Systemic risk of Chinese financial institutions

M

T

Systemic Risk of Chinese Financial

Institutions

Author:

Chuchu YANG

Supervisor: Prof. Peter BOSWIJK

A thesis submitted in fulfillment of the requirements for the degree of Master of Science

in the

Faculty of Economics and Business Amsterdam School of Economics

i

Declaration of Authorship

I, Chuchu YANG, declare that this thesis titled, “Systemic Risk of Chinese Financial Institutions” and the work presented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for a re-search degree at this University.

• Where any part of this thesis has previously been submitted for a de-gree or any other qualification at this University or any other institu-tion, this has been clearly stated.

• Where I have consulted the published work of others, this is always clearly attributed.

• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Signed: Date:

UNIVERSITY OF AMSTERDAM

Abstract

Amsterdam School of Economics

Master of Science

Systemic Risk of Chinese Financial Institutions

by Chuchu YANG

In this thesis, we perform a `1norm penalized quantile regression using

LASSO techniques to investigate the risk spillovers within Chinese finan-cial institutions and also construct a tail risk network to show the current network structure. Furthermore, we investigate the systemic relevance by calculating the realized systemic risk betas and deliver the dynamic rele-vance rankings. On one hand, it has been proved that risk spillovers are widely spread within Chinese financial network; on the other hand, the im-portance of commercial banks has been identified through the constructed network. It has been evidenced in our thesis that commercial banks in China are highly interconnected within the network, and they also consid-ered to be systemic important, considering the realized systemic risk betas.

iii

Acknowledgements

I would like to express my deep gratitude to Professor Boswijk, my re-search supervisor, for his patient guidance, enthusiastic encouragement of this research work.

I also wish to thank my parents and my boyfriend for their support through-out my study.

Contents

2.1 Sources of Systemic Risk . . . 3

2.1.1 Correlated Investment . . . 3

2.1.2 Liquidity Risk . . . 4

2.2 Contagion and Financial Network . . . 4

2.3 Global Measures of Systemic Risk. . . 6

2.3.1 MES and SES . . . 6

2.3.2 SRISK . . . 6

2.3.3 ∆CoVaR . . . 7

2.3.4 Other Measures . . . 7

3 Model and Methodology 9 3.1 VaR . . . 9

3.2 General settings for quantile regression . . . 10

3.3 Company-specific VaR Estimation . . . 10

3.4 System VaR Estimation . . . 11

3.4.1 Company-specific Tail Risk Network . . . 11

Identification of Potential Company-specific Risk Drivers 11 3.4.2 Evaluation of the Goodness of the Model . . . 12

3.5 Topological Graphic Network Model . . . 13

3.6 Measuring Systemic Risk Contributions . . . 13

4 Data and Variables 16 4.1 Analyzed Financial Institutions . . . 16

4.2 Data and Variables . . . 18

4.2.1 Company-Specific Variables . . . 18

4.2.2 Macroeconomic Variables . . . 19

4.2.3 Stationarity Check . . . 20

4.3 System VaR . . . 20

4.4 Data Processing . . . 21

4.4.1 Dealing with Low Frequency Data . . . 21

5 Analysis and Results 23 5.1 Company-specific Tail Risk . . . 23

5.1.1 LASSO Selection of Tail Risk Drivers. . . 23

v

5.2 Measuring Systemic Risk Contributions . . . 26

5.2.1 Example: ABC . . . 27 Unrestricted Model . . . 27 H1: Restricted Model 1. . . 27 H2: Restricted Model 2. . . 27 H3: Restricted Model 3. . . 27 Test Results . . . 28 5.2.2 Example: BCL . . . 28 5.3 Discussion . . . 29 6 Conclusions 31 6.1 Conclusion . . . 31 6.2 Future Work . . . 32 A Appendix I 33 B Appendix II 36 Bibliography 37

List of Figures

3.1 Markov Blanket for node A . . . 13

4.1 Stock Price by Date . . . 18

4.2 Daily log Returns of System . . . 21

5.1 The full network of 32 listed financial institutions in Chinese stock market . . . 25

vii

List of Tables

4.1 Analyzed Financial Institutions . . . 17

4.2 Arithmetic Mean of All Companies, 2010-2016 . . . 19

4.3 Augmented Dicky Fuller Test . . . 20

5.1 Explanations of Variables . . . 23

5.2 Variables Selected by LASSO for V aRi_{with q = 0.05 . . . . . 24}

5.3 Tail Risk Cross-dependencies . . . 27

5.4 Test Statistics and p-value for ABC . . . 28

5.5 Test Statistics and p-value for BCL . . . 28

5.6 Companies with Significant βs|i . . . 29

5.7 βs|i_{Rankings for Specific Date. . . . 30}

A.1 LASSO results for V aRi_{with q = 0.05 . . . . 33}

List of Abbreviations

LASSO Least Absolute Shrinkage and Selection Operatior

CSRC China Securities Regulatory Commission

MES Marginal Expected Shortfalls

SES Systemic Expected Shortfalls

CoVaR Co VaR

1

Chapter 1

Introduction

In ensuring that the risk of the financial system as a whole stays at “pru-dent” levels, regulators are tasked to meet two forms of regulatory chal-lenges. One is microprudential regulation, which needs to ensure that risk-taking at the individual bank level is not excessive. The other is macropru-dential regulation, which seeks to contain the systemic risk that banks may be excessively exposed to collective failure. There is a long history of aca-demic research on microprudential regulation, while it is only recently that academics started to analyze macroprudential tool (Hanson, Kashyap, and Stein,2011) though it has been long proposed (Crockett,2000, Borio,2003). The global financial crisis gives us a lesson that considering only about in-dividuals’ risk, which is at the microprudential level, is not enough. Hence, a proper measure of systemic risk at the macroprudential level is essential to monitor the stability of financial system by regulatory authorities.

According to the Bank for International Settlements, systemic risk in the financial system is the risk that a failure of a participant to meet its contrac-tual obligations may in turn cause other participants to default, with the chain reaction leading to broader financial difficulties (Tarashev, Borio, and Tsatsaronis,2010). “Too big to fail” has been evidenced to become “too in-terconnected to fail” during the 2007-2009 financial crisis, which indicates that cross-sectional dependencies between the risk exposures can threaten the stability of financial system as a whole (Rajan,2009). Hence, measuring the interconnectedness within the financial system and quantify the contri-bution of each financial institution to overall systemic risk can help identify which company contributes more to systemic risk. Stricter regulatory re-quirements for institutions with larger systemic risk contributions would break the tendency to generate systemic risk. The failure of one institution spreads to other institutions through financial links between them. These links include interbank loans, payment systems or OTC derivatives posi-tions. Such an intricate structure of linkages can be captured by a network representation of the financial system. A classic example of a financial net-work is constructed to illustrate how systemic risk (i.e., contagious bank failures) may occur through financial independences among financial insti-tutions (Hu et al., 2012). This "source-specific approach" relies on several families of qualitative models, which deliver predictions that can be con-firmed by empirical analyses, often based on supervisory data. Another approach aims to deliver global measures of systemic risk contributions using market data and balance-sheet data, potentially encompassing all the

mechanisms studied in the first type of financial network. Particularly pop-ular examples include the systemic risk measure (SRISK) and the delta con-ditional value-at-risk (∆CoVaR) (Brownlees and Engle, 2015, Adrian and Brunnermeier,2011), while this "global approach" is more statistical in na-ture and does not take a particular stand on the cause of systemic risk.

As a result, a general empirical assessment of systemic relevance can-not build on the vast theoretical literature on financial network models and financial contagion, as such studies typically require detailed information on intra-bank asset and liability exposures. However, these data are not publicly available and even supervisory authorities can only collect par-tial information, which lead to an unclear understanding of how complex structures eventually translate into dynamic and predictable measures of fi-nancial system. Hence, a proper integration between these two approaches can help us to map a full view of financial network and corresponding sys-temic risk.

