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Rongjie Tian[1],Beijing Institute of Technology and

Jiawen Yang[2],The George Washington University


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 ?, 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 became a reviving focus of concern.

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 Blaschke et al, 2001 and Sorge, 2004). Most researchers design macro stress testing by modeling the link between macroeconomic variables and credit risk measures. Sensitivity analysis, scenario analysis, and extreme values are usually employed to implement the stress testing.

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 relationship 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 autoregression model to generate a comprehensive indicator and then use an extended version of Wilson's model by imposing feedback effects between default rates and macroeconomic variables. Scenario analysis is also employed as part of our stress testing. We design four "exceptional but plausible" scenarios and use Monte Carlo simulation to get the credit loss distribution. Finally, we generate a conditional probability distribution of loss 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.

We find that GDP, CPI, exchange rate, nominal interest rate, real property index and unemployment rate have prolonged impacts on the default rate. The coefficient of the lagged default rate is found to be positive and significant, suggesting that the default rate of banks in the past period can produce a prolonged impact on the default rate in the current period. From the impulse tests, we observe that default rate responds most to the impulse of one standard error change of CPI, real property index, and unemployment rate.

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 establishes the macroeconomic credit risk model. Section 5 carries out the macroeconomic stress testing and presents our results. Section 6 concludes.


Wilson (1997) and Merton (1974) are known for stress test using macro credit models. Wilson establishes a direct model based on sensitivity of many macro economic variables for default probability in each industry department. The model analyzes the relationship between default probability and macroeconomic factors, then simulates the path of default probability distribution in the future to get the expected abnormal losses on asset portfolio. Furthermore, the model simulates the default probability value under the impact on the macroeconomic fluctuations. In comparison, the Merton model integrates asset price changes into default probability evaluation. The Wilson model is more intuitive and involves less computation while the Merton model has high data and computational requirements.

Many empirical studies have employed these macro credit models. Boss (2002) uses the macroeconomic credit model to analyze the stress situation for bank default probability in Australia and finds that industrial production, inflation rate, stock index, nominal short-term interest rates, and oil prices are the determinant factors of default probability. Sorge and Virolainen (2006) adopt the Wilson framework to perform a macro stress test on credit default probability in Finland and find that default probability distribution by Monte Carlo simulation is significantly different from its normal distribution in stress situations. VaR value is far higher than the base VaR value. Kafai, Choi, and Fong (2008) establish a stress test framework for Hong Kong retail banks on macroeconomic fluctuation, including macroeconomic factors such as gross domestic product (GDP), interest rates (HIBOR), real estate prices (RE), and Mainland China's GDP. Their results show that, even under all stress situations, some banks can still remain profitable at the confidence level of 90%.

Some researches integrate bad loans, loan loss amount or composite index and macroeconomic factors into a matrix vector to measure stability of the financial system. Hanschel and Monnin (2003) establish a compound stress index for the Swiss banking system, which contains a market index in an unstable financial situation and the derivatives deformation index on a bank balance sheet. Kalirai and Scheicher (2002) construct a regression estimation of time series data, the accumulated loan losses and a wide range of macroeconomic variables including GDP, industrial output gap, the consumer price index, the money supply growth rates, the stock market index, exchange rate, exports, and oil prices.

Studies of macro stress testing on credit risk of Chinese commercial banks are still at an early stage. Efforts have been made to estimate links between credit risk indicators and macroeconomic factors in China. Xiong (2006) employs a multiple Logit regression model on macroeconomic factors and finds that GDP and inflation rate are significant factors that affect the stability of the Chinese banking system. Li and Liu (2008) test the relationship between probability of default (PD) and nominal value of macroeconomic factors, which shows a statistical significance. They also provide a framework of macro stress testing on credit risk of Chinese commercial banks, but their results just provide a point estimation result based on stress scenarios. Simulation methods have not been seen in stress testing for Chinese banks.


China's banking system has some unique features. First, four largest commercial banks, often being referred to as "the big four," dominate China's banking industry. During the period between 1985 and 2008, China's banking sector has undergone significant reforms. Our study has to consider these reforms on the big four banks in China.

