Identifying the systemic importance and systemic vulnerability of ﬁnancial institutions based on portfolio similarity correlation network

The indirect correlation among ﬁnancial institutions, stemming from similarities in their portfolios, is a primary driver of systemic risk. However, most existing research overlooks the inﬂuence of portfolio similarity among various types of ﬁnancial institutions on this risk. Therefore, we construct the network of portfolio similarity correlations among diﬀerent types of ﬁnancial institutions, based on measurements of portfolio similarity. Utilizing the expanded ﬁre sale contagion model, we oﬀer a comprehensive assessment of systemic risk for Chinese ﬁnancial institutions. Initially, we introduce indicators for systemic risk, systemic importance, and systemic vulnerability. Subsequently, we examine the cross-sectional and time-series characteristics of these institutions’ systemic importance and vulnerability within the context of the portfolio similarity correlation network. Our empirical ﬁndings reveal a high degree of portfolio similarity between banks and insurance companies, contrasted with lower similarity between banks and securities ﬁrms. Moreover, when considering the portfolio similarity correlation network, both the systemic importance and vulnerability of Chinese banks and insurance companies surpass those of securities ﬁrms in both cross-sectional and temporal dimensions. Notably, our analysis further illustrates that a ﬁnancial institution’s systemic importance and vulnerability are strongly and positively associated with the magnitude of portfolio similarity between that institution and others.


Introduction
With the gradual advancement of financial innovation in recent years, a complex network of correlations between financial institutions has been created as a result of closer contact and mixed business operations across financial institutions.This will lead to the risk that a single financial institution in distress will propagate through the correlation network across the system, ultimately creating financial systemic risk [1,2].Because of this risk formation mechanism, many scholars already focus on the central role of financial link-ages that cause systemic risk [3,4].Now, the study on the financial correlation network is broadly divided into two categories.The first is the direct correlation network, which forms by connecting different market entities via direct creditor-debtor relationships [5].When a market entity fails to deliver on a debt contract, the risk spreads to the direct correlation network.The second is the indirect correlation network, which is created by the entities' indirect connection through the ownership of common assets [6].When some banks experience asset losses, they must sell some assets due to leverage ratio constraints, which causes asset values to fall, affecting other banks that hold the assets and causing risk contagion.Many studies have analyzed the systemic risk in the direct correlation network [7,8].A significant number of articles have examined bank systemic risk by constructing interbank lending [9,10] and credit networks [11,12].And the two most typical research methods are the EN algorithm [13] and the DebtRank algorithm [14].
However, with the increasing portfolio similarity and mixed business operations among financial institutions, the indirect correlation network among financial institutions has gradually attracted the interest of scholars.Numerous scholars have examined the systemic risk from the perspective of indirect networks and indirect contagion using simulation and empirical methodologies [15].The research has confirmed that the indirect network is an important channel of the risk contagion and should not be ignored [16].In addition, scholars have also made a detailed analysis of the risk contagion mechanism in the indirect network.Currently, there are two major categories of contagion models.One is the threshold model, which holds that banks will only liquidate assets when they go bankrupt [6,17].The other is the leverage targeting model.It assumes that if the leverage ratio of the bank does not meet the requirements, it will liquidate the assets [18][19][20].In addition to the research mentioned above, many studies have built indirect networks using real data to study the risk contagion of financial systems across various countries [15,21,22].Of course, a few scholars have also examined the systemic risks of financial institutions like funds [23,24] and insurance firms [25] from the perspective of indirect contagion in order to provide new insights for asset managers and policymakers [26].
