MACRO STRESS TESTING ON CREDIT RISK OF COMMERCIAL BANKS IN CHINA BASED ON VECTOR AUTOREGRESSION MODELS Rongjie Tian* Beijing Institute of Technology Email:
[email protected] Jiawen Yang The George Washington University Email:
[email protected]
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. 1
Electronic copy available at: http://ssrn.com/abstract=1909327
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 2
Electronic copy available at: http://ssrn.com/abstract=1909327
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 3
Electronic copy available at: http://ssrn.com/abstract=1909327
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
4
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. 5
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 6
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:
p yt y a i t i Zt Wt i 1 Xt X t i
(t 1, 2,..., N )
(1)
where yt denotes the default rate of banks, Xt is the (n1) vector of macroeconomic variables at time t
7
(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).
PCA1 u11 x1 u12 x2
u1n xn
PCA2 u21 x1 u22 x2
u2n xn (2)
PCAp u p1 x1 u p 2 x2
ui21 ui22
uin2 1
ui1u j1 ui 2u j 2
u pn xn
i 1,
uinu jn 0
p
(3)
for all i j
8
(4)
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:
p yt yt i a i Zt Wt i 1 PCAt PCAt i
(t 1, 2,..., N )
(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, 9
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 yt 1 yt 1 2 yt 2
p yt p t , t 1, 2,
,T
(6)
where the vector yt includes the variables of interest and εt is a vector of error terms with variance-covariance matrix Σ.
1 12 1 0 21 21 22
1n 2 n
11(i ) 12(i ) (i ) 22(i ) , i 21 (i ) (i ) 1 1n 2 n
1(ni ) 2(in) nn(i )
, i 1, 2,
1t 2t , p , t nt
A moving average representation of Equation (6) could be presented as follows.
( L)Yt ut , E (ut ut ') I k ,
(7)
( L) 0 1L 2 L2 ... p Lp ,
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,
10
A( L) yt t , t 1, 2,..., T
(8)
Let A,B be invertible KK matrices, then multiply A on the left to both sides of Equation (8),
AA( L) yt A t , t 1, 2,..., T
(9)
If A,B satisfy the conditions as follows:
A t But , E(ut ) Ok , E(ut , ut ') I k , (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
11
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
12
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 13
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.
14
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.
15
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 16
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 17
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
18
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 19
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( Loss VaR) 1 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
20
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.
21
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 22
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.
23
References Boss, M. (2002). “A Macroeconomic Credit Risk Model for Stress Testing the Austrian Credit Portfolio.” Financial Stability Report 4: The Oesterreichische National bank (OeNB), 64-82. Boss, M., Fenz, G., Pann, J., Puhr, C., Schneider, M. Ubl, E. (2009). “Modeling Credit Risk through the Austrian Business Cycle: an Update of the OeNB.” Financial Stability Report 17: The Oesterreichische Nationalbank (OeNB), 92-108. Dey, S., Misina, M., Tessier, D. (2007). “ Stress Testing the Corporate Loan Portfolio of Canadian Banking Sector. ” Bank of Canada Financial System Review, June, 59-62. Dovern, Jonas, Carsten-Patrick Meier, Johannes Vilsmeier. (2010). “How Resilient is the German Banking System to Macroeconomic Shocks?” Journal of banking and finance 34(8), 1839-1848. Drehmann,M. , Manning, M. (2004). “Systematic Factors Influencing UK Equity Returns. ” Bank of England, Mimeo. Hoggarth, G., Sorensen, S., Zicchino, L. (2005).“Stress Tests of UK Banks Using a VAR approach.” Working paper 282, Bank of England. Hotelling, Harold. (1933). “Analysis of a Complex of Statistical Variables into Principal Components.” Journal of Educational Psychology 24(6 & 7), 417-441 & 498-520. Li, J., Liu, L. (2008). “An Assessment on the Credit Risk for China Commercial Bank System Based on Macro Stress Testing.” Modern Economic Science 30(6), 66-74. Jolliffe, I. T. (2002). “Principal Component Analysis.” Second ed. New York: Springer Series in Statistics. Kalirai, H., Scheicher, M. (2002). “Macroeconomic Stress Testing: Preliminary Evidence for Austria.”Financial Stability Report: Austrian National Bank 3, 77-98. Merton, R. (1974). “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates.” Journal of Finance 29(7), 449-470. Kumiko, O. (2007). “Banking System Reform in China: The Challenges of Moving Toward a 24