Hautsch, Schaumburg, and Schienle (2014) proposed systemic risk mea-sure based on a tail-risk network, which properly combined the two strands of approaches by applying tail risk as a specific source of systemic risk and constructing a tail-risk network to investigate the dependencies and spillover effect through the network. Following their method, we performed a `1norm penalized quantile regression using the Least Absolute Shrinkage

and Selection Operator (LASSO) techniques to address the importance of the risk spillovers within a financial institution, and constructed a tail risk network to show the interconnectedness of financial institutions in China as well as the marginal effect of the tail risk of a specific financial institu-tions on the whole financial system’s tail risk. The reason why we adopt a dataset consisting of 32 Chinese financial institutions is as follows: first, China reached a 249% debt-to-GDP ratio in the first quarter of 2016, and the financial systems in China is facing with the problem of the expansion of highly leveraged private and corporate debt. It appears to be an emerg-ing acceptance of the fact that increases in debt (leverage) seem to increase the collective fragility of financial institutions after the global financial cri-sis (Acharya, Schnabl, and Suarez, 2013). Hence, it helps us to study the interconnectedness of financial institutions under pressure; second, there is no related literature on the tail risk network construction of Chinese fi-nancial institutions so far, so we add additional empirical analysis to study systemic risk in China.

The rest of the thesis is organized as follows. Chapter 2 provides a review of the literatures on general measures of systemic risk, including methods based on network topology and global measurement. Chapter 3 outlines and explains the models and methods, that is, tail risk definition, quantile regression using LASSO techniques. Chapter 4 describes the em-pirical data, selected variables and data processing procedures. Chapter 5 shows the results of the models. Then, Chapter 6 discusses what we have found and what it implies in practice, plus some possible directions for fur-ther research.

3

Chapter 2

Literature Review

There seems to be no unique definition for systemic risk, and it is usually seen as a phenomenon that is difficult to define and quantify while it is there "when we see it"1(IMF,2009, Benoit et al.,2016). Haldane and May,

2011 proposed ’financial ecosystem’ to emphasize the importance of the network dynamics and its complexities after the global financial crisis that began in 2007, and concluded that evolutionary forces have often been sur-vival of the fattest rather than the fittest. "Too interconnected to fail" or " too systemic to fail" (Bernanke, 2009, Rajan, 2009) has been proposed as well as "too big to fail". However, the item of "too big to fail" has been criticized for its validity: Zhou,2009studied the relationship between the size of a financial institution with its systemic importance under the frame-work of multivariate Extreme Value Theory (EVT) and concluded that size should not be considered as a proxy of systemic importance. Meanwhile, researches focusing on the "interconnectedness" of financial systemic have raised attention.

2.1

Sources of Systemic Risk

Despite the general characteristic of the system, the mechanisms behind systemic risk have also been widely studied.

2.1.1 Correlated Investment

Financial institutions are likely to be involved and exposed to same risks if they choose to invest in the same assets. Acharya (2009) show that the failure of one bank leads to a lower aggregated level of risky investment, as a result, the return on safety assets are increasing in equilibrium, thus the surviving bank’s profit is squeezing. Hence, the failed bank poses a nega-tive externality to the system, which is denoted as a "recessionary spillover" . Thus banks have incentives to invest in the same assets to avoid being in-fluenced by it. Acharya and Yorulmazer (2008) also investigated another mechanism similar to this. The externality is that creditors rationally inter-pret the default of a given bank as a signal that the other banks may fail in the future. However, when banks fail together, the liquidation of their assets would have a large impact on the economy, which forces the govern-ment to organize a bailout. Hence, it seems like a "too-may-to-fail" guaran-tee for banks to take the same risks. Farhi and Tirole (2012) also derive that

bailouts are optimal when banks fail at the same time, so it is also optimal for banks to get engaged in herding.

2.1.2 Liquidity Risk

Liquidity risk represents another form of risk that banks are likely to be exposed to in a correlated way. Bhattacharya and Gale (1987) show that banks invested too much in illiquidity risk, which generated the risk of liquidity shortages to the whole financial system. Banks’ liabilities can also be too liquid, thus resulting in a mismatch between the company’s assets and liabilities. Brunnermeier and Oehmke (2013) derive the results that a company can dilute the claims of existing creditors by issuing new debt at a shorter maturity. Hence, it leads to a "maturity rat race" that all banks have the incentives to rely on short-term debt.

2.2

Contagion and Financial Network

Several sources of systemic risk are discussed above, and both of them re-late to close interaction. However, the mechanism behind systemic risk also takes effect through the "financial ecosystem". In other words, the inter-connectedness of a firm within the financial system, instead of its size and idiosyncratic, has raised the potential of increasing the risk of the entire system. Then we can use the definition that systemic risk refers to the risk or probability of the breakdowns of the entire system, while in a financial sector, it indicates a joint default incidence of various financial institutions which is captured by the correlations of observed equity returns (De Nicolo and Kwast,2002). Hence, the way of how to construct the financial network has a large impact of the measurement and systemic risk as well as the con-tagion between financial institutions.

Depended on different perspectives of systemic risk formation, there are two main approaches of constructing financial network and the correspond-ing systemic risk. The first one focused on one specific source of systemic risk, particularly using confidential data. The second method mainly inves-tigated the systemic risk through a global aspect using market data.

Regulatory institutions monitor the dynamic of financial system through linkages and network topologies. A typical example of links is interbank claims with a clear contagion of how much firm j owes to i denoted as bi,j.

Allen and Gale (2000) used a network structure of four banks to demon-strate that a complete network is more robust than connected but incom-plete network. In this framework, the network is defined as comincom-plete when bi,j is positive between all financial institutions, while an incomplete

net-work summarized a condition that i has linkages to j and j to k, but there is no direct linkages between i and k. Hence, it gave an idea of the instabil-ity of financial network in realinstabil-ity.

Network topology generates an insight and shape the behavior of under-lying financial institutions. It defines a way that different financial insti-tutions can be represented as nodes, of which nodes are placed and inter-connected with respect to each other, and the overall patterns that emerge out of this. One the one hand, since bilateral exposures between banks and other financial institutions are generally not reported to central banks or

Chapter 2. Literature Review 5 regulatory institutions, the entire network structure is not likely to be ob-served thus it leads to difficulty to identify the systemic importance of in-volved financial institutions. Several methods have been proposed to fill in the blank. Maximum Entropy (ME) (Upper,2011, Elsinger, Lehar, and Sum-mer, 2013) is one of the widely used method in reconstructing interbank networks using balance sheet data (assets and liabilities). Suppose the in-terbank linkages are represented by a N x N matrix with components of xij

denoting the total amount of lending from bank i to bank j. The problem to estimate bilateral exposures is that the maximization of X∗becomes as close as possible to matrix X∗ with the components of x∗_ij = PN

j=1xIJPNi=1xij,

of which the first item denotes the total lending from bank i to all the other banks and the latter item denotes the total borrowing of bank j from other banks. RAS algorithm2has been performed to minimize the cross entropy of the following matrices to solve the proposed question:

min ˆ xij N X i=1 N X j=1 ln(xˆij x∗_ij) (2.1)

which is subject to following constraints as

N X i=1 ˆ xij = N X j=1 xij, N X j=1 ˆ xij = N X i=1 xij, ˆxij ≥ 0 ∀i 6= j, ˆxij = 0 ∀i = j

However, it is only optimal for "complete network" as explained in Allen and Gale (2000), while the typical financial network are sparse as interbank activity is usually depended on relationships (Cocco, Gomes, and Martins,

2009). An alternative benchmarking method to deal with "incomplete mar-ket" is defined as Minimum Density (Anand, Craig, and Von Peter, 2015), which minimums the number of links necessary for distributing a given volume of loans in the interbank market. Maximum Entropy tends to de-liver upper bound of the systemic importance, while Minimum Density gives a lower bound. Minimum Spanning Trees algorithms has also been adopted to construct financial networks in Huang et al.,2016.