In the above-mentioned studies on financial systemic risk, scholars have proposed many measures of systemic risk, but most of them only focus on one aspect of systemic risk.i.e., only pay attention to the systemic importance of financial institutions [27,28] or the risk exposure of financial institutions [29,30].In fact, Systemic risk consists of two aspects: risk spillover caused by network connections among financial institutions and risk exposure to financial institutions, where risk spillovers and exposures reflect the systemic importance and systemic vulnerability of financial institutions, respectively.When considering the correlation network of financial institutions, systemic importance evaluates each financial institution's risk contribution in the risk contagion process.The network model method, the Sharpley value method [31], and CoVaR [32] are the primary systemic importance measurement methods.Ref. [33] first used the network model method to study the risk contagion among banks, but the data required by this method are the transaction data of each financial institution, which are difficult to collect and process in a timely manner.This has a significant impact on China's monitoring of systemic risk.As a result, the Sharpley value method was proposed to assess the degree of systemic importance of various financial institutions by allocating systemic risk to each institution based on the size of each individual contribution [34,35].However, the above methods are more complicated to calculate; in contrast, CoVaR can directly measure the risk spillover effects of financial institutions, which is convenient and quick, and therefore is gradually being widely used in the field of risk management [36,37].Furthermore, some researchers have used indicators to measure the systemic importance of financial institutions [38].For the systemic vulnerability, it evaluates the risk borne by each financial institution from other financial institutions, i.e., the entire financial system, in the risk contagion process.The marginal expected loss (MES) method and the SRISK method are the main systemic vulnerability measurement methods.The MES method measures the expected loss of a financial institution in the event of severe turbulence in the financial system and reflects the sensitivity of the financial institution to changes in systemic risk [39], whereas the SRISK indicator measures a financial institution's capital shortfall in the event of a severe market downturn as a function of the institution's size, leverage, and risk [40].Some other scholars have analyzed the factors influencing systemic importance and systemic vulnerability [41] or constructed contagion and vulnerability indices to measure the degree of systemic importance and vulnerability of banks, respectively [42].
The review of the above literature reveals that the study of systemic risk under the portfolio similarity correlation channel has become popular.Nevertheless, most research has only analyzed the systemic risk caused by a single type of financial institution under this channel and has mainly used banks as a case study.The characteristics of portfolio similarity correlation networks between different types of financial institutions have not been elucidated.Therefore, in order to further investigate systemic risk under the portfolio similarity correlation channel, we concentrate on the portfolio similarity correlation network among different types of financial institutions and measure the systemic risk of financial institutions according to the expanded fire sale contagion model.At the same time, while studying the modeling of portfolio similarity among various financial institutions, the works of Barucca et al. [43] and Caccioli et al. [44] align with our research.Nevertheless, both studies rely on the leverage target model to measure fire sale losses, which deviates from the actual liquidation process of financial institutions.Therefore, we refer to the research conducted by Ramadiah et al. [21] to estimate asset liquidation amounts and price changes in the fire sale process of financial institutions.Using the Ramadiah et al. model, we expand the fire sale model by including real regulatory leverage rates for different financial institutions.Moreover, we study more asset classes held by financial institutions to understand systematic risks related to similarities in their portfolios.This helps us calculate losses for financial institutions more precisely during a crisis.Additionally, most of the literature on assessing systemic importance and vulnerability of financial institutions is based on market data [41,45].And there are fewer relevant studies in China.Therefore, considering the complex connections between Chinese financial institutions, we use balance sheet data and complex network methods to study their systemic importance and vulnerability over time and across different institutions.This not only broadens our research perspective, but also provides regulators with more comprehensive references for preventing and mitigating financial systemic risks.

