Systemic risk of China's financial system : 2007-2018 : a comparison between CoVar, MES and SRISK across banks, insurance and securities firms

China's stock market crash in 2015 aroused scholarly attention on financial systemic risk in China. Using data on China's stock market from January 5, 2007 to September 28, 2018, this study calculated three different measures of systemic risk, i.e., temporal fluctuation of financial institutions' contribution to systemic risk (CoVaR), sensitivity of financial institutions to systemic risk (MES) and long-run expected capital shortfall (SRISK), to assess the formation, occurrence, and consequences of systemic risk in China. The results show that Δ CoVaR and MES exhibited an abnormal rise during the outbreak of the 2008 global financial crisis and the 2015 domestic stock market crash, whereas SRISK showed a steady increase throughout the observation window, indicating China's ever-growing SRISK despite the CoVaR and MES. More importantly, regardless of temporal fluctuation, (1) the vast majority of systemic risk comes from banks, followed by insurance firms, which is shown by the institutions' ranking in terms of Δ CoVaR; (2) securities firms followed by insurance firms are exposed to more systemic risk as indicated by short-run expected equity loss (i.e., MES); and (3) banks accumulate more SRISK than any other financial institution. The findings suggest that, in the event of a severe Chinese financial crisis, likely banks will endure the greatest amount of capital shortfall, whereas securities firms will suffer more short-run loss proportionally and thus risk a higher probability of bankruptcy. We conclude with a comparison of systemic risk in financial systems between China and the USA and policy implications.

Keywords: Systemic risk; China; financial institutions; CoVaR; MES; SRISK

Introduction

A financial crisis occurred in the United States in 2007 and spread to global financial markets and other economic sectors. After the outbreak of the crisis, relevant international organizations, national supervisory authorities and scholars conducted in-depth research on the formation and occurrence of the financial crisis, and the external characteristics of financial institutions' risks were widely recognized to harm the stability and security of financial systems. This situation will lead to a series of financial regulatory issues (Basel Committee on Banking Supervision, [9], [10]; Acharya, Philippon, Richardson, & Roubini, [1]; Zhou, [39]) and could theoretically explain the reasons for the risk externalities of financial institutions (Allen & Gale, [8]; Acharya & Yorulmazer, [4]; Brunnermeier & Pedersen, [16]; Diamond & Rajan, [20]; Pedersen, [33]).

The externality of financial institution risk means that a single financial institution increases its profits by expanding its balance-sheet and off-balance-sheet business scale and leverages and controls its own risks through financial innovation; however, the risks within the entire financial system do not simply disappear but are instead transferred and redistributed. Thus, the health of a single financial institution does not necessarily mean that the entire financial system is safe (Borio, [12]). The degree of association between financial institutions is constantly increasing and becoming increasingly complicated through various ties. Once a single financial institution is in crisis, its individual risks will be rapidly transmitted through relationships of assets and liabilities, the irrational herd effect of investors and market expectations. Subsequently, other financial institutions will further magnify the external influence of the financial institutions' risks and may even cause catastrophic damage and huge systemic losses to the entire financial system and seriously jeopardize the sound and smooth operation of the entire economic society (Allen & Gale, [7]). The traditional financial supervision of individual financial institutions has made it difficult to monitor the systemic risk of such financial institutions. After the crisis, Adrian and Brunnermeier ([5]) proposed the Conditional Value-at-Risk indicator (CoVaR), Acharya, Pedersen, Philippon, & Richardson ([3]) proposed the new monitoring indicators Systemic Expected Shortfall (SES) and Marginal Expected Shortfall (MES), and Brownlees and Engle ([15]) proposed the Systemic Risk Measure (SRISK). All of these indicators are intended to reflect this newly exposed systemic risk of financial institutions.

Due to the reform and opening-up that began in 1978, China's financial industry achieved rapid development. By the end of 2017, the total assets of China's banking industry, insurance industry, securities industry and trust industry reached 245 trillion yuan, 16.64 trillion yuan, 6.14 trillion yuan, and 25 trillion yuan, respectively. Moreover, in recent years, with changes in the international financial environment and the deepening of China's domestic financial reforms, the trend of China's financial industry shifting from a separate business model to a mixed business model has become more apparent and resulted in the establishment of a number of comprehensive financial holding groups represented by CITIC, Ping An, and China Merchants, whose business scopes cover the major financial sectors: banking, insurance, securities and trusts. In addition, the continuous innovation of financial products and the gradual relaxation of supervision and financing channels have made China's financial market more active and created a large number of systemic risks. In short, the expansion of China's financial industry, the continuous innovation of financial products, and the hybridization of financial formats have reduced the threat of risk contagion among financial institutions and increased the impact of potential systemic risk. As such, it is important to assess the systemic risk of China's financial industry from a holistic perspective (Ding and Tay, [21]).

Derbali ([18]) uses the SRISK indicator to measure the systemic risk of Chinese financial institutions after 2008. This indicator reflects the expected size of a financial institution's crisis when a system crisis occurs and reflects the ability of financial institutions to act as a firewall in the event of a financial crisis. However, when a financial institution itself has a crisis, it may trigger a systemic financial crisis. The CoVaR indicator measures this risk. Based on Chinese stock market and bond market data after January 5, 2007, this paper uses three systemic risk indicators,

Graph

$\Delta$ CoVaR, MES and SRISK, to measure the systemic risk of Chinese financial institutions. This paper ranks the risks of financial institutions, discusses the size of the systemic risk of banks, insurance companies and securities companies in China, and notes the differences in systemic risk in various industries during crisis and non-crisis periods.

The study finds that

Graph

$\Delta$ CoVaR and MES exhibited an abnormal rise during the outbreak of the 2007–2009 global financial crisis and the 2014–2016 domestic stock market crash, whereas SRISK witnessed a steady increase throughout the observation window, indicating China's ever-growing SRISK despite the temporal fluctuation of financial institutions' contribution to systemic risk (

Graph

$\Delta$ CoVaR) and the sensitivity of financial institutions to systemic risk (MES). More importantly, regardless of temporal fluctuation, (1) the vast majority of the systemic risk comes from banks, followed by insurance firms, as shown by the ranking of the institutions by

Graph

$\Delta$ CoVaR; (2) securities firms, followed by insurance firms, are exposed to more systemic risk, as indicated by short-run expected equity loss (i.e., MES); and (3) banks accumulate more SRISK than any other financial institution. The findings suggest that, in the event of a severe Chinese financial crisis, likely banks will endure the greatest amount of capital shortfall, whereas securities firms will suffer more short-run loss proportionally and thus risk a higher probability of bankruptcy.

As such, we argue that policy makers should take a holistic approach when monitoring and managing systemic risk of China's financial market, and in particular should establish proactive regulatory measures to address the possibility of the systemic risk accumulating and spilling over from the primary source (i.e., securities and insurance firms) to the ballast of the system (i.e., banks). The establishment of Financial Stability and Development Committee under the State Council of China (国务院金融稳定发展委员会) in 2017 demonstrated the Chinese government's determination to deal with financial mixed operations by enhancing the sharing of information and coordination across the previously divided financial supervisory agencies. A real-time overarching monitoring framework, including the three systemic risk indicators used in this study, will prove to be vital for monitoring and warning against systemic financial risks.

The remainder of this paper is structured as follows. The second section provides a literature review, the third section introduces the theoretical method used in this paper, the fourth section explains the dataset, the fifth section conducts an empirical analysis and discusses the systemic risk rankings of Chinese financial institutions, and the final section concludes the paper.

Literature review

The research on systemic risk focuses primarily on two types of content: the first is the construction of early warning indicators for systemic risk and the other is the problem of systemic risk transfer and size measurement of financial institutions.

Conducting the first type of systemic risk warning research, Illing and Liu ([28]) proposed that the description and measurement of systemic risk status can be achieved by synthesizing the financial stress index. Alessi and Detken ([6]) used data on the 18 Organization for Economic Co-operation and Development (OECD) countries from 1970 to 2007, with 5 real economic variables and 13 financial variables, constructed 89 simple early warning indicators and sorted the indicators to select the most effective early warning indicators. Borio and Drehmann ([13]) selected some indicators from real estate prices, stock prices and credit spread and combined them with the credit index to build three different versions of the indicator signals and then test indicators within and outside the sample.

After the US financial crisis, measurements of systemic risk and financial institutions' contribution to systemic risk have become important components of global financial regulatory reform. In view of the shortcomings of traditional measurement methods, after the crisis broke out, regulators and scholars proposed a series of methods to measure systemic risk and marginal risk contribution of individual financial institutions. These methods can be divided mainly into the following two categories according to data types.