General network structure has also been discussed. Gai and Kapadia (2010) developed an analytical model of contagion in financial networks with arbi-trary structure and showed a "robust yet fragile" tendency which indicates that the probability of contagion may be low while the outcome can be ex-treme when it occurs. Allen, Babus, and Carletti (2010) also developed a model where the number and shape of financial connections interact with the funding structure in financial institutions in determine systemic risk. Meanwhile, they also proved that the structure of financial network mat-ters for systemic risk when they are using short-term finance. It has been noticed that in this approach most networks builds on a certain source of systemic risk, so the complex structure of systemic risk is neglected.

2.3

Global Measures of Systemic Risk

Suppose the markets are efficient, the current prices of securities and the derivatives written on them are also assumed to convey all the available information. The global measure, which did not concentrate on a single source of systemic risk or the transmission channel, is constructed under this assumption. Contrary to measures targeted on network topology of a particular source, it take a global, multi-channel approach to assess sys-temic risk.

There are four prominent examples of market-data based measures.

2.3.1 MES and SES

Acharya et al. (2010) proposed the marginal expected shortfall (MES) and the systemic expected shortfall (SES). MES is a measurement of the marginal contribution of a financial institution i to systemic risk considering the rel-ative market capitalization of i (which is defined as ωitat time t). Given the

systemic risk is measured by Expected Shortfall (ES), it can be interpreted as ESsys(C) = N X i=1 ωitEt−1(rit| rsys < C)

where ESsys(C)refers to the expected shortfall of the system, rsysis defined

as the weighted average of the return of all individual institutions (rsys =

PN

i=1ωitrit, N is the number of all financial institutions within the system),

and C is a threshold defined as the tail risk of the system using Value-at-Risk (VaR). All terms are calculated conditional on the information set up to time t − 1. By taking the partial derivative of ESsys(C)with respect to

ωit, it yields the value of MES for each financial institution i at time t within

the system

MESit(C) =

∂ESsys(C)

∂ωit = Et−1

(rit| rsys < C)

SES is an extended version of MES, as it include the effect of actual drop of a company’s equity into MES. In this sense, SES is defined as

SESit= (kLit− 1 + θMESit+ ∆i)Wit

where Lit refers to the leverage ratio of company i at time t, k is used to

construct a threshold that the system is considered as under distress when the market capitalization of company i is below k times the total assets of i, and θ and ∆iare constant items.

2.3.2 SRISK

SRISK can also be considered by an extended version of MES, which is pro-posed by Brownlees and Engle (2015) to investigate an individual firm’s conditionally capital shortfall given distress of the system and identified the contribution of it to systemic risk. For company i at time t, it can be

Chapter 2. Literature Review 7 defeined as

SRISKit= max[0; k(Dit+ (1 −LRMERSit)Wit)

| {z } Required Capital − (1 − LRMERSit)Wit | {z } Avalable Capital ]

where Ditis the book value of total liabilities, and LRMESitis defined as the

long-run MES. Acharya, Engle, and Richardson (2012) proposed a method to approximate LRMESit using daily MESit as LRMESit ' 1 − exp(18 ×

MESit)over a six-month horizon.

2.3.3 ∆CoVaR

∆CoVaR is proposed by Adrian and Brunnermeier (2011), as the Value-at-Risk of the financial system conditional on institutions under distress. CoVaRj|iq is defined as the VaR of institution j (j can also represent the

whole system) conditional on event C(rsys)of institution i,

P r(rsys ≤ CoVaR

j|rsys=V aRiq

q )

where q = P r(rsys≤ V aRiq).

Then the contribution of institution i to j is defined by CoVaRj|iq =CoVaR

j|rsys=V aRiq

q − CoVaRj|rsys=Median

i

q

where CoVaRj|rsys=Mediani

q refers to the median state of the institution.

2.3.4 Other Measures

Billio et al. (2012) use a quarterly returns on hedge funds, banks, broker-dealers, and insurance companies to develop several measures of intercon-nectedness based on Granger causality test and principle component anal-ysis. In the same vein, Diebold and Yılmaz,2014model stock returns in a vector autoregressive framework to empirically estimate directional volatil-ity connectedness measures among major US financial institutions. These measure provide direct estimates of statistical connectivity within a system of financial institutions, and show that banks have played a predominant role in transmitting shocks comparing with other types of financial institu-tions.

Hautsch, Schaumburg, and Schienle (2014) proposed the realized systemic risk beta to measure firm’s contribution given network interdependencies between firm’s tail risk exposures. Similar with ∆CoVaR, it calculated the contribution institution i on j including the influence of i’s tail risk on j, which maps a more complete view of the influencing factors on j’s tail risk. The contribution of institution i to system risk was defined as the marginal effect of the tail risk of i on the whole system.

Hence, we are going to adopt the method used in Hautsch, Schaumburg, and Schienle (2014) to perform a quantile regression using LASSO tech-nique and construct the tail risk network, of which we set tail risk spillovers between financial institutions as a proxy for liability claims. It uses the gen-eral econometric model as a foundation to construct the tail risk network,

and to investigate the spillovers of a specific company to other companies and further to the whole financial system.

9

Chapter 3

Model and Methodology

Assessing and predicting dependence between company-specific risk and systemic risk require modeling regression relations in the (left) tail of under-lying asset return distributions, rather than in the center. This is sharp con-trast to a standard correlation analysis in (conditional) means which cannot quantify spillovers in a tail situation of financial distress, and also goes be-yond simple descriptive correlations between tails. Tail correlations do not allow detecting causal dependencies between tail and do not permit fore-casting systemic risk contributions.

Therefore, our model does not feature a general equilibrium framework, but is exclusively designed to provide a practically feasible measure of a company’s marginal contribution to systemic risk in the presence of risk spillovers from other companies. These underlying network linkages be-tween tails risks of firms in the system should be identified in the first step.

3.1

VaR

Value of Risk (VaR) will be used as our risk measure for companies as well as the whole financial system to evaluate their market risks. Since the 1990s, it has been adopted as the most popular and widely accepted mea-sure of tail risk among regulators and financial institutions. It builds on extreme conditional quantiles, which also corresponds to our requirements of model settings. VaR is used to determine capital requirements required to cover possible losses with a significance level q over a certain horizon `. Let {Vt}t≥1be the value of asset, then VaR can be written as:

P r[Vt+`− Vt≥ −V aR(`)] = q (3.1)

where t corresponds to the time index from when we become interested in the risk of a financial position of an asset. V represents the value of underly-ing asset. Denote the cumulative distribution function (CDF) of Vt+`− Vtas

F`(x). Hence, VaR(`) equals to minus the qth quantile of distribution F`(·),

which can be described as the following equation:

−V aR(`) = inf {x ∈ R : F`(x) ≥ q} = xq (3.2)

where inf denotes the smallest real number x that satisfies F`(x) ≥ p. By

defining VaR as the negative q-quantile ensures that it is positive and rep-resents a loss position.

3.2

General settings for quantile regression

A standard linear quantile regression is introduced by Koenker and Bassett Jr (1978), and it is proved to be well suited and is generally used for VaR estimation. Let’s denote ˆxq as the estimates of the qth quantile of F`(x),

then we have an alternative characterization of VaR, which can be used to proceed a generalized quantile regression approach:

ˆ xq= arg min β T X t=1 wq(Xt− β) (3.3)

where wq(·)is check function:

wq= (q − 1{x<0})x =

(

qx, if x ≥ 0 (q − 1)x, if x < 0

Suppose that we adopt this setting into a linear regression and obtain the corresponding estimates ˆ xq|zt = ˆβ 0 zt, ˆβ = arg min β T X t=1 wq(Xt− β 0 zt) (3.4)

where ztincludes the explanatory variables.

