2012 International Conference on Management Science & Engineering (19th)
September 20-22, 2012
Dallas, USA
Applying Modified KMV Model to Analyze the Credit Risk
of Listed Firms in Chinese Cement Industry
XU Ying-peng
School of Economics and Management, Beijing Jiaotong University, P.R.China, 100044
Abstract: Cement industry is the mainstay industry
in China. The development of cement industry is highly
correlated with the national economic development.
However, cement industry requires a huge capital
injection and financing is more difficult for this industry.
So, the credit risk management of this industry is
becoming a fundamental and crucial work. In this paper,
we develop a novel model based on the original KMV
model to measure the credit risk of Chinese cement
industry. By adjusting some parameters in the basic model,
we improve the predictive accuracy and find the adjusted
model is more suitable for the cement industry in China.
The KMV model assumes that the firm goes into
bankruptcy with its default point at short-term debt plus
half of the long-term debt. However, by using significance
test of the difference of DD (default distance), we think
default point in cement industry should be short-term debt
plus 10% long-term debt. In addition, we think the value
of the company’s equity should include both tradable
shares and limit sell shares and we find a way to calculate
the value of the limit sell shares. Finally, by analyzing the
total asset value, DD and EDF (expected default
frequency) of 4 selected firms from year 2006 to 2011, we
find financial crisis has great impact on Chinese cement
industry. However, in the year 2009 and 2010, the large
range of the establishment of the economic affordable
housing and low-rent housing in China gives cement
industry a chance to improve their products’ quality and
change their strategy to better meet the challenges in the
future.
Keywords: credit crisis, industry analysis, KMV
model, paired sample t-test
1 Introduction
The cost of the cement contains coal, electric power,
depreciation and raw material, of which coal and electric
power occupy almost 60% of the total cost. However, the
low concentration degree of cement industry causes low
bargaining power for cement enterprises when facing
coal or electric power enterprises. So, the price of cement
always fluctuates with the price of coal and electric
power. The cement industry has poor ability in shielding
against price fluctuation risks. At the same time, Chinese
cement industries usually consume more resources and
978-1-4673-3014-5/12/$31.00 ©2012 IEEE
make larger environment damage during the
production[1], which weakens their international
competitiveness. Moreover, the cement industry is a
capital-intensive industry. Especially the NSP process
cement which Chinese government encourages needs
large capital investment[2]. This industry also needs huge
liquidity to maintain their production and operation. But
the operation cycle usually lasts for more than one year,
which virtually increases the credit risk of the cement
industry. Another aspect is annexation and reorganization
of enterprises also needs large credit funds to be involved
in. Based on the analysis above, the credit risk of cement
industry is a fundamental and urgent issue need to
considerate.
After the establishment of the CBRC(China
Banking Regulatory Commission), the rate of troubled
loan of the four major commercial banks in China has
been fallen from 24.12% to 1.14% during nine
years(2003-2011). However, according to the statistics
published by CBRC, the rate of troubled loan of
commercial banks in fourth quarter 2011 begin to
increase compared with third quarter, which ends the
continuous downtrend from 2005. The total number of
troubled loan in fourth quarter 2011 is 427.9billion,
raised by 20.1billion compared with last quarter [3]. This
is a signal that the banks should take more measures to
deal with the aggravated financial environment.
In the increasing competitive financial world, there
is an urgent need for Chinese banks to develop an
effective model to measure the default probabilities of
various firms [4]. In this way, the banks could improve the
quality of the loans and reduce the rate of troubled loan.
Nowadays, KMV model is one of the most popular
models in credit risk assessment. This model has already
been adopted by plenty of commercial banks [5]. Many
studies proved its accuracy and feasibility.
