Electronic copy available at: http://ssrn.com/abstract=1909327

1

MACRO STRESS TESTING ON CREDIT RISK OF COMMERCIAL BANKS

IN CHINA BASED ON VECTOR AUTOREGRESSION MODELS

Rongjie Tian*

Beijing Institute of Technology

Email: tianmemory@163.com

Jiawen Yang

The George Washington University

Email: jwyang@gwu.edu

Abstract

This paper develops a framework for stress-testing the credit risk of Chinese commercial banks to

macroeconomic shocks. Using data over the period 1985-2008, this study establishes a vector

auto-regression (VAR) model to describe the links between default rate and macroeconomic factors, and

then designs three stress scenarios to implement the stress testing by Monte Carlo simulation. As a result,

a credit loss distribution is generated. Our results indicate that the shocks in real property and CPI bring

long term and worst impact on credit risk to commercial banks in China.

JEL: G21,G32,E17

Keywords: Credit risk; Macro stress testing; Commercial bank; VAR model

* This research was conducted while Rongjie Tian stayed at the George Washington University as a visiting scholar

from September 2009 to September 2010.

Electronic copy available at: http://ssrn.com/abstract=1909327

2

MACRO STRESS TESTING ON CREDIT RISK OF COMMERCIAL BANKS

IN CHINA BASED ON VECTOR AUTOREGRESSION MODELS

1. INTRODUCTION

The global financial crisis that started in the United States in 2007 highlights the importance of

macroeconomic (macro) stress testing in the financial sector. Macro stress testing refers to a range of

techniques used to assess the vulnerability of a financial system to “exceptional but plausible”

macroeconomic shocks (see Virolainen, 2006). Most researchers design macro stress testing by modeling

the link between macroeconomic variables and credit risk measures. Sensitivity analysis, scenario

analysis, and extreme values theory are usually employed to implement the stress testing. In recent years,

a lot of effort has been put into stress testing on credit risk of banks all over the world. The New Basel

Capital Accord, Basel Ⅱ, imposes the rigorous stress testing requirements: banks which implement the

Internal Ratings-Based Approach (IRB) must conduct stress tests. The China Banking Regulatory

Commission (CBRC) also requires all Chinese commercial banks to implement stress testing to manage

credit risk. During the current financial crisis, stress testing on credit risk has become a reviving focus of

concern.

Within the framework of credit risk modeling and macro stress testing, we seek to address the

following issues in this paper: What are the most important macroeconomic variables that affect credit

risk for Chinese commercial banks? What is the specific relation between credit risk of banks and the

macroeconomic variables? How does banks’ credit risk react to macroeconomic shocks? We adopt the

default rate as our indicator of credit risk for Chinese commercial banks, and construct a Vector

auto-regression (VAR) model to generate a comprehensive indicator and then use an extended version of

Wilson (1997) model by imposing feedback effects between default rates and macroeconomic variables.

Scenario analysis is also employed as part of our stress testing. We design three “exceptional but

Electronic copy available at: http://ssrn.com/abstract=1909327

3

plausible” scenarios and use Monte Carlo simulation to get the credit loss distribution. Finally, we

compare the credit loss distribution under these stressed scenarios based on the concept of Value-at-Risk

(VaR).

The data employed in this study spans a time period from 1985 to 2008, which covers multiple

episodes of severe macroeconomic shocks such as the Asian financial crisis in 1997, the Russian crisis in

1998, and the current global financial crisis that started in 2007. The macroeconomic variables we have

examined include GDP growth, the Chinese currency exchange rate, nominal interest rate, real property

index, CPI, and unemployment rate. We find that GDP growth, exchange rate, nominal interest rate, real

property index, CPI and unemployment rate have prolonged impacts on the default rate. In order to

describe the feedback effects between variables, we employ vector auto-regression framework to assess

the impact of macroeconomic variables on firms’ probabilities of default.

The rest of the paper is organized as follows. Section 2 provides a brief literature review. Section 3

describes main features of Chinese commercial banks. Section 4 describes our methodology and data. We

lay out three specific methodological frameworks for our macroeconomic credit risk model: VAR model

with raw macroeconomic variables, VAR model with principal components analysis (PCA) and structural

VAR model. Section 5 presents our empirical results for the macroeconomic credit risk model with

different methodological framework. We also carry out our stress tests with impulse, scenario, and

variance decomposition. Section 6 concludes.

2. LITERATURE REVIEW

As Dovern et al. (2010) point out, as a field of academic research, macroeconomic stress testing is

relatively new. There are two approaches to estimating the linkage between credit risk and

macroeconomic factors. The first one is linked to the work of Wilson (1997a and 1997b), who establishes

a direct model based on sensitivity of many macro economic variables for default probability in each

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industry. Studies by Boss (2002), Virolainen (2004), Choi, Fong and Wong (2006) have followed and

advanced the work of Wilson. In comparison, the second approach is based on the work of Merton (1974),

in which asset price changes are integrated into default probability evaluation (see Drehmann and

Manning (2004), Pesaran et al. (2006)). Compared with the Wilson (1997) methodology, the Merton

approach has some disadvantages, including high data and computational requirements. According to

Sorge (2006), in the Merton approach, equity prices may be noisy indicators of credit risk. Therefore, we

adopt the first approach in this paper.

Researchers have identified macroeconomic variables that affect credit risks according to specific

macroeconomic situations of the target countries involved. Boss (2002) finds that industrial production,

inflation rate, stock price index, nominal short-term interest rates, and oil prices are the determinant

factors of default probability in Australia. Virolainen (2004) reveals that GDP growth, interest rates,

corporate indebtedness, inflation, industrial production, real wages, the stock price index and the oil

prices are the related factors for the probability of default for banks in Finland. In investigating the

determining factors for credit risk in Hong Kong, Wong, Choi, and Fong (2008) recognize the importance

of GDP growth rates in both Hong Kong and mainland China, interest rates, and real estate prices. In

order to solve the problem of a certain degree of arbitrariness in choosing macroeconomic variables, Boss

(2009) applies a principal component analysis (PCA) to a set of Austrian macroeconomic variables.