3.3

Company-specific VaR Estimation

In this thesis, we adopted the two-step quantile regression setting used in Hautsch, Schaumburg, and Schienle (2014) to estimate company-specific VaR and system VaR. We define the underlying asset return as Xti, where t

denotes a fixed point of time and i corresponds to a specific company. The company’s conditional Value-at-Risk, V aRi

q,t, is measured as its tail risk

given a class of company-specific tail risk drivers W(i)_t . It represents the qth quantile of Xi

t. Three types of risk drivers are included in V aRip,t, one is

lagged company-specific variables, Ci

t−1, which are publicly available; one

is lagged macroeconomic state variables, Mi_t−1, which are proper proxies for financial system circumstances; another is the empirical tail risk of com-panies within the financial system other than company i, E−i_t−1= (Ej_t−1)_i6=j, and we continue to define it as "loss exceedances" as in Hautsch, Schaum-burg, and Schienle (2014). Loss exceedances are defined conditional on a stress scenario, and we only consider the influence of of company j on VaR of company i if the former one is under pressure of undercapitalization. Then we rewrite E−i_t−1 in a conditional format as E_t−1j = X_t−1j 1(X_t−1j ≤

ˆ

Q0.1), and ˆQ0.1 represents the unconditional sample quantile of the

distri-bution of X_t−1j . (1 is an indicator.) However, different from what is in Hautsch, Schaumburg, and Schienle (2014), we use one-period lagged loss exceedances instead of that of time t to avoid the potential simultaneity issue. P r(−X_ti≥ V aRi q,t| W (i) t ) = P r(Xti ≤ Qiq,t | W (i) t ) = q (3.5)

Chapter 3. Model and Methodology 11 where Qi

q,tdenotes the qth quantile of the underlying asset returns.

3.4

System VaR Estimation

Similarly, as is measured as the conditional VaR of the entire financial sys-tem return, the estimation of the contribution of company i to syssys-temic risk also follows a linear quantile regression settings. Denote V aRsp,tas the

mea-sure of systemic risk, it interprets the negative pth quantile of systemic re-turn Xs

t, which is obtained as the value-weighted average return of major

financial institutions in Chinese financial system. To measure the systemic impact of company i on the system, we derived the marginal effect of com-pany i’s VaR on the system VaR

∂V aRs_p,t(Vt, V aRiq,t)

∂V aRi_q,t = β

s|i

p,q (3.6)

where V aRp,ts is a function of V aRiq,tand Vt, with the latter one consisted

of additional control variables. It is defined as the realized systemic risk

beta. If βp,qs|i of company i is of statistical significance, the product of it and

the tail risk of company i will be defined as a company’s realized systemic

risk contribution.

3.4.1 Company-specific Tail Risk Network

For each time point t, we model the conditional VaR of company i as a linear function of its specific tail risk drivers W_t(i),

V aRi_q = Wi

0

t ξiq (3.7)

Hence, the coefficients can be estimated using a linear function in return quantiles

X_ti = −Wi

0

t ξiq+ εit, with Qq(εit| Wi) = 0 (3.8)

If all risk drivers in W(i)t have already been determined from the pool of all

potential risk drivers Wt, the estimates ˆξiqof ξqi can be derived in a standard

quantile regression setting by minimizing 1 T T X t=1 ρq(Xti+ Wi 0 tξqi) (3.9)

where ρq(u)is a check function as we defined in3.2. And it yields an

esti-mate of company-specific VaR of the ith company ˆ

V aRi_q,t = Wi

0

tξˆqi (3.10) Identification of Potential Company-specific Risk Drivers

We can only run the estimation for company-specific tail risk if the relevant risk drivers (∈ W(i)_{) are determined in advance. As discussed in Chapter2,}

2014) and (possibly high) collinearity between the covariates, we choose a statistical shrinkage technique to determine the relevant covariates, and it is called Least Absolute Shrinkage and Selection Operator (LASSO). LASSO steps into quantile regression by adding an `1 penalty term, which is controlled by a fixed penalty parameter λi for each company i.

˜ ξi_q=argmin_ξi 1 T T X t=1 ρq(Xti+ W 0 tξiq) + λi pq(1 − q) T K X k=1 ˆ σk | ξki | (3.11)

where K is the size of the pool of potential company-specific risk drivers, and Wt = (Wt,kK_k=1) with componentwise variation ˆσk2 = 1

T

PT

t=1Wt,k2.

If the absolute value of the estimated marginal effect | ˜ξi | of the poten-tial risk driver is below a certain threshold (τ ), then it will be eliminated from our interested regressors. Since the estimated coefficients | ˜ξi | are generally downward biased in finite sample after penalization in3.11, the unstructured model 3.9 will be re-estimated with the selected risk drivers by LASSO. An increasing λ indicates a larger penalty, which will sharply decrease the absolute value of estimated coefficient and thus more regres-sors will be eliminated. The λ of company i will be selected automatically through the given algorithm in the Appendix of Hautsch, Schaumburg, and Schienle (2014).

3.4.2 Evaluation of the Goodness of the Model

We will use a likelihood ratio (LR) version of dynamic quantile (test) devel-oped by Engle and Manganelli (2004). First, we generate a binary variable to measure VaR exceedances as Ii

t ≡ I(Xti < −V aRiq,t)

E[Iti | Ωt] (3.12)

where Ωt contains the information set up to t. If the model is correctly

defined, then 3.12will hold. Denote At = (It−1i , It−2i , It−3i ,V aRˆ i t−1)

0

, the condition3.12can be checked via estimating a logistic regression model

I_ti= α + A0_tθ + Ut (3.13)

Then under the joint hypothesis,

H0 : α = qand θ1= θ2 = θ3= θ4 = 0

LR = −2(lnLr− lnLu)∼ χa 25 (3.14)

where the subscript r denotes the likelihood function under H0, while u

Chapter 3. Model and Methodology 13

3.5

Topological Graphic Network Model

Markov blanket is used to construct the tail risk network, which contains all relevant information for predicting the node’s role in the network (Fried-man, Geiger, and Goldszmidt,1997). It can be illustrated using the follow-ing graph

FIGURE3.1: Markov Blanket for node A

The Markov blanket for a node A in a Bayesian network is the set of nodes ∂A composed of all relevant information about A. In a Markov net-work, the Markov blanket of a node is its set of neighboring nodes, which only reflects the direct relationship between different nodes. Take all inter-ested companies as nodes in such network, if Ej is selected by LASSO in the identification of tail risk drivers, the coefficient ξi

k,q will be used as the

measure of impact of company j on company i. Otherwise, there will be no arrows between company j and company i. The layout and allocation will be determined by minimizing the cross-company distance.

To graph a directed relation, we denote the source node (the influencing company) as s, the target node (the influence company) as t, and weights ωij as the influencing coefficient as we calculated in the previous tail risk

estimation ξi k,q.

First, we construct an indicator variable, xij, to check whether edge (i,j) is

a part of the shortest path.

X j xij− X j xji =      1, if i = s −1, if i = t 0, otherwise

Then, our goal of constructing the shortest-paths network will be to mini-mizeP

ij∈A ωijxij.

