Download Research on Financial Early Warning

Research on Financial Early Warning
SHANG Hongtao, SONG Shan
School of Economic and Management, Beijng University of Technology, China
[email protected]
，100124
Abstract: The change process of the enterprise financial rate is a random process. It’s difficult to find a
precise forecast result through the normal analytical method which according to some historical data.
However Markov mainly used to analyze the future trend of development and change of random
incident. So this paper selects rate of return on common stockholders’ equity(ROE), total assets increase
and operating cash flow per share to forecast the enterprise finance with totally twenty quarterly data
from 2003 to 2007 of Zhongwugaoxin Co. Ltd. Markov is also used to research their change rules
empirically. The result of empirical study may forecast promptly the business finance risk.
Key Words:Financial Crisis, Financial Early-Warning, Markov
，
1 Introduction
，
Markov was produced by Audrey Markov, a Russian mathematician then developed by Monte
Carlo. It mainly used to analyze the future trend of development and change of random incident. In
other words, the present state and pulse of a variable are used to forecast the future state and pulse of the
variable, so that the relevant countermeasure can be adopted.[1]
The change process of the enterprise financial rate is a random process. It’s difficult to find a
precise forecast result through the normal analytical method which according to some historical data.
The changes of state are called transitions. Markov researches the transitions of the system which looks
as a whole to explain the random of the change of financial index. So Markov is used to analyze the
change rules of financial indexes in this paper to forecast the risk of company finance.[2]
2 Introduction of Markov
（） ∈
Process of random is a sequence of random variables X t ,t T. The possible values of t form a
countable set T call the parameter space. The possible values of X(t) form a countable set S call the state
space. The process of random can be divided into four kinds according to whether S and T are discrete
aggregate or not. Markov is only refer part of it in the process of random. We often call it Markov
process. Definition: Let {Xn n=0 1 2 …} is a sequence of random variables. Xn=i means a event that
the system is in the state i at the moment n. pij n =p Xn+1│Xn=i means that at the condition Xn=i, the
condition probability of Xn+1=j . We also call it one step transition probability of the system. {Xn} is
claimed a Markov Chain if p (Xn +1 = j │ Xn = i, Xk = ik, k = 1,2,…, n-1) = p(Xn +1 = j │ Xn = i) = pij (n)
for any of the non-negative integer i1 , i2,…, i, j and all n ≥ 0. The definition means the states in every
moment depend on the states in former process but they are independent of the past states. This is
non-aftereffect or non-memory of Markov chain. If one step transition probability pij (n) = p (Xn +1 = j │
Xn = i) has nothing to do with the initial moment n, pij can be recorded shortly. Clearly, one step
transition probability has the property as follows:
pij≥0 i nj=1 2 … n
∑pij=1 i=1 2 … n
One step transition probability in every state can form a matrix:
， ，，，
（ ， ， ， ， ），
（）（
（ ，， ，）
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）
 p11
p
 21
P=  M