Research model and risk indicator 2.1 Portfolio similarity correlation network
The portfolio similarity correlation network is an undirected weighted network of financial institutions that are correlated with each other according to the similarity of their asset portfolio holdings, as shown in Fig. 1.The network's nodes stand for financial institutions, The yellow nodes represent insurance companies; the blue nodes represent securities firms and the orange nodes represent banks with different colors denoting various kinds of financial institutions.The connected edges between nodes indicate that the portfolios held by the financial institutions are similar, and the thickness of the edge indicates how much more similar the assets are between the institutions; the thicker the edge, the higher the portfolio similarity between the financial institutions.
There are various ways to measure the level of portfolio similarity between financial institutions, but we employ the cosine similarity proposed by Girardi et al. to more accurately assess the portfolio similarity between different types of financial institutions [46].The level of portfolio similarity between financial institution i and financial institution j is defined as: Where C im is the value of asset m held by financial institution i, V i is the vector parametrization of the asset portfolio held by financial institution i.The size of portfolio similarity between financial institutions ranges from 0 to 1, with larger values indicating higher portfolio similarity between financial institutions.

Expanded fire sale contagion model
The portfolio similarity correlation network reveals that financial institutions are interconnected due to the similarity of their asset portfolios.The fire sale contagion model takes portfolio similarity among financial institutions into account and assumes that as asset prices fall, financial institutions will sell the related assets at a lower price to meet regulatory leverage requirements.A massive sell-off of assets leads to a glut of assets in the market, resulting in a further decline in asset prices, which causes other financial institutions associated with them to suffer losses, triggering systemic risk.Consequently, the fire sale contagion model is good for measuring the systemic risk that financial institutions suffer from price declines under the portfolio similarity correlation channel.
Two main types of fire sale contagion models are included in the existing studies: one is the threshold model, which assumes that financial institutions liquidate their assets only when losses are large enough to cause insolvency and no longer participate in the subsequent contagion process [6].The other is the leverage targeting model.This model assumes that when the financial institutions' leverage falls short of their goal leverage, they must liquidate part of their assets [18].Nevertheless, Ramadiah et al. discover that the actual fire sale behavior of financial institutions lies between the threshold model and the leverage target model [47].Therefore, in order to capture a more realistic systemic risk, we refer to the results of Ramadiah et al. to estimate the liquidation volume and price fluctuations of assets during the fire sale process of financial institutions.Using Ramadiah et al. 's model, we incorporate the actual regulatory leverage rates of different types of financial institutions as leverage targets.Additionally, we expand the asset classes held by financial institutions to develop an expanded fire sale model.This model serves as a tool for exploring systematic risk under the correlation channel of portfolio similarity among financial institutions.

Structure of the balance sheet
In this study, we consider a financial system with N financial institutions (including banks, insurance companies, and securities firms) and M categories of illiquid assets (see the data description section for specific categories).
Assume that at time t, the cash held by financial institution i is C t i , its portfolio of illiquid assets is A t i , and its other assets is Q t i .P t m is the price of asset m at time t, and {O t i1 , . . ., O t iM } ≥ 0 is the portfolio of illiquid assets of financial institution i at time t.Therefore, A t i = M m=1 (O t im × P t m ) indicates the overall value of the financial institution's portfolio of illiquid assets.For simplicity, we assumed that the initial price of each illiquid asset is one, i.e., P 0 m = 1, ∀m ∈ M.And illiquid assets may suffer price losses throughout the fire sale process, but the price of cash always remains constant; other assets Q t i , which are asset types other than cash and illiquid assets, such as interbank assets, are also unaffected by the fire sale.
Moreover, we assume that the liabilities of financial institution i is L t i and the equity is E t i .Therefore, the total assets T t i and total liabilities B t i of financial institution i are expressed as: ( 2 )

Contagion process of fire sale under external shocks
Assume that after a shock θ m (θ m ∈ [0, 1]), the price of asset m falls to P 1 m at time t = 1, thus For any asset m,there is P 1 m ≤ P 0 m , and there must be at least one class of asset prices that satisfy P 1 m < P 0 m .Financial institution i owning asset m will experience a direct loss as a result of the shock, i.e., Loss i = M m=1 (O 1 im × (P 0 m -P 1 m )).At this point, the total assets, equity, and liabilities of the financial institution i are described as: Subsequently, financial institution i then acts in response to the direct losses it experiences.If the loss is great for E 1 i < 0, the financial institution i becomes insolvent, and it must liquidate all of its assets.And the financial institution i exits the portfolio similarity correlation network and is not involved in the subsequent contagion process.On the other hand, if the financial institution experiences a loss and its regulatory leverage no longer complies with regulatory requirements, it must sell off part of its assets.Here, the regulatory leverage ratio is defined as capital divided by total assets.Hence, financial institution i must liquidate some of its assets when Eq. ( 4) is no longer satisfied.
Where λ 1 i is the regulatory leverage ratio at time t = 1, λ α i is the regulatory leverage ratio requirement, where α is used to differentiate the regulatory leverage ratios of different types of financial institutions.
In this paper, a one-parameter non-linear function H 1 i (σ ) is introduced to capture the liquidation process of financial institutions [47].By introducing regulatory leverage into the Ramadiah et al. model, we can get the total value of assets to be liquidated by financial institution i is represented in Eq. ( 5).
In Eq. ( 5), , where σ i is the absolute return on assets, σ 1 i = - . And q (q ∈ (0, ∞)) is a parameter that is related to a financial institution's propensity to follow threshold liquidation dynamics.
For ease of exposition, we suppose that financial institution i will keep its current asset portfolio weighting unchanged, i.e., sell off its assets proportionally.Meanwhile, the price of an asset will alter as a result of its fire sale.And referring to the model of Ramadiah et al. [47], the price of asset m after it has been affected by the fire sale can be described as: Where μ is a parameter reflecting the market response to asset liquidation, with higher values of a indicating greater illiquidity of assets.φ 1 im denotes the total amount of assets m sold by financial institution i, When financial institutions conduct the fire sale, they will experience two types of losses: a mark-to-market loss on their remaining assets and a loss on the decline in value of the assets sold at the time of the sale [19].Additionally, it is presumed that the asset price at the midpoint of the pre-selling and post-selling times is subtracted from the selling assets.Therefore, the contagion loss for financial institution i after the first round of the fire sales is: In Eq. ( 7), the portion preceding the plus sign represents the mark-to-market loss on the remaining assets, and the portion following the plus sign represents the loss on the portion of the assets sold off.
The preceding is a summary of the improved fire sales contagion model's first round of contagion.As asset prices are updated, i.e., as losses from the fire sale contagion occur, the total assets and leverage of the financial institutions will change again, which causes them to liquidate some of their assets once more, triggering a new round of contagion.And this cycle will continue until there are no more financial organizations in the network that need to liquidate their assets.