3.6

Measuring Systemic Risk Contributions

As mentioned in equation 3.6, the impact of a specific company i to the whole system is estimated as the marginal effect of systemic V aRsp,t on

company-specific V aRi

q,t. It can be estimated in the following linear model

V aRs_p,t= V(i)

0

t γps+ βp,qs|iV aRiq,t (3.15)

To capture a time-varying effect of systemic risk beta, a linear relationship is imposed to model the potential time variation of βs|i

β_p,q,ts|i = β_p,q,0s|i + Zi_t−1

0

ηs|i_p,q (3.16) where Zi_t−1is a set of lagged observed variables, which represent a finan-cial company’s propensity to be under a distress. ηs|ip,qis corresponding

pa-rameters driving the time-varying effects. Choosing Zit = Cti, then we can

rewrite the model as following V aRs_p,t= V(i) 0 t γps+ β s|i p,q,0V aR i q,t+ (V aRiq,t· Zit−1) 0 η_p,qs|i (3.17) Since V aRs

p,tand V aRq,ti are not directly observed, the estimates from first

step quantile regression are used as generated regressors X_ts= − ˆV(i) 0 tγps− β s|i p,q,0V aRˆ i q,t−V aRˆ i q,t· Zit−1 0 ηs|i_p,q+ εs_t (3.18) with Qp(εst |V aRˆ i q,t, ˆV (i) t , Zit−1) = 0

Hence, parameter estimate are obtained via quantile regression by mini-mizing 1 T T X t=1 ρp(Xst+ ˆV(i) 0 tγps+ β s|i p,q,0V aRˆ i q,t+V aRˆ i q,t· Zit−1 0 ηs|i_p,q) (3.19)

As a result, we yields the estimates of ˆηp,qs|i and ˆβs|ip,q,0, and the corresponding

time-varying marginal effect ˆβ_p,q,ts|i can be obtained as ˆ

β_p,q,ts|i = ˆβ_p,q,0s|i + Zi_t−1

0

ˆ

ηs|i_p,q (3.20) In the end, we will run a joint significance test for linear hypothesis based on the following statistics

ST = min ξs_∈σ 0 T X t=1 ρp(Xts− B 0 tξs) − min ξs_∈RKB T X t=1 ρp(Xts− B 0 tξs) (3.21) where Bt≡ (V aRti, V aRit· Zit−1, V (i)

t ), corresponding KB-parameter vector

ξs, and σ0refers to the constrained set of parameter under H0. However, the

parameter vector is involved in the test statistic, so we cannot deliver valid inference from it since the asymptotic distribution is unknown. Chen et al. (2008) proposed an adjusted version of the test statistic we can resample

Chapter 3. Model and Methodology 15 from, S_T? = min ξs_∈σ 0 T X t=1 ωtρp(Xts− B 0 tξs) − min ξs_∈RKB T X t=1 ωtρp(Xts− B 0 tξs) − ( T X t=1 ωtρp(Xts− B 0 tξˆcs) − T X t=1 ωtρp(Xts− B 0 tξˆs)) (3.22)

where ˆξs_c denotes the constrained estimate of ξs_{, and ω}

t is a sequence of

standard exponentially distributed random variables, with both mean and variance equal to one. And they also showed that S?_T delivers a good ap-proximation of the distribution of the original format of the test statistic. As a result, the distribution of ˆξ_cswill be set as a benchmarking, and if ST

yields a given significance level of ˆξs_c, we reject the null hypothesis. In our case, 10% is set as the threshold to define significant effects. The company is considered to be systemically relevant if an increase in its potential loss position causes significantly higher tail risk of the system, after control for the general economic state variables as well as the risk inflows from other companies. To test the joint significance of the model, we proposed three hypothesis:

H1 : β₀s|i= η_Sizes|i = η_Leverages|i = 0

And then, in the second hypothesis, we want to test if whether marginal effects on the system are time-varying, which yields:

H2 : η_Sizes|i = η_Leverages|i = 0

While, if H2 is not rejected, the we re-specify the systemic risk beta as a

constant. Reconstruct the model without the interaction variables, and test the hypothesis:

H3 : β0s|i= 0

If the model is well defined, we can then start to construct the systemic relevance ranking using a time-varying realized systemic risk contribution.

Chapter 4

Data and Variables

4.1

Analyzed Financial Institutions

In order to capture a comprehensive view of the network structure of fi-nancial institutions in China, we employ the dataset following the criteria as stated:

• The company should be actively traded in the stock exchange market in mainland China, either is listed on Shanghai Stock Exchange (SSE) market or Shenzhen Stock Exchange (SZSE) market. Since the regu-latory environment between mainland China and other stock market are different, we only explore the relationship within the same regu-latory frame to control for the external influence caused by potential omitted variables;

• The company should be actively traded from the beginning of 2010 till the recent financial fundamental release date of March 31 of 2016. China has adopted its “4-trillion economic stimulus program” in the late phrase of 2008, and is comprehensively implemented after 2009. It has been criticized to cause the debt issue in China since a large amount of hot money rushed into high-return sector such as real es-tate and financial sector. Our aim is to investigate the systemic risk after the widespread implementation of this program;

• The company should be recognized and classified as a financial insti-tution during the selected time period. This criteria is made to main-tain that our selected company keeps playing as a financial institution thus it makes sense when we analyzing its relevant systemic impor-tance. We follow the Guidelines for the Industry Classification of Listed Companies issued by China Security Regulatory Commission (CSRC) to make this judgment.

It results in a dataset consisting of 32 publicly traded financial institutions in Chinese stock market, which exists from January 2010 to March 2016. These financial institutions are grouped into four sectors: commercial banks, security-broker dealers, insurance companies, and other financial services such as trust companies. We also add the sub-industry classification from Bloomberg as a reference in Table4.1.

Chapter 4. Data and Variables 17

TABLE4.1: Analyzed Financial Institutions

Symbol Institution Name Stock Code Bloomberg Sub-Industry CSRC Sector

ABC Agricultural_{Bank of China Limited∗} 601288 Banks Commercial Banks ATI Anxin

Trust Co., Ltd. 600816 Instl Trust, Fiduciary & Custody Other Financial Institutions BKB Bank of_{Beijing Co., Ltd.} 601169 Banks Commercial Banks BCL Bank of_{China Limited} 601988 Banks Commercial Banks BOC Bank of_{Communications Co., Ltd.} 601328 Banks Commercial Banks BNN Bank of_{Nanjing Co., Ltd.} 601009 Banks Commercial Banks BON Bank of_{Ningbo Co., Ltd.} 002142 Banks Commercial Banks SOA Changjiang_{Securities Company Limited} 000783 Institutional Brokerage Security Brokers-Dealers CNB China_{Citic Bank Corporation Limited} 601998 Banks Commercial Banks CCBN China_{Construction Bank Corporation} 601939 Banks Commercial Banks CLF China_{Life Insurance (Group) Co., Ltd.} 601628 Life Insurance Insurance MER China_{Merchants Bank Co., Ltd.} 600036 Banks Commercial Banks CMZ China_{Merchants Securities Co., Ltd.} 600999 Institutional Brokerage Security Brokers-Dealers CMB China_{Minsheng Banking Corp.,Ltd.} 600016 Banks Commercial Banks CNP China

Pacific Insurance (Group) Co., Ltd. 601601 Life Insurance Insurance

CSC Citic_{Securities Company Limited} 600030 Institutional Brokerage Security Brokers-Dealers EBS Everbright_{Securities Company Limited} 601788 Institutional Brokerage Security Brokers-Dealers YAR Gf_{Securities Co., Ltd.} 000776 Wealth Management Security Brokers-Dealers BEH Guoyuan_{Securities Company Limited} 000728 Institutional Brokerage Security Brokers-Dealers SMT Haitong_{Securities Co., Ltd.} 600837 Institutional Brokerage Security Brokers-Dealers HXB Hua Xia_{Bank Co., Limited} 600015 Banks Commercial Banks SRX Huatai_{Securities Co., Ltd.∗} 601688 Institutional Brokerage Security Brokers-Dealers ICBC Industrial_{And Commercial Bank of China Limited} 601398 Banks Commercial Banks IBC Industrial_{Bank Co., Ltd.} 601166 Banks Commercial Banks LIU Northeast_{Securities Co., Ltd.} 000686 Banks Commercial Banks DEV Ping An_{Bank Co., Ltd.} 000001 Life Insurance Insurance

PING Ping An_{Insurance (Group) Company of China, Ltd.} 601318 Instl Trust, Fiduciary & Custody Other Financial Institutions SIT Shaanxi

International Trust Co., Ltd. 000563 Instl Trust, Fiduciary & Custody Other Financial Institutions SAC Shanghai_{Aj Group Co., Ltd.} 600643 Banks Commercial Banks SPU Shanghai_{Pudong Development Bank Co., Ltd.} 600000 Institutional Brokerage Security Brokers-Dealers CDC Sinolink_{Securities Co., Ltd.} 600109 Institutional Brokerage Security Brokers-Dealers CCW Southwest_{Securities Co., Ltd.} 600369 Institutional Brokerage Security Brokers-Dealers

4.2

Data and Variables

4.2.1 Company-Specific Variables

We use publicly available data to determine a company’s propensity to be involved in financial distress. Stock prices are obtained from Datastream with a daily frequency, and the others are from Compustat quarterly .