Dovern et al. (2010) model the interaction between the banking sector and the macro-economy for

German banks and their VAR analysis indicates that the level of stress in the banking sector is strongly

affected by monetary policy shocks.

For the dependent variable, loan loss provisions (LLPs) and non-performing loans (NPLs) have been

used as a proxy of default rate. However, details of the default rate used for macro stress testing vary from

country to country, depending on the availability of data. For example, a central bank with limited access

to detailed data for individual banks tends to focus on aggregate data, such as LLPs in the banking sector

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and the default rate of the corporate sector as proxies for the quality of bank loan portfolios.

Current studies of macro stress testing have mainly focused on advanced economies. Kalirai and

Schleicher (2002) use single equations and a large array of macroeconomic variables to test the soundness

of the Austrian banking sector. Hoggarth et al. (2005b) employ a vector autoregressive model for macro

stress tests of the banking sector in the UK. Dey et al. (2007) modify the Wilson (1997) and Virolainen

(2004) approach to investigate the delayed effects of macroeconomic variables on default risks for banks

in Canada. Sanvi Ai et al. (2009) simulate default probabilities for the French manufacturing sector for

several macroeconomic scenarios. Peter Spencer and Zhuoshi Liu (2010) develop a multi-country

macro-finance KVAR model to study international economic and financial linkage among the US, the UK

and other OECD countries.

However, studies of macro stress testing on credit risk of Chinese commercial banks are still at an early

stage due to special features of the Chinese bank system and data deficiencies. Xiong (2006) and Ren

(2007) employ a multiple Logit regression model on macroeconomic factors and finds that GDP, inflation

rate and interest rate are significant factors that affect the stability of the Chinese banking system. Li

(2008) may be the first one to test the relationship between probability of default (PD) and

macroeconomic factors in China based on the frameworks of Wilson (1997) and Virolainen (2004).

However, their results just provide a point estimation result based on stress scenarios. Simulation methods

have not been seen in stress testing for Chinese banks, which is accomplished in this paper.

3. MAIN FEATURES OF THE BANKING SYSTEM IN CHINA

China’s banking system has some unique features. First, four largest commercial banks, often referred

to as “the big four,” dominate China’s banking industry. Between 1985 and 2008, China’s banking sector

went through significant reforms. Our study reflects the performance and defaults of these big four banks

in China.

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Second, the management and disposition of non-performing loans (NPLs) has been a main focus in

China’s banking reform. As this study chooses the default rate or NPL rate as an indicator of credit risk,

special attention has to be paid to the reforms involving NPLs in our analysis. From 1985 till the

mid-1990s, the big four, designated as specialized state owned commercial banks, took the responsibility

of financing most of the capital needs for investment and constructions by the state owned enterprises

(SOEs). They even had to lend to inefficient sectors, such as stagnant SOEs and, as a result, they

accumulated large volumes of NPLs (see Kumiko (2007)). In the mid-1990s, the Chinese government

decided to turn these specialized banks into truly commercial banks. Since 1999, China took measures to

recapitalize the state-owned banks and peel off NPLs from their balance sheets. As a result, the level of

NPLs has significantly declined ever since.

Third, as the big four had the responsibility to lend to SOEs for a long time, the NPLs in China have

been tightly related to macroeconomic policies in China. According to a survey by the central bank of

China, central and local government intervention and mandatory credit support for state owned

enterprises contributed 60% of the NPLs, while the banks’ own problems contribute for only 20% (Zhou,

2004). Therefore, there may be a more tight relationship between NPLs and macroeconomic factors in

China.

4. METHODOLOGY AND DATA

4.1 The macro VAR framework

We try different methodologies in our study to see which fits our data the best: (1) VAR model with

original or raw macroeconomic variables (Model A family), (2) VAR model with principle component

analysis (Model B family), and (3) structural VAR (SVAR) model with original macroeconomic variables.

The advantage of using original or raw data to establish VAR model is that the model could reflect all the

information of data and we could explain the result obtained easily. However, in order to avoid

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multicollinearity among these variables, the number of macroeconomic variables may have to be limited.

In our case, four variables are selected. In order to save more macroeconomic information in our model,

we also consider the PCA method to integrate six variables into four principle components, which may

improve the performance of the VAR model. Thirdly, we estimate an SVAR model for the relationship

between NPLs and macroeconomic variables as such a model may reflect the contemporaneous

information of macroeconomic variables.

4.1.1 The macro credit framework – The VAR model. The macroeconomic credit risk model is based on

the Credit Portfolio View model proposed by Wilson (1997a and 1997b) and developed by McKinsey

(1998). This approach is well suited to macro stress tests because it relates the default rate in a given

economic sector to macroeconomic factors. Hence, when the model is estimated, the default rate can be

simulated through the effects of macroeconomic shocks applied to the system. In turn, these default rates

can be used to simulate the loss distribution for a given credit portfolio.

Our macroeconomic credit risk model is very close to the Wilson model. However, there is one major

difference -- we use a Vector Auto-regression model (VAR) with all variables. The VAR approach, made

popular by Sims (1980), has become an important tool in empirical macroeconomics. The popularity of

this approach arose both out of the inability of economists throughout the 1970s to agree on the true

underlying structure of the economy and from the Lucas critique, that changes in policy systematically

alter the structure of econometric models.