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 revolving 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 capital needed for investment and constructions by the State owned enterprises (SOEs). They even had to provide lending to inefficient sectors, such as stagnant SOEs, and they accumulated large volumes of NPLs (Kumiko O., 2007). Till 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 have significantly declined.

Third, the four state owned commercial banks have been responsible for lending to SOEs for a long time, so the performance of NPLs may be tightly related to macro policy in China. According to Zhou Xiaochuan, Governor of the People's Bank of China (PBOC), the PBOC conducted a survey on the formation and composition of NPLs of state-owned commercial banks by April 2004. The result of this survey is shown in Table 1.

According to the PBOC's survey, the first four causes represent policy loans or systemic problems and contributed 80% of the NPLs, while the banks' own problems contribute the remaining 20%. Therefore, there may be a more tight relationship between NPLs and macroeconomic factors than bank's internal management in China. That is a major reason why we focus on the impact of macroeconomic variables on credit risks of Chinese commercial banks.

Table 1 PBOC NPL Breakdown Survey



Central and Local Government Intervention


Mandatory Credit Support for State Owned Enterprises


Poor Legal Environment and Weak Law Enforcement


Industrial Restructuring in Enterprises


Bad Business Operation and Management of State Owned Commercial Banks



4.1 Model Description

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 resembles the Wilson model. However, ours differ in that we use a Vector Autoregression model with all variables. The macroeconomic credit risk model is presented as follows:



where is the vector of macroeconomic variables at time (), is the vector of constants, are autoregressive matrices, for i=1, 2, , p. Finally, is a vector of serially uncorrelated innovations, vectors of length n. The is multivariate normal random vector with a covariance matrix, where is an identity matrix, unless otherwise specified.

The estimated model can be used to simulate the future path of the default rate for given values of the macroeconomic factors. Using Monte Carlo methods, it is then possible to estimate the credit loss portfolio for the underlying macroeconomic environment.

4.2 Model Specification

4.2.1 Independent Variables

The macroeconomic variables used in the VAR analysis are described in Table 2. For comparison, we list variables in studies of other countries in Table 3.

Table 2 Macroeconomic variables we choose




Seasonally adjusted nominal GDP


1 year nominal bench interest rate on savings


Exchange rate


Consumer Price Index


Unemployment rate


Real property index

Table 3 Macroeconomic variables which other scholars choose in the world




Hong Kong

Interest rate,

Exchange rate

Nominal exchange rate

Interest rate


Asset price

overnight call rate

Real GDP growth

Real GDP growth

Nominal GDP growth


Mainland real GDP growth

Savings ,


the amount outstanding of bank lending

Corporate spreads



Real property price

International balance of payment

We chooses six major variables as independent variables. Nominal GDP, unemployment rate, and inflation rate allow us to investigate the effect of the business cycle on default rates. CPI is used to measure inflation. Interest rate has a direct impact on the level of corporate loans, which is related to credit risk of banks. We use the 1-year bank loan interest rate, which is linked to the majority of loans taken by the Chinese corporations. Real property index is considered in this paper for several reasons. First, housing mortgages have grown rapidly in China. Real estate loans in China rose to RMB 5.24 trillion in November 2008 with an annual growth rate of 10.3%. The proportion of real estate loans in total banks' loans has grown steadily. 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 are decreasing, the risk that borrowers cannot get money from selling houses will increase so that they will probably default their loans. Third, the experience in the subprime lending crisis tells us that banks' stability collapses along with the housing market. Therefore, we should consider the impact of real estate on banks' credit risk. Exchange rate is considered as an indicator of macroeconomic environment in the world.

These variables are found to be significant factors that affect banks' credit risk, as indicated by the adjusted R-squared values of the regressions and the p-values of the coefficients. We have also included other macroeconomic variables such as consumer confidence, oil price, retail sales, and stock market index in our regressions, but find that they have no additional explanatory power.