Market-Oriented Economy.” Rand National Security Research Division. Pesaran, H., Shin, Yongcheol. (1998). “Generalized Impulse Response Analysis in Linear Multivariate Models.” Economics Letters, Elsevier 58(1), 17-29. Pesaran, M.H., Schnermann,T., Treutler, B. J., Weiner, S.M. (2006). “Macroecnomic dynamics and credit risk: A global perspective.” Journal of Money, Credit and Banking 38(5), 1211-1262. Peter, S., Liu, Z. (2010). “An Open-Economy Macro-finance Model of International Interdependence: The OECD, US and the UK.” Journal of Banking and Finance 4(3), 667-680. Pearson, K. (1901). “On Lines and Planes of Closest Fit to Systems of Points in Space.” Philosophical Magazine Series 6 2(11), 559–572. Philippe, Jorion. (2006). “Value at Risk: The New Benchmark for Managing Financial Risk.” 3rd edition. McGraw-Hill, ISBN 978-0071464956. Sanvi, A., Caroline, J., Ludovic, K., Jeremy, M., Mireille, B. (2009). “Macro Stress Testing with a Macroeconomic Credit Risk Model: Application to the French Manufacturing Sector.” www.banque-france.fr. Virolainen, K. (2004). “Macro Stress Testing with a Macroeconomic Credit Risk Model for Finland.” Discussion Papers No. 18, Bank of Finland. Sorge, M., Virolainen, K. (2006). “A Comparative Analysis of Macro Stress Testing Methodologies with Application to Finland.” Journal of Financial Stability 17(2), 113-151. Stock, J., Watson, M. (2001). “Vector Auto-regressions.” Journal of Economic Perspectives 15(4), 101-115. Wilson, T. C. (1997a). “Portfolio credit risk (I).” Journal of Risk 9(10), 111-170. Wilson, T. C. (1997b). “Portfolio credit risk (II).” Journal of Risk 10(10), 56-61. Wong, J., Choi, K. F., Fong, T. (2006). “A Framework for Macro Stress Testing the Credit Risk of Banks in Hong Kong.” Hong Kong Monetary Authority Quarterly Bulletin 10, 1-38. Ren, Y., Sun, X., Cheng, G., Xian, E. (2007). “Applied Study on Stress Testing Approaches of 25
Credit Risk.” Statistics and Decision 14, 101-103. Xiong, B. (2006). “An Assessment on the Stability of Chinese Bank’s System: Indicator Analysis and Stress Tests.” Unpublished PhD Dissertation, University of Southwest, Chengdu, China. Zhou, Xiaochuan (2004a). “Some Issues Concerning the Reform of the State Owned Commercial Banks.” Speech at the IIF Spring Membership Conference, Shanghai, 16 April 2004. Bank of International Settlement’s Website: http://www.bis.org/list/cbspeeches/from_01072004/page_3.htm.
26
Table 1. Descriptive statistics of variables
Mean Std.dev. JB-test ADF-test Correlation NPL GDPG UEP NR ER CPI
NPL 16.82 9.55 0.35 NPL(-1) -2.98* NPL 1 -0.29 0.06 -0.13 0.53 -0.33
GDPG 9.95 2.67 0.61 GDPG(-1) -4.19* GDPG -0.29 1 -0.08 0.12 0.01 0.3
UEP 3.08 0.82 0.42 UEP(-1) -3.36* UEP 0.06 -0.08 1 -0.7 0.7 -0.46
NR 5.94 3,25 0.39 NR(-1) -2.47* NR -0.13 0.12 -0.7 1 -0.43 0.8
ER 6.71 2.00 0.18 ER(-1) -3.99* ER 0.53 0.01 0.7 -0.43 1 -0.34
CPI 107.40 2.95 0.66 CPI(-1) -4.00* CPI -0.33 0.3 -0.46 0.8 -0.34 1
RPI 115.3519 20.70 0.34 RPI(-1) -5.58* RPI 0.22 -0.1 0.74 -0.75 0.64 -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.
27
Table 2. VAR models using original variables Model A1 NPL 0.79***
ER
NR -0.12
GDPG
RPI
Model A2 NPL 0.98***
ER NPL(-1) -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* 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*** RPI(-2) -0.14** dummy Classes Macro -6.80*** C 6.51*** 25.18*** R-squared 0.95 0.96 0.95 0.71 0.93 0.97 0.96 Adj. R-squared 0.89 0.93 0.92 0.45 0.88 0.95 0.92 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.
NR
0.62***
-0.04** -
3.99*** 0.94 0.88
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).