McQuown(1993)[6] pointed out that the financial report
could reflect the history of the company and the market
price could predict the future development trend. Kurbat
and Korablev(2002)[7] prove that the KMV model was
very effective after analyzing 1000 US. Companies in
three years. Peter Crobie and Jeff Bohn(2003)[8] found
that EDF(expected default frequency) could accurately
and sensitively manifest the credit changes before
insolvency. It is clearly that KMV model is effective in
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the assessment of credit risk. We, however, pay more
attention to applying KMV model to estimate the credit
crisis of the listed companies in China. Many researchers
have already contributed a lot to this issue. Zhang
Miao(2005)[9] pointed that KMV is the most suitable
model for China after comparing KMV with Credit
Metrics[10], Credit Portfolio View[11] and CreditRisk+. Gu
Qianping and Wang Tao(2009)[12] created a new function
of DD(default distance) and EDF(expected default
frequency) to replace normal distribution in KMV model.
Tang Zhenpeng(2010)[13] found that EGARCH-M
volatility modeling is more accurate to evaluate the
equity of the firms. Zhao Jihong and Xie Shouhong
(2011) [14] proved that the default point in the basic KMV
model is not fit for the Chinese firms. Wo Chiang (2011)
[15]
redefined the optimal default point based on genetic
algorithms and found that GA-KMV model performs
best.
From the above, we find that most of the earlier
studies concern with the modification of the KMV model
to get a more accurate result of the listed firms’ DD and
EDF, especially to the whole stocks market. We, however,
focus on a single point---cement industry, and try to
redefine the meaning of variables in the model based on
actual Chinese financial environment. In this paper, we
also discuss the relationships between debts, equity and
DD. Finally, we will analyze the influence of the credit
crisis and policies on the cement industry based on the
DDs(default distances) and EDFs(expected default
frequencies) we get.
The structure of this paper is organized as follows.
Section 2 reviews the KMV model and explains its
theories. Section 3 discusses the modification when
applying the model to the listed cement industry. Section
4 compares the related coefficient of different factors in
the KMV model. Section 5 uses advanced KMV model
to analyze the statistics of cement industry from year
2006 to 2011. This section also connects these results to
the policies of China and the financial environment in the
world. In the end, we get some conclusions and make
some suggestions for further studies.
Where V denotes the total asset value of the firm,
is
E the market value of the firm’s equity, N (⋅) is the
cumulative standard normal distribution function. D
denotes the face value of the firm’s debt; r is the
instantaneous risk-free rate; t denotes the debt maturity.
The value of the equity as a function of the total
value of the firm can be described by the
Black-Scholes-Merton formula. The Merton model gives
relationship between the volatility of equity value and
the volatility of total asset value [16]:
2 Review the KMV model
3 Parameter setting and results analysis
The well-known KMV model developed by KMV
Company is based on the modern corporate finance
theory and the options theory. The principle of the
options theory is simple. When the value of the assets of
the company is changed, the shareholders will reassess
the relationship between the value and debts. When the
total assets value exceeds the debts, they will pay back
the loan to the bank. However, if the debts exceed the
value of the company, the shareholders will choose not to
pay back the loan and let the company go bust.
According to the above analysis, the value of the
equity is a function of the value of the firm and time. We
can derive from the Black-Scholes option pricing
formula that:
(1)
E = VN (d1 ) − De − rt N (d 2 )
3.1 Data description
Now we use KMV model to calculate the DD and
EDF of different firms in the cement industry. We collect
data from the financial statements of 4 listed firms in the
cement industry (stock code: 000401, 600539, 600217
and 000877).
VN (d1 )
(2)
σV
E
where σV is the volatility of the firm’s asset value,
σE =
σE is the volatility of the equity value of the firm. In
equation (1), d1 and d 2 are given by
V
1
+ (r + σV 2 )T
(3)
2
d1 = D
σV T
(4)
d 2 = d1 − σV T
From the four equations (1) (2) (3) and (4), we can
conclude that d1 , d 2,V , σV need to be inferred. Other
variables can be got or calculated based on the statistics
in the financial statements of the listed firms.