4.2.2 Dependent Variables

We choose default rate, defined as default ratio of loan assets, as our dependent variable to assess credit risk in Chinese commercial banks. Default rate is the most direct indicator to assess loan quality of banks. Default risk can be measured by the borrower's default probability within a given period. Various measures have been used to indicate the default rate in empirical studies. The ratio of the number of bankrupt institutions to the total number of bank institutions faced with is used to gauge the default probability in Finland banks (Virolainen K ,2006); ratio of NPLamount over three months total loan amount is used to approximate the default probability in Wong, Choi, and Fong (2006).

We use NPL ratio of main commercial banks in China as 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 to the default rate that other researchers have used in their studies. Before 1998, bank loans in China were classified into four categories delineated by the status of payment: (1) normal; (2) over due (loans on which interest or principal had not been paid on time); (3) long overdue (loans that were overdue for an extended time period, or the borrowers' legal entity status expired or their businesses were closed); and (4) dead loans (loans long overdue that were confirmed to be non-recoverable). Loans in the last three categories were regarded as NPLs. In 1998, the PBOC released guiding principles for loan classification based on risk characteristics, which divide all loans into five categories: normal, concern (special mention), substandard, doubtful, and loss. Loans in the last three categories were regarded as NPLs. Since 1998, the due classification system exited until the end of 2003, when all commercial banks were required to adopt the five-category system that resembles international norms.

As the five-category classification system after 1998 is not in accord with the previous four-category system, we need to adjust our data between 1985 and 1998 by a factor that is obtained by computing the proportion of five-category NPL in four-category NPL using the data between 1998 and 2003.

4.3 Model Test

4.3.1 Data description

The data for our study are retrieved from China's Statistical Yearbook and China's Financial Yearbook. 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, every variable's average value 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 of all data are presented in Table 4.

Figure 1 line graph of NPL

Table 4 Statistic description of data




































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.

4.3.2 Number of lags

To determine the correct lag length order for the VAR system, the Likelihood Ration Test, Residual Normality Test, and Residual Serial Correlation LM Test are performed. We find that a lag length of four is optimal (see table 5).

The number of lags in this multivariate model, p, is based on conventional criteria but, due to the size of our dataset, we impose some constraints on the system. We do not go further than 4 for p. We check whether the residuals of our equations corroborate with the required properties by applying the Ljung and Box white noise test.

4.3.3 Parameter estimation results

Table 5 VAR Lag Order Selection Criteria











































* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

We use maximum likelihood estimate method to estimate the parameters for the empirical macroeconomic credit risk model .The results are presented in Table 6.

As shown in Table 6, the LNY is positively related to the lag effects on nominal GDP growth ,CPI, exchange rate , nominal interest rate , real property index series, and unemployment rate series. The results imply that these macroeconomic factors have a prolonged impact on the default rate, which are respectively. Surprisingly, the coefficient of the lagged default rate, are positive and significant, so there is positive autocorrelation in , suggesting that the default rate of banks in the past period can produce a prolonged impact on the default rate in the current period. Therefore, we should consider analyzing the development of the default rate over a time horizon that is longer than the duration of the artificial shock in order to reflect the long-term impact of the stress.

4.3.4 Impulse response

We use generalized impulse response analysis for unrestricted vector autoregressive (VAR) and co-integrated VAR models which Pesaran and Shin(1998) proposed. This approach does not require orthogonalization of shocks and is invariant to the ordering of the variables in the VAR. Our impulse response result is shown in Figure 2.

When CPI has a shock of one standard error, will increase by 0.2 and start to increase until becoming flat after the tenth time horizon. Similarly, when the exchange rate, unemployment rate and real property index have an impulse shock of one standard error, will present a negative path

until the sixth period. Specially, the shock of one standard error of GDP growth does not appear to exert significant changes in Additionally, we observe that LNY responds most to the impulse of CPI, RPI and UEP, which are about 0.3, -0.3, -0.27 of one standard error respectively.

4.4. Model Prediction

One of the main features of a model is its ability to provide good out-of-sample simulations.

Actually, over-parameterized models usually perform very well in in-sample tests, but their out-of-sample performances are often rather weak. We prepare some data to test the predictability of our model, which are out of samples and account for ten percent of our data set.