The macroeconomic credit risk model we employ (namely the Model A family) is described as follows:

1

( 1,2,..., )p

t t i

i t t

it t i

y ya Z W t N

X X

(1)

where yt denotes the default rate of banks, Xt is the (n1) vector of macroeconomic variables at time t

8

(Xt=(x1,x2,…,xn)’), Zt is the (m1) vector of exogenous variables, a is the ((n+1) 1) vector of constant, Φi

is an ((n+1)(n+1)) autoregressive matrix with lag i, for i=1,2,…,p, B is the (m1) coefficient vector of

exogenous variables, and Wt is a vector of serially uncorrelated innovations, vectors of length n. Wt is a

multivariate normal random vector with a covariance matrix Q, where Q is an identity matrix, unless

otherwise specified.

4.1.2 The principle component analysis (PCA). Principle components analysis (PCA) was invented in

1901 by Karl Pearson, developed by Hotelling (1933) and the best current time reference is Jolliffe (2002).

The aim of PCA is to reduce data dimensionality by performing a covariance analysis between variables.

As such, it is suitable for data sets in multiple dimensions. Instead of estimating the probabilities of

default by the changes of individual macroeconomic variables, we use a PCA and take the resulting

factors as input for the regression analysis. A PCA is an orthogonal linear transformation that places the

projection of the data with the greatest variance on the first coordinate. The other coordinates are chosen

subsequently, so that they explain the maximum remaining variance subject to the condition of

orthogonality. In this paper, the first four components are taken into account and they explain 95% of the

variance of the seven variables. The relationship between components and variables could be explained as

follows (Jolliffe, 2002).

1 11 1 12 2 1n nPCA u x u x u x

2 21 1 22 2 2n nPCA u x u x u x

(2)

1 1 2 2p p p pn nPCA u x u x u x

2 2 2

1 2 1 1,i i inu u u i p (3)

1 1 2 2 0 for all i j i j in jnu u u u u u i j (4)

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where PCAi (i=1,…,p) is a set of principle components, xi (i=1,…,n) is a set of macroeconomic variables

and uij (i,j=1,…,n) is a set of unknown coefficients which need to be estimated. The first principal

component, PCA1, accounts for the maximum variance in the data, the second principal component, PCA2,

accounts for the maximum variance that has not been accounted for by the first principal component, and

so on.

In this paper, we also establish credit risk model with principle components (model B family namely),

which is computed from the original macroeconomic variables through principle component analysis. The

macroeconomic credit risk model with principle components we employ is described as follows:

1

( 1,2,..., )p

t t i

i t t

it t i

y ya Z W t N

PCA PCA

(5)

where yt denotes the default rate of banks, PCAt is the (n1) vector of macroeconomic variables at time t

(Xt=(x1,x2,…,xn)’), Zt is the (m1) vector of exogenous variables, a is the ((n+1) 1) vector of constant, Φi

is an ((n+1)(n+1)) autoregressive matrix with lag i, for i=1,2,…,p, B is the (m1) coefficient vector of

exogenous variables, and Wt is a vector of serially uncorrelated innovations, vectors of length n. Wt is a

multivariate normal random vector with a covariance matrix Q, where Q is an identity matrix, unless

otherwise specified.

4.1.3 The macro SVAR model. Structural VARs (SVAR) are an extension of traditional VAR analysis.

The structural VAR approach aims to provide the VAR framework with structural content through the

imposition of restrictions on the covariance structure of various shocks. Two features of the structural

form make it the preferred candidate to represent the underlying relations. First of all, error terms are not

correlated. The structural, economic shocks which drive the dynamics of the economic variables are

assumed to be independent, which implies zero correlation between error terms as a desired property. This

is helpful for separating out the effects of economically unrelated influences in the VAR. Second,

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variables may have a contemporaneous impact on other variables. This is a desirable feature especially

when low frequency data is used since contemporaneous data can be included in the SVAR model.

In our paper, we consider the situation of n multi variables in structural vector auto-regression, as in

Sims (1980). A structural vector auto-regression model with lag p, SVAR(p), is presented as follows

(neglecting a possible intercept and/or exogenous variables for notational simplicity):

0 1 1 2 2t t t p t p ty y y y , 1,2, ,t T (6)

where the vector yt includes the variables of interest and εt is a vector of error terms with

variance-covariance matrix Σ.

12 1

21 2

0

21 22

1

1

1

n

n

,

( ) ( ) ( )

11 12 1

( ) ( ) ( )

21 22 2

( ) ( ) ( )

1 2

i i i

n

i i i

n

i

i i i

n n nn

, 1,2, ,i p ,

1

2

t

t

t

nt

A moving average representation of Equation (6) could be presented as follows.

( ) ,t tL Y u

( ') ,t t kE u u I

(7)

2

0 1 2( ) ... p

pL L L L ,

where Ψ(L) is the parameter matrix of lag polynomial L, Ψ0≠Ik. If Ψ0 is a lower triangular matrix, the

SVAR model is called a recursive SVAR model.

Consider a moving average representation of unrestricted VAR model,

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( ) , 1,2,...,t tA L y t T (8)

Let A,B be invertible KK matrices, then multiply A

on the left to both sides of Equation (8),

( ) , 1,2,...,t tAA L y A t T (9)

If A,B satisfy the conditions as follows:

, ( ) , ( , ')t t t k t t kA Bu E u O E u u I , (10)

Equation (10) is called a SVAR model of AB type.

This SVAR model of AB type not only builds the contemporary relations among the endogenous

variables, but also reflects the response of the model to independent stochastic disturbance ut shock. If

matrix A is a identify matrix, it means that there is no contemporary relationship among the endogenous

variables and the response of every variable to orthogonal disturbance is simulated by matrix B. If matrix

B is a identify matrix, the contemporary relationship among the endogenous variables exists and is

decided by matrix A.

4.2 Data

The data for our study are retrieved from China Statistical Yearbook published by China Statistics Press

and Almanac of China’s Finance and Banking published by China Financial Publishing House. We use

the piecewise cubic Hermit interpolating polynomial method to match any missing data. Since the model

is based on the whole economic system in China, the average value of every variable is applied instead of

the value in each sector. When there are multiple changes in the interest rate in one year, the weighted

average is used for the relevant year. A line graph of NPLs is shown in Figure 1 and descriptive statistics

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of all data are presented in Table 1.