Indicators for measuring systemic risk
When performing a fire sale of assets, multiple rounds of contagion processes frequently occur.However, including too many cycles of asset liquidation can often reduce the effectiveness of stress testing models [47].Therefore, we utilize the frameworks proposed by Greenwood et al. and Duarte et al. to establish a metric for assessing systemic risk based on the contagion losses following the initial round of fire sales [18,48].

Systemic risk indicator: SR
Systemic risk (SR) is a measure of the financial system's systemic risk.In this study, it is defined as the ratio of contagion losses to the initial total equity after the first round of fire sales for financial institutions in the improved fire sale contagion model, as in Eq. ( 8).

Systemic important financial institution indicator: SIFI
Systemically important financial institutions (SIFI) assess how much each financial institution contributes to the spread of risk; the higher the risk share, or the higher the value of the indicator, the more important the financial institution.Therefore, the indictor is defined as the ratio of the contagion loss of each financial institution after the first round of fire sales to the contagion loss of all financial institutions in the improved fire sale contagion model, as shown in Eq. (9).

Systemic vulnerable financial institution indicator: SVFI
Systemic Vulnerable Financial Institutions (SVFI) measure the risk that each financial institution faces from other financial institutions, i.e., the financial system, during the risk contagion process.The financial institution is more vulnerable, and the more risk it takes on, the higher the measure's value.Therefore, the systemic vulnerable financial institution indicator is defined as the ratio of the contagion loss of each financial institution after the first round of fire sales to its initial equity value in the improved fire sale contagion model, as shown in Eq. (10). 3 Description of data and parameters

Descriptive statistics of data
We used the balance sheet data of financial institutions from 2017 to 2021 and selected the sample financial institutions according to the following principles: 1) The listing time is earlier than January 1, 2017; 2) There were no ST or ST* situation during the sample period, that is there are no abnormalities in the financial or other conditions during the sample period, posing a risk of delisting; 3) The industry classification results for financial institutions remained unchanged during the sample period.In conclusion, 56 financial organizations were chosen as the research objects, and they were categorized into 24 banks, 4 insurance companies, and 28 securities firms based on the China Securities Regulatory Commission's industry categorization findings for the third quarter of 2021.The research data were obtained from the CSMAR1 database and the annual reports of financial institutions, with the data unit being millions of RMB.This paper represents the institution's portfolio by considering multiple asset classes, specifically including the following 10 illiquid assets.In this section, we provide the descriptive statistics for cash and balances with central banks, the total assets, and the ten illiquid assets.The ten illiquid assets are derivative financial instruments, net loans and advances to customers, investment properties, fixed assets, intangible assets, deferred tax assets, other assets, debt investments, other debt investments, and investments in other equity instruments, which will be impacted by the fire sale.The amount of assets held by financial institutions varies greatly, as shown in Table 1.Net loans and advances to customers, along with other assets, debt investments, and cash and balances with central banks, are significantly larger in size compared to investment properties and intangible assets, which are comparatively smaller.