• Daily Stock Price Return

Our tail risk calculation is based on a company’s daily stock price. Company stock price return is used as the underlying asset return in the calculation of tail risk V aRi

t for company i. Denote that the

stock price of company i at time t is Pti, then we use the log-return of

the stock price as the asset return for the company, which is defined as Xi

t = logPti− logPt−1. The daily stock price return of companies

selected from different sector are displayed in Figure4.1.

FIGURE4.1: Stock Price by Date

We can see that from 2015, there is large volatility in stock prices al-most for all companies. Hence, it is expected to be a system distress of financial sector.

• One-period Lagged Daily Stock Price Return

We also include a one-period lagged daily stock price return to ac-count for the potential volatility clustering, which refers to a general observation in financial market that "large changes tend to be fol-lowed by large changes, of either sign, and small changes tend to be followed by small changes. (Berger and Mandelbrot,1963)".

• Leverage

We use_{Shareholders’ Equity}Total Liability to measure a company’s leverage. It is argued that high financial leverage has resulted in the widespread failures of financial institutions during the 2007-2009 crisis (Acharya, Schnabl, and Suarez, 2013,Goel, Song, and Thakor, 2010, Shleifer and Vishny,

Chapter 4. Data and Variables 19

2010). A company with a leverage ratio which is larger than 1 is con-sidered to be highly leveraged. Table4.2shows the arithmetic mean of the leverage ratio of all companies from 2010 to 2016.

TABLE4.2: Arithmetic Mean of All Companies, 2010-2016

Year 2010 2011 2012 2013 2014 2015 2016

Leverage 9.8369 8.7666 8.4534 8.4859 8.5823 8.9372 8.2871

• Size

The size of the company is measured as the logarithm of its market capitalization. A small-sized company maybe more exposed to mar-ket risks, and it is evidenced by an empirical analysis from Akbari, Rostami, and Veismoradi (2012).

• Stock Return Volatility

Stock return volatility is calculated on a daily base as moving aver-age of 5 trading days of the standard deviation of the returns, which captures the degree of variation of a company’s stock price.

• One-period Lagged Loss Exceedances of Company j

Loss exceedances are defined conditional on a distress scenario, and we only consider the influence of of company j on VaR of company i if the former one is under pressure of undercapitalization. Then we rewrite E−i_t in a conditional format as E_tj = X_tj1(X_tj ≤ ˆQ0.1),

and ˆQ0.1 represents the unconditional sample quantile of the

distri-bution of Xtj. (1 is an indicator.) Since we are interested in using tail

risk spillovers as a potential proxy of liability claims between differ-ent financial institutions, simultaneous issue might occur due to the unknown relationship between a conditional quantile and the condi-tional distribution of loss exceedances for time period t. Hence, in-stead of using loss exceedances for time index t, we use the value from t − 1 to maintain the order of presence of independent variables and dependent variables.

4.2.2 Macroeconomic Variables

We also use 4 lagged-macroeconomic variables to account for the general state of the economy. The daily equity market return and real estate sec-tor return are obtained from Datastream, and the 1-year Government bond yields are from Bloomberg in a daily base.1

• Daily Equity Market Return

The daily equity market return is a good proxy of the general perfor-mance of the whole financial market. For example, when the govern-ment adopts a new policy, it may create a good or a bad signal of the

1_{We would like to follow the macroeconomic variable set suggested and used by Adrian}

and Brunnermeier,2011, while some data are not available in China. As for the implied volatility index, VXFXI, computed by the Chicago Board Options Exchange (CBOE), it launched on March 16, 2011, which is not within our time range.

economic or industry development. It will influence the level of confi-dence of the investors, thus leading to a volatile stock market climate which will also affect the existing financial institutions.

• Real Estate Sector Return

The financial market is highly correlated with the performance of real estate sector in China. The previous global financial crisis also started from the bursting of housing bubbles. In this case, we run a Pearson’s product-moment correlation for the daily log-returns of financial sec-tor and real estate secsec-tor, the correlation coefficient is 0.773 with a p − valueof 0.000 (2.2e-16) rejecting the null hypothesis of there is no correlation between the performance of the two sectors.

• The Change of 1-yr Government Bond Yield

The government bond is the basis of financial market. Since it is backed by Chinese government or government-linked agencies, it gives an idea of future interest rate changes and economic activity of the country. A short-term government bond with maturity of 1 year is picked as the proxy to indicate the predictable economic and politi-cal stability. Financial market is sensitive to any changes of economic and political environment, so it is also used for us to control for the macroeconomic status.

4.2.3 Stationarity Check

We run a stationarity check for macroeconomic variables before includ-ing them into the model. The Augmented Dicky-Fuller test has been per-formed. The test results are displayed in Table4.3:

TABLE4.3: Augmented Dicky Fuller Test

Dickey-Fuller Lag order p-value Real Estate Sector Return -9.5927 11 0.01 Daily Equity Market Return -8.7997 11 0.01 Change of Government Bond Yield -9.4726 11 0.01

As a result, all of our macroeconomic variables are stationary, so they will all be included in the model.

4.3

System VaR

In modeling systemic risk contributions, we use the price index of financial sector, which represents the general performance of 63 financial institutions in China, and our analyzed companies are all involved in this list. We also take the log return of the index as the dependent variable for system VaR. It is also captured in a daily base. As for the drivers of system VaR, since we are going to use the same sets of data and variables as in company-specific VaR, we will only list the variables instead of making detailed descriptions. The log returns of the whole financial sector is displayed in Figure4.2

Chapter 4. Data and Variables 21

FIGURE4.2: Daily log Returns of System

4.4

Data Processing

It is noticed that the financial fundamentals of a company are captured quarterly, while for the rest of observations, the data frequency is based on daily. In order to achieve a balanced and consistent data set for our chosen time interval, we process our current variables through temporal disaggregation method.

4.4.1 Dealing with Low Frequency Data

The book value of Total Liabilities and Shareholders’ Equity are used to calculate a company’s leverage ratio, and they are released in the compa-nies’ financial reports quarterly. However, there will only be 25 observa-tions if we adopt a quarterly calender for estimation, thus the asymptotic property of the quantile estimators will be affected due to the small sam-ple size (Wooldridge,2015). Hence, we adopt the temporal disaggregation method to convert a low frequency variable into a relatively high frequency series as daily for both Total Liabilities and Shareholders’ Equity.

The standard methods for temporal disaggregation can be classified into two categories: one is estimated using one or several indicators and per-form a Generalized Least Squares (GLS) regression on the low frequency series, such as Chow-Lin (Chow and Lin, 1971) for stationary or cointe-grated series, and Fernandez (Fernandez,1981) and Litterman (Litterman,

1983) for non-cointegrated series; the other can deal with the disaggrega-tion of a series without an indicator, such as Denton (Denton, 1971) and

Denton-Cholette (Dagum and Cholette, 2006). Chow-Lin method is cho-sen to disaggregate Total Liabilities into daily base since there is no high frequency data can be used as an indicator for it. Denton-Chollete is cho-sen for Shareholders’ Equity as we can pledge it to Market Capitalization of a daily base. For both variables, the average of the resulting daily-based series (high frequency) is consistent with the quarterly-based series (low frequency).

As a results, the constructed dataset contains 1630 daily observations of 32 publicly traded financial institutions with a time range from January

2010 to March 2016. However, the dataset is not balanced, due to: 1) miss-ing values for stock prices; 2) lagged variables construction. Hence, before running the models, all missing variables are dropped, which results in 1385 daily observations for all companies.