[FIGURE 1 GOES ABOUT HERE]

[TABLE 1 GOES ABOUT HERE]

As shown in Figure 1, the trend of nonperforming loans in China’s commercial banks resembles a bell,

with 1999 and 2004 as major turning points. China's main commercial banks NPLs started to decline in

1999 and declined dramatically since 2004. In 1999 and 2004, the Chinese government injected funds

into the four state owned commercial banks to offset their large amount of bad assets, paving the way for

their initial public offering. Since the big four accounted for more than 60% of the total assets in China’s

banking sector, major changes in the asset quality of the big four exert a significant impact on changes of

the overall index.

According to the pairwise correlations between macroeconomic variables, we choose six

macroeconomic variables: Nominal GDP growth (GDPG), unemployment (UEP), nominal interest rate

(NR), exchange rate (ER), Consumer Price Index (CPI), and real property index (RPI). Nominal GDP

growth and unemployment rate allow us to investigate the effect of business cycle on default rates. We

use the 1-year nominal bank loan interest rate for the interest rate variable. This rate is linked to the

majority of loans taken by corporations in China. As is known, it includes both inflation and the real rate

of interest. Interest rate has a direct impact on the cost of loans and hence the credit risk of banks.

Exchange rate is measured by the ratio of RMB, the Chinese currency, to the U.S. dollar, which is

considered as an indicator of China’s international economic environment. An increase in the exchange

rate (a depreciation of the RMB) is viewed as a weakening of the Chinese economy relative to the rest of

the world. CPI is used to measure inflation.

The real property index (RPI) measures the construction units of real property. We consider this

variable for several reasons. First, housing mortgages have grown rapidly in China. Real estate loans in

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China rose to RMB5.24 trillion in November 2008 with an annual growth rate of 10.3%. The proportion

of real estate loans in total bank loans has grown steadily as well. Second, when the real estate market

booms, even borrowers with financial hardships can pay mortgages or pay back their loans by selling

their properties. However, when the real estate market is down and house prices decline, the risk of

mortgage default increases. Third, the experience of the subprime mortgage crisis in the United States

tells us that banking stability collapses along with the housing market. Therefore, we should consider the

impact of real estate market on banks’ credit risk.

We use NPL ratio of main commercial banks in China is a proxy for default rate for two reasons. First,

the NPL data is available for the period 1985 to 2008. Second, the definition of NPL is similar with the

default rate that other researchers have used in their studies.

5. EMPIRICAL RESULTS AND STRESS TEST

5.1 Empirical results

5.1.1 Results from VAR with original macroeconomic variables. We start estimation of the VAR model

using a limited set of variables (Model A family). The pairwise correlations presented in Table 1 are taken

into account in our variable selection. This selection not only helps to identify which variables are more

correlated with default frequencies, but also to avoid possible multicollinearity problems. As a result, four

variables are selected: exchange rate (ER), nominal interest rate (NR), GDP growth (GDPG), and real

property index growth (RPI). Table 2 presents the results we have obtained using the VAR framework

with these four macroeconomic variables.

[TABLE 2 GOES ABOUT HERE]

In the first model (Model A1) presented in Table 2, the set of endogenous variables comprises the four

macroeconomic variables we have selected. As shown in the column of NR in Table 2, note that the

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coefficient of NPL(-1) is negative and significantly different from 0.This result shows that an increase in

the default rate in the t-1 period is followed by a sharp cut in nominal interest rate in period t.

Consequently, the lagged values of the default rate affect the future path of some macroeconomic factors.

This is an ex-post corroboration of the use of a multivariate framework to model macroeconomic factors

and the default rate. In addition, the negative correlation between the nominal interest rate and the lagged

default rate could stem from the assumption that a higher default rate reflects a bad economic

environment. So, even though output is not a formal target of the central bank of China, the business

cycle seems to influence the conduct of the monetary policy. For instance, a cut in the nominal interest

rate could be viewed as the response of the monetary authorities to the deterioration of the

macroeconomic environment. Besides, the coefficient of NR(-2) in Table 2 describing the evolution of

NPLs is positive and significant, so that it confirms that an increase in the nominal interest rate in (t-2)

period leads to an increase in the default rate. This result is also in line with the expectation that the

default rate increases along with interest rates owing to higher borrowing costs. In this way, there is a

feedback effect between the default rate and the nominal interest rate. This is a second argument in favor

of a multivariate framework. Exchange rate in (t-1) period displays a negative coefficient to NPLs,

suggesting that RMB currency appreciation leads to a rise in NPLs. However, Exchange rate in (t-2)

period shows a positive effect on NPLs. We will discuss this problem later.

We find no significant relations between NPLs, GDP growth, and RPI growth in Model A1. In Model

A2, we modify GDP growth and RPI growth as an exogenous variable to see if the explanatory power of

the model increases. We also add two dummy variables, a macro dummy and a loan class dummy, to

Model A2. The loan class dummy is intended to control for the change from four to five categories of loan

quality classification in China, which is 1 for the year when the loan grating reform occurred and 0 for the

other years. The macro dummy is to control for the effects of capital injection by the Chinese government

in the banking industry, which is 1 when there was capital injection and 0 otherwise.

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The AIC and SC values for Model A2 are smaller as compared with those for Model A1, indicating that

the fitting ability of Model A2 is better than Model A1. The VAR stability test is passed as well. In Model

A2, the coefficient of macro dummy is negative whereas the coefficient for the loan class dummy is not

significant. The result suggests that the effect of loan grating reform had no effect on NPLs but the capital

injection did. This finding confirms with a common notion that a change in loan classification has no real

effect on loan performance while capital injection changes the capital structure of the banking sector and

loan performance.