Description of parameters
This research focuses on four key parameters: regulatory leverage ratio requirements for financial institutions (λ α i ), propensity parameters for financial institutions to follow the threshold model (q), market response parameters for asset liquidation (μ), and the percentage of external shocks (θ m ).The values used in the empirical analysis for these parameters are described below.
(1) Regulatory leverage ratio requirements for financial institutions (λ α i ).According to the provisions in the Guidelines for the Supervision of Leverage Ratios of Commercial Banks, the Measures for the Management of Capital of Financial Assets Investment Companies, and the Measures for the Management of Risk Control Indicators of Securities Firms, we set the regulatory leverage ratio requirements for banks, insurance companies and securities firms at 4%, 6% and 8%, respectively.
(2) Propensity parameters for financial institutions to follow the threshold model (q).The range of the propensity parameters in the real liquidation model of financial institutions is between 20 and 30 [47].Here, for convenience in the calculation, we set q = 20.
(3) Market response parameters for asset liquidation (μ).Except for cash, all assets are assumed to have the same market response parameters.According to Ramadiah et al., the range of the market response parameters for illiquid assets is between 0.6 and 1 [47].Since the assets considered in this research are illiquid, we set μ = 0.6.
(4) The percentage of external shocks (θ m ).The interval of change for external shocks during the systemic risk phase is [deleveraging minimum shock, all bankruptcy minimum shock].External shocks within this interval will lead to risky contagion within the financial system.Therefore, to ascertain the percentage of external shocks that cause risk contagion in the financial system during the sample period, we set the external shocks to [0.001, 1] and simulate them in the model in steps of 0.001.Based on the simulation results, the proportion of external shocks is set to 0.037 in order to ensure that risk contagion occurs in all years of the sample period and to analyze the systemic importance and vulnerability of financial institutions more accurately in both cross-sectional and temporal dimensions.This value represents the minimum proportion of shocks that is necessary for risk contagion to occur in all years of the sample period.

Portfolio similarity correlation network of 56 Chinese financial institutions
Based on the description of the portfolio similarity correlation network in Sect.2.1, we calculated the size of portfolio similarity among individual financial institutions using the balance sheet data of 56 financial institutions in China from 2017 to 2021 and plotted the portfolio similarity correlation network of 56 financial institutions in China from 2017 to 2021 as shown in Fig. 2.
As seen in Fig. 2, financial institutions have a strong portfolio similarity correlation among themselves, providing a channel for systemic risk contagion.And from 2017 to 2021, portfolio similarity between financial institutions of the same type was high, while there was a significant change in portfolio similarity among different types of financial institutions, particularly from 2017 to 2018.In addition, to provide a more visual representation of the changes in the portfolio similarity association among financial institutions, we calculate the average portfolio similarity size among multiple financial institutions for each year, and the results are shown in Table 2 and Table 3.
Tables 2 and 3 show that portfolio similarity between financial institutions of the same type is strong and varies less, while portfolio similarity between different types of financial institutions is relatively low and varies substantially.It is noteworthy that the greatest portfolio similarity is found between banks and insurance companies, which remains at around 0.5, indicating that risks from banks or insurance companies have a high potential to be transmitted to each other.On the other hand, banks and securities firms show a    lower portfolio similarity, with assets remaining largely similar at around 0.2 from 2018 to 2021, except for a significant upward trend from 2017 to 2018, so the risk spread between banks and securities firms through this channel is relatively low.From the perspective of changing trends, portfolio similarity between banks and insurance companies follows a similar trend to the size of portfolio similarity between banks and securities firms, both increasing and then stabilizing, whereas portfolio similarity between insurance companies and securities firms is more variable, increasing significantly from 2017 to 2018, but then decreasing from 2018 to 2021.In addition, Barucca et al. found that some institution types hold debt and equity portfolios that are more similar to those held by other types, which is similar to our findings  [43].Furthermore, their research showed that both unit-linked and non-unit-linked insurance company debt holdings are highly similar to each other's debt holdings as well as to those of banks.To a lesser extent, they are also similar to those of investment funds.
In our study, we observed that the overall asset similarity between insurance companies and banks is higher than that between insurance companies and securities firms.Therefore, banks and insurance companies need to be particularly aware of risks from the asset similarity channel with respect to each other.
In conclusion, we have achieved a preliminary knowledge of the portfolio similarity correlation among financial institutions and its changes by analyzing the portfolio similarity correlation network of financial institutions in China.Nevertheless, the risk propagation information reflected in the network is limited.As a result, we have examined the systemic importance and systemic vulnerability of financial institutions on this basis in order to better capture the systemic risk of financial institutions under this portfolio similarity connection.

Systemic risk based on portfolio similarity correlation network
Table 4 depicts the trend of the systemic risk for each year of the sample period at a shock of 0.037.As shown, the systemic risk of China's financial system increases and then decreases from 2017 to 2021, with a significant increase from 2017 to 2018, confirming the impact of the 2018 "stock market crash" on China's financial system to some extent.And from 2019 to 2021, the systemic risk has been at a low level, with a small fluctuation.This indicates that our financial system as a whole is in a more stable state as a result of the implementation of various policies in recent years to avoid systemic risk in China.
To ensure the accuracy of the results, we set out to investigate whether propensity parameters for financial institutions to follow the threshold model (q) and market response parameters for asset liquidation (μ) have an impact on systemic risk.Figures 3 and 4 present the data and trends related to systemic risk under different values of parameters q and μ.As seen in these figures, the trend of systemic risk in China remains unchanged in 2017-2021 regardless of how the parameters q and μ change.And, both figures indicate a higher level of systemic risk in 2018.These findings strengthen our confidence in the robustness of the results.Specifically, we note that as the value of parameter q increases, the level of systemic risk decreases.Conversely, as the value of parameter μ rises, the level of systemic risk also rises; yet, it's worth mentioning that even under these conditions, the overall change remains quite small.