The first category is the network analysis approach, which measures the associated data based on actual assets and liabilities between financial institutions. This approach uses data on inter-bank bilateral mutual assets and liabilities to measure the risk of infection in the system and the degree of systemic risk contribution and relative systemic importance of individual banks to the banking sector (IMF, BIS, & FSB, 2009) by simulating bank bankruptcy, bankruptcy loss and the difficulty of inducing a systemic crisis caused by single or multiple banks in the banking network system (Degryse & Nguyen, [17]; Mistrulli, [32]; Upper, [37], [38]). In the network analysis method, the actual inter-bank assets and liabilities data are used to estimate the bilateral relationship between banks. Therefore, this method is used mainly to measure the systemic risks of the banking sector, the systemic importance of individual banks, and the contribution to systemic risks. In practice, except for a few countries (Italy, Hungary, Mexico), actual bilateral exposure data between banks are generally difficult to obtain; therefore, the existing research on inter-bank risk contagion mainly uses the maximum entropy method, which analyzes the total interbank assets and liabilities of individual banks to estimate the bilateral relationship between banks (Upper, [37]); however, the difficulty of obtaining data makes the method less useful.

The second type of method is collectively referred to as the reduced-form approach. This approach assumes that financial markets are efficient so that financial market data (including financial institution stock prices, credit default swaps, CDS spreads, etc.) can be used to measure the systemic risk of financial institutions. Such methods have the following advantages. First because the changes in financial institutions' asset prices reflect the market's expectations of their future performance, the adoption of market data is more forward-looking (Duffie, Eckner, Horel, & Saita, [23]; Huang, Hao, & Zhu, [27]; Lehar, [31]); the market data are convenient to obtain, and this method is more time-sensitive. Thus, it can rapidly reflect the changes in the financial sector's systemic risk in the time dimension (Huang et al., [27]; Segoviano & Goodhart, [35]), which is conducive to timely risk control and supervision. Third, financial market data are relatively easy to obtain, which makes them conducive to researching and applying such indicators. Therefore, after the US financial crisis, systemic risk measurement methods based on public financial market data, such as financial institutions' stock returns, have been widely favored by academic circles and regulatory authorities.

The simple method can be divided into two types: The first measures the systemic risk of the financial sector by examining the correlation change in the financial institution's stock return rate as performed by Huang et al. ([27]). Although this method can identify systemic risk changes, it is difficult to measure a single financial institution's degree of risk contribution to the entire financial system or other financial institutions. The second method measures the systemic risk and the financial institution's contribution to the entire financial system or other financial institutions (or risk spillover) mainly through the statistical tail behavior of the financial institution's asset returns. It can also be divided into "top-down" and "bottom-up" analysis methods (Drehmann & Tarashev, [22]).

The "top-down" analysis first derives systemic risk and then assigns this systemic risk to a single financial institution through a distribution method. For example, Acharya et al. ([3]) proposed the SES and MES methods based on the Expected Shortfall (ES). SES and MES measure all losses beyond the threshold (the α quantile of the loss distribution) and have additive properties, which take into account the influence of financial institutions' leverage on systemic risk as well as the contribution of financial institutions to the marginal risk. Based on the microeconomic theory model and extreme value theory, these indicators prove that financial institutions' contribution to the marginal risk of the overall system during a systemic financial crisis can be predicted by the MES and leverage ratio of financial institutions during a period with no financial crisis (Acharya et al., [3]). More importantly, this method is in good agreement with the macroprudential supervision theory. The regulatory authorities can effectively regulate financial institutions that have a high contribution to marginal risk and high leverage and thus achieve the regulatory purpose of reducing systemic risks and preventing the outbreak of financial crises. Therefore, the SES and MES methods have been widely praised by scholars (Brownlees & Engle, [15]; Tarashev, Borio, & Tsatsaronis, [36]). MES focuses on the rate of return rather than the actual deficient amount. Based on this aspect, Brownlees and Engle ([15]) proposed the SRISK systemic risk measurement method for financial institutions. This indicator measures the risk of capital shortage in a single financial institution when a financial crisis occurs. Since then, many scholars have used this indicator to measure the systemic risk of financial institutions in various countries. For example, Derbali, Hallara, and Sy ([19]), Derbali ([18]), and Acharya, Engle, and Richardson ([2]) use the SRISK index to assess the degree of systemic risk contribution of Greek, Chinese and American financial institutions.

The "bottom-up" analysis estimates the systemic risk of the entire financial system when a single financial institution goes bankrupt. The main representative of such methods is the Conditional Value at Risk (CoVaR), which was proposed by Adrian and Brunnermeier ([5]) based on the Value at Risk indicator (VaR). CoVaR measures a financial institution's contribution to the overall systemic risk and reflects the risk spillover effects across the financial network (Adrian & Brunnermeier, [5]). Of course, as a systemic risk metric, CoVaR also has certain limitations. Because CoVaR measures the systemic risk and the marginal risk contribution of a single financial institution, similar to VaR, only the α quantile of the loss distribution is considered; thus, the tail risk in extreme cases below the CoVaR threshold cannot be well captured. The CoVaR indicator itself is not additive, which increases the difficulty of estimating the systemic risk faced by the entire financial system through the aggregated risk contribution of individual financial institutions (Adrian & Brunnermeier, [5]; Gauthier, Lehar, & Souissi, [24]).

The "top-down" and "bottom-up" approaches measure the degree of loss of a single financial institution in the event of a systemic risk and the likelihood of a systemic risk occurring at the risk of a single institution, respectively. The former assesses the "fire retardance" of financial institutions, while the latter assesses the "combustibility" of financial institutions. As such, we posit that the combination of the two can provide an integrative description of systemic risk and help reveal the formation, occurrence, and consequences of financial system systemic risk. In this study, we analyze the systemic risk of China's financial system (2007–2018) by comparing ΔCoVaR, MES and SRISK across China's banks, insurance firms and securities firms.

Econometric methodology

Definition and estimation of CoVaR

In 2009, the first draft of Adrian and Brunnermeier ([5]) introduced CoVaR to capture systemic risk. Boyle and Kim ([14]) proposed the generalized Co-Conditional Tail Expectation (

Graph

$\mathit{CoCTE}$ ) risk measure, which is relatively new and considered a good evaluator of risk because it is a coherent risk measure. However, the

Graph

$\mathit{VaR}$ has been used for a wide range of risks, which increases the wide applicability of CoVaR, albeit incoherently. We follow the contribution by Adrian and Brunnermeier ([5]) to analyze the systemic risk derived by individual institutions in China's financial market.

To emphasize the systemic nature of the risk measure, Adrian and Brunnermeier ([5]) add to existing risk measures the prefix "Co", which stands for conditional, contagion, or co-movement. This measure focuses primarily on CoVaR, where the institution's CoVaR relative to the system is defined as the VaR of the whole financial sector conditional on the institution being in distress. The difference between the CoVaR conditional on the distress of an institution and the CoVaR conditional on the "normal" state of the institution is ΔCoVaR, which captures the marginal contribution of a particular institution (in a non-causal sense) to the overall systemic risk.

We focus on ΔCoVaR as a measure of systemic risks, and it presents several advantages. First, ΔCoVaR focuses on the contribution of each institution to overall system risk, while traditional risk measures focus on the risk of individual institutions. Moreover, regulation based on the risk of institutions in isolation can lead to excessive risk-taking along systemic risk dimensions. Another merit is that ΔCoVaR is generally sufficient to study the risk spillovers from institution to institution across the whole financial network.

There are several possible methods of measuring CoVaR. Here, we primarily use quantile regressions because of their simplicity and efficient use of data. We also provide a time-varying estimation of CoVaR with macro state variables. The specific methodologies of these estimations are presented in the appendices, and the detailed descriptions of macro state variables are described in the next section.

Definition and estimation of MES

MES measures a firm's equity loss conditional on the event of a market decline (Brownlees & Engle, [15]). There are two standard measures of firm-level risk: VaR and ES, both of which seek to measure the potential loss incurred by the firm as a whole in an extreme event (Acharya et al., [3]). MES is defined as the expected equity loss invested in a particular financial institution if the overall market declines by a certain amount, and it measures the marginal contribution of an institution i to systemic risk, measured by the ES of the system.

According to Brownlees and Engle, the MES can then defined as the partial derivative of the system's ES with respect to the weight of a firm i in the economy. Therefore, to estimate this measure, we need to first estimate ES. The detailed estimation via the DCC-GARCH model is presented in the appendices.

Definition and estimation of SRISK

The SRISK index of an individual firm measures the expected capital shortage a financial firm would suffer in case of a substantial market decline over a given time period, which is subject to the firm's degree of leverage, its size and its equity loss conditional on a market decline (i.e., MES) (Brownlees & Engle, [15]). Moreover, this index measures the systemic risk contribution of a financial institution as well as the aggregate systemic risk of the whole financial system (Brownlees & Engle, [15]).