 pi1
 M
p12 L p1 j L
p22 L p2 j L

M
M

pi 2 L pij L

M
M
（）
＜ （＜ ）
（） ，
P11 P12 … P1n…P21 P22 P2nP= … … Pn1 Pn2 Pnn is a transition matrix. Let parameter of X n means
Time. tm means present state while tm+1
tm are future states and t1 t2 t3…… tm-1
tm are past
states. {X tm =im} is claimed Present shortly. {X tm＋1 =im＋1} is Future and {X t1 =i1 …….. X
tm-1 =im-1} is Past. We can describe it like this:
P{Future Past Present} P{ Future Present }
Easily we can find:
P{ Future Past Present } P{ Future Present }P{ Past Present }
P{ Past Present Future } P{ Past Present }
Markov equation is applied to have the conclusion: P（n） =P（n-1） •P= Pn in the other words, n steps
transition matrix is equal to the power of n of one step transition matrix.
（ ）
（）
∣ ，
， ∣
∣ ，
（＞ ）
＝
＝
＝
＜＜
（ ）
∣
∣
∣
∣
，
，
3 Selection of variable index for financial early warning
Selection of variable index for financial early warning must consider every factor fully.
Zhao Xiangtao(2007) chose seventy companies of financial crisis which were treated specially and
seventy companies of non-financial crisis as the model. He used some statistical analysis methods like
independent-samples test, factor analysis and relevance analysis integrally to select twelve variables.
Then Logistic regression analysis was handled to regress twelve variables. Logistic discriminance model
was produced to test Logistic model. [3] Test results showed that: In these twelve variables, ROE, total
assets increase and operating cash flow per share have the important influence on the financial situation
of enterprise. The formula is:
……………………………(1)
(X1 is ROE. X2 is total assets increase. X3 is operating cash flow per share). P<0.5 means the
enterprise is on the state of non-financial crisis, otherwise, it is on the state of financial crisis. From
testing of 30 listed companies which were first treated specially in 2006, its prediction accuracy rate
reached 85.33%.
So this paper chooses ROE, total assets increase and operating cash flow per share as the early warning
indexes. Markov is also used to research their change rules. Finally, according to formula (1) we can
forecast the risk of enterprise finance.
4 The process of empirical research
4.1 Samples selection
China Tungsten and High-tech Materials Co. Ltd formerly named Hainan Jinhai Co. Ltd. Its former
company was Hainan Jinhai Materials Co. which wholly owned by Hainan Jinhai Industrial Co. The
main business of the company is manufacturing and the processing of non-ferrous metal and the hard
alloy product.
This paper selects twenty quarterly data from 2003 to 2007 to analyze the sample.
4.2 Indicators summary
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Below are data summary of three indicators of China Tungsten and High-tech Materials Co. Ltd.
(1)ROE Rate of Return on Common Stockholders’ Equity = net profit /Stockholders’ Equity
As shown in table1.
（
）
Tab.1 Summary of ROE in varies period
2003-6-30
2003-9-30
2003-12-31
Time
2003-3-31
2004-3-31
Sequence
1
2
3
4
5
ROE
1.19%
3.00%
3.84%
6.39%
0.99%
Time
2004-6-30
2004-9-30
2004-12-31
2005-3-31
2005-6-30
Sequence
6
7
8
9
10
ROE
1.44%
1.40%
3.43%
0.31%
0.87%
Time
2005-9-30
2005-12-31
2006-3-31
2006-6-30
2006-9-30
Sequence
11
12
13
14
15
ROE
1.52%
0.56%
-0.79%
-1.65%
-1.91%
Time
2006-12-31
2007-3-31
2007-6-30
2007-9-30
2007-12-31
Sequence
16
17
18
19
20
ROE
-14.82%
-0.90%
-4.42%
-7.27%
-54.96%
(2) Operating cash flow per share= operating cash flow / Stockholders’ Equity As shown intable2.
Tab.2
Time
Summary of operating cash flow per share in varies period
2003-3-31
2003-6-30
2003-9-30
2003-12-31
2004-3-31
Sequence
1
2
3
4
5
operating cash flow per
share
Time
-0.61
0.07
0.12
0.41
-0.68
2004-6-30
2004-9-30
2004-12-31
2005-3-31
2005-6-30
Sequence
6
7
8
9
10
operating cash flow per
share
Time
-0.71
-0.49
-0.41
-0.04
0.12
2005-9-30
2005-12-31
2006-3-31
2006-6-30
2006-9-30
Sequence
11
12
13
14
15
operating cash flow per
share
Time
0.09
0.19
0.00
0.34
1.07
2006-12-31
2007-3-31
2007-6-30
2007-9-30
2007-12-31
Sequence
16
17
18
19
20
operating cash flow per
share
0.68
-0.23
-0.16
0.18
-0.11
(3) Total assets increase= (total assets this year-total assets last year)/ total assets last year As shown
in table3.
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Tab.3 Summary of total assets increase in varies period
2003-6-30
2003-9-30
2003-12-31
2004-3-31
2004-6-30
Time
2004-9-30
Sequence
1
2
3
4
5
6
Total assets increase
5.89%
-1.54%
-3.69%
11.78%
11.04%
2.92%
Time
2004-12-31
2005-3-31
2005-6-30
2005-9-30
2005-12-31
2006-3-31
Sequence
7
8
9
10
11
12
Total assets increase
-4.31%
-2.60%
0.06%
-1.05%
1.64%
1.67%
Time
2006-6-30
2006-9-30
2006-12-31
2007-3-31
2007-6-30
2007-9-30
Sequence
13
14
15
16
17
18
Total assets increase
-2.77%
-12.88%
-3.79%
9.69%
-10.66%
2.87%
4.3 Analyze data with Markov chain
Let’s use Markov chain analyze the above information.
4.3.1Construct state and determine the appropriate state probability
According to the data we select, the change range of ROE, the first indicator, is mainly between
-1%-2%. We must consider the limited data and data distribution when we classify it. The state range
is shown in table4.
Indicator state
Tab.4
S1
Indicator range
below-1%
（-1%,2%）
（2%，5%）
above5%
6
8
5
1
Frequence
Calculation of earning per share base on varies status
S2
S3
S4
ROE is divided into four ranges, the range is 3%. Frequence is the number that data of samples
fall into the four ranges. The frequence in the first range is 6. The frequence in the second range is 8.
The frequence in the third range is 5. The frequence in the last range is 1.
The change range of operating cash flow per share, the second indicator, is mainly between
0.05-0.35. The state range is shown in table5.
Indicator state
Tab.5 Calculation of operating cash flow per share base on varies status
S1
S2
S3
S4
below-0.6
（-0.6,0.1）
（0.1，0．7）
above0 7
3
9
7
1
Indicator range
Frequence
．
Operating cash flow per share is divided into four ranges, the range is 0.7. Frequence is the number
that data of samples fall into the four ranges. The frequence in the first range is 3. The frequence in the
second range is 9. The frequence in the third range is 7. The frequence in the last range is 1.
The change range of total assets increase, the third indicator, is mainly between -5%-5% The state
range is shown in table6.
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Tab.6
Calculation of total assets increase base on varies status
Indicator state
S1
Indicator range
below-5%
（-5%，0）
（0，5%）
above5%
3
7
5
4
Frequence
S2
S3
S4
4.3.2 The state transfer probability matrix is constructed by the state transfer
According to the information shown in the above two, transform condition of ROE is shown in
Table7.
Tab.7
The next state
The current state
Transform of ROE in different state
S1
S2
S3
S1
S2
S3
S4
5
1
2
0
1
5
1
1
0
1
3
0
S4
0
1
1
0
One step transition probability matrix:
0 
 5 / 6 1/ 6 0