Cross-sectional characteristics of systemic importance and systemic vulnerability of financial institutions
Table 5 shows the cross-sectional characteristics of the systemic importance of 56 financial institutions in China.And the names of financial institutions in Table 5 are represented by their English abbreviations, and the specific correspondence is shown in the Appendix.
The systemic importance ranking is based on the mean value of SIFI for each financial institution from 2017 to 2021, while the portfolio similarity ranking is based on the mean value of the size of portfolio similarity between each financial institution and other finan- From the perspective of different types of financial institutions, the mean values of SIFI for banks, securities firms, and insurance companies are 0.03882, 0.00041, and 0.01722, respectively, as shown in Table 5.That means banks have the highest systemic importance, followed by insurance companies and securities firms.Hence, banks and insurance companies should be a top concern for financial regulators because they contribute more to the systemic risk resulting from portfolio similarity correlations than securities firms.
Next, from the perspective of a single type of financial institution, firstly, the mean of SIFI for China's five largest state-owned banks is high, reflecting their high systemic importance, greater contribution to the risk of the financial systems, and the fact that they are a top concern for financial regulators.Second, urban commercial banks are ranked low overall, with joint-stock commercial banks like Hua Xia Bank being ranked medium in terms of systemic importance.However, some banks, like China Everbright Bank and Bank of Beijing, also have relatively high mean values of SIFI, so their potential risk contribution to the financial system cannot be ignored.For securities firms, the mean values of SIFI are significantly lower than those of banks and insurance companies.Even the mean values of SIFI for the top two securities firms, GF Securities and CITIC Securities, are at the low end of the range for banks and insurance companies.As a result, the risk contribution of securities firms to the systemic risk resulting from portfolio similarity correlation is lower, which is related to the smaller range of assets held by securities firms themselves and the lower total assets.Finally, Ping An of China has the highest mean values of SIFI among insurance companies as well as the highest mean among banks and a large portfolio similarity size.This reflects Ping An of China's importance in the overall financial system and is inextricably linked to its strong overall strength and the adoption of a business model that spans multiple businesses across multiple financial sectors.
In addition, we calculated the Spearman correlation coefficient between the value of systemic importance and the value of portfolio similarity for the 56 financial institutions to determine whether the size of portfolio similarity between a financial institution and other financial institutions impacts the systemic importance of that institution.The correlation coefficient came out to be 0.4785, which is significant at the 0.001 level.This indicates that the correlation of financial institutions based on portfolio similarity is one of the factors that triggers systemic risk in the financial system.Additionally, the systemic importance of a financial institution is strongly and positively associated with the magnitude of portfolio similarity between that institution and other financial institutions.
Table 6 shows the cross-sectional characteristics of systemic vulnerability for 56 financial institutions in China.Similarly, the names of financial institutions in Table 6 are represented by their English abbreviations, and the specific correspondence is shown in the Appendix.The systemic vulnerability ranking is based on the mean value of each financial institution from 2017 to 2021 according to the different types of financial institutions, and the portfolio similarity ranking is also based on the mean value of the size of portfolio similarity between each financial institution and other financial institutions from 2017 to 2021 before the shock.
As shown in Table 6, the mean values of SVFI for banks, securities firms, and insurance companies are 0.03837, 0.00480, and 0.02703, respectively, which exhibit the same characteristics as systemic importance.Therefore, securities firms have lower systemic From the perspective of a single type of financial institution, the mean values of SVFI for China's four largest banks are high, indicating that negative shocks to the financial system will be transmitted more to these four banks.Furthermore, Minsheng Bank and China Everbright Bank ranked highly in terms of systemic vulnerability, even higher than large banks like Bank of China and Industrial and Commercial Bank of China, which could be attributed to their strong portfolio similarity.As a result, in the event of a crisis, Minsheng Bank and China Everbright Bank would face a greater risk of spillover.At the same time, we observe that the mean values of SVFI for national joint-stock commercial banks like Hua Xia Bank and city commercial banks like Bank of Shanghai are not significantly different but are higher than those of insurance companies like China Pacific Insurance.This implies that national joint-stock commercial banks and city commercial banks are exposed to similar spillovers but still have significant risk exposures in the event of a crisis.In addition, with the overall risk of China's securities firms having increased in recent years, the regulator should pay attention to securities firms with relatively high values of SVFI in this area to achieve the goal of preventing and mitigating systemic risk, even though the overall systemic vulnerability ranking of securities firms is low.For insurance companies, Xinhua Insurance has a high level of systemic vulnerability but a low level of systemic importance.This indicates that Xinhua Insurance has a smaller contribution to the overall financial systemic risk than other insurance companies, but is subject to more risk spillover and is likely to trigger extreme situations such as insolvency when shocks are too large.
Similarly, we calculated the Spearman correlation coefficient between the value of systemic vulnerability and the value of portfolio similarity for the 56 financial institutions.Similar to the findings regarding systemic importance, the correlation coefficient turned out to be 0.6585, which is highly significant at the 0.001 level.This indicates that the systemic vulnerability of a financial institution is strongly and positively associated with the magnitude of portfolio similarity between that institution and other financial institutions.
In conclusion, the analysis of the cross-sectional characteristics of systemic importance and systemic vulnerability of financial institutions under the portfolio similarity correlation network can help regulators target individual regulators from three aspects.First, regulators should concentrate their efforts on financial institutions with high systemic importance and vulnerability, such as China's large four banks, which are inherently more stable.Particularly Minsheng Bank, as it has a high SIFI and SVFI value; even though its systemic vulnerability is higher than that of the Four banks, its ability to resist risk is much lower.In the event of a shock, such financial institutions will increase the likelihood of risk contagion and financial system instability.Second, regulators should be concerned about the financial institutions with a mismatch between systemic importance and systemic vulnerability.One is that financial institutions like Xinhua Insurance, which have significant systemic vulnerability but low systemic importance, should work to increase their ability to resist risks.The other is a financial institution like the Bank of Communications, with great systemic importance but low systemic vulnerability.Losses in this category of financial institutions are more likely to cause risk spillovers to the financial system, and the key to its regulation lies in reducing its level of risk spillovers.Finally, it's worth focusing on the financial institutions with low systemic importance and vulnerability.They cannot significantly affect the stability of the financial system in the short term, but it is crucial to prevent them from endangering it by engaging in risky investment practices themselves.

