volume of transactions between security businesses and other institutions, the risk has swiftly transferred from security companies to other financial sectors.

Table 3 shows that all statistical measures, i.e. VaR, CVaR, and DCVaR, increased significantly from 2012 to 2014 and peaked in 2015. In the same year, the Chinese stock market suffered a major drop in prices. China's stock markets saw abnormally high volatility from June to August 2015. In 53 trading days, the Shanghai Composite Index plummeted by more than 45%, from 5,178 points to 2,851 points. The stock market value quickly dwindled, from a high of 5,178 on June 12, 2015, to a low of 2,850 points on August 26, 2015. The total market value of the Shanghai and Shenzhen markets evaporated by about 33 trillion yuan. The severe capital market crash transferred risk to other institutions and raised risk measures of the whole financial system. The stock market progressively recovered till the end of 2015, and the financial market progressively stabilized over the next few years. Insurance and security firms, in general, contribute more to systemic risk. But other institutions, such as trust funds, financial companies, etc. may bring about severe loss and endanger the financial system as a whole. The mean value of ΔCoVaR of Chinese listed banks is lower than 166.9 between 2007 and 2014, compared with Huang (2017). It suggests that, from the standpoint of VAR, the systemic risk of Chinese banking sector is decreasing. Adrian (2016) investigates the ΔCoVaR of 1,226 US financial institutions between 1986 and 2010, and discovers a value of 120. It means the systemic risks of Chinese banks are similar with US banks, from the perspective of VAR (see Table 4)

The measures of MES and LRMES exhibit a similar trend with VaR and CVaR. the MES and LMES values of banks are the lowest among all types of financial institutions. The values of security companies are higher than other types of institutions. This result demonstrates that banks contributes less than other kinds of institutions, while security companies are the major contributor to the systemic risks. Both measures keep increasing from 2012 to 2015, and reach the peak values in 2015. After that, a decreasing trend is observed for all kind of institutions. This result confirms our analysis above, when the economy expands, the systemic risk of all financial institutions is heavily accumulated. However, when the stock market crash, the systemic risks of all financial institutions begin to release quickly. It proves the existence of pro-cyclical effect between the financial risk and the stock market. According to Xu et al. (2020), the hot listing market is the result of governmental subsidies and the removal of entry restrictions in the junior market, the profitability of listed firms depends on the combination of stockholder's equity, long-term liabilities, provisions and deferred revenues positively. The effective supervision on capital markets can lower the systematic risk of the whole financial market. On the other hand, the early warning system of financial bubbles is crucial to prevent the contagion of systemic risks in the system.