28
Table 3. VAR models using PCA Model B1 NPL 0.69*** -0.34***
PC1
PC2
PC3 0.05*** 0.06*
PC4
Model B2 NPL 1.14***
Model B3 PC2 -0.12***
NPL(-1) NPL(-2) PC1(-1) 0.65*** -1.04** PC1(-2) PC2(-1) -3.76** 0.89** -1.39*** 0.54*** PC2(-2) 2.96*** PC3(-1) 0.57* -0.43** -3.26* PC3(-2) 3.19*** 0.48*** 2.49** PC4(-1) 2.46** 1.46*** -1.45** PC4(-2) Dummies Macro -6.66*** C 11.29*** -1.90*** 1.63** R-squared 0.96 0.99 0.77 0.87 0.89 0.96 0.76 Adj. R-squared 0.94 0.98 0.56 0.75 0.79 0.93 0.59 Determinant resid covariance (dof adj.) 1.72 E-04 0.43 Determinant resid covariance 5.38E-06 0.07 Log likelihood -22.61 -64.51 Akaike information criterion 7.05 8.59 Schwarz criterion 9.78 10.08 VAR stability No Yes Note: Standard errors are in parentheses.*,** and*** indicate significance at the 10%,5% and 1% levels, respectively.
PC3 0.08** -0.26*** 0.59*
0.36*** 1.56*** -
-1.84*** 0.86 0.75
NPL(-1) NPL(-2) PC2(-1) PC2(-2) PC3(-1) PC3(-2) PC4 PC1
Dummies Macro C
NPL 1.18***
PC2 -0.09***
-1.30** 3.03** -2.89*** 2.42**
0.87** -0.35*** -0.55**
-0.95***
PC3 0.04*** 0.04** 0.28* 0.38**
-1.44*** 0.15***
0.96*** -0.28**
1.72** 0.90 0.83
-1.35*** 0.87 0.78
-7.40*** 0.95 0.92 0.12 0.02 -50.75 7.34 8.82 Yes
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. 29
Table 4. Structural VAR estimates assumption
A=
B=
1 C(1) C(2) C(4) 0 0
0 1 C(3) 0 C(5) 0
0 0 1 0 0 C(6)
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).
30
Table 5. Structural VAR estimates
C(1) C(2) C(3) C(4) C(5) C(6) Log likelihood
Coefficient 0.04 -0.02 -0.08 2.08*** 0.93*** 0.59*** -96.79
Std. Error z-Statistic Prob. 0.09 0.41 0.67 0.06 -0.28 0.77 0.13 -0.59 0.55 0.31 6.63 0.00 0.14 6.63 0.00 0.09 6.63 0.00
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.
31
Table 6. Expected default rate for each macroeconomic scenario (%) Period Benchmark Scenario2 Scenario3 Scenario4 2007:1 2007:2 2008:1 2008:2
3.10 4.15 4.35 3.62
3.10 7.93 7.02 3.93
3.10 6.57 5.33 7.01
3.10 7.02 5.96 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.
32
Table 7. Loss distribution in half year horizon Default rate% Confidence% Benchmark 80 3.16 90 3.64 95 3.79 99 4.13 99.9 4.39 Credit loss (billion RMB) Confidence% Benchmark 80 1079.75 90 1127.57 95 1176.39 99 1254.01 99.9 1330.21
Scenario2 3.52 3.81 3.94 4.22 4.57
Scenario3 4.13 4.29 4.38 4.78 4.93
Scenario4 3.69 3.70 3.79 4.05 4.34
Scenario2 1127.40 1180.98 1221.92 1301.31 1386.40
Scenario3 1263.04 1317.90 1359.65 1446.56 1528.67
Scenario4 1081.36 1131.56 1174.87 1255.32 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.
33
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.
34
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.
35
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.
36
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. Response to Generalized One S.D. Innovations Response of NPL to NR
Response of NPL to ER
3
3
2
2
1
1
0
0
-1
-1
-2
-2 1
2
3
4
5
6
7
8
9
10
1
2
Response of NR to NPL
3
4
5
6
7
8
9
10
9
10
Response of ER to NPL
1.00
.8
0.75
.6
0.50 .4 0.25 .2 0.00 .0
-0.25 -0.50
-.2 1
2
3
4
5
6
7
8
9
10
1
37
2
3
4
5
6
7
8
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. Variance Decomposition Percent NPL variance due to NR
Percent NPL variance due to ER
100
100
80
80
60
60
40
40
20
20
0
0 1
2
3
4
5
6
7
8
9
10
1
Percent NR variance due to NPL 100
2
3
4
5
6
7
8
9
10
Percent ER variance due to NPL 100
80
80
60
60
40
40
20
20
0 1
2
3
4
5
6
7
8
9
10
38
0 1
2
3
4
5
6
7
8
9
10
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
90
80 Frenquency
80
70
70 60
60 50
50 40
40 30
30
20
20
10
10
0 2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
0 2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
credit loss(%)
(c) Scenario 3
(d) Scenario 4
90
100
Frequency
Frequency 90
80
80
70
70
60 60
50 50
40 40
30 30
20
20
10
10
0 2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
0 2.2
credit loss%
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8 credit loss%
39
4