23

Chapter 5

Analysis and Results

5.1

Company-specific Tail Risk

5.1.1 LASSO Selection of Tail Risk Drivers

LASSO selection procedure has been performed for a tail risk setting with q equals to 0.05, which represents the 5% quantile of distribution of log-returns for each individual companies. Since the added penalty term will induce a downward estimation risk, we rerun quantile regression with same confidence level to get an accurate estimates. The complete results are shown in TABLEAin AppendixA. In Table5.2, we present the risk drivers selected by LASSO for four companies as representatives for Big Fours, commercial banks other than the Big Fours, insurance companies, and security broker-dealers. The explanation of different risk drivers can be checked in Table5.1.

TABLE5.1: Explanations of Variables

Item Explanation

Symbol-1 One period (day) lagged logreturns of company Symbol Ex.Symbol-1 One period (day) lagged loss exceedance of company Symbol

MktCap Size of the company

logReturnsM-1 One period (day) lagged logreturns of market equity logReturnsRE-1 One period (day) lagged logreturns of real estate sector

Note: Symbol refers to the abbreviation of a specific company.

As a result, for most of the analyzed companies, the selected drivers for individual company’s tail risk are risk exceedances from other companies as E−i_t . Hence, we not only captured the extent of how a company’s tail risk is affected by relevant drivers, we also obtain the direction of such in-fluence. Most of the coefficients related to loss exceedances are negative, which gives an insight that company i’ s tail risk V aRi_{increase while}

com-pany j is facing with a high negative return.However, intuitively for those with positive coefficients, it describes a situation that when company j is under stress, the company i will benefit from this situation which results in a lower tail risk V aRi, a further detailed analysis of the mechanism should be done to investigate this issue. To construct a tail risk contagion network, we will drop this part from our thesis.

Two signals have raised our attention that 1) the tail risk interconnected-ness between company i and E−i_t usually exists when j refers to commercial

TABLE5.2: Variables Selected by LASSO for V aRi_{with q =}

0.05

Big Fours Security Broker-dealers

BCL Value Std.Error t value Pr(>|t|) SOA Value Std.Error t value Pr(>|t|) Ex.CMZ-1 0.27758 0.1239 2.24037 0.02523 Ex.ABC-1 0.70977 0.32533 2-18172 0.0293 Ex.BEH-1 -0.18419 0.08998 2.04711 0.04084 Ex.BCL-1 -0.2649 0.10102 -2.62218 0.00884 BCL-1 -0.10668 0.03491 -3.05549 0.00229 Ex.MER-1 -0.42965 0.21695 -1.98044 0.04786 Ex.EBS-1 -0.20725 0.09066 -2.28591 0.02241 Insurance Company Ex.DEV-1 0.34946 0.15673 2.22977 0.02593

PING Value Std.Error t value Pr(>|t|) Ex.SIT-1 0.31262 0.07393 4.22855 0.00003 (Intercept) -0.36385 0.08542 -4.25957 0.00002 Ex.SAC-1 -0.24725 0.07109 -3.47804 0.00052 Ex.BCL-1 -0.32964 0.09243 -3.56639 0.00037 logReturnsM-1 0.418 0.19941 2.09618 0.03625 Ex.CCBN-1 0.33855 0.14521 2.33139 0.01988

Ex.HXB-1 0.41946 0.12735 3.29383 0.00101 Commercial Banks

MktCap 0.02819 0.00673 4-18854 0.00003 SPU Value Std.Error t value Pr(>|t|) logReturnsRE-1 0.18329 0.07282 2.51696 0.01195 Ex.HXB-1 -0.34048 0.1286 -2.6476 0.0082

Note: A complete result is displayed in TableAin Appendix IA.

banks. It indicates that the tail risk of company i will increase especially when commercial banks are involved in potential financial stresses with tail risk linkages; 2)connections between close competitors of commercial banks are evidenced in our model.

To evaluate the goodness of fit of the model specification, first, we per-form a F-test for joint linear hypothesis to test the joint significance of se-lected loss exceedances E−i_t for company i; and then, we perform a Like-lihood Ratio version of the dynamic quantile test to investigate how well the model predicts the size and frequencies of tail risks. The corresponding test statistics can be checked inB.1in AppendixB. For most of the cases, F statistic shows that the LASSO-selected tail risk spillovers are significant. Meanwhile, comparing to the models only with balance-sheet variables and macroeconomic variables, the model, of which variables selected by LASSO, generally with tail risk linkages between different financial insti-tutions, the results of LR test also show significance in most of the cases. It addresses the importance of including tail risk spillovers into the model, thus confirms our intention of building the tail risk network to investigate financial network properties.

5.1.2 Tail Risk Network

By assigning the directions, we can classify the drivers" and "risk-takers" for any given pairs of individual companies. A general overview of such relationship is shown in Table5.3. The column "Influenced Company" refers to companies whose lagged loss exceedances are selected by LASSO as risk drivers of V aRit for company i; The column "Influencing

Compa-nies" refers to companies which are influenced by the loss exceedances of company i. Correspondingly, influenced companies will be classified as "risk-drivers" with in the system, while influencing companies will be clas-sified as "risk-takers" in the sense. Given the tail risk cross dependencies, we construct the network with the chosen layout that satisfied the condi-tion that the sum of cross-company distance is minimized. Hence, the most highly connected companies are located in the center. The full network graph is shown in Figure5.1.

Chapter 5. Analysis and Results 25 ABC ATI BCL BEH BKB BNN BOC BON CCBN CCW CDC CLF CMB CMZ CNB CNP CSC DEV EBS HXB IBC ICBC LIU MER PING SAC SIT SMT SOA SPU SRX YAR

FIGURE 5.1: The full network of 32 listed financial institu-tions in Chinese stock market

As we can see from the graph, in the center lies the "Big Four"1 commer-cial banks with the most outgoing arrows but less incoming arrows. Mean-while, the most influenced companies are also located in the center of our network, with more incoming arrows than out going arrows. To address the systemic importance, we classify those companies into three groups. The companies in the first group act as the risk-drivers within the system as they have more outgoing arrows than incoming arrow. For those compa-nies, their failure may affect a large portion of the companies in the market, while they are unlikely to be affected by the distress of other companies.

1_{The Big Four commercial banks consists of Bank of China, China Construction Bank,}

Industrial and Commercial Bank of Chinaand Agricultural Bank of China. All of the Big Fours are included in our empirical analysis.

Since a shock created by these companies can cause a domino effect within the whole system, these companies should be closely monitored by supervi-sory authorities.Besides the "Big Four" commercial banks as we mentioned before, several researched commercial banks are also been classified in this group2. For commercial banks such as ICBC, IBC and CMB, they don’t have any incoming arrows which they only act as risk drivers within the system. We consider it as the most influential financial institution within our tail risk network. Hence, it has a relatively larger probability to deliver a nega-tive impact on systemic risk than being influenced by the neganega-tive impact of the system. It is noticed that PING, identified as an insurance company, are also classified into this group. PING stands for Ping An Insurance Group. It is a "group of financial activity" rather than an insurance company since it also operates as a commercial bank, as well as an investment bank. Hence, it is not difficult to explain that the joint role of PING results in its position within the system.

The second group contains companies that mainly act as risk-takers. It only has inflow arrows that indicates these companies are not systemically risky, while they are likely to suffer from the distress of other companies. It may give an insight for these companies to account for the spillover effect of other companies in their internal risk management. These companies are generally security-broker dealers.

The third group contains companies that act as both drivers" and "risk-takers", while to separate them from the first group, they contains less out-going arrows than incoming arrows. These companies are main systemic players who receive and transmit risks within the financial network. There is no specification for different sectors in this group, commercial banks, in-surance companies These companies should also be supervised properly as they create new channels for systemic risk to contagion.