After we get V σV , DD and EDF of the firm can
be calculated by the following two equations[17]:
V − DP
DD =
(5)
V * σV
EDF = 1 − N ( DD)
(6)
According to the KMV model, the default will
occur when the value of the asset decrease to a level
between the short-time debts and the total debts. This
point is called DP (default point).
When the DD(distance-to-default) decreases, the
firm will become more likely to default. So, DD or EDF
is a suitable measure to decide whether a firm will
default in the future. In other words, the company will be
more creditable when it has a high DD.
ln
3.2 Variable definition
1) Equity value evaluation (E). Earlier studies
usually directly regard the company’s share value as the
company’s equity value[18]. However, the Chinese
government has taken stock equity reform from 2004.
After the equity reform, the non tradable shares in the
company change into limit sell shares. However, the
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Stock code
Short-term debts
Long-term debts
Tradable shares
Limit sell shares
The total shares
Net asset value per share
Market value of firm equity
Stock code
σEm
σE
000401
Tab.1 Basic information of the selected firms
000401
600539
13005978100
136081900
12053100000
3802850
1212245980
160435890
135276930
69564110
1347522910
230000000
7.83220
2.63710
22503655055
943018065.2
Tab.2 The volatility of equity
600539
600217
000877
0.194857958
0.141589478
0.125046954
0.431633145
0.675007767
0.490480342
0.433175357
_
1 n
(m i − m ) 2
∑
n − 1 i =1
mean value of µ i :
_
µ=
1 n
∑ µi
n i =1
000877
5153050000
4219210000
435651910
53293230
488945140
11.34050
14358588723
0.124601756
calculation of the value of the limit sell shares does not
have an exact way. Chen Xiaohong, Wang Xiaoding, Wu
Desheng(2010)[19] pointed out the value of limit sell
shares should be net assets per share multiply the number
of limit sell shares. But this method does not consider the
additional value when non tradable shares become the
limit sell shares. In this point, we find that Song
Shujuan(2006)[20] put forward the average discount of the
non tradable state-owned shares and corporate shares is
23% when they change into limit sell shares. In this
paper, we regard 23% as the discounted value of the limit
sell shares.
So, the value of the equity can be calculated as
follows:
(7)
E = S * n1 + (1 + 23%) * NAVPS * n2
E : Market value of firm equity
S : Stock Price in the market
n1 : The total number of the tradable shares
NAVPS : Net asset value per share
n2 : The total number of the limit sell shares
In this step, we choose four listed firms in the cement
industry as example. Tab.1 represents some basic
information from the financial statements of these four
firms.
2) Volatility of the equity value of the firm ( σE )
In this article, we use Historical Volatility Model to
calculate σE [21] [23] . We assume that the price of the
shares obey logarithmic normal distribution. The rate of
the returns of the stock monthly ( µ i ) can be calculated as
follows:
µ i = ln(S i / S i −1 )
(8)
S
Where i means the closing price of i month.
The standard deviation of µ i :
σ Em =
600217
1426140000
142912000
660800000
0
660800000
0.29000
2006000000
(9)
The rate of the returns of the stock yearly can be
calculated by σ Em
σE = σ Em * T = σ Em * 12
(11)
We collect the closing price of these four firms in
2011 and take these data into the equations (8) (9) (10)
and (11) to calculate σE . Tab.2 shows the results of the
calculations.
3) Definition of the DP in the cement industry
The default point of the company has a very
important role in the KMV model. Zhao Jihong and Xie
Shouhong(2011)[14] have already proved that the default
point in the basic KMV model is not fit for the Chinese
firms. Li Leining and Zhang Kai(2007)[22] pointed that
the percent of the long-term liability should be 10% after
studying 80 listed firms in the stock market.
Different industries might have different DPs. In
this paper, we are going to calculate the DP in the cement
industry.