SRISK is simply given by the capital shortfall, which tells us how much capital the firm needs to add if other crises were to happen. In this perspective, the firms with the largest capital shortfall are assumed to be the greatest contributors to the crisis and the most systemically risky. Because the numerical definition of SRISK is associated with LRMES, which is closely related to MES, we also apply a DCC-GARCH model to the estimation of SRISK. These definitions and estimations are also available in the appendices.

Here, we notice again the differences between CoVaR (or ΔCoVaR) and SRISK.

Graph

$\mathit{CoVaR}$ represents the risk contribution of a certain firm to the system and measures the overall systemic risk when an individual institution breaks down, which is apparently the "bottom-up" analysis. Meanwhile, SRISK is a "top-down" method of analyzing systemic risk, which measures the risk of an individual firm when the overall system suffers a financial crisis. We take these two indicators into consideration to examine the systemic risks of China's financial market more comprehensively.

Data

This paper aims to assess the systemic risk of the Chinese financial market from January 5, 2007 to September 28, 2018, with CoVaR, MES and SRISK representing the three indices of systemic risk. The study sample includes all 43 financial institutions that were publicly listed on either the Shanghai Stock Exchange or the Shenzhen Stock Exchange before January 1, 2007, including 16 banks, 4 insurance companies and 23 security companies (see Table 1 for a complete list of the financial institutions included in the study). The primary dataset is the daily return of the 43 Chinese financial institutions as well as the daily return of the Chinese stock market, which was extracted from the China Stock Market and Accounting Research Database (CSMAR). In addition, we obtained the financial statements of the 43 financial institutions from the RESSET database as well as other data on the financial market (e.g., the three-month treasury bill rate, credit spreads, etc.) from the Wind database.

Table 1. Summary statistics of Chinese financial institutions.

	Returns	Market Capitalization (millions)
	Mean	Std. Dev	Max	Min	Mean	Std. Dev	Max	Min
Bank
Ping An Bank	0.00076	0.02582	0.19617	−0.10020	107.15	53.28	259.27	25.41
Bank of Ningbo	0.00099	0.03640	1.40544	−0.10016	44.34	21.25	109.61	15.00
Pudong Development Bank	0.00066	0.02415	0.10031	−0.10026	221.56	86.15	400.66	62.33
Hua Xia Bank	0.00067	0.02507	0.10070	−0.10048	80.06	27.46	158.06	28.81
China Minsheng Bank	0.00050	0.02229	0.10101	−0.10000	185.32	60.65	317.09	73.22
China Merchants Bank	0.00073	0.02300	0.10026	−0.10007	308.63	124.72	719.74	134.30
Bank of Nanjing	0.00074	0.02668	0.72182	−0.10013	37.72	17.66	87.11	13.90
Industrial Bank	0.00081	0.02553	0.38799	−0.10020	219.82	83.13	403.23	58.60
Bank of Beijing	0.00049	0.02680	0.81440	−0.10013	97.91	31.09	164.92	41.60
Agricultural Bank of China	0.00049	0.01417	0.10122	−0.09899	892.16	147.58	1396.76	673.39
Bank of Communications	0.00037	0.02466	0.71392	−0.10058	211.23	57.78	435.88	108.13
Industrial and Commercial Bank	0.00032	0.01751	0.10053	−0.10043	1233.80	248.55	2218.51	854.64
China Everbright Bank	0.00045	0.01867	0.18065	−0.09917	144.07	29.76	253.99	93.16
China Construction Bank	0.00043	0.01931	0.32248	−0.10094	51.55	12.49	101.88	33.12
Bank of China	0.00020	0.01751	0.10164	−0.10040	719.93	166.59	1330.09	479.57
China CITIC Bank	0.00052	0.02961	0.96035	−0.10025	182.93	47.70	334.76	106.91
Insurance
Ping An Insurance	0.00089	0.02585	0.38432	−0.10004	320.05	164.76	853.18	99.46
New China Life Insurance	0.00088	0.02729	0.13720	−0.10008	82.60	26.80	149.57	40.25
China Pacific Insurance	0.00051	0.02770	0.60567	−0.10007	160.25	47.14	387.39	80.70
China Life Insurance	0.00056	0.03192	1.06197	−0.10007	527.23	205.86	1563.43	268.83
Security
Shenwan Hongyuan	0.00239	0.10397	3.04321	−0.10037	141.22	48.68	295.65	95.33
Northeast Securities	0.00248	0.11888	5.96083	−0.10025	19.24	9.18	52.24	1.63
Guoyuan Securities	0.00135	0.07066	3.26916	−0.10016	29.57	13.69	78.25	3.61
Sealand Securities	0.00216	0.06890	2.57540	−0.10024	18.08	12.55	53.35	0.78
GF Securities	0.00011	0.02697	0.10040	−0.10029	94.37	24.16	182.79	56.29
Changjiang Securities	0.00157	0.07662	3.59313	−0.10042	34.11	16.96	91.29	9.40
Shanxi Securities	0.00044	0.03350	0.70128	−0.10032	26.22	10.16	69.67	12.60
Western Securities	0.00115	0.03624	0.66667	−0.10015	40.40	25.07	114.20	12.50
Guosen Securities	0.00099	0.03271	0.44082	−0.10008	130.38	42.28	284.62	65.27
CITIC Securities	0.00072	0.02895	0.10043	−0.10016	163.42	54.81	386.29	81.84
Sinolink Securities	0.00115	0.04154	1.29621	−0.10032	25.71	14.47	100.50	5.58
Southwest Securities	0.00079	0.02765	0.10039	−0.10027	28.40	14.27	76.94	0.72
Haitong Securities	0.00094	0.03214	0.10050	−0.10019	109.28	44.75	244.54	2.29
Orient Securities	0.00044	0.03266	0.43968	−0.10022	92.41	30.73	216.39	47.85
China Merchants Securities	0.00011	0.02477	0.10039	−0.10013	84.62	33.51	222.45	38.17
The Pacific Securities	−0.00003	0.02959	0.10095	−0.10030	22.94	11.36	69.35	7.64
Dongxing Securities	0.00078	0.03584	0.44009	−0.10015	53.10	13.94	106.27	26.75
Guotai Junan Securities	0.00014	0.02839	0.43988	−0.10017	145.99	23.24	265.50	105.53
Industrial Securities	0.00046	0.02956	0.48600	−0.10048	40.84	16.79	98.23	17.51
Soochow Securities	0.00046	0.02903	0.13077	−0.10027	29.36	14.55	78.81	12.44
Huatai Securities	0.00030	0.02674	0.10038	−0.10022	81.62	29.52	186.42	40.71
Everbright Securities	0.00009	0.02730	0.29981	−0.10005	56.11	20.12	128.72	25.81
Founder Securities	0.00063	0.02925	0.43590	−0.10050	54.80	24.06	135.58	22.33
	Total Liabilities (billions)	Total Assets (billions)
	Mean	Std. Dev	Max	Min	Mean	Std. Dev	Max	Min
Bank
Ping An Bank	1508.66	962.22	3128.04	267.33	1605.31	1036.81	3359.73	274.12
Bank of Ningbo	441.41	294.18	997.30	64.65	468.83	310.97	1062.57	70.17
Pudong Development Bank	3054.32	1616.66	5611.09	671.54	3246.53	1748.27	6032.51	696.74
Hua Xia Bank	1361.69	593.32	2350.42	422.78	1440.28	645.12	2527.18	434.58
China Minsheng Bank	2807.37	1573.43	5449.41	676.63	2989.72	1687.74	5833.69	696.48
China Merchants Bank	3219.23	1504.94	5650.55	903.16	3448.61	1636.24	6140.41	959.40
Bank of Nanjing	476.29	353.33	1127.12	68.49	507.60	373.06	1200.51	78.03
Industrial Bank	3058.45	1815.68	5957.74	639.91	3241.94	1943.23	6387.64	664.57
Bank of Beijing	1119.71	621.51	2290.45	304.09	1202.64	664.38	2474.53	330.49
Agricultural Bank of China	10673.81	7087.84	20640.52	421.41	11398.56	7573.01	22237.32	485.05
Bank of Communications	5024.01	2002.91	8355.18	1867.59	5387.33	2183.64	9007.13	1975.50
Industrial and Commercial Bank	15379.11	4888.26	23958.65	7214.27	16565.23	5417.59	26098.19	7694.96
China Everbright Bank	4174.45	2453.00	9730.78	1406.79	4452.99	2608.55	10324.43	1487.50
China Construction Bank	12802.49	4672.47	20519.11	5040.88	13788.53	5118.29	22366.20	5464.46
Bank of China	10752.02	3471.36	16606.74	5040.88	11591.09	3795.72	17999.80	5464.46
China CITIC Bank	2871.60	1556.43	5161.79	0.60	3078.35	1666.05	5534.50	0.86
Insurance
Ping An Insurance	641.97	754.98	3555.88	6.78	794.81	760.57	3830.36	133.49
New China Life Insurance	3376.44	4321.82	12150.57	12.50	3597.68	4584.52	12876.08	21.25
China Pacific Insurance	262.69	225.01	739.57	0.74	351.23	232.88	909.92	87.22
China Life Insurance	1595.66	628.35	2714.41	609.15	1825.71	691.12	3040.68	722.83
Security
Shenwan Hongyuan	4.14	8.75	49.66	0.02	17.25	24.72	78.04	0.80
Northeast Securities	23.88	19.92	64.85	0.06	30.82	24.21	75.10	0.54
Guoyuan Securities	18.68	14.12	52.61	0.20	32.59	19.33	71.01	0.61
Sealand Securities	16.48	18.62	53.04	0.18	21.76	23.78	67.42	0.39
GF Securities	111.87	108.63	358.36	0.08	146.26	134.34	427.67	0.35
Changjiang Securities	36.97	28.89	101.52	3.37	49.51	35.01	117.39	2.74
Shanxi Securities	439.88	630.18	1977.81	5.59	462.41	652.47	2080.10	11.68
Western Securities	686.34	837.13	2581.94	0.01	723.05	876.72	2734.81	1.11
Guosen Securities	722.43	810.80	2581.94	0.01	768.90	844.09	2734.81	1.11
CITIC Securities	186.48	115.37	418.94	52.16	267.02	137.88	527.58	84.06
Sinolink Securities	13.35	10.74	43.77	1.72	21.27	16.63	59.50	2.38
Southwest Securities	20.12	18.44	64.01	0.53	30.87	24.50	81.67	0.55
Haitong Securities	120.71	90.98	362.17	0.28	182.96	117.03	459.95	1.19
Orient Securities	118.37	123.25	729.62	43.55	145.65	126.10	763.49	68.14
China Merchants Securities	133.49	129.22	729.62	43.55	167.06	136.34	763.49	68.14
The Pacific Securities	73.26	206.54	816.53	1.96	80.71	214.68	854.48	3.40
Dongxing Securities	5226.89	6069.68	15239.81	34.78	5558.42	6421.87	16315.36	53.37
Guotai Junan Securities	5622.33	6170.07	15928.77	195.79	6000.26	6516.74	17048.73	297.08
Industrial Securities	3081.24	4516.33	12150.57	12.09	3284.74	4790.70	12876.08	20.77
Soochow Securities	194.18	211.09	739.57	6.96	236.96	250.97	909.92	14.48
Huatai Securities	1465.59	2622.12	8374.26	31.06	1599.27	2786.47	8872.13	47.93
Everbright Securities	1415.82	2646.56	8374.26	24.13	1535.22	2817.85	8872.13	46.40
Founder Securities	3283.72	4095.72	10880.73	10.50	3516.43	4353.81	11628.82	24.61