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5.1.2 Results from VAR with principle components. We include six macroeconomic

variables in our principle component analysis: GDP growth, exchange rate, nominal interest

rate, real property index, CPI, and unemployment rate. The results are presented in Table 3.

The first four principle components can describe 95% of data information, so we employ

these four principle components as endogenous variables in VAR Model B1.Some coefficients

of the variables in Model B1are significant, suggesting that VAR Model B1 can describe the

character of the data. However, as Table 3 shows, there is at least one root outside the unit

circle, so the VAR model does not pass the stability test. We adjust PC1(-1) and PC4(-1) as

exogenous variables and add a macro dummy to get Model B2. Model B2 is a stable VAR

system although the fitting ability does not improve over Model B1, as shown by values of

AIC and SC. In Model B3, we make PC1 and PC4 as exogenous variables to test the

influence of variables in the current period. The coefficient of PC1 and PC4 become

significant and the fitting ability of Model B3 is much better than that of Model B2. Moreover,

Model B3 satisfies the VAR stability condition. Our result suggests that the PCA method does

help retain information and improve the VAR model with original variables. Model B3 shows

that, with PC1 and PC4 as exogenous variables, different linear combination of

macroeconomic variables produces different impact on the default rate. As for the fitting

ability, the results from PCA are better than those from VAR with original variables.

Nonetheless, the PCA models are less intuitive from an economic perspective because every

component is a linear combination of the original macro variables.

[TABLE 3 GOES ABOUT HERE]

5.1.3 Results from SVAR. To test if there is a contemporaneous relationship between NPLs

and the macroeconomic variables, we estimate a structure VAR (SVAR) model in AB type.

We use scoring as the estimation method and short-run pattern matrix as the restriction type.

Table 4 shows the type of A and B matrices we need to estimate. The estimation results are

presented in Table 5. The estimated coefficients of Matrix B are significantly different from

17

zero, indicating that Matrix B is not an identity matrix. However, the estimated coefficients of

Matrix A are not significant, suggesting that Matrix A is an identity matrix. The results of

Matrix A and Matrix B imply that there is no contemporaneous relationship among the

variables. Therefore, SVAR is not a proper model for our data.

[TABLE 4 GOES ABOUT HERE]

[TABLE 5 GOES ABOUT HERE]

Based on the above analysis, Models A2 and B3 are good fits for our data. Figure 2 and

Figure 3 depict the fitting charts of the two models respectively. Comparing the fitting charts

of NPLs, Model A2 is more accurate than model B3. Moreover, as mentioned before, Model

B3 is based on principle component analysis which is difficult to interpret economically.

Therefore, in the stress testing that follows, we choose Model A2 as our basic model.

5.2 Stress test on China’s banking system

5.2.1 Impulse response analysis. We use generalized impulse response analysis for

unrestricted vector autoregressive (VAR) and co-integrated VAR models proposed by Pesaran

and Shin (1998). This approach does not require orthogonalization of shocks and is invariant

to the ordering of the variables in the VAR. Our estimated impulse responses of NPLs to

macroeconomic variables are depicted in Figure 4.

[FIGURE 4 GOES ABOUT HERE]

When the nominal interest rate (NR) has a positive shock of one standard error, NPLs

decrease by 0.2 and start to increase and stay on a positive value after four years. It is

plausible that the rise in NR may discourage consumption and encourage savings in the short

run, leading to an increase loan repayment rate and a decline in NPLs. However, a rise in NR

increases the cost of loans in the long run, resulting in an increase in NPLs after several

periods. NPLs are negatively affected by exchange rate (ER) shocks, although the effect

18

fluctuates slightly at first. Our interpretation is that a rise in the exchange rate (home currency

depreciation) is a sign of bad economy. Turning to the NPLs shocks, they have persistent

effects over ten years on NR and ER, with NR trending down while ER trending upwards.

Finally, we find that NPLs have obvious external time lag effects. As Figure 4 shows, the

impulse of NPLs to ER produces longer time lag effects than NR. That is, a change in the

exchange rate impacts the default rate for a longer time than the nominal interest rate.

5.2.2 Variance decomposition. While an impulse response function describes the influence

of a shock in one endogenous variable on other endogenous variables in VAR models,

variance decomposition analysis is performed to identify the contribution of each shock to the

changes in the endogenous variables, which are usually measured by their variances. Hence,

variance decomposition presents the relative importance of every stochastic disturbance

which affects the variables in VAR models.

Figure 5 shows the result of our variance decomposition analysis. Changes in NPLs due to

an NR shock gradually rises up to 40% after 10 years, while the maximum percentage change

in the variance of NPLs due to an ER shock is 28% in the second year. It means the influence

of NR on NPLs is a long term effect and becomes more important than ER over time. It is

economically plausible that NPLs are more closely related to NR than ER.

[FIGURE 5 GOES ABOUT HERE]

5.2.3 Scenario analysis. Four scenarios of macroeconomic variables are selected for our

stress test on Chinese commercial banks as follows. Here, 2007:1 and 2007:2 represent the

first half and the second of the year of 2007 respectively while 2008:1 and 2008:2 are denoted

in the same way.

(1) The benchmark scenario, in which there is no shock;

(2) A fall in China’s nominal GDP growth by 5%, 7%, and 3% respectively in each of the

19

three consecutive half years starting from 2007:1;

(3) A rise of nominal interest rate by 400 basis points in 2007:1, followed by a rise of 500 bps

in 2007:2, and another rise of 300 basis points in 2008:1; and exchange rate increases by 5%，

8%, and 10% respectively;

(4) Reductions in real property index by 4.2%, 12.3%, and 20% respectively in each of the

three consecutive half years starting from 2007:1.