There are two kinds of listed firms in China: ST
(special treated) companies and non ST companies. ST
companies usually have some financial trouble. We
consider that the ST firms are more likely to default than
non ST firms. So, based on this assumption, we can
compare the differences of DDs (default distances) of
these firms and select the m, which can better distinguish
the ST from non ST firms. So, in this paper, we choose 6
firms in the cement industry (three of them are ST firms
and others are non ST firms; stock code: 000401, 000789,
000877, 600217, 600539, 000673) to calculate DP of the
cement industry.
The equation to get DP:
(12)
DP = SD + m * LD
SD: short-term debts
LD: long-term debts
0 ≤ m ≤1
We add the m by 0.1 and take paired sample t-test.
Results are shown in Tab.3 and Tab.4.
From Tab.3, we can know that all the DDs decrease
(10)
- 985 -
m
0.1
Tab.3 Different DDs of the listed firms when m chooses different number
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DD 000401
2.284
2.2812
2.2783
2.2754
2.2725
2.2696
2.2667
2.2638
2.2609
2.2579
DD 000789
1.7398
1.7386
1.7374
1.7362
1.735
1.7338
1.7326
1.7314
1.7302
1.7289
DD 000877
2.2886
2.287
2.2855
2.284
2.2825
2.2809
2.2794
2.2778
2.2763
2.2747
DD 600217
2.0047
2.0044
2.004
2.0036
2.0033
2.0029
2.0025
2.0022
2.0018
2.0014
DD 600539
1.4766
1.4766
1.4766
1.4765
1.4765
1.4765
1.4765
1.4765
1.4765
1.4764
DD 000673
2.1157
2.1157
2.1157
2.1157
2.1157
2.1157
2.1157
2.1157
2.1157
2.1157
Tab.4 Significance test of the difference of DDs
Mean value
Pair T test
m
Non-ST
ST
Mean Difference
t-value
p-value(double tail)
0.1
2.1041
1.8657
0.23847
7.202
0.018739
0.2
2.1023
1.8656
0.23670
7.178
0.018863
0.3
2.1004
1.8654
0.23497
7.160
0.018952
0.4
2.0985
1.8653
0.23327
7.140
0.019056
0.5
2.0967
1.8652
0.23150
7.124
0.019141
0.6
2.0948
1.8650
0.22973
7.095
0.019293
0.7
2.0929
1.8649
0.22800
7.073
0.019408
0.8
2.0910
1.8648
0.22620
7.045
0.019559
0.9
2.0891
1.8647
0.22447
7.021
0.019689
1
2.0872
1.8645
0.22267
6.990
0.019858
when m becomes bigger. What’s more, the DD of a non
ST company decrease more quickly than a ST company.
This can be explained by the structure of the liability of
the company. Through the statistics we collect, we can
know that in China, a non ST company usually has more
long-term liability than a ST company. The banks are not
willing to borrow money to the ST companies when
considering the higher risk. In addition, the ST
companies concern more about the survival of the firm,
which means they are more likely to deal with the extant
problems than resolve future problems. So they do not
need many long-term debts to develop. Another
phenomenon is the DDs of the firms do not change much
following m, which means when analyzing a selected
industry, m is not that important.
Moreover, all the firms, in general, have the same
development trend. In other words, the structure of the
liability might not be the most important factor when
evaluating the DD of a cement company.
From Tab.4, all the p-values are blow 0.05, which
means the DDs of non ST and ST have significant
differences. When m=0.1, the p-value is at a minimum,
which means m at this value can best distinguish the ST
firms from non ST ones. Then when m is growing, the
p-value becomes bigger. So, m=0.1 is the suitable value
to calculate DP.
In Tab 4, we can also find that the p-value does not
have much difference. Moreover, we do not have many
ST companies to take Paired Sample test. This may be
another reason to get these close results.
Based on the discussion above, we choose m=0.1 and
calculate the DP of the four firms. The results are shown
as Tab 5.
4) The instantaneous risk-free rate (r)
We choose the RMB one-year deposit interest rate
of 2011 as the value of r. r=2.25%
5) Time (T)
We choose one year as a period and T=1.