The assets and liabilities in Table 1 show that the bank sector accounts for the largest proportion of the financial industry while security companies account for the smallest proportion. However, few Chinese insurance firms have been listed, which increases the difficulty of drawing certain absolute conclusions. As for the returns, security companies generally have higher returns than the other two sectors, although some of them also suffer relatively low or even negative returns. The volatility of the returns of the security sector is higher than others due to the characteristic of their businesses.

To calculate CoVaR, the macro state variables should be carefully selected. Following Adrian and Brunnermeier ([5]), the risk factors we selected for

Graph

$M_t$ are as follows.

• Real Estate Index (RESI). The real estate index is used to measure changes in real estate prices. With March 1, 2013 as the cutoff point, the previous stock exchange index code is 399200 and the subsequent index code is 399241. We select the index daily logarithmic rate of return as the data sample.
• Volatility (VIX). Generally, the implied volatility is calculated from options that expired at approximately 30 days, thus reflecting the investor's volatility (risk) expectations for the next 30 days. Since the volatilities we extracted from RESSET are calculated from historical data, we choose the daily volatility of logarithmic returns based on the GARCH model of the CSI 300.
• Three-month Treasury Bill Rate (TBR3M). We use the rate of return of the three-month treasury bill announced by Chinabond (www.chinabond.com.cn/).
• Liquidity Spread (LIQSPR). Adrian and Brunnermeier ([5]) measure LIQSPR by the yield spread between the ten-year treasury rate and the three-month bill rate. We choose to use the spread between China's 3-month treasury bill yield and SHIBOR 7-day repo rate as the liquidity spread.
• Credit Spread (CRESPR). Here, we use the spread between the 1-year AAA corporate bond yield and the 1-year government bond yield.
• Yield Spread (YIESPR). We indicate this factor by the spread between 10-year and 3-month government bill yields.

Table 2 provides the summary statistics of the above six macro state variables. This table shows that RESI has the highest volatility with a standard variance of 0.0228. The average LIQSPR is negative, which represents that higher liquidity usually brings higher returns.

Table 2. Summary statistics of macro state variables.

	Mean	Std. Dev	Max	Min
RESI	0.0005	0.0228	0.0997	−0.0961
VIX	0.0168	0.0077	0.0410	0.0060
TBR3M	0.0258	0.0079	0.0511	0.0080
CRESPR	0.0119	0.0039	0.0269	0.0043
LIQSPR	−0.0034	0.0078	0.0164	−0.0652
YIESPR	0.0112	0.0065	0.0263	−0.0148

When estimating SRISK, we need to know the liability and market capitalization of the individual institutions. We obtain the liabilities from firms' seasonal financial reports and assume that the liabilities of any day in a season are the same and equal to the average of the liabilities at the end of the last season and the end of this season. Regarding market capitalization, we consider the daily data on the total stock market value of each institution.

Empirical findings

The study aims to use the three systemic risk measures, i.e., CoVaR, MES, and SRISK, to analyze the Chinese financial market and its systemic risks over time, the differences across financial industries, and the divergent implications of the three measures. Figures 1–4 show the changes in China's financial systemic risk over time as indicated by the arithmetic average of the systemic risks of 43 financial institutions in the three measures. We focus on two special time periods: the 2007–2009 financial crisis and the 2014–2016 China stock market crash. The results showed that ΔCoVaR and MES were both high during these two periods, which is in line with our expectations: when the entire financial system suffers a shock, the risks faced by financial institutions increase. However, SRISK presents no obvious volatility during these periods, although it shows continuous growth, which may be due to the close relationship between SRISK and the financial institutions' liabilities and market capitalization, and the continuous expansion of financial institutions also increases their risk capital.

Graph: Figure 1. CoVaR of the Chinese financial institutions (1/5/2007 – 9/30/2018).

Graph: Figure 2. ΔCoVaR of the Chinese financial institutions (1/5/2007 – 9/30/2018).

Graph: Figure 3. MES of the Chinese financial institutions (1/5/2007 – 9/30/2018).

Graph: Figure 4. SRISK (￥billions) of the Chinese financial institutions (1/5/2007 – 9/30/2018).

Next, we split the sample time into four time periods representing the financial crisis period, the stationary period, the Chinese stock market crash period and the recent period: 2007 to 2009, 2010 to 2013, 2014 to 2016, and 2017 to 2018, respectively. For each time period, we examine the average of the three systemic risk indicators of the banking sector, the insurance sector and the security sector in this interval.

In Figures 5–7, we report the fluctuation of Chinese financial institutions measured by ΔCoVaR, MES and SRISK, respectively, during the period from 2007 to 2009, namely the financial crisis period. The results show that both ΔCoVaR and MES showed an increase trend in 2008, which was a proof of the increasing systemic risks during the financial crisis. For a comparison among the three financial sectors, the banking sector suffered most of the systemic risks and accounted for most of them as well. However, when we focus on SRISK, we cannot find obvious volatility and the banking sector showed the highest SRISK, which was quite different from the other two measures. This difference may result from the sharp increase of the magnitude of Chinese banks during that period.

Graph: Figure 5. ΔCoVaR of the Chinese financial institutions (1/5/2007 – 12/31/2009).

Graph: Figure 6. MES of the Chinese financial institutions (1/5/2007 – 12/31/2009).

Graph: Figure 7. SRISK of the Chinese financial institutions (1/5/2007 – 12/31/2009).

In Figures 8–10, we report the fluctuation of Chinese financial institutions measured by ΔCoVaR, MES and SRISK respectively, during the stationary period from 2010 to 2013. In this time interval, ΔCoVaR and MES were relatively steady. ΔCoVaR indicates that the banking sector played an important role in the contribution of systemic risks, while MES shows that the security sector was the most systemically risky. At the same time, SRISK grew steadily and the banking sector still presented the highest SRISK, followed by the insurance sector.

Graph: Figure 8. ΔCoVaR of the Chinese financial institutions (1/1/2010 – 12/31/2013).

Graph: Figure 9. MES of the Chinese financial institutions (1/1/2010 – 12/31/2013).