We have designed the scenarios according to several principles. First, there is a plausible

probability that these changes in the macroeconomic variables will occur. Second, the

scenarios are supposed to be extreme situations. That is, they appear rarely. Third, if one of

the scenarios occurs, it may bring high credit risk to Chinese commercial banks, which will

lead to enormous credit losses to them. All scenarios we have designed are more severe than

what actually happened in prior financial crises. In addition, every scenario has a group of

macroeconomic variables involved. That is, the scenario is more comprehensive than those

that consider shocks of a single macro factor. Last but not least, the macroeconomic variables

in every scenario are a sequence of shocks with a worsening trend. The situation is plausible

in the real world because economic stimulus policies may not be effective immediately to

stem the crisis.

We assume that these shocks occur only in 2007:1 and we analyze their consequences on

default rates and credit losses for 2007:2, 2008:1and 2008:2. In particular, we compare the

simulated default rates and loss distributions in 2008:2 with the ones obtained from the

benchmark or basic scenario (in which no shocks occur in 2007:1). Table 6 reports the

response of default rates for each macroeconomic scenario.

[TABLE 6 GOES ABOUT HERE]

Here we introduce the concept of Value at Risk (VaR) to measure the losses of a given

20

portfolio over time horizon H. Value at Risk (VaR) calculates the maximum losses expected

(or worst case scenario) on an given portfolio, over a given time period and given a specified

degree or confidence. We can describe it as follows (Philippe Jorion, 2006):

Pr( ) 1Loss VaR c (11)

where Loss means the losses of a given portfolio over time horizon H, c is the given

confidence level. From calculating VaR, the bank can know what is the most they can loss on

the NPLs.

Monte Carlo simulation is a good method to calculate VaR, which can get the loss

distribution of a given portfolio overtime horizon H. In this paper, we conduct Monte Carlo

simulation as follows.

According to Equation (1), we first produce a large number of random variables from the

multivariate normal distribution with mean being zero and variance-covariance matrix being

the estimated Q

, which represents a realization of the vector of disturbances Wt. Given the

current and past values of the X, macroeconomic variables, the default rate and the realization

Wt, the associated one-period-ahead values yt+1 and xt+1 can be calculated based on Model A2

we have described earlier.

Similarly, the two-period-ahead values can be calculated with another independently

random variables and one-period-ahead values previously obtained. Repeating the same

procedure yields a future path of the joint sector specific default rates, given the time horizon.

By simulating a large number of such paths, a frequency distribution of the horizon-end

default rates of benchmark scenario can be constructed.

In constructing the distribution of possible credit losses for a stressed scenario, we

introduce a hypothesized adverse macroeconomic development into the simulation procedure

above and generate another set of future path of the joint sector specific default rates, given

21

the time horizon. The difference from the benchmark scenario is that we change the value of

macroeconomic variables in the stressed year. A shock in one variable also leads to

disturbances in other variable through the transmission effect built in the model. In order to

estimate the loss distribution, the simulation is replicated over 2000 times. Table 7 and Figure

6 show the results of such simulations.

[TABLE 7 GOES ABOUT HERE]

[FIGURE 6 GOES ABOUT HERE]

In the benchmark scenario (no shocks), default rates are the real values in every half year.

Because we assume the macro shock begins at 2007:1, there is no response of default rate for

each shock in this period.

As shown in Table 6, compared to the benchmark scenario, the default rate in every other

scenario has strong responses to the specified shocks. From 1998, China’s GDP growth and

unemployment rate were increasing till 2007, so we design this scenario to test the respond of

default rate in China for the sustained increase of GDP growth and unemployment rate. From

Table 6, we can see that the GDP growth and unemployment rate shocks of Scenario 2 have

the strongest impact on the default rate: 7.93% in 2007:2 and 7.02% in 2008:1. But the

influence becomes much less, 3.93%, in 2008:2. The result means that the rise on GDP

growth and unemployment would lead to a quick respond to the default rate in the next period

and the effect would become weak in the next period.

Scenario 4, real property index and CPI shocks, has the longest influence on the default rate,

with the influence being the strongest in 2008:2. In recent years, price increases in

commodities and houses in China have become a major concern. Any price decrease, be it

caused by government policy or otherwise, may cause default rates to rise in the banking

sector. As shown in the Table 6, a decline in commodity and house prices would produce the

longest impact on the default rate.

22

Scenario 3, shocks in interest and exchange rates, has the same trend as scenario 4, but it is

less severe than scenario 4. Increasing interest rate and exchange rate will impose more

pressure on repaying debt owing to the cost of borrowing for both individuals and export

enterprises in China.

As shown in Table 7 and Figure 6, even in the worst situation, commercial banks in China

could still make profits. As shown in Table 7, however, at the confidence level of 90%, banks’

credit losses with shocks from different macroeconomic variables range from 3.64% to 4.29%

of the portfolios. At the 99% confidence level, the losses range from 4.05% to 4.78%. The

estimated maximum losses are very similar to the 5% loss of U.S. banks in November 2008,

when the U.S. market experienced severe financial crisis.

6. SUMMARY AND CONCLUSION

This paper describes a framework for macro stress-testing on credit risk in commercial

banks in China. The framework enables us to measure the vulnerability of commercial banks

against various macroeconomic shocks. The results show that the framework successfully

simulates the related responses of credit risk between severe financial crisis and subsequent

economic recovery.

A distinguishing feature of our study is that the sample period employed to estimate the

model includes several severe financial crises. Thus, we have avoided the shortcoming of

performing stress tests with a model based on benign historical data. Another distinctive

feature of the study is that the relationships between default rate and macroeconomic

variables are jointly estimated in a multivariate framework. Several models – VAR models

with original macroeconomic variables, VAR models with principal components, and

structure VAR model – are tested before we select the best one. We find that after principle

component analysis, VAR model ability could be improved significantly and structural VAR

model does not fit our data. Finally, we simulate the distribution of credit losses by the Monte

23

Carlo method and calculate VaR to report credit risk for commercial banks in China. The

macroeconomic credit risk model with explicit links between default rates and macro factors

is well suited for macro stress testing purposes. We use the model to analyze the impact of

stress scenarios on the credit risk of aggregated Chinese commercial banks. It should be noted

that using NPLs as a proxy of default rates is still a relatively crude approximation. For

further studies or extensions of the model, default rates for specific industry sectors may be

used. Company level rating information and credit rating transition probability matrix may

also be considered.

