107Acta všfs, 1/2008, roč. 2
Credit risk and stress testing of the Czech
Banking Sector
Kreditní riziko a stresové testování českého
bankovního sektoru
1	 Introduction
In the globalization world the financial crises can spread easily between countries. Crossborder
contagion can threaten countries with the week banking sector. From this point
of view, the stress test exercise should be regularly processed in order to detect financial
system fragility. The important part of such exercise is the evaluation of the credit risk
under certain macroeconomic scenario. For this reason it is very important to know the
link between credit risk and macroeconomic environment. Using these tools for monitoring
purpose, reformative measures can be adopted by regulator to prevent the potential
financial crises in the country in advance. Due to these facts, macroeconomic credit risk
modeling is the new challenge for the economic research.
Our recent experience with the effects of economic downturn on banks’ loan portfolios
in the Czech economy in the late 1990s provides an opportunity to investigate the link
between macroeconomic development and credit portfolio quality. These findings can
help to improve the stress test calculation employed by the Czech National Bank for the
purpose of financial stability. Despite a very good shape of the Czech economy at this moment,
the central bank needs to have reliable tools to detect potential instability within
the economy.
From financial stability point of view, credit risk of the banking sector portfolio should be
investigated. Rapid credit growth in the Czech Republic creates pressure for the improvement
in credit risk management at the present time. Loans to households’ growth rate
reach 30% on average during last years. After deep recession in the end of the nineties and
consequential credit crunch period, credit growth to corporate sector was recover since
2002. Despite of significant growth, level of the private credit in the economy is still far to
EU-15 average. The estimation of the sectoral credit risk models together with stress test
can be useful tool for the central bank. These models can provide better knowledge about
5th
Place – Profesor František Vencovský Award
5. místo – Cena profesora Františka Vencovského
Petr jakubík*
*	 Czech National Bank and the Institute of Economic Studies of Charles University in Prague. The findings,
interpretations and conclusions expressed in this paper are entirely those of the author and do not represent
the views of any of the above institutions.
108 Acta všfs, 1/2008, roč. 2
potential instability of the banking sector. Different unfavorable, but plausible scenario
can be tested in this manner. Although sectoral models can better explain credit risk in the
economy, sectoral data is difficult to obtain. Especially in the case of Central and Eastern
European transitional economies, time series are still short with a lot of structural breaks.
It makes empirical analyses hard.
This paper follows methodology used by Jakubík (2006a). It extends the study of Jakubik
(2007), who estimated macoreconomic credit risk model for the Czech aggregate
economy. Besides the credit risk modeling, the paper focuses on difficulties with data of
sectoral default rate. It shows how to deal with incomplete data in order to distinguish
credit risk for the household and corporate sector. It is structured as follows. Section 2 introduces
related studies. Section 3 describe available data, one-factor model as a selected
approaches to credit risk modeling and its estimation for the corporate and households
sectors. Section 4 presents using of the estimated models for the stress test purpose. The
last section concludes and discusses possible further research topics.
2	 Related Study
In the context of the New Basel Capital Accord, there are studies investigating cyclical
effects in credit risk models on the bank capital requirement. Catarineu-Rabell, Jackson,
Tsomocos (2003) investigate the impact of different forms of implementation of the rating
system on the bank capital requirement. Verónica Vallés (2006) discuss difficulties with the
implementation of Basel II. She focus on the through the cycle rating system and its construction
for the emerging economies with financial information affected by macroeconomic
crisis. A survey of the literature on cyclical effects on default probability, loss given
default and exposure at default can be found in (Allen, Saunders 2003). There are studies
investigated which factors drive the corporate credit risk in the economy. Elizalde (2005)
studies the importance of credit risk correlation in bond market prices. By decomposing
the firms’credit spreads on different credit risk factors is able to compute the importance
of each credit risk factor on the evolution of the firms’ credit risk, identifying their credit
risk correlation. The other studies use the idea of decomposition of the credit risk on the
common observable factors for all firms in the economy and firms’ specific unobservable
factor. This is also assumption of the popular one-factor model belonging to class of latent
factor models. The firms’specific factor is unobservable, but the assumption about its distribution
is made. This model is employed for example by Rösch (2005), Hamerle, Liebig,
Scheule (2004) or Jakubík (2006a).