Graph: Figure 10. SRISK of the Chinese financial institutions (1/1/2010 – 12/31/2013).

In Figures 11–13, we show the fluctuation of Chinese financial institutions measured by ΔCoVaR, MES and SRISK, respectively, during the Chinese stock market crash period from 2014 to 2016. It is obvious that ΔCoVaR and MES significantly increased in 2015, when the Chinese stock market suffered greatly. Similar to the stationary period, the banking sector showed the highest ΔCoVaR while the MES of the security sector varied most dramatically. Both ΔCoVaR and MES indicated that these three sectors had similar fluctuating trends. However, the SRISK of the banking sector continued to increase, the insurance sector varied in 2014 and then remained stable, and the security sector showed a significant increase in 2015. Therefore, the security companies in China may suffer the most systemic risks when there is negative turbulence in the stock market.

Graph: Figure 11. ΔCoVaR of the Chinese financial institutions (1/1/2014– 12/31/2016).

Graph: Figure 12. MES of the Chinese financial institutions (1/1/2014– 12/31/2016).

Graph: Figure 13. SRISK of the Chinese financial institutions (1/1/2014– 12/31/2016).

In Figures 14–16, we report the recent fluctuations of the Chinese financial institutions measured by ΔCoVaR, MES and SRISK respectively, from 2017 to 2018. The results show that all three measures went through steady fluctuations because a severe crisis was not observed over the past two years. We focus on the sector differences in this interval. The ΔCoVaR results showed that the insurance sector seemed to bear the same systemic risk as the banking sector, which is quite different from the previous periods. As for the MES, the security sector had more obvious variations and was considered the most systemically risky. The changes in SRISK remained the same, where banks still suffered the most systemic risks because of their huge liabilities and market capitalizations.

Graph: Figure 14. ΔCoVaR of the Chinese financial institutions (1/1/2017– 9/28/2018).

Graph: Figure 15. MES of the Chinese financial institutions (1/1/2017– 9/28/2018).

Graph: Figure 16. SRISK of the Chinese financial institutions (1/1/2017– 9/28/2018).

All of these variations are visually represented in Table 3 and Figures 17–19, which shows that 2015 witnessed a distinct increase in all three measures of systemic risk, thus indicating that the domestic financial crush could impact greatly on financial institutions. In contrast, although ΔCoVaR and MES reacted sensitively to the global financial crisis in 2009, the variation was relatively slight compared to that in 2015.

Graph: Figure 17. ΔCoVaR of the Chinese financial institutions (1/5/2007– 9/28/2018).

Graph: Figure 18. MES of the Chinese financial institutions (1/5/2007– 9/28/2018).

Graph: Figure 19. SRISK of the Chinese financial institutions (1/5/2007– 9/28/2018).

Table 3. Systemic risk measures of Chinese financial institutions (2007–2018).

	ΔCoVaR	MES	SRISK
	Financial	Banking	Insurance	Security	Financial	Banking	Insurance	Security	Financial	Banking	Insurance	Security
2007	0.0172	0.0195	0.0191	0.0152	0.0206	0.0262	0.0288	0.0153	133.80	79.06	12.124	0.328
2008	0.0153	0.0194	0.0178	0.0120	0.0089	0.0256	0.0222	−0.0050	143.32	143.25	30.110	0.865
2009	0.0173	0.0227	0.0218	0.0128	0.0312	0.0376	0.0362	0.0258	173.81	174.72	36.184	0.568
2010	0.0141	0.0171	0.0150	0.0119	0.0238	0.0298	0.0274	0.0190	173.72	209.76	44.653	1.407
2011	0.0140	0.0155	0.0135	0.0130	0.0287	0.0251	0.0243	0.0319	182.95	299.91	54.733	1.590
2012	0.0140	0.0134	0.0178	0.0137	0.0285	0.0217	0.0258	0.0337	191.39	349.55	89.942	1.358
2013	0.0166	0.0181	0.0180	0.0154	0.0398	0.0311	0.0344	0.0468	202.54	399.07	54.887	1.372
2014	0.0144	0.0162	0.0148	0.0131	0.0285	0.0282	0.0295	0.0285	221.32	439.51	47.055	2.255
2015	0.0278	0.0302	0.0273	0.0261	0.0596	0.0425	0.0508	0.0729	249.85	480.91	68.380	6.031
2016	0.0177	0.0174	0.0189	0.0176	0.0482	0.0244	0.0376	0.0667	209.91	536.95	55.455	9.263
2017	0.0116	0.0122	0.0128	0.0109	0.0218	0.0092	0.0146	0.0318	235.51	606.12	61.183	8.015
2018	0.0127	0.0136	0.0166	0.0114	0.0177	0.0157	0.0211	0.0185	247.54	636.91	64.627	8.486

Conclusions and discussion

This paper aims to use the data on China's financial market from January 5, 2007 to September 28, 2018 to describe the different influences on the formation, occurrence, and consequences of the financial system of Chinese financial institutions from three aspects: ΔCoVaR, MES and SRISK. Among these, ΔCoVaR reflects the impact of the loss of a single financial institution on the entire financial system, which is a "bottom-up" analysis; and MES and SRISK reflect the effects of risks of the system to a single financial institution when the entire financial system is in crisis, which is a "top-down" analysis. These three indicators have different meanings, although they can measure systemic risk to a certain extent and are widely used in the study of systemic risk.

First, we observe the changes in the systemic risk of Chinese financial institutions over the past 11 years. Our research focuses on two special time periods within the sample interval: before and after the 2008 global financial crisis and during the 2015 China stock market crash. For the Chinese financial market, the former is affected by the external financial system risk while the latter is affected by the domestic financial crisis risk. Through the study of these two time periods, we can also explore whether the systemic risks faced by Chinese financial institutions are related to the internal and external nature of the financial crisis. The results show that ΔCoVaR and MES have obvious fluctuations during the financial crisis, which can reflect that financial institutions are facing greater risk during the crisis, while

Graph

$\mathit{SRISK}$ gradually increases with time and cannot intuitively observe the crisis, which may because SRISK is closely related to the financial institution's liabilities and market capitalization. In the past decade, China's financial institutions have experienced a period of rapid development. Their assets, liabilities, and market capitalization are constantly growing; thus, their risk exposure is also increasing. Therefore, although ΔCoVaR and MES exhibited abnormal increases during the outbreak of the 2007–2009 global financial crisis and the 2014–2016 domestic stock market crash, SRISK witnessed a steady increase throughout the observation window, indicating China's ever-growing SRISK despite the ΔCoVaR and the sensitivity of MES.

Second, for each time period, we consider the differences among the various Chinese financial sectors in accordance with the systemic risk during that time period. For each interval, we show the simple average of the financial risk indicators of the financial institutions in each sector. According to these figures, we obtained the following results. (1) With ΔCoVaR as the standard, during the 2008 financial crisis and the 2015 stock crush, banks ranked first and insurance companies ranked second, while at other times, particularly the recent two years, the systemic risk of insurance companies was higher. (2) With MES as the standard, we find that banks ranked first and the insurance sector ranked second from 2007 to 2009, which is similar to the results for ΔCoVaR. However, starting in 2010, the systemic risk of security companies witnessed the highest rank among the three sectors while the insurance sector had ranked second until 2016 and replaced by the banking sector in 2017. We speculate that in recent years, the income structure of the security industry has shifted slightly to the "heavy assets" business, such as capital intermediation and investment, which has led to an increase in the size of security companies, an increase in capital demand, and an increase in demand for leverage. Security companies have diversified into the banking and insurance sectors by offering many new financial products, which makes the business relationship between securities companies and other financial institutions very close and further increases the systemic risk of securities companies. (3) With SRISK as the standard, we find that banks always occupy the top position followed by insurance companies because SRISK is closely related to the financial institutions' liabilities and market value while banks and insurance companies are larger than securities companies.

The findings suggest that banks are the primary source of systemic risk in China and will be burdened with the greatest capital shortfall in the event of a severe financial crisis in the future. The securities companies are more sensitive to fluctuations of the stock market, and the insurance companies may play a more important role in systemic risks as time passes.

The results as found in this study point to the similarities and differences between China and the USA in terms of the systemic risks of their financial systems. As Brownlees and Engle ([15]) found, similar to China, the US banking sector scored much higher than the insurance and security sectors in terms of SRISK after the 2008 financial crisis, which means that in the event of a severe financial crisis, either in China or the USA, banks will suffer more capital shortfall. However, prior to the 2008 financial crisis, in the USA, the capital shortfall risk in the banking sector is nearly neglectable while brokers and dealers, such as Lehman Brothers, were exposed to such risk. The bankruptcy of Lehman Brothers during the crisis fundamentally shifted the systemic risk burden from security firms to banks in the USA. Additionally, the SRISK of the US banking sector experienced a decline after 2009 and was roughly the same in 2013 as the insurance and security sectors combined, although in China, the SRISK of the banking sector continued increasing and is at least a few times greater compared with the other two sectors. This finding indicates that the banking sector of China's financial sector is the primary reservoir in the event of a financial crisis, whereas the banking sector in the USA is less burdened with such a systemic risk.