3.3 Calculations
Now, from equation (1)，(2)，(3)and(4), we can
calculate V and σV . Then, we can get DD and EDF of
the firms with equation (5) and (6). The results are
shown in Tab 6.
3.4 Result analysis
From Tab.6, we can know that KMV model can
effectively assess the credit risk of Chinese listed firms
and distinguish the good-perform firms from the bad
ones. Another discovery is big companies perform better
than small ones. The total values of the two non ST
companies are 411.12 billion and 214.6 billion. While the
total values of the ST companies are 10.779 billion and
34.701 billion. We can conclude that the total value asset
has great relevance with DD.
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Stock code
000401
DP
19032528100
Tab.5 Stock code and DP
600539
137983325
Tab.6 V
σV
600217
000877
1497596000
7262655000
DD and EDF
Stock code
000401
600539
600217
000877
V（billion）
411.12
10.779
34.701
214.6
σV
0.2363
0.5906
0.2837
0.2898
DD
2.2725
1.4765
2.0033
2.2825
EDF
0.0115
0.0699
0.0226
0.0112
Tab.7 Correlations
SD
LD
σE
E
V
σV
DD
Pearson Correlation
1
0.997**
0.965*
-0.688
0.989*
-0.658
0.726
Sig. (2-tailed)
0.003
0.035
0.312
0.011
0.342
0.274
Pearson Correlation
0.997**
1
0.962*
-0.632
0.987*
-0.595
0.677
LD
Sig. (2-tailed)
0.003
0.038
0.368
0.013
0.405
0.323
Pearson Correlation
0.965*
0.962*
1
-0.744
0.993**
-0.662
0.798
E
Sig. (2-tailed)
0.035
0.038
0.256
0.007
0.338
0.202
Pearson Correlation
-0.688
-0.632
-0.744
1
-0.717
0.976*
-0.994**
σE
Sig. (2-tailed)
0.312
0.368
0.256
0.283
0.024
0.006
Pearson Correlation
0.989*
0.987*
0.993**
-0.717
1
-0.657
0.765
V
Sig. (2-tailed)
0.011
0.013
0.007
0.283
0.343
0.235
Pearson Correlation
-0.658
-0.595
-0.662
0.976*
-0.657
1
-0.948
σV
Sig. (2-tailed)
0.342
0.405
0.338
0.024
0.343
0.052
Pearson Correlation
0.726
0.677
0.798
-0.994**
0.765
-0.948
1
DD
Sig. (2-tailed)
0.274
0.323
0.202
0.006
0.235
0.052
Pearson Correlation
-0.658
-0.600
-0.711
0.999**
-0.685
0.982*
-0.987*
EDF
Sig. (2-tailed)
0.342
0.400
0.289
0.001
0.315
0.018
0.013
**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).
SD
4 Related coefficient of different factors
EDF
-0.658
0.342
-0.600
0.400
-0.711
0.289
0.999**
0.001
-0.685
0.315
0.982*
0.018
-0.987*
0.013
1
when the company has more assets, it will be more likely
to pay back the loan.
From the discussion above, we can know that total
asset value of a company has relevance with DD. Now
we use related coefficient to evaluate the relevance
between different factors and DD. We choose the
statistics in Tab.1, Tab.2, and Tab.6 as the sample. The
results of calculation are shown in Tab.7.
Tab.7 shows the relationships of the factors in the
KMV model. From Tab.7, we can get many discoveries.
First, There is great connection among SD(short-term
debt), LD(long-term debt), E and V. This illustrates the
company’s total value increases in proportion to the raise
of debt. Second, σE is highly correlated with DD and
EDF. The related coefficient between DD and σE is
-0.994. And the related coefficient between EDF and
σE is 0.999. When σE raises, DD decreases and EDF
raises. From this connection, we can get the conclusion
that steady rise of the value of the equity might add a
company’s resistance to financial crisis. On the contrary,
the great fluctuation of the stock price suggests the
potential risk of the company. Third, the related
coefficient between V and DD is 0.765. This means
5 Applying KMV model to cement industry
analysis
In order to analyze the development of the Chinese
cement industry and to evaluate the influence of financial
crisis on this industry, we collect the statistics from 4
listed firms (stock code: 000877, 000401, 600802,
000789) from 2006 to 2011, and calculate the V, DD and
EDF of these firms. The results are shown as Fig.1 and
Fig.2.