24

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27

Table 1. Descriptive statistics of variables

NPL GDPG UEP NR ER CPI RPI

Mean 16.82 9.95 3.08 5.94 6.71 107.40 115.3519

Std.dev. 9.55 2.67 0.82 3,25 2.00 2.95 20.70

JB-test 0.35 0.61 0.42 0.39 0.18 0.66 0.34

NPL(-1) GDPG(-1) UEP(-1) NR(-1) ER(-1) CPI(-1) RPI(-1)

ADF-test -2.98* -4.19* -3.36* -2.47* -3.99* -4.00* -5.58*

Correlation NPL GDPG UEP NR ER CPI RPI

NPL 1 -0.29 0.06 -0.13 0.53 -0.33 0.22

GDPG -0.29 1 -0.08 0.12 0.01 0.3 -0.1

UEP 0.06 -0.08 1 -0.7 0.7 -0.46 0.74

NR -0.13 0.12 -0.7 1 -0.43 0.8 -0.75

ER 0.53 0.01 0.7 -0.43 1 -0.34 0.64

CPI -0.33 0.3 -0.46 0.8 -0.34 1 -0.62

This table shows descriptive statistics on the data series used in the empirical analysis. The

means, standard deviations (std.dev.) and correlations are computed over the period

1985-2008. Figures in row 4 refer to p-values corresponding to Jarque-Bera-tests on

normality of the variables. The figures in row 6 refer to test statistics from

Augmented-Dickey-Fuller-tests; an “*” indicates rejection of the hypothesis of a unit root at a

5% confidence level. Note that unit root exists in the level of every variable but there is no

unit root in the first difference.

28

This table shows the result obtained by using VAR with original macroeconomic variables.

Two models we constructed are listed in the table. In model A1, we take exchange rate(ER),

nominal rate (NR), GDP growth (GDPG) and real property index growth (RPI) as endogenous

variables. In model A2, we modify GDP growth and RPI growth as exogenous variables and

add two dummy variables. The macro dummy is to control funds injection by Chinese

government into the four state owned commercial banks in some years. The classes dummy is

to control loan grading change in 1998. In each model, each column represents a sub-equation

in Equation (1).

Table 2. VAR models using original variables

Model A1 Model A2

NPL ER NR GDPG RPI NPL ER NR

NPL(-1) 0.79*** -0.12 0.98*** -0.16**

NPL(-2) 0.14**

ER(-1) -3.00* 0.49*** 0.29***

ER(-2) 3.25* 0.48*** 0.98* 0.44***

NR(-1) -3.11** -2.84* 0.62***

NR(-2) 1.34*** 0.41*** 3.17**

GDPG(-1) 0.52** 0.55*** 0.52**

GDPG(-2) 0.14** 2.03** - - -

RPI(-1) -0.03** 0.45*** -0.04**

RPI(-2) -0.14** - - -

dummy

Classes

Macro -6.80***

C 6.51*** 25.18*** 3.99***

R-squared 0.95 0.96 0.95 0.71 0.93 0.97 0.96 0.94

Adj. R-squared 0.89 0.93 0.92 0.45 0.88 0.95 0.92 0.88

Determinant resid covariance (dof adj.) 150.71 1.33

Determinant resid covariance 4.71 0.16

Log likelihood -173.12 -73.91

Akaike information criterion 20.74 9.72

Schwarz criterion 23.46 11.35

VAR stability Yes Yes

Note: Standard errors are in parentheses.*, ** and *** indicate significance at the 10%, 5% and 1% levels

respectively.

29

Table 3. VAR models using PCA Model B1 Model B2 Model B3

NPL PC1 PC2 PC3 PC4 NPL PC2 PC3 NPL PC2 PC3

NPL(-1) 0.69*** 0.05*** 1.14*** -0.12*** 0.08** NPL(-1) 1.18*** -0.09*** 0.04***

NPL(-2) -0.34*** 0.06* NPL(-2) 0.04**

PC1(-1) 0.65*** -1.04** -0.26*** PC2(-1) -1.30** 0.87** 0.28*

PC1(-2) - - - PC2(-2) 3.03** -0.35***

PC2(-1) -3.76** 0.89** -1.39*** 0.54*** 0.59* PC3(-1) -2.89*** -0.55** 0.38**

PC2(-2) 2.96*** PC3(-2) 2.42**

PC3(-1) 0.57* -0.43** -3.26* PC4 -1.44*** 0.96***

PC3(-2) 3.19*** 0.48*** 2.49** 0.36*** PC1 -0.95*** 0.15*** -0.28**

PC4(-1) 2.46** 1.46*** -1.45** 1.56***

PC4(-2) - - -

Dummies Dummies

Macro -6.66*** Macro -7.40***

C 11.29*** -1.90*** 1.63** -1.84*** C 1.72** -1.35***

R-squared 0.96 0.99 0.77 0.87 0.89 0.96 0.76 0.86 0.95 0.90 0.87

Adj. R-squared 0.94 0.98 0.56 0.75 0.79 0.93 0.59 0.75 0.92 0.83 0.78

Determinant resid covariance (dof adj.) 1.72 E-04 0.43 0.12

Determinant resid covariance 5.38E-06 0.07 0.02

Log likelihood -22.61 -64.51 -50.75

Akaike information criterion 7.05 8.59 7.34

Schwarz criterion 9.78 10.08 8.82

VAR stability No Yes Yes

Note: Standard errors are in parentheses.*,** and*** indicate significance at the 10%,5% and 1% levels, respectively.