From the regulators point of view credit risk on the aggregate level is important. The most
of the central bank employ some kind of sensitivity analyses or stress test exercise for the
financial sector. They try to estimate sectoral credit risk in the economy. Sorge, Virolainen
(2006) illustrate the main analytical approaches to macro stress test in the literature and
estimate macroeconomic credit risk models for stress test purposes using data for Finland.
In order to model corporate credit risk they use bankruptcy data as well as loan loss provisions.
Wagner, Marsh (2006) study credit risk transfer in the economy with endogenous
financing. They find the transfer of credit risk from banks to non-banks to be more beneficial
than credit risk transfer within bank sector. The results of the economic research on the
issue credit risk and stress testing is highly demanded by central banks. Boss, Krenn, Puhr,
109Acta všfs, 1/2008, roč. 2
Summer (2006) gives an overview of the general ideas used by Austrian central bank for
the monitoring of systematic risk in the economy. They integrated credit risk into the stress
test exercise. They used bankruptcy data as a proxy for default rate for 13 industry sectors.
Time series of default frequencies is explained by macroeconomic risk factor changes.
The estimated equation enable them translate macroeconomic risk factor changes into
probabilities of default for each industry sector. Bario, Furfine, Lowe (2001) covered the
relationship between credit risk, financial cycles and financial stability. They found limited
number of macroeconomic variables to predict episode of financial turbulence. Danmarks
Nationalbank analyzed the financial vulnerability of the Danish household sector (Danmarks
Nationalbank (2007)). Macro stress test of Danish households simulates the effect
of higher unemployment and interest-rate increases on the households’ability to service
their debt. Macroeeconomic credit risk model is also employ in stress test exercise of
Bank of England. Pain (2003) found the empirically relationship between banks’provision
and macroeconomic indicators as a GDP growth rate, real interest rates, credit growth or
concentration of the domestic loan portfolio.
Further related studies to the issues of credit risk and stress testing can be found e.g. in
Jakubík (2007).
3	 Credit Risk in the Czech Economy
From the central bank point of view it is necessary to assess the change in the credit risk of
a loan portfolio in relation to change in the macroeconomic environment within a stress
test exercise. To this end, a macroeconomic credit risk model for the Czech aggregate loan
portfolio was developed by Jakubík (2006b).
One disadvantage of the aggregate model is that it cannot capture the different sensitivities
of corporate and households sectors to change in the macroeconomic environment.
The structure of the loan portfolio has changed considerably over the past five years in the
Czech economy. The share of loans to households in banks’ total loan portfolio increased
from 10% in 2001 to almost 40% at the end of 2006. It is thus apparent that the household
sector is becoming increasingly significant in the total loan portfolio. For this reason, it
would be appropriate to estimate the macroeconomic credit risk model separately for the
corporate and household sectors. The main obstacle to the estimation of such models is
the non-availability of data on the dependent variable.
The aggregate risk model for the Czech economy was estimated on quarterly data on
inflow of non-performing loans (NPLs).
However, such data is only available on an aggregate
basis and cannot be obtained separately for the household and corporate sectors.
The sectoral breakdown shows NPL stocks, not flows. To obtain flows, one has to estimate
the decrease in NPLs as a result of write-offs, sales or enforcement of such classified liabilities
of banks. The following relationship applies to the stock of NPLs, the default rate
and the rate of gross NPLs decrease.
			 (1)
	 NPLs are loans with a classification of three or higher, i.e. substandard, loss and doubtful.
110 Acta všfs, 1/2008, roč. 2
where NPL is the stock of NPLs in the relevant period, u the rate of gross NPLs decrease,
df the default rate and Loans1
volume of outstanding loans at the beginning of the
period under review. This enables us to derive the following relationship (2) for the
default rate.
						 (2)
Depending on the frequencies monitored, equation (2) can be used to compute the quarterly
or annual default rate.
Except for the rate of gross decrease, all the variables in
relationship (2) are usually known. Volumes of total loans and NPLs are available for the
Czech economy broken down by sector. The rate of decrease was only available for aggregate
loans. This figure is highly volatile, mainly due to non-recurring massive write-offs at
the end of the 1990s and at the beginning of the new millennium as a result of clean-ups
of large banks’ balance sheets. It can be assumed that most of the problem loans related
to corporations rather than households and that the rate of decrease for the household
sector is relatively stable over time. The period of write-off, sale or enforcement of NPLs to
households was chosen to be two years as an expert estimate. If we work with the annual
default rate, the corresponding rate of decrease is 0.5.
Based on this assumption, the
default rate of households in the economy can be derived using relationship (2).