Time-series characteristics of systemic importance and systemic vulnerability of financial institutions
Through the analysis of cross-sectional characteristics in Sect.4.3, we understand the status of systemic importance and systemic vulnerability of individual financial institutions at the time point.Furthermore, to help regulators understand the trend of risk changes in the financial system over a certain period, so that they can formulate more scientific and reasonable initiatives to prevent and warn financial risks, the time-series characteristics of systemic importance and systemic vulnerability of different financial institutions from 2017 to 2021 will be explored next.Tables 7 and 8 show the results.Overall, the relative systemic importance and systemic vulnerability of different types of financial institutions did not remain constant over the sample period, and the mean values of SIFI and SVFI for banks and insurance companies are consistently higher than for securities firms.Moreover, during the 2018 stock market crash period, the risk spillover from banks and insurance companies to the overall financial system was significantly higher than that of the securities firms, and the risk spillover from the financial system to banks and insurance companies was also significantly higher than that of the securities firms.This is consistent with the findings of Caccioli et al. [44].Consequently, banks are predominantly the most systemically important institutions in different financial systems.
On the other hand, we observe from Table 7 that the mean values of SIFI for banks and securities firms did not change significantly over the sample period and remained largely stable, indicating that the systemic importance of banks and securities firms was relatively stable over the sample period, while insurance companies experienced a small amount of volatility.However, as shown in Table 8, the time-series characteristics of financial institutions' systemic vulnerability exhibit very different characteristics of change from systemic importance.From 2017 to 2018, the systemic vulnerability of banks, insurance companies, and securities firms increased substantially, with banks showing the largest change, while from 2018 to 2019, the systemic vulnerability of banks, securities firms, and insurance companies showed a clear downward trend, and from 2019 to 2021, they exhibited a lower level of systemic vulnerability with minimal change.This indicates that as China  has strengthened its prevention and safeguards against financial systemic risks in recent years, financial institutions have become exposed to lower levels of risk spillovers and the financial system has become relatively more stable.It is also worth noting that the variation tendency in systemic risk under the portfolio similarity correlation channel is similar to the variation tendency in the time-series characteristics of systemic vulnerability.This reflects the fact that systemic risk measured in terms of contagion loss is overwhelmingly a reflection of the vulnerability of financial institutions.As a result, analyzing the systemic importance and systemic vulnerability of financial institutions separately provides a more comprehensive understanding of the evolution of systemic risk.