This table presents results obtained by using Principle Component Analysis (PCA). In each model, each column represents a sub-equation in Equation (5).

We add some variables in the set of macroeconomic variables in order to produce 4 or more principle component to analyze. We choose first four principle

components because they can describe 95% of data information. In Model B1, the first four principle components are endogenous variables without dummies.

In Model B2, we adjusted PC1(-1) and PC4(-1) as exogenous variables and add macro dummy to control for the influence of bank fund injection by Chinese

government in some years. In Model B3, we adjust PC1 and PC4 as exogenous variables to test the influence of variables in the current period.

30

Table 4. Structural VAR estimates assumption

This table shows the types of A and B matrices we need to estimate when we build the

structural VAR model in AB type (see Equation (10).

A = 1 0 0

C(1) 1 0

C(2) C(3) 1

B = C(4) 0 0

0 C(5) 0

0 0 C(6)

31

Table 5. Structural VAR estimates

Coefficient Std. Error z-Statistic Prob.

C(1) 0.04 0.09 0.41 0.67

C(2) -0.02 0.06 -0.28 0.77

C(3) -0.08 0.13 -0.59 0.55

C(4) 2.08*** 0.31 6.63 0.00

C(5) 0.93*** 0.14 6.63 0.00

C(6) 0.59*** 0.09 6.63 0.00

Log likelihood -96.79

This table shows estimated results from the structural VAR model. Standard errors, z-statistic

and probability (Prob.) are in Columns 2, 3, and 4. ***, **, * indicate 1%, 5%, 10% levels of

significance respectively.

32

Table 6. Expected default rate for each macroeconomic scenario (%)

Period Benchmark Scenario2 Scenario3 Scenario4

2007:1 3.10 3.10 3.10 3.10

2007:2 4.15 7.93 6.57 7.02

2008:1 4.35 7.02 5.33 5.96

2008:2 3.62 3.93 7.01 7.87

This table presents the response of default rates in each macroeconomic scenario. Numbers in

the table represent the percentage changes of default rate in the four periods.

33

Table 7. Loss distribution in half year horizon

Default rate%

Confidence% Benchmark Scenario2 Scenario3 Scenario4

80 3.16 3.52 4.13 3.69

90 3.64 3.81 4.29 3.70

95 3.79 3.94 4.38 3.79

99 4.13 4.22 4.78 4.05

99.9 4.39 4.57 4.93 4.34

Credit loss (billion RMB)

Confidence% Benchmark Scenario2 Scenario3 Scenario4

80 1079.75 1127.40 1263.04 1081.36

90 1127.57 1180.98 1317.90 1131.56

95 1176.39 1221.92 1359.65 1174.87

99 1254.01 1301.31 1446.56 1255.32

99.9 1330.21 1386.40 1528.67 1315.31

This table shows Value at risk (VaR) at different confidence levels in each scenario. We

design four scenarios which are explained in short as follows:

(1) Benchmark: no shocks;

(2) Scenario2: GDP growth and unemployment shocks;

(3) Scenario3: Interest rate and exchange rate shocks;

(4) Scenario4: real property index and CPI shocks.

34

Figure 1. Line graphs of variables

This figure presents the data that is used to estimate the VAR models. NPL figures are given

in percentage. NPLs are defined as the ratio of the sum of total non-performing loans to the

total amount of outstanding loans. GDP growth refers to the annual growth rate of real gross

domestic product for China. Interest rate is the 1-year nominal interest rate. Unemployment

rate refers to the ratio of the number of unemployed people to the total number of workers in

any given year. Exchange rate is expressed as the value of the U.S. dollar in terms of RMB

units.

35

Figure 2. Fitting graph of forecasting data by Model A2

This table shows the fitting ability of Model A2. The solid line represents the actual default

rate and the dotted line represents our forecast through Model A2.

36

Figure 3. Fitting graph of forecasting data by Model B3

This table shows the fitting ability of Model B3. The solid line represents the actual default

rate and the dotted line represents our forecast through Model B3.

37

Figure 4. Impulse responses to generalized one S.D. innovations

The figure shows the impulse responses to generalized one S.C. innovations based on VAR

Model A2 with three endogenous variables (GDP growth, nominal rate and exchange rate

respectively) and two exogenous variable (GDP growth and RPI). The blue lines indicate the

median of the impulses.

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Response of NPL to NR

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Response of NPL to ER

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1 2 3 4 5 6 7 8 9 10

Response of NR to NPL

-.2

.0

.2

.4

.6

.8

1 2 3 4 5 6 7 8 9 10

Response of ER to NPL

Response to Generalized One S.D. Innovations

38

Figure 5. Variance decomposition

This figure shows the different contribution percentage of NPL due to shocks in NR and ER

shocks on the first row, and the contribution of NR and ER due to NPL shock in the second

row.

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent NPL variance due to NR

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent NPL variance due to ER

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent NR variance due to NPL

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

Percent ER variance due to NPL

Variance Decomposition

39

Figure 6. Simulated loss distribution under benchmark and stressed scenarios

This figure reports the histogram of credit loss for each macroeconomic scenario. We design

four scenarios as follows:

(1) Benchmark: no shocks;

(2) Scenario2: GDP growth and unemployment shocks;

(3) Scenario3: Interest rate and exchange rate shocks;

(4) Scenario4: real property index and CPI shocks.

(a) Benchmark scenario (b) Scenario 2

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.80

10

20

30

40

50

60

70

80

Frenquency

credit loss(%)

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.80

10

20

30

40

50

60

70

80

90

(c) Scenario 3 (d) Scenario 4

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.20

10

20

30

40

50

60

70

80

90

100

credit loss%

Frequency

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 40

10

20

30

40

50

60

70

80

90

credit loss%

Frequency