The question is how to deal with the corporate sector. Using of the equation (2) is not
appropriate for the corporate sector due to unstable behaviour of the rate of gross NPLs
decrease. However having an aggregate data on the gross inflow of NPLs and default rate
for the households sector we can derive gross inflow of NPLs for the corporate sector.
Nevertheless the time series of the sectoral loans are available, we can estimate corporate
default rate as a ratio of the gross NPLs inflow and outstanding loans at the given time.
For the better figure of the corporate sector credit risk, we can use credit register to compare
our estimation and real figure. However the central credit register contains data only
since November 2002. We use this data only for the latest values. However we checked
that our estimate well fit to credit register data.
3.1	 One-factor Model
The one-factor model is the popular version of the latent factor model which belongs to
the class of the Merton structural model. This model appear in many papers, for example
in (Rösch 2005), (Lucas, Klassen, Spreij, Straetmans 1999) (Cipollini, Missaglia 2005),
(Jakubík 2006a), (Jakubík 2006b), (Jakubík 2007). The model is able to good explain credit
	 An alternative approach to approximating annual default rate is to use bankruptcy data. This approach was
used for example by Virolainen (2004) or Bos, Krenn, Puhr, Summer (2006).
	 Parameter u in the equation (1) may not in fact be constant over time. Nonetheless, we believe that the level
of 0.5 is relatively realistic and consistent with anecdotal evidence.
	 Data on the gross inflow on NPLs for the corporate sector were calculated as a difference between this variable
for the aggregate economy and households sector. This number was finally adjusted, because there are
still others sector in the economy as a government, entrepreneurs and financial sector. We used the share of
the corporate sector on the total NPLs for the adjustment.
111Acta všfs, 1/2008, roč. 2
risk in the economy due to its nonlinearity. This section briefly describes the model and
way how to use this concept for the macroeconomic credit risk modeling.
A random process with a standard normal distribution is assumed for the standardised
logarithmic return on assets of a firm. The discrete normal logarithmic return satisfies the
following equation for each firm in the economy.
						 (3)
R denotes the logarithmic return on assets for each firm i at time t. F corresponds to the
logarithmic return in the economy independent of firm i at time t, which is assumed to be
a random variable with a standard normal distribution. This variable represents the part
of the return which is not specific to the firm and can thus satisfy the general conditions
for profitability of firms in the economy. U denotes the return specific to the firm, which
is again assumed to be random with a standard normal distribution. The two random
variables are also assumed to be serially independent. Given these assumptions, the logarithmic
return on assets of each firm i at time t also has a standard normal distribution. The
model is based on the Merton approach, according to which a default event occurs if the
return on a firm’s assets falls below a certain threshold. Formally,
,						 (4)
where Y denotes a random variable with the two potential state (1/0 – borrower i defaults/
non-defaults at time t). Different macroeconomic indicators can be considered if the applied
variant of the model assumes that the value of this threshold changes depending
on changes in the macroeconomic environment. The value can be modelled as a linear
combination of macroeconomic variables (xjt
). The final version of the model is described
by the equation (5) in the case that macroeconomic indicators are included into the model
(Ψ denotes the distribution function of the standard normal distribution).
(5)
The conditional default probability on realization ft
of random unobservable factor at time
t corresponding to the default probability (5) is given by formula (6).
									 (6)
If we furthermore assume a homogenous portfolio of firms in the economy whose returns
on assets correspond to process (3), the average default rate in the economy is then
– based on the law of large numbers – equivalent to the probability of default of a firm.
Given the assumption of homogeneity of firms in the economy, it is more appropriate to
estimate the model on the basis of sectoral data.
112 Acta všfs, 1/2008, roč. 2
In order to estimate the model (5), a relationship with a conditional number of defaults
of firms depending on the realisation of the random variable F representing the latent
factor was used. The conditional number of defaults depending on the realisation of the
random factor is a random variable which, under the given assumptions, has a binomial
distribution, with the parameters of conditional probability pi
(ft
) given by equation (6) and
the number of firms Nt
.
						 (7)
The model can be estimated by maximising a likelihood function containing a random
latent factor, which was assumed to have a standard normal distribution. Full description
of the one-factor model and way how to estimate it can be found for example in Jakubík
(2007). We employed this concept in this paper. 