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Fig.1
Fig.2
Fig.1 presents the change of the total asset value of
the 4 firms. From Fig1, we can see that the total asset
value has a growing trend in the five years. In general,
Chinese cement firms grow rapidly. Some special
company (000401) double its total assets value in just 3
years. However, in 2008, the value of 000877 and
600802 decreases compared with 2007. The total value
of 000401 and 000789 remain the same as last year.
From the statistics in 2008, we can know that financial
crisis make large damage to cement industry in China.
Fortunately, in 2009, the total values of the 4 firms are all
increasing, which means the cement firms have already
taken some measures to deal with the crisis. Another
phenomenon we need to pay attention is the value of the
4 firms decreases or remains the same in 2011, which
means the development of cement industry might meet
another crisis in the next few years.
Fig.2 shows the change of default distances of the 4
firms from 2006 to 2011. From Fig 2 we can see that the
DDs decrease greatly from 2007 to 2008, which means
the 4 firms are most likely to default in 2008. It is clearly
that the financial crisis has a great impact on the cement
industry in China. However, there is another signal we
should concern is the DD of the 4 firms begin to decrease
even in 2006, which means KMV model can predict the
development trend of the cement industry. So, the banks
and the government can change the policies according to
the change of the default distance in order to better help
the companies to return to their normal condition. They
can also take some measures to prevent larger damage
when they find DD of the firms decreases. In addition,
the DDs of the 4 companies are decreasing in 2011,
which means cement industry need to change their
strategy to take more chances to overcome the potential
crisis, and the growth of this industry might slow down
in the future.
6 Conclusion
In this paper, we use KMV model to analyze the
development of the cement industry in China. The KMV
model assumes that the firm goes into bankruptcy with
its default point at short-term debt plus half of the
long-term debt. However, we change the percent of
long-term debt to find the suitable percent for the cement
industry. By using significance test of the difference of
DD, we think default point should be short-term debt
plus 10% long-term debt. By further research, we can
know that short-term debts usually play an import role in
the debt structure in ST companies. Another reason
contributed to this situation is that the banks are not
willing to loan money to ST companies when
considering the higher risk. So, the ST companies are
more likely to fault and short-term debt is more
important when assessing the risk of these companies.
That’s why the ratio is only 10% in cement industry in
China.
In addition, we consider the additional value when
non tradable shares change into limit sell shares and we
give a way to calculate the value of the limit sell shares,
which can help us better evaluate the value of the equity
of the companies.
Moreover, by analyzing the total asset value, DD
and EDF of the 4 selected firms in cement industry, we
conclude that KMV model can predict the development
tendency of a company. In 2008, the total asset value of
these four firms gets down and the DDs of these
companies are at their lowest point, which means the
financial crisis has great impact on the cement industry.
However, in the 2009 and 2010, the cement industry has
a fast development. This might be related to the large
range of the establishment of the economic affordable
housing and low-rent housing motivated by Chinese
government. But the DDs and the value of the firms get
down in 2011, so the cement industry should change
their normal strategy and use more high-tech ways to
enhance the quality of their products. Sometimes they
may even change their management structure to better
adapt to the financial environment in the world.
Finally, there still a lot of work need to do to better
apply KMV model to China. First, the analysis of the 4
listed firms might not represent all the companies in the
cement industry. We should also find some models to
calculate DD of the non listed firms. Second, the way to
calculate non tradable shares should be improved to get
more accurate results. In addition, KMV model is based
on the assumption that the volatility of the price of stock
obeys normal distribution. However, the actual volatility
might not fit this assumption. A better distribution model
should be promoted to advance KMV model.
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