In terms of the source of the systemic risk, the banking sector in the USA exhibited a higher ΔCoVaR than both the insurance and security sectors prior to the financial crisis (Bernal, Gnabo, & Guilmin, [11]; Girardi and Tolga Ergün, [25]), indicating that the USA banking sector has accumulated systemic risk among financial systems. However, as discussed above, the banking sector scored very low in SRISK, indicating that banks as lenders of subprime mortgage were able to transfer the systemic risk they created by reselling mortgage-backed securities. Similar to the 2008 financial crisis in the USA, the regulatory authorities of China's financial system are increasingly troubled with the possibility that the creators of systemic risk channel the risk to other parts of the system, although in China, security firms seem to create systemic risk while banks represent an eventual ballast of the system. Regardless, this misalignment in the financial system will prove to be a major challenge for Chinese regulatory authorities as was previously observed in the financial system of the USA.

Acknowledgements

Comments and suggestions from Chinese Economy editor Professor Ligang Zhong and reviewers are gratefully acknowledged.

Appendices

Definition and estimation of CoVaR

Definition of CoVaR and ΔCoVaR

Suppose that a system consists of m different financial firms and that the aggregate result of the system is modeled as follows:

(1)

Graph

$$S=\sum _{i\in I}^{}{X}_i,I=\left\{1,...m\right\}$$

where

Graph

$X_i$ is the representative random variable of the ith firm, which can be the firm's assets, liabilities, surplus, rate of return or loss. Here, we choose the rate of return.

Recall that

Graph

$Va{R}_q(X_i)$ or

Graph

$Va{R}_q^i$ is implicitly defined as the q quantile or percentile:

(2)

Graph

$$\mathrm{Pr}(X_i\le Va{R}_q^i)=q$$

Definition:

Graph

$\mathit{CoVa}{R}_q^{j|i}$ denotes that the

Graph

$\mathit{VaR}$ of institution j (or the financial system) is conditional on some event

Graph

$C(X_i)$ of institution i. That is,

Graph

$\mathit{CoVa}{R}_q^{j|i}$ is implicitly defined by the q-quantile of the conditional probability distribution:

(3)

Graph

$$\mathrm{Pr}(X_j\le \mathit{CoVa}{R}_q^{j|C(X_i)}|C(X_i))=q$$

We denote institution i's contribution to j as follows:

(4)

Graph

$$\Delta \mathit{CoVa}{R}_q^{j|i}=\mathit{CoVa}{R}_q^{j|X^i=Va{R}_q^i}-\mathit{CoVa}{R}_q^{j|X^i=\mathit{media}{n}^i}$$

In this paper, we focus on the conditioning event of

Graph

$\{X_i=Va{R}_q^i\}$ and primarily study the case where j = system, i.e., when the return of the portfolio of all financial institutions is at its

Graph

$\mathit{VaR}$ level. In this case,

Graph

$\mathit{CoVa}{R}_q^i$ denotes the

Graph

$\mathit{VaR}$ of the financial system conditional on the distress of a certain financial institution i.

Additionally,

Graph

$\mathit{CoVa}{R}_q^{j|X_i=\mathit{media}{n}_i}$ reflects the stress of the financial system when the ith individual company stands in a normal standard. We remove the constraint of

Graph

$X_i=\mathit{media}{n}_i$ because this condition indicates that no risk is caused by individual i. According to the above assumptions, the following equation can be adopted:

(5)

Graph

$$\Delta \mathit{CoVa}{R}_q^i=\mathit{CoVa}{R}_q^i-Va{R}_q^{\mathit{sys}}$$

This indicator denotes the difference between the

Graph

$\mathit{VaR}$ of the system conditional on the distress of the individual i and the unconditional

Graph

$\mathit{VaR}$ of the financial system and reflects the degree to which systemic risk increases when the ith firm is involved in risk. In other words, this definition can be treated as a systemic risk measure caused by individual i.

CoVaR Estimation via Quantile Regressions

To estimate the generalized

Graph

$\mathit{CoVaR}$ from empirical data, we use a quantile regression method based on the contribution by Koenker and Bassett ([30]).

Assume that dependent variable y is a linear function of explanatory variables x:

(6)

Graph

$$y=\alpha +x\beta +\epsilon$$

We can obtain

Graph

$\beta$ (containing a column 1) by the ordinary least squares (OLS) method, maximum likelihood estimation or other econometric methods. The quantile regression is an approach that specifies coefficient

Graph

$\beta$ by the following derivation:

(7)

Graph

$$\underset{\beta \in R^2}{\min }\sum _{k=1}^n(y_k-x_k\beta )(q-I(y_k<x_k\beta ))$$

where

Graph

$y_k$ and

Graph

$x_k$ are observations of variables y and x, respectively. The indicator function

Graph

$I(y_k<x_k\beta )$ equals 1 when

Graph

$y_k<x_k\beta$ and 0 otherwise.

Thus, after minimizing

Graph

$\beta ,$

(8)

Graph

$$\widehat{y}={\widehat{\alpha }}_q+x{\widehat{\beta }}_q$$

Graph

${\widehat{\beta }}_q$ is called the q-quantile coefficient estimator.

The quantile regressions incorporate estimates of the conditional mean and the conditional volatility to produce conditional quantiles without the distributional assumptions that would be needed for an estimation via OLS. This characteristic makes the quantile regression method useful for broad application.

Consider the predicted value of the financial sector

Graph

$X^{\mathit{sys}}$ on a certain institution i for the q-quantile:

(9)

Graph

$${\widehat{X}}_q^{\mathit{sys},i}={\widehat{\alpha }}_q^i+{\widehat{\beta }}_q^i{X}^i$$

Using a particular predicted value of

Graph

$X^i=Va{R}_q^i$ yields the

Graph

$\mathit{CoVaR}$ measure. More formally, within the quantile regression framework, our specific

Graph

$\mathit{CoVaR}$ measure is simply given as follows:

(10)

Graph

$$\mathit{CoVa}{R}_q^{\mathit{sys}|X^i=Va{R}_q^i}:={\widehat{\alpha }}_q^i+{\widehat{\beta }}_q^{i}Va{R}_q^i$$

Graph

$\Delta \mathit{CoVa}{R}_q^{\mathit{sys}|i}$ is then given as follows:

(11)

Graph

$$\Delta \mathit{CoVa}{R}_q^{\mathit{sys}|i}={\widehat{\beta }}_q^i(Va{R}_q^i-Va{R}_{50\%}^i)$$

Time-varying estimation of CoVaR with systemic macro state variables

In addition to the previous method that focuses on the estimation of a constant

Graph

$\mathit{CoVaR}$ over time, we estimate the conditional distribution as a function of macro state variables to capture the time variation. Still, we run quantile regressions on the data, where

Graph

$M_{t-1}$ indicates the vector of lagged macro state variables:

(12)

Graph

$$X_t^i={\alpha }^i+{\gamma }^i{M}_{t-1}+{\epsilon }_t^i$$

(13)

Graph

$$X_t^{\mathit{sys}}={\alpha }^{\mathit{sys}|i}+{\beta }^{\mathit{sys}|i}{X}_t^i+{\gamma }^{\mathit{sys}|i}{M}_{t-1}+{\epsilon }_t^{\mathit{sys}|i}$$

Then, we can obtain the following:

(14)

Graph

$$Va{R}_t^i(q)={\widehat{\alpha }}_q^i+{\widehat{\gamma }}_q^i{M}_{t-1}$$

(15)

Graph

$$\mathit{CoVa}{R}_t^i(q)={\widehat{\alpha }}^{\mathit{sys}|i}+{\widehat{\beta }}^{\mathit{sys}|i}Va{R}_t^i(q)+{\widehat{\gamma }}^{\mathit{sys}|i}{M}_{t-1}$$

With the previous effort, we compute

Graph

$\Delta \mathit{CoVa}{R}_t^i:$

(16)

Graph

$$\Delta \mathit{CoVa}{R}_t^i(q)={\widehat{\beta }}^{\mathit{sys}|i}(Va{R}_t^i(q)-Va{R}_t^i(q))$$

Definition and estimation of MES

Definition of MES

Graph

$Va{R}_{\alpha }$ represents the maximum that a financial institution loses with confidence

Graph

$1-\alpha ;$ that is,

Graph

$\mathrm{Pr}(R<-Va{R}_{\alpha })=\alpha .$

Graph

$ES$ is the expected loss conditional on the loss being greater than the

Graph

$\mathit{VaR}$ :

(17)

Graph

$$E{S}_t^m=-E\left[r_t^i\right|r_t^m\le -Va{R}_{\alpha }]=-\sum _{i=1}^N{w}_t^i{E}_{t-1}(r_t^i|r_t^m<-Va{R}_{\alpha })$$

where

Graph

$w_t^i$ is the weight of institution i in the financial system at time t,

Graph

$r_t^m$ is the aggregate return of the system at time t,

Graph

$r_t^i$ is the return of institution i at time t,

Graph

$Va{R}_{\alpha }$ represents the maximum that the financial institution loses with

Graph

$1-\alpha$ confidence, while

Graph

$E{S}_{\alpha }$ indicates the average of returns on days when the loss exceeds its

Graph

$Va{R}_{\alpha }.$

Therefore, we can obtain the

Graph

$\mathit{MES}$ by the following expression:

(18)

Graph

$$ME{S}_t^i=\frac{\partial E{S}_t^m}{\partial w_t^i}=-E_{t-1}(r_t^i|r_t^m<-Va{R}_{\alpha })$$

Graph

$ME{S}_t^i$ shows how institution i's risk taking adds to the whole system; that is, institution i's contribution to the risk of the system at time t is

Graph

$ME{S}_t^i.$

Estimation of MES via the DCC-GARCH method

Here, we estimate

Graph

$\mathit{MES}$ based on the methodology raised by Brownlees and Engle ([15]).