3.2	 Macroeconomic Credit Risk model for the Corporate Sector
As was described at the beginning of the chapter Credit Risk in the Czech Economy, the
proxy for the credit risk in the corporate sector can be calculated. The credit register, which
is operated by the Czech National Bank and contains credit data of the corporate sector,
can be used for the more precise calculation of the corporate credit risk in the economy.
However this register is operated only since October 2002. We used data from the credit
register since 2003 to check our proxy credit risk time series. This data confirmed good
construction of the proxy variable.
Key macroeconomic determinants for the development of the corporate sector are interest
rates, exchange rates, price of the inputs, and growth rate of the domestic economy and the
economy of the key business partners.
These indicators also affect default rate in the corporate
sector. 90% of the newly granted loans to the Czech corporate sector are with short
fixation less then one year. It means that increase of the interest rate cause raise the price
of firms´ financial sources at the one year horizon ceteris paribus. More expensive sources
decline the ability of the firms to meet their financial obligations. Consequently, corporate
default rate increase. Appreciation of the exchange rate can also affect positively default
rate of the corporate sector.
Stronger exchange rate raises price of the goods in foreign currency.
Firms are becoming les competitive. In general the price of goods in foreign currency
at the world market is given. Hence the ratio between cost and sales is changed and profit
of firms decline. It can lead in the higher default rate in the corporate sector. The increase
of the price of firms’inputs can also affects companies in the negative way. On the contrary,
	 Although this model was originally derived for the bankruptcy data, it can be applied for the loans data as
well - see Jakubík (2007).
	 The register contains data on legal entities and individual entrepreneurs and can be used to obtain information
on the payment discipline of banks’ clients.
	 Key macroeconomic determinants of the profitability of the non-financial corporations are discussed for
example in CNB (2007).
	 The relationship between profitability and real effective exchange rate was empirically confirmed e.g. by
CNB (2007).
113Acta všfs, 1/2008, roč. 2
growth of the market price of firms’outputs can affects firms in the opposite way. From the
debtor point of view, the increase of the price level in the economy means decrease of the
real value of the obligation. Although permanent inflation leads to the additional cost and
harms the economy, in the short run the inflation improves the financial situation of the
debtors and decrease probability of the companies’ default. The period of the economic
boom has positive effect on the corporate sector. Demand for the goods and services produced
by the non-financial firms increases. Consequently the profit of companies increases
and corporate default rate decreases. The same effect on the corporate credit risk has the
growth of the economies of the key business partner. How strongly corporate sector is
influenced by foreigner economies depends on the openness of the domestic economy.
Vulnerability of the corporate sector also depends on its indebtedness. Higher debt of the
company corresponds to the higher financial leverage and higher potential profit or lost.
Such a company is more vulnerable to the unexpected macroeconomic shock and its default
probability is higher.
In order to estimate credit risk model for the corporate sector we took into account all
macroeconomic indicators mentioned above. We were looking for the model which would
be able to explain corporate sector credit risk and capture the effect of the key macroeconomic
determinant changes. Such a model could be used for the stress test scenario of
the Czech banking sector. We used credit data to derive a proxy variable for the credit risk
modelling. This variable was derived from the gross inflow of the NPLs for the aggregate
economy and households default rate calculated according the equation (2). Such derived
time series of the corporate default rate was available from 1997 Q1 to 2007 Q1. However
due to the others considered macroeconomic indicators, the final model was estimated
for the time period from 1998 3Q.
We employed one-factor model in all analyses. The best performance was obtained for
the model where GDP, exchange rate, inflation and indebtedness of the corporate sector
were included as macroeconomic indicators. The model was estimated for quarterly time
series from 1998 Q3 to 2006 Q4. Resulting estimated model corresponds to equation (8).
The estimate of the coefficients is shown in Table 1.
			 (8)
Table 1 – Default rate model for the corporate sector
114 Acta všfs, 1/2008, roč. 2
All the estimates were significant at least at the 5% confidence level. According the estimated
model, corporate default rate in the Czech economy depends negatively on the non-lagged
growth rate of the annual real gross domestic product. The growth rate of the Czech economy
improves the situation of the firms and their default probability decrease. Our empirical analysis
demonstrates the influence of the exchange rate on the credit risk. We used real effective
exchange rate of the Czech koruna deflated by consumer price index lagged by two quarters.
Stronger real exchange rate of the domestic currency affects corporate credit risk positively.