Given past values of macroeconomics factors and default rates, and the parameters of our macroeconomic credit risk model, we can conduct forecasts of all the variables of the model iterating their equations forward.

Figure 2 Impulse Responses of LNY to Macroeconomic variables

There are two methods we can choose to conduct forecasts:

Compute all the future processes in one time by our model;

In addition, parameter estimates can be revised if new data for the variables become available. In this way, we assume that the model can be revised at a semiannual frequency. We called this method a step-by-step dynamic forecast.

Figure 3 the forecasting process of variables

Figure 3 presents the forecasting processes of every variable by the first forecasting method. Our model can predict the future value of every variable. Here, however, we focus on LNY variable because it can be transformed to default rate and it implies the change of default rate. As we have defined before, the trend of LNY is adverse to default rates. From Figure 3, the future trend of LNY is slightly downward sloping, which indicates the future trend of default rate is moderately upward.

Figure 4 shows the fitting line graph between actual data and forecasting data by the first method. As Figure 4 shows, the forecasting result severely overestimate the default rate in the future.

About the second forecasting method, using the assumption that the model is estimated on a semiannually sample from 1985sa1 to 2006sa2, which 'sa' means seme-annual,we perform the following out-of-sample forecasting exercise by a step-by-step forecasting method. In every step for forecasting one period, the model is re-estimated for each additional period and the forecasted value of default rate for the next period is computed.

Figure 5 presents the fitting line graph between actual data and forecasting data by the second method. Although it underestimates slightly the default rate in future periods, it performs better than the first forecasting method.

Figure 4 Fitting graph of forecasting data by the first forecasting method

Figure 5 Fitting graph of forecasting data by the second forecasting method

In addition, we build a benchmark model - the ARMA(1,1)model. The ARMA(1,1) specification is a reasonable benchmark, as also used by Stock and Watson (2001) in the context of forecasting macro series. Table 7 shows the parameters estimated of ARMA (1, 1) model by our sample data.


The result for our benchmark model is presented as follows:


We could compare these two models effects with Root Mean Square Errors (RMSE). If the RMSE of the model we established before is smaller than the benchmark model, it suggests that the new model will be better than the benchmark model.

Comparing to the actual value of LNY, RMSE of our model is 0.011631, which is less than RMSE of the benchmark model, 0.0938. It suggests that our model is preferred to the benchmark model.

Table 7 ARMA model parameters



Std. Error























Stress testing can be thought of as a process (Jones, Hilbers, and Slack, 2004) that includes:

(i) Identification of specific vulnerabilities or areas of concern;

(ii) Construction of a scenario;

(iii) Mapping the outputs of the scenario into a form that is usable for an analysis of financial institutions' balance sheets and income statements;

(iv) Performing the numerical analysis;

(v) Considering any second round effects; and

(vi) Summarizing and interpreting the results.

The aim of this exercise is to illustrate the stages of this process. It will also illustrate that these stages are not necessarily sequential, as some modification or review of each component of the process may be needed as work progresses.

Scenario Analysis is the main method in recent application. It defines some scenario with a group of risk factors and analyzes the stress losses under each scenario. There are two kinds of event designing methods: historical scenario and hypothetical scenario. Other methods are sensitivity analysis and sensitivity of extreme value theory method (EVT).

Based on the literatures of credit risk pressure test and the FASP handbook jointly developed by the World Bank and the IMF, the stress test execution procedures are shown in Figure 6.

Prostokt zaokrglony:  Bank internal data
  Market data 
  Credit database
Prostokt zaokrglony: Collecting data
Prostokt zaokrglony: Identifying risk factors
Prostokt zaokrglony:  Event analysis
  Stress events
Prostokt zaokrglony: Determining risk factor shocks
Prostokt zaokrglony: Reporting test result

Figure 6 Stress Testing Framework

5.1 Scenario Analysis

Scenario analysis is selected to conduct a stress test on Chinese commercial banks. For the macroeconomic factors we have selected, we set up four scenarios as follows:

(1) The first one, 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 three consecutive half years starting from 2007:1; unemployment rate increase by 5.6%, 7.4%, and 9.8% respectively;

(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 the exchange rate increases by 5%,8%, and 10% respectively;

(4) Reduction in real property index by 4.2%, 12.3% and 20% respectively in each of the three consecutive half years starting from 2007; CPI decreases by 3.6%, 6.2%,and 8.5% respectively.