First, we build a bivariate process of the firm and market returns:

(19)

Graph

$$\begin{array}{c}{r}_t^m={\sigma }_t^m{\epsilon }_t^m\\ r_t^i={\sigma }_t^i{\rho }_t^i{\epsilon }_t^m+{\sigma }_t^i\sqrt{1-{({\rho }_t^i)}^2}{\xi }_t^i\\ ({\epsilon }_t^m,{\xi }_t^i)\sim F\end{array}$$

where

Graph

${\sigma }_t^m$ and

Graph

${\sigma }_t^i$ are the conditional standard deviation of the market and firm i's return, respectively,

Graph

${\rho }_t^i$ is the conditional correlation between market and firm i, and

Graph

$({\epsilon }_t^m,{\xi }_t^i)$ are the shocks to the system and firm i, which are independent and identically distributed over time with zero mean, unit variance and zero covariance.

Let

Graph

${\beta }_t^i={\rho }_t^i\frac{{\sigma }_t^i}{{\sigma }_t^m},$

Graph

$C=-Va{R}_{\alpha };$ thus, we can obtain the following:

(20)

Graph

$$r_t^i={\beta }_t^i{r}_t^m+{\sigma }_t^i\sqrt{1-{({\rho }_t^i)}^2}{\xi }_t^i$$

(21)

Graph

$$\begin{array}{c}ME{S}_t^i={\sigma }_t^i{\rho }_t^i{E}_{t-1}({\epsilon }_t^m|{\epsilon }_t^m<C/{\sigma }_t^m)+{\sigma }_t^i\sqrt{1-{({\rho }_t^i)}^2}{E}_{t-1}({\xi }_t^i|{\epsilon }_t^m<C/{\sigma }_t^m)\\ ={\beta }_t^i{E}_{t-1}(r_t^m|r_t^m<C)+{\sigma }_t^i\sqrt{1-{({\rho }_t^i)}^2}{E}_{t-1}({\xi }_t^i|{\epsilon }_t^m<C/{\sigma }_t^m)\end{array}$$

Second, we estimate the tail expectation in (21) via the non-parameter methodology proposed by Scaillet ([34]):

(22)

Graph

$${\widehat{E}}_{t-1}({\epsilon }_t^m|{\epsilon }_t^m<\kappa )=\frac{\sum _{t=1}^{T}K\left(\frac{\kappa -{\epsilon }_t^m}{h}\right){\epsilon }_t^m}{\sum _{t=1}^{T}K\left(\frac{\kappa -{\epsilon }_t^m}{h}\right)}{\widehat{E}}_{t-1}({\xi }_t^i|{\epsilon }_t^m<\kappa )=\frac{\sum _{t=1}^{T}K\left(\frac{\kappa -{\epsilon }_t^m}{h}\right){\xi }_t^i}{\sum _{t=1}^{T}K\left(\frac{\kappa -{\epsilon }_t^m}{h}\right)}$$

where

Graph

$\kappa =Va{R}_t^m/{\sigma }_t^m,K(x)={\int }_{-\infty }^x\kappa (u)\mathrm{d}u,$

Graph

$\kappa (u)$ is the kernel function, and

Graph

$h$ is the bandwidth. Here, we assume that

Graph

$h=T^{-0.2}$ and

Graph

$x$ have a standard normal distribution.

Third, we estimate

Graph

${\sigma }_t^i$ and

Graph

${\sigma }_t^m$ via the GJR-GARCH model (Glosten, Jagannathan, & Runk, [26]):

(23)

Graph

$$\begin{array}{c}{\sigma }_t^m={(w_{m,G}+{\alpha }_{m,G}{r}_{t-1}^m{}^2+{\gamma }_{m,G}{r}_{t-1}^m{}^2{I}_{t-1}^m+{\beta }_{m,G}{\sigma }_{t-1}^m{}^2)}^{0.5}\\ {\sigma }_t^i={(w_{i,G}+{\alpha }_{i,G}{r}_{t-1}^i{}^2+{\gamma }_{i,G}{r}_{t-1}^i{}^2{I}_{t-1}^i+{\beta }_{i,G}{\sigma }_{t-1}^i{}^2)}^{0.5}\end{array}$$

where

Graph

$I_t^f=\{\begin{array}{c}1{\mathrm{r}}_t^f<0\\ 0{\mathrm{r}}_t^f\ge 0\end{array},f=m,i.$ Taking the heavy tail into account, we also assume that the standard residual follows a t distribution.

Finally, we estimate

Graph

${\rho }_t^i$ using the DCC model. Assuming that

Graph

$P_t$ is the time-varying dynamic correlation matrix of institution i and the market rate of return, then the conditional covariance matrix of the two can be expressed as follows:

(24)

Graph

$$H_t=D_t{P}_t{D}_t=\left[\begin{array}{c}{\sigma }_t^{i}0\\ 0{\sigma }_t^m\end{array}\right]\left[\begin{array}{c}1{\rho }_t^i\\ {\rho }_t^{i}1\end{array}\right]\left[\begin{array}{c}{\sigma }_t^{i}0\\ 0{\sigma }_t^m\end{array}\right]$$

Based on the previous estimation, we can derive the

Graph

$ME{S}_t^i$ for each institution i at any time t.

Definition and estimation of SRISK

Definition of SRISK

Because

Graph

$\mathit{MES}$ measures the tail expectation of the firm's return conditional on the systemic event, we consider here the long-run marginal expected shortfall (

Graph

$\mathit{LRMES}$ ), which is the estimated loss when investors expect the market to fall by at least 40% in 6 months. Thus, we define the

Graph

$\mathit{SRISK}$ as follows:

(25)

Graph

$$\mathit{SRIS}{K}_t^i=\max (0,-k{D}_t^i+(1-k)W_t^i(1-\mathit{LRME}{S}_t^i))$$

where

Graph

$D_t^i$ and

Graph

$W_t^i$ denote the book value of firm i's debt and the market value of its equity, respectively, and k is the prudential capital ratio between 0 and 1. Additionally, its percentage version is as follows:

(26)

Graph

$$\mathit{SRISK}{\%}_t^i=\mathit{SRIS}{K}_t^i/\sum _{i=1}^I\mathit{SRIS}{K}_t^i$$

Here, we notice again the differences between

Graph

$\mathit{CoVaR}$ (or

Graph

$\Delta \mathit{CoVaR}$ ) and

Graph

$\mathit{SRISK}.$

Graph

$\mathit{CoVaR}$ represents the risk contribution of a certain firm to the system and measures the overall systemic risk when an individual institution breaks down, which is apparently the "bottom-up" analysis. Meanwhile,

Graph

$\mathit{SRISK}$ is a "top-down" method of analyzing systemic risk, which measures the risk of an individual firm when the overall system suffers a financial crisis. We take these two indicators into consideration to examine the systemic risks of China's financial market more comprehensively.