Impact of the inflation on the firms’ default rate was confirmed. In the case of inflation, the
annual rate of growth of the average quarterly price consumer index lagged by one quarter
was the most significant. A positive effect of the inflation on the situation of debtor was empirically
shown. A real value of outstanding debt decreases with the inflation. We consider the
debt indicator as a ratio of loans to GDP lagged by four quarters. As the loans we used total
outstanding banking loans to the non-financial corporate sector. Latent factor which is the
part of the estimation was still significant. However its coefficient is not part of the final model
expressed by equation (8). Obtained result implies that corporate default rate in the economy
is also affected by other factors then the macroeconomic indicators included.
However only the macroeconomic indicators mentioned above were included into the
final model, also the others were considered. We employed for example real and nominal
interest rates, real gross domestic product growth rate in the EU-15, EU-25, EA-12 and
Germany or unemployment rate. Although some of them had significant prediction power
for the corporate defaults rate, due to the correlation with the included indicators they did
not contribute to the prediction power of the whole model.
Figure 1 demonstrates the performance of the estimated one-factor model for the Czech corporate
sector. It confirms ability of the model to explain corporate default rate in the economy.
Figure 1 – Performance of the Estimated Model for the Czech Corporate Sector
0%
5%
10%
15%
20%
25%
30%
1998 2000 2002 2004 2006
Observed Default Rate Estimated Default Rate
Due to nonlinearity of the model, standard methodology for quality measurement of estimate
can not be applied. Nevertheless a number of the less common indicator can be
used. One of the tests of model quality is a test of the hypothesis that all the coefficients
115Acta všfs, 1/2008, roč. 2
except the constant term are zero (H0
: β1 
= β2
= β3 
= β4
=0). This hypothesis can be tested by
likelihood ratio -2lnλ = -2ln(Lc
/Lu
), where Lc
denotes likelihood function of the constrained
model and Lu
likelihood function of the unconstrained model. This ratio is an asymptotic
chi-squared distributed variable with 4 degrees of freedom due to four macroeconomic
indicators included into the estimated one-factor model. The test rejected null hypothesis
at the confidence level less then 1%. Instead of the standard coefficient of determination
which can not be used due to nonlinearity, the pseudo-coefficients of determination were
employed. All these coefficients are based on the likelihood functions of the restricted and
unrestricted model. They should be in the interval [0;1]. Our results close to 1 pointed out
the good quality of the estimated model.
				 Estrella (1998) (9)
				
Cragg-Uhler (1970) (10)
Cragg-Uhler (1970) (11)
Veall-Zimmermann (1992) (12)
The residuals of the model (8) were tested for autocorrelation using the Q-statistics. These
values demonstrate absence of the autocorrelation in the residuals at the 5% confidence
level (see figure 2).
Figure 2 – Autocorrelation function of the residuals
116 Acta všfs, 1/2008, roč. 2
Furthermore the heteroskedasticity was investigated by Breusch-Pagan test. We ran the
following regression.
			 (13)
We tested following null hypothesis H0
against alternative hypothesis H1
. H0
means that
square residuals do not vary with any of the original regressors.
We were not able to reject the null hypotheses. The present of the heteroskedasticity was
not proved. It seems that estimated standard errors of the coefficients are not biased.
Overall the estimation of the model (8) is not probably biased due to the properties of
the residuals.
3.3	 Macroeconomic Credit Risk Model for the Household Sector
In order to estimate credit risk model for the household sector in the Czech economy we
follow one-factor model methodology. The same approach as for the corporate sector was
applied. The resulting model was estimated for the annual default rate time series from
1997 Q3 to 2006 Q3.
The ability of the households meet their financial obligation depends mainly on the income
to instalment ratio. The households usually have a regular income as a salary, pension
or some kind of rent. Besides that, they can own financial assets, real or personal
estates. If their disposable income decreases under the certain threshold, they have to
sell owned assets. If they already have nothing to sell they fall to the default. From the
point of banks, it is easier to assess payment ability of the households then firms. One of
the key macroeconomic determinants for the households default is unemployment rate
which significantly affects the households’ income. In the case that the key breadwinner
of the heavy indebtedness household is fired from the job the household is usually not
able to compensate his income and fall to the default under the condition that all owned
assets are already sold. Gross domestic product is usually correlated with the households’
income and therefore can be used as a proxy for it. Instalment of the debt depends on
the interest rates in the economy. Default probability of the indebted household increases
with increase of the interest rate under the consideration that interest rate for the loan is
not fixed. Besides the indicators influencing the income to instalment ratio, principal of
the debt can be also affected. Increase in the price level declines the real value of the debt.