Conclusions
In this study, we first constructed the portfolio similarity correlation network model and improved the fire sales contagion model to describe the risk contagion mechanism under the portfolio similarity correlation channel.And then we defined risk indicators such as systemic risk, systemically important financial institutions, and systemically vulnerable financial institutions to measure the changes in systemic risk and the systemic importance and vulnerability of financial institutions under the portfolio similarity correlation channel.Finally, we used the balance sheet data of 56 financial institutions from 2017 to 2021 for the empirical study.In the empirical study, we built the portfolio similarity correlation networks of 56 Chinese financial institutions, revealing portfolio similarity correlation and risk propagation among financial institutions.Meanwhile, we also analyzed the cross-sectional and time-series characteristics of the systemic importance and systemic vulnerability of China's financial institutions and explored the relationship between the size of portfolio similarity between financial institutions and other financial institutions and their systemic importance and systemic vulnerability.
In general, this paper draws some useful conclusions.First, we found that the density of the portfolio similarity correlation network among 56 financial institutions in China is high, i.e., there is a strong portfolio similarity association among the 56 financial institutions in the sample period.Among them, banks and insurance companies show a high level of portfolio similarity to each other, while banks and securities firms show a low level of portfolio similarity to each other, and this variability changes over time.Meanwhile, the analysis of the cross-sectional and time-series characteristics of financial institutions' systemic importance and systemic vulnerability reveals that banks and insurance companies have higher systemic importance and securities firms have lower systemic importance during the sample period, as does financial institutions' systemic vulnerability.Especially, the systemic importance and systemic vulnerability of a particular financial institution are strongly and positively associated with the magnitude of portfolio similarity between that institution and others.Also, we found that the systemic risk indicator set from the contagion loss is overwhelmingly a reflection of the vulnerability of financial institutions.Therefore, it is necessary to analyze systemic risk in terms of both systemic importance and systemic vulnerability.In addition, a thorough analysis of the cross-sectional and timeseries characteristics of these two aspects will assist government regulators in developing more scientific and rational regulatory policies.In addition, it would be interesting to expand the study to a wider time period, and to a wider range of financial institutions, and we will be working on this in future studies.

Figure 1
Figure 1 Portfolio similarity association network of financial institutions.(Origin from Barucca et al. (2021)) The yellow nodes represent insurance companies; the blue nodes represent securities firms and the orange nodes represent banks

Figure 2
Figure 2 Portfolio similarity correlation network from 2017 to 2021 for 56 financial institutions in China.Figure 2(a) to Fig. 2(e) depict the portfolio similarity correlation network map from 2017 to 2021, with orange nodes representing banks, yellow nodes representing insurance companies, and blue nodes representing securities firms, and the thickness of the connected edges reflecting the magnitude of portfolio similarity between financial institutions.Note that the names of financial institutions in Fig. 2 are represented by their English abbreviations, and the specific correspondence is shown in the Appendix

Figure 2 (
Figure 2 Portfolio similarity correlation network from 2017 to 2021 for 56 financial institutions in China.Figure 2(a) to Fig. 2(e) depict the portfolio similarity correlation network map from 2017 to 2021, with orange nodes representing banks, yellow nodes representing insurance companies, and blue nodes representing securities firms, and the thickness of the connected edges reflecting the magnitude of portfolio similarity between financial institutions.Note that the names of financial institutions in Fig. 2 are represented by their English abbreviations, and the specific correspondence is shown in the Appendix

Figure 2
Figure 2 Continued

Figure 3 Figure 4
Figure 3 Systemic risk under changes in parameter q

Table 1
Descriptive statistics table of the data

Table 2
The change in average portfolio similarity between the same types of financial institutions

Table 3
The change in average portfolio similarity between different types of financial institutions

Table 5
Cross-sectional characteristics of the systemic importance of 56 financial institutions

Table 6
Cross-sectional characteristics of systemic vulnerability of 56 financial institutions

Table 7
Time-series characteristics of systemic importance of different financial institutions from 2017 to 2021

Table 8
Time-series characteristics of systemic vulnerability of different financial institutions from 2017 to 2021