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 changed, which means the scenario is more comprehensive than other scenarios that consider shocks of a single macro factor. Last but not least, the macroeconomic variables in every scenario we have designed 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.

5.2 Stress Testing

The goal of this section is to examine the response of the default rate to a macroeconomic shock. Here we focus on the effects of an output shock. First, we assume that these shocks occur only in 2007:1 and we analyze their consequences on default rates and credit loss for 2007:2, 2008:1and 2008:2. In particular, we compare the default rates and loss distributions in 2008:2 derived from the simulations carried out under the assumption of the presence of shocks with the ones obtained with the basic scenario (in which a shock does not occur in 2007:1).

5.2.1 Response of default rates to an output shock

Using the macroeconomic credit risk model, we compute the responses of the default rate in the next three periods (2007:2, 2008:1, 2008:2) by step-by-step forecasting method we have described before. Table 8 reports the response of default rates for each macroeconomic scenario.

In the benchmark scenario (no shock), default rates are the real values in every half year. Because the macro shock begins at 2007:1, there is no response of default rate for each shock in 2007:1.

Compared to the benchmark scenario, the default rate in every scenario has strong response for the output shocks. Scenario 2, GDP and unemployment shocks, has the strongest impact on the default rate in 2007:2 and 2008:1, but the influence becomes much less in 2008:2. 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. Scenario 3 has the same trend as scenario 4, but it is less severe than scenario 4.

Table 8 Expected default rate for each macroeconomic scenario (%)


























5.2.2 Loss distribution simulation

The loss distribution of a given portfolio over time horizon H can be determined by means of a Monte Carlo simulation. In order to estimate the loss distribution, the simulation is replicated over 2000 times.

For each macro crisis scenario (presence of shocks), we proceed in two steps: Firstly, using the macroeconomic credit risk model, we compute the responses of the default rate by Monte Carlo simulation; Secondly, the corresponding simulated default rates are used to assess credit loss distributions. In what follows we detail this two-step procedure.

Table 9 and Figures 7 to 10 present the corresponding distribution of total loss in every scenario. The simulation result shows that even in the worst situation, Chinese commercial banks can still keep a healthy state of development. In addition, scenario 3 is the most severe scenario in the four scenarios. The result is not different from the previous result by using step-by-step dynamic forecasting methods. The difference may be caused by the simulation error.

Table 9 Loss distribution in half year horizon

Default rate%































credit loss(billion RMB)































Figure 7 loss distribution and VaR graph for benchmark scenario

Figure 8 loss distribution and VaR graph for scenario 2

Figure 9 loss distribution and VaR graph for scenario 3

Figure 10 loss distribution and VaR graph for scenario 4


This paper describes a framework for macro stress-testing on credit risk in Chinese commercial banks. The framework enables us to measure the vulnerability of commercial banks against various macroeconomic shocks. The results show that the framework successfully simulated 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 avoid the shortcoming of performing stress tests with a model based on "too benign historical data." Another distinctive feature of the study is that we considered six macroeconomic variables in VAR models, which is more than any other study. In addition, in order to improve the forecasting accuracy, we employ a step-by-step dynamic forecasting method. Finally, we simulate the loss distribution of credit loss by the Monte 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 an aggregated Chinese corporate credit portfolio.

In addition, from the standpoint of macro-prudential policy, it would be helpful to encourage private banks to establish frameworks for micro stress-testing and to discuss the state of robustness in the banking sector with them. For example, it is possible to examine the robustness of the results of macro stress-testing through cross-checking with those from micro stress-testing for each bank's data.


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[1] This research was carried out while Rongjie Tian stayed at the George Washington University as a visiting scholar.

[2]Jiawen Yang is a professor of International Business at the George Washington University.


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