Hence, the inflation decreases the default probability of the households.
	 The quarterly time series of the annual default rate was generated from the monthly series of the annual
default rate calculated using relationship (2) by averaging the three monthly figures corresponding to the
relevant quarter. Although the default rate obtained using equation (2) was available from 1994, the time
series on which the model was estimated had to be shortened as a result of some lags in the model and due
to the shorter series of the other macroeconomic indicators included in the model.
117Acta všfs, 1/2008, roč. 2
A whole range of macroeconomic indicators were considered for the estimate. The model
chosen as the statistically best model, in line with the economic theory, was one containing
the unemployment rate and the real interest rate.10
The unemployment rate was
lagged by four quarters, which corresponds to the lagged impact on payment discipline
in the event of loss of employment.11
The statistically best results were achieved with a lag
in the real interest rate of three quarters. This result expresses the lagged impact of an
interest rate change on debtors resulting from interest rate fixation. The real interest rate
was calculated by deflating the annual PRIBOR by the CPI. Latent factor which is the part
of the estimation was still significant as well as in the case of the model for the corporate
sector (8). Obtained results imply that default rate of the households sector in the economy
is also affected by other factors then the considered macroeconomic indicators. The
resulting estimated model corresponds to equation (14). The estimate of the coefficients
is shown in Table 3.12
						 (14)
Table 2– Default rate model for the household sector
The hypothesis that all the coefficients except the constant term are zero (H0
: β1 
= β2
=0)
was tested by the likelihood ratio -2lnλ = -2ln(Lc
/Lu
). This ratio is an asymptotic chi-squared
distributed variable with 2 degrees of freedom. The test rejected null hypothesis at the
confidence level less then 1%. However pseudo coefficients of determination show worse
performance of the model compare the corporate sector. It could be caused by the lower
prediction power of the macroeconomic indicators to explain households default. Another
reason could be instability of the parameter u in the equation (2) which was assumed
to be constant.
10	 Also considered for the estimation of the model were nominal interest rates, inflation, the interest rate gap,
the real GDP growth rate, the output gap, the ratio of interest paid to income or disposable income, etc.
Disposable income was modelled using average wages and household consumption, while interest paid
was modelled as the product of the credit volume and the annual PRIBOR increased by a certain interest
rate spread.
11	 The loan is initially repaid from savings or the redundancy payment; payment discipline is affected only
after that.
12	 Danmarks Nationalbank employs unemployment and interest-rate within the macro stress test of Danish
households (Danmarks Nationalbank (2007)).
118 Acta všfs, 1/2008, roč. 2
Figure 3 – Performance of the Estimated Model for the Czech Household Sector
0%
2%
4%
6%
1997 1999 2001 2003 2005
Observed Default Rate Estimated Default Rate
			 Estrella (1998) (15)
			
	 Cragg-Uhler (1970) (16)
				 Cragg-Uhler (1970) (17)
Veall-Zimmermann (1992) (18)
The residuals of the model (14) were tested for autocorrelation using the Q-statistics.
These values demonstrate absence of the autocorrelation in the residuals at the 5% significance
level (see figure 4).
Furthermore the heteroskedasticity was investigated in the same way as in the case of the
corporate credit risk model (8). In contrast to model (8), the estimated model (14) records
the heteroskedasticity of the residuals. Due to this result the standard errors of the estimated
coefficients can be biased.
119Acta všfs, 1/2008, roč. 2
Figure 4 – Autocorrelation function of the residuals
4	 Use of Models in Stress Testing
The Czech National Bank (CNB) employs the stress test exercise of the Czech banking sector
for the purpose of financial stability.This methodology was gradually elaborated since 2004
by Čihák (2004), Čihák Heřmánek (2005), Čihák, Heřmánek a Hlaváček (2007).The basic stress
tests based on extreme value from the past were complemented by interbank contagion
test. These tests were followed by model scenarios within in-built estimated macroeconomic
factors from the CNB’s quarterly forecast and estimated growth in non-performing
loans from the macroeconomic credit risk model for the aggregate economy developed by
Jakubík (2007). This model enables to link development of the non-performing loans and
macroeconomic environment. However different sensitivity of the households and corporate
sectors was not able to capture. Although the aggregate model records good quality
of the estimation, the forecast can be biased due to rapid growth of the loans to household
and increasing share on the total banks’portfolio in the present time.The estimated sectoral
credit risk models can better capture the real credit risk in the economy. We can test affect
of the macroeconomic changes separately for the households and corporate sector. Both
of these models can be incorporated into the current stress test methodology of the Czech
National Bank. The models can evaluate the effect of the macroeconomic scenario on total
non-performing loans to the corporate and households sector.