Estimation of SRISK

The key to estimating

Graph

$\mathit{SRISK}$ is to predict

Graph

$\mathit{LRMES},$ which can be achieved through a Monte Carlo simulation. Let the present time be t, the prediction interval be h, and the estimation process be divided into four steps. In the first step, a standardized residual sequence of length h is randomly extracted S times from the sample, namely,

Graph

$\{{\epsilon }_{m,t+\tau }^s,{{\xi }_{i,t+\tau }^s\}}_{\tau =1}^h,s=1,...,S.$ In the second step, the dynamic volatility and correlation coefficient of the last period (t period) in the sample are taken as the initial values, and the normalized residuals extracted in the first step are substituted into the GJR-GARCH and DCC equations. Then, the next period of volatility can be calculated iteratively; thus, we can obtain the relative market and individual returns. In the third step, we calculate the accumulative returns as follows

(27)

Graph

$$R_{f,t+1:t+h}^s=\text{exp}\{\sum _{\tau =1}^h{r}_{f,t+\tau }^s\}-1,f=m,i$$

In the last step, we compute the

Graph

$\mathit{LRMES}$ :

(28)

Graph

$$\mathit{LRME}{S}_{t+1:t+h}^i=\frac{\sum _{s=1}^S{R}_{i.t+1:t+h}^{s}I\{R_{m,t+1:t+h}^s<C\}}{\sum _{s=1}^{S}I\{R_{m,t+1:t+h}^s<C\}}$$

Substituting

Graph

$\mathit{LRMES}$ and the corresponding firm liability, equity market value, and appropriate k-value into Equation (25) yields the

Graph

$\mathit{SRISK}$ value at that moment.

To maintain consistency for these three indices, let

Graph

$q=5\%$ in the quantile regression for CoVaR and

Graph

$\alpha =5\%$ when computing MES and SRISK. Generally, we choose

Graph

$k=8\%$ for Equation (25).

1 Acharya, V., Philippon, T., Richardson, M., & Roubini, N. (2010). The financial crisis of 2007-2009: Causes and remedies. Financial Markets, Institutions & Instruments, 18 (2), 89 – 137. doi: 10.1111/j.1468-0416.2009.00147_2.x 2 Acharya, V. L., Engle, R., & Richardson, M. (2012). Capital shortfall: A new approach to ranking and regulating systemic risks. American Economic Review, 102 (3), 59 – 64. doi: 10.1257/aer.102.3.59 3 Acharya, V. L., Pedersen, L. H., Philippon, T., & Richardson, M. P. (2017). Measuring systemic risk. Review of Financial Studies, 30 (1), 2 – 47. doi: 10.1093/rfs/hhw088 4 Acharya, V. L., & Yorulmazer, T. (2007). Too many to fail: An analysis of time-inconsistency in bank closure policies. Journal of Financial Intermediation, 16 (1), 1 – 31. doi: 10.1016/j.jfi.2006.06.001 5 Adrian, T., & Brunnermeier, M. K. (2016). CoVaR. American Economic Review, 106 (7), 1705 – 1741. doi: 10.1257/aer.20120555 6 Alessi, L., & Detken, C. (2011). Quasi real time early warning indicators for costly asset price boom/bust cycles: A role for global liquidity. European Journal of Political Economy, 27 (3), 520 – 533. doi: 10.1016/j.ejpoleco.2011.01.003 7 Allen, F., & Gale, D. (2000). Financial contagion. Journal of Political Economy, (1) 108, 1 – 33. doi: 10.1086/262109 8 Allen, F., & Gale, D. (2007). Understanding financial crises. New York : Oxford University Press. 9 Basel Committee on Banking Supervision. (2009). Strengthening the resilience of the banking sector: Consultative document. Retrieved from http://www.bis.org/publ/bcbs164.pdf Basel Committee on Banking Supervision. (2010). Basel III: A global regulatory framework for more resilient banks and banking systems. Retrieved from http://www.bis.org/publ/bcbs189.pdf Bernal, O., Gnabo, J., & Guilmin, G. (2014). Assessing the contribution of banks, insurance and other financial services to systemic risk. Journal of Banking & Finance, 47 (C), 270 – 287. doi: 10.1016/j.jbankfin.2014.05.030 Borio, C. (2003). Towards a macroprudential framework for financial supervision and regulation. BIS Working Papers, 49 (2), 1–18. doi: 10.2139/ssrn.841306 Borio, C., & Drehmann, C. M. (2009). Towards an operational framework for financial stability: "Fuzzy" measurement and its consequences. Social Science Electronic Publishing, 15 (9), 3295 – 3303. doi: 10.2139/ssrn.1458294 Boyle, P. P., & Kim, J. (2012). Designing a counter-cyclical insurance program for systemic risk. Journal of Risk and Insurance, 79 (4), 963 – 993. doi: 10.1111/j.1539-6975.2012.01473.x Brownlees, C., & Engle, R. F. (2017). SRISK: A conditional capital shortfall measure of systemic risk. Review of Financial Studies, 30 (1), 48 – 79. Brunnermeier, M. K., & Pedersen, L. H. (2009). Market liquidity and funding liquidity. Review of Financial Studies, 22 (6), 2201 – 2238. doi: 10.1093/rfs/hhn098 Degryse, H., & Nguyen, G. (2007). Interbank exposures: An empirical examination of systemic risk in the Belgian banking system. International Journal of Central Banking, 3, 123 – 171. Derbali, A. (2017). Systemic risk in the Chinese financial system: Measuring and ranking. The Chinese Economy, 50 (1), 34 – 58. doi: 10.1080/10971475.2016.1211904 Derbali, A., Hallara, S., & Sy, A. (2015). Systemic risk of the Greek financial institutions: application of the SRISK model. African Journal of Accounting, Auditing and Finance, 4 (1), 7 – 28. doi: 10.1504/AJAAF.2015.071751 Diamond, D. W., & Rajan, R. G. (2005). Liquidity shortages and banking crises. The Journal of Finance, 60 (2), 615 – 647. doi: 10.1111/j.1540-6261.2005.00741.x Ding, X., & Tay, N. S. P. (2016). Some challenges to economic growth and stability in China. The Chinese Economy, 49 (5), 301 – 306. doi: 10.1080/10971475.2016.1193394 Drehmann, M., & Tarashev, N. A. (2011). Systemic importance: Some simple indicators. BIS Quarterly Review, March 2011. Available at SSRN: https://ssrn.com/abstract=1785264 Duffie, D., Eckner, A., Horel, G., & Saita, L. (2009). Frailty correlated default. The Journal of Finance, 64 (5), 2089 – 2123. doi: 10.1111/j.1540-6261.2009.01495.x Gauthier, C., Lehar, A., & Souissi, M. (2012). Macroprudential capital requirements and systemic risk. Journal of Financial Intermediation, 21 (4), 594–618. Girardi, G., & Tolga Ergün, A. (2013). Systemic risk measurement: Multivariate GARCH estimation of CoVaR. Journal of Banking & Finance, 37 (8), 3169 – 3180. doi: 10.1016/j.jbankfin.2013.02.027 Glosten, L. R., Jagannathan, R., & Runk, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, (5) 48, 1779 – 1801. doi: 10.1111/j.1540-6261.1993.tb05128.x Huang, X., Hao, Z., & Zhu, H. (2009). A framework for assessing the systemic risk of major financial institutions. Journal of Banking & Finance, 33 (11), 2036 – 2049. doi: 10.1016/j.jbankfin.2009.05.017 Illing, M., & Liu, Y. (2003). An index of financial stress for Canada (Bank of Canada Working Paper), 1 – 63. IMF, BIS, & FSB. (2009). Guidance to assess the systemic importance of financial institutions, markets and instruments: Initial considerations. Report to the G-20 Finance Ministers and Central Bank Governors, October, 1–27. Retrieved from https://www.imf.org/external/np/g20/pdf/100109.pdf Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46 (1), 33 – 50. doi: 10.2307/1913643 Lehar, A. (2005). Measuring systemic risk: A risk management approach. Journal of Banking & Finance, 29 (10), 2577 – 2603. doi: 10.1016/j.jbankfin.2004.09.007 Mistrulli, P. E. (2011). Assessing fnancial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns. Journal of Banking & Finance, 35 (5), 1114 – 1127. doi: 10.1016/j.jbankfin.2010.09.018 Pedersen, L. H. (2009). When everyone runs for the exit. International Journal of Central Banking, 5 (4), 177 – 199. Scaillet, O. (2005). Nonparametric estimation of conditional expected shortfall. Insurance and Risk. Management Journal, 74, 639 – 660. Segoviano, M. A., & Goodhart, C. A. E. (2009). Banking stability measures. IMF Working Papers, 23 (2), 202–209. Tarashev, N., Borio, C., & Tsatsaronis, K. (2016). Risk Attribution using the shapley value: Methodology and policy applications. Review of Finance, 20 (3), 1189 – 1213. doi: 10.1093/rof/rfv028 Upper, C. (2007). Using counterfactual simulations to assess the danger of contagion in interbank markets. BIS Working Papers, 7 (3), 111–125. Upper, C. (2011). Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability, 7 (3), 111 – 125. doi: 10.1016/j.jfs.2010.12.001 Zhou, X. (2011). The response of financial policy to financial crisis: Background, internal logic and main forms of macroprudential policy framework. Finance Research, 2011 (1), 1 – 14. Chinese version.

By Hua Zhou; Wenjin Liu and Liang Wang

Reported by Author; Author; Author