Hence, the structure of our network can be classified into three circles. The circle within the center contains those large commercial banks, while most security broker-deals are classified into the outward circle since they convey and transmits the least risk. The circle in the middle, taking risks from the center-located financial institutions and transmits them within its own range or towards the outside circle. Within our tail risk networks, banks are playing an important role in generating systemic risk to the whole system, and this feature has already been evidenced by a vast of literatures (Allen and Gale,2007,Anand et al.,2013).

5.2

Measuring Systemic Risk Contributions

We are going through the results by comparing two different types of com-panies, one fails to yield a significant marginal effect, and the other one re-sults in a significant marginal effect. Two examples are given in the follow-ing part, one is ABC as the representative of companies which are consid-ered not to be systematically relevant, the other is BCL as the representative of the systemically relevant companies.

2_{Among the "Big Four" banks, China Construction bank acts as a risk-taker rather than a}

Chapter 5. Analysis and Results 27

TABLE5.3: Tail Risk Cross-dependencies

Commercial Banks Influenced Company Influencing Company ABC BOC, MER,CMB,DEV,SPU CSC,SMT,ARX,BNN.SOA,CMZ

BKB CLF,CNP,SRX,IBC SIT,CCBN

BCL CMZ,BEH ATI,PING,SOA,CDC,CLF

BOC BON,SMT CCBN,CCW,ABC

BNN ABC,HXB,SAC,CCW SAC,CDC,CLF

BON CSC,LIU BOC,CNP,CSC

CNB EBS,SMT CCBN BKB,BOC,MER,EBS,SMT,PING ATI,PING,CDC,EBS MER CLF,CNP ABC,SOA,SAC,CCBN,CLF,CDC CMB ABC,SIT,SAC HXB SOA ATI,BNN,DEV,PING,SPU ICBC CLF,EBS IBC EBS,BKB,SIT DEV HXB SOA,CLF,CDC,CMZ,ABC SPU HXB CCW,ABC Insurance Company CNP BON,SRX,PING BKB,AMT,MER CLF ATI,BCL,BNN,MER,CSC,SRX,ICBC,DEV,SIT BKB,SIT„CDC,MER,EBS PING BCL,CCBN,HXB SRX,CCBN,SAC,SNP.CSC Security &Broker-dealers &Others

LIU BON,SAC

SAC BNN,MER,CMZ,CMB,EBS,LIU,PING EBS,BNN,SOA

SOA ABC,BCL,MER,EBS,DEV,SIT,SAC HXB,EBS

CMZ ABC,DEV BCL,SAC

CSC ABC,BON,PING BON,CLF

EBS SOA,CCBN,CLF,ICBC,IBC,SIT,SAC SRX,SOA,CNB,CCBN,SA,CDC,CCW

YAR SAC CDC,CCW BEH SIT,SAC BCL SMT ABC,CNP BOC,CNB,CCBN,CDC SRX ABC,EBS,PING,SIT CLF,CNP CDC BCL,BNN,CCBN,CLF,EBS,SAC,CCW SIT,CCW,ATI CCW BOC,EBS,YAR,SIT,SPU,CDC BNN,CDC ATI BCL,CCBN,HXB,CDC CLF

SIT BKB,CLF,CMB,IBC,CDC SRX,SOA,CLF,CDC,CCW

5.2.1 Example: ABC

ABC refers to the Agricultural Bank of China, which is one of the "Big Fours" commercial banks in China. We are going to take ABC as an example to go through the procedure of estimating systemic risk contributions.

Unrestricted Model

Recall from the previous section, we selected the tail risk drivers by LASSO. And for ABC, it is influenced by BOC, MER,CMB,DEV,SPU. The unrestricted model will only include the tail risk of these companies, and we will use the pre-estimated resultsV aRˆ i_q,t, which are obtained by LASSO to capture the time varying systemic betas βp,qs|i.

H1: Restricted Model 1

As illustrated in3.6, in the restricted model under H1, the tail risk estimates of ABC, Size as well as the Leverage Ratio are also included based on the unrestricted model.

H2: Restricted Model 2

Referring to3.6, the VaR of ABC is excluded based on models under H1.

H3: Restricted Model 3

Under H3, we will only have all tail risk estimates of ABC and all other in-fluencing companies, which tries to capture the tail risk of the whole system only by V aRs of all related companies.

Test Results

For each of the model, we use "wild type" of bootstrap to yield the nec-essary statistics and the corresponding p-values with resampling of 1000 iterations. The test statistics and p-value are displayed in Table5.4

TABLE5.4: Test Statistics and p-value for ABC

Hypothesis ST p-value

H1 0.0237 0.0814

H2 0.0108 0.1970

H3 0.0071 0.2784

However, the null hypothesis that time-varying β equals to zero is not rejected, which concludes that ABC is not considered to be systemically rel-evant through our tail risk network.

We run the models for all 32 countries to check the systemically relevance of company i.

5.2.2 Example: BCL

BCL refers to Bank of China Ltd, which is also one of the "Big Fours" commer-cial banks. The tail risk influencing companies for BCL consists of CMZ and BEH selected by LASSO in previous steps. The test statistics and p-value are displayed in Table5.5

TABLE5.5: Test Statistics and p-value for BCL Hypothesis ST p-value

H1 0.0433 0.0054

H2 0.0312 0.0081

H3 0.0297 0.0008

Hence, we calculated the realized systemic risk betas for BCL and it has been shown in the following Figure5.2

Chapter 5. Analysis and Results 29

FIGURE5.2: Realized Systemic Risk Betas for BCL

We can read from the Figure5.2that when it is before 2015, the realized systemic risk beta stays around 0 in a relatively stable status. While, when it goes to 2015, as what we have showed in Chapter4, the whole systemic experienced a volatile period. The risk contributions measured by realized systemic risk beta started to increase sharply.

5.3

Discussion

The financial companies with significant marginal effect are listed in the following Table5.6

TABLE5.6: Companies with Significant βs|i

Symbol PH1 PH2 PH3 BCL 0.0054 0.0081 0.0008 BEH 0.0227 0.0031 0.0005 BOC 0.0026 0.0004 0.0002 BON 0.0679 0.0339 0.0101 CNB 0.0359 0.0450 0.0245 CSC 0.1268 0.0182 0.0048 MER 0.0333 0.0185 0.0882 SMT 0.1999 0.1201 0.0613 YAR 0.0092 0.0070 0.0035

Hence, by their rankings of βs|i, we also address the systemically rele-vance of these financial institutions. Since βs|i_{is time-variant, we are going}

to pick up the values of the March 2015 and the March 2016 to see the rel-ative systemic contribution of these financial institutions. It confirms our

TABLE5.7: βs|i_{Rankings for Specific Date}

Rankings 2015 Symbol Mar-15 Rankings 2016 Mar-16

1 BOC 0.3459 1 0.2630 2 BON 0.2192 4 0.1772 3 BCL 0.2009 2 0.1855 4 CNB 0.1984 3 0.1823 5 MER 0.1982 6 0.1631 6 SMT 0.1753 7 0.1618 7 YAR 0.1629 5 0.1643 8 BEH 0.1357 8 0.1175 9 CSC 0.1047 9 0.1061

analysis in the tail risk network that banks are playing an important role within the financial system in China. However, it is a bit surprising that ABC and CCBN are not of systemically importance when considering the marginal effect the tail risk of it shed on the whole financial system. Be-sides, we’ve also noticed that from March 2015 to March 2016, the absolute value of realized systemic risk beta is decreasing, while the rankings did not change much comparing to the previous year. Some other important fac-tors may explain more about the variation of the financial sector’s tail risk, such as shadow banking as Acharya et al. (2010) emphasized that shadow banking system was precisely used to organize such a "manufacturing of tail risk" in the run-up yo the crisis. Besides, investors may also fail to ade-quately discipline his form of risk-taking by financial institution. However, we captures the property of a tail risk network of the financial system in China and delivers a generally consistent importance through the network linkages as well as the marginal effect of companies’ tail risks.