In order to forecast credit risk for the corporate sector, we have to set the inputs of the model
(8).These include the non-lagged real GDP growth rate, real effective exchange rate lagged by
two quarters, annual inflation lagged by one quarter and aggregate corporate loans to GDP
ratio lagged by four quarters. These values can be set either expertly or as a percentage deviation
from the CNB’s quarterly macroeconomic forecast (see CNB (2003)). All these indicators
are the part of the CNB’s forecast except loans to the corporate sector. In the case that stress
test exercise assume one-year horizon, we do not need to predict this variable due to four lags
in the model. For longer horizon some kind of the credit growth model could be applied. The
models based on the panel regression are used most frequently for the loan portfolio growth
rate.This sort of models was also applied to the countries of Central and Eastern Europe, for example
by Cottarelli, Dell’Ariccia,Vladkova – Hollar (2003) or Duenwald, Gueorguiev, Schaechter
120 Acta všfs, 1/2008, roč. 2
(2005). The vector error correction model (VEC) is generally used for estimates for individual
country as well as for aggregate data for several countries – e.g. Hofman (2001) or Schadler,
Murgasova, Elkan (2005). In many studies the volume of loans in the economy is expressed
as a ratio of loans to the private sector to GDP and is often estimated on the basis of a set of
macroeconomic variables. Other studies try to model directly the rate of growth of the absolute
volume of loans in the economy as for instance Fabrizio, Igan, Mody, Tamirisa (2006) who
modeling credit growth for the countries of Central and Eastern Europe.
Table 3 – Sensitivity Analysis of the Credit Risk Model for the Corporate Sector
(annual default rate in response to the value of exogenous variables)*
Inflation
(in %)
Real
Effective
ER
Loans
to GDP
(in %) 1 2 3 4 5 6
15 6.01 5.14 4.37 3.70 3.11 2.61
35 19.64 17.56 15.63 13.84 12.20 10.70
50 37.07 34.18 31.37 28.68 26.09 23.63
15 7.28 6.26 5.36 4.57 3.87 3.26
35 22.48 20.22 18.10 16.13 14.30 12.62
50 40.84 37.85 34.94 32.11 29.38 26.77
15 8.73 7.57 6.52 5.59 4.77 4.04
35 25.53 23.10 20.81 18.65 16.64 14.77
50 44.70 41.64 38.64 35.71 32.85 30.10
15 4.63 3.93 3.31 2.78 2.32 1.92
35 16.30 14.46 12.76 11.21 9.80 8.53
50 32.36 29.62 26.99 24.49 22.11 19.88
15 5.67 4.84 4.10 3.47 2.91 2.43
35 18.84 16.81 14.93 13.20 11.61 10.16
50 35.96 33.10 30.34 27.68 25.14 22.73
15 6.88 5.91 5.05 4.29 3.63 3.05
35 21.60 19.40 17.34 15.42 13.65 12.02
50 39.70 36.74 33.86 31.06 28.38 25.80
15 3.52 2.96 2.47 2.06 1.70 1.40
35 13.35 11.75 10.29 8.96 7.77 6.70
50 27.91 25.36 22.94 20.65 18.51 16.51
15 4.35 3.68 3.10 2.59 2.16 1.79
35 15.58 13.80 12.16 10.66 9.30 8.08
50 31.31 28.61 26.03 23.57 21.25 19.07
15 5.34 4.55 3.85 3.25 2.72 2.27
35 18.05 16.08 14.26 12.58 11.05 9.65
50 34.87 32.04 29.32 26.70 24.21 21.85
0.9
1.0
1.1
GDP Growth Rate (in %)
1
3
5
0.9
1.0
1.1
0.9
1.0
1.1
Note:*
The sensitivity analysis uses non-lagged real GDP growth, CPI inflation lagged by one
quarter, real effective exchange rate lagged by two quarters and corporate loan-to-GDP ratio
lagged by four quarters.
Table 3 shows the sensitivity of the corporate credit risk to the change in real GDP growth
rate, real effective exchange rate, inflation and corporate loans to GDP ratio. The coefficients
of the equation (8) cannot be interpreted as the commonly used elasticities of impacts of
the relevant macroeconomic factors on credit risk, due to recalculation by the cumulative
distribution function of a normal distribution. For this reason the effect of the change in one
macroeconomic indicator depends on the value of the others indicators. This fact points out
121Acta všfs, 1/2008, roč. 2
the table 3. For example the effect of slow down in GDP growth from 5% to 3% depends on
the actual corporate loans to GDP ratio, real effective exchange rate and inflation.
The CNB’s quarterly macroeconomic forecast for unemployment rate, 12-month PRIBOR and
CPI can be used to predict credit risk in the household sector according to the equation (14).
However the model (14) does not record so good statistical performance as the model (8) for
the corporate sector.
Table 4 shows the sensitivity of households’ credit risk to the change in the unemployment
rate and real interest rate in the economy.We observe low sensitivity of the model to the exogenous
macroeconomic shocks. It can be caused by lower sensitivity of the households sector
to the macroeconomic environment as well as inaccurate estimation of the proxy variable for
the households’credit risk in the economy according to equation (2).
Table 4 – Sensitivity Analysis of the Credit Risk Model for the Households Sector
(annual default rate in response to the value of exogenous variables)*
Note: *
The sensitivity analysis uses unemployment rate lagged  by four quarters and real interest
rate lagged by tree quarters.
5	 Conclusions
Credit risk modelling is an important part of the stress test exercise.We investigated different
sensitivity of the corporate and households sector credit risk to the change of macroeconomic
environment in the Czech economy. In order to improve banking sector stress test,
sectoral macroeconomic credit risk models can be incorporated into the exercise. While the
performance of the estimated model for the corporate sector records very good quality, the
performance of the model for the households sector was worse. Further work in this area
could be done. Data from the credit register for individuals would be possible to use in the
future for the credit risk modelling for the households sector. Nevertheless this research
study is important step to capture different impact of the macroeconomic change on the sectoral
credit risk. One-factor model was employed in all analyses. This methodology enables
to capture nonlinearities of the credit risk determinants. All these results can contribute to
detect potential fragility of the banking sector and prevent the financial crises.
Abstract
This paper deals with sectoral credit risk in the Czech economy. It follows structural Merton‘s
approach. Latent factor models are employed within this framework. The credit risk
122 Acta všfs, 1/2008, roč. 2
models for the corporate and household sectors in the Czech Republic were estimated in
this manner. They are able to capture the effects of macroeconomic changes on the sectoral
credit risk in the economy. The results of this study can be used for the improvement
of the Czech banking sector stress test. The models enable the stress tests to be linked to
the Czech National Bank’s official quarterly macroeconomic forecast.
JEL Classification / JEL klasifikace
G21, G28, G33
Souhrn
Tato práce se zabývá sektorovým kreditním rizikem v české ekonomice a vychází z mertonovského
strukturálního přístupu. Pro modelování kreditního rizika jsou použity latentní faktorové
modely. Na datech české ekonomiky byly odhadnuty makroekonomické modely kreditního
rizika pro sektor podniků a domácností.Tyto modely jsou schopny zachytit dopad změn makroekonomického
prostředí na sektorální kreditní riziko v ekonomice.Výsledky této studie mohou
být použity k zpřesnění stresového testování českého bankovního sektoru. Modely umožňují
navázání stresového testování na oficiální čtvrtletní prognózu České národní banky.
Kontaktní adresa / Contact address
PhDr. Ing. Petr Jakubík, Ph.D.
Česká národní banka a Institut ekonomických studií Fakulty sociálních věd Univerzity
Karlovy v Praze
(e-mail: Petr.Jakubik@cnb.cz)
PhDr. Ing. Petr Jakubík, Ph.D.
Vystudoval ekonomii na Fakultě sociálních věd Univerzity Karlovy
v  Praze, statisticko-pojistné inženýrství na Fakultě informatiky
a statistiky VŠE v Praze, inženýrskou informatiku na Fakultě jaderné
a fyzikálně inženýrské ČVUT v Praze. Ph.D. v oboru finance obhájil
na Fakultě financí a účetnictví v Praze. V průběhu své odborné praxe
vystřídal několik bankovních institucí, v současné době působí jako
vrchní ekonom ČNB v Praze. Je členem představenstva a výkonného
výboru České společnosti ekonomické, Centra základního výzkumu
pro dynamickou ekonomii a ekonometrii a členem Evropské ekonomické
společnosti.“
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