 1 / 8 5 / 8 1 / 8 1/ 8 
P= 
0 1/ 5 3 / 5 1/ 5



 0
1
0
0


The matrix means the probability that index of sample transfer from one state to another state.
Transform condition of operating cash flow per share is shown in table8.
Tab.8
The next state
The current state
Transform of operating cash flow per share in different state
S1
S2
S3
S1
S2
S3
S4
1
0
1
0
2
3
4
0
One step transition probability matrix:
0 
1/ 3 2 / 3 0


 0 3/8 5/8 0 
P= 
1 / 7 4 / 7 1/ 7 1/ 7 



 0
0
1
0


Transform condition of total assets increase is shown in table9.
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0
5
1
1
S4
0
0
1
0
Tab.9
The next state
The current state
Transform of total assets increase in different state
S1
S2
S3
S1
S2
S3
S4
0
1
1
1
1
2
3
1
1
2
1
1
S4
0
2
0
1
One step transition probability matrix:
 0

1 / 7
P= 
1/ 5

1 / 4

1/ 2
2/7
3/5
1/ 4
1/ 2
0 

2/ 7 2 / 7
1/ 5
0 

1 / 4 1 / 4 
4.3.3 The state vector of various states are inferred by the transition probability matrix
According to one step transition probability matrix and -54.96%, the current status of ROE , we can
find:
Л 0
1 0 0 0
（ ）＝（ ， ， ， ）
0 
 5 / 6 1/ 6 0


 1/ 8 5 / 8 1/ 8 1/ 8 
Л 0 ×P (1 0 0 0)
0 1/ 5 3 / 5 1/ 5 



 0
1
0
0


（ ）＝ （ ） ＝
Л 1
（ ）＝（5/6,1/6,0,0）
So, Л 1
The annual report in March 31, 2008 is forecasted under the stability condition. The probability of
ROE falls into the range S1 is 5/6. The probability of ROE falls into the range S2 is 1/6. The probability
of ROE falls into the range S3 is 0. The probability of ROE falls into the range S4 is 0. So Л 1 of
ROE is -5%.
According to one step transition probability matrix and -0.11, the current status of operating cash
flow per share , we can find:
Л 0
0 1 0 0
（）
（ ）＝（ ， ， ， ）
0 
1/ 3 2 / 3 0


 0 3/8 5/8 0 
Л 0 ×P (0 1 0 0)
1/ 7 4 / 7 1/ 7 1/ 7 


 0
0
1
0 

（ ）＝ （ ） ＝
Л 1
， （ ）＝（0,3/8,5/8,0）
So Л 1
The annual report in December 31, 2007 is forecasted under the stability condition. The probability
of operating cash flow per share falls into the range S1 is 0. The probability of operating cash flow per
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share falls into the range S2 is 3/8. The probability of operating cash flow per share falls into the range
S3 is 5/8. The probability of operating cash flow per share falls into the range S4 is 0. So Л 1 of
operating cash flow per share is 1.825.
According to one step transition probability matrix and -17.63%, the current status of total assets
increase, we can find:
Л 0
1 0 0 0
（）
（ ）＝（ ， ， ， ）
 0

1 / 7
Л 0 ×P (1 0 0 0 )
1/ 5

1 / 4

1/ 2
2/7
3/ 5
1/ 4
（ ）＝ （ ） ＝
Л 1
， （ ）＝（0,1/2,1/2,0）
1/ 2
0 

2 / 7 2 / 7
1/ 5
0 

1 / 4 1 / 4 
So Л 1
The annual report in December 31, 2007 is forecasted under the stability condition. The probability
of total assets increase falls into the range S1 is 0. The probability of total assets increase falls into the
range S2 is 1/2. The probability of total assets increase falls into the range S3 is 1/2. The probability of
total assets increase falls into the range S4 is 0. So Л 1 of total assets increase is -2.0433.
Finally, let’s put the three data into formula (1):
（）
ln
p
= −10.454 X 1 − 3.869 X 2 − 3.271X 3 + 0.828
1− p
Because P=0.9>0.5 , So the company is on the state of financial crisis.
5 Conclusion
This paper selects rate of return on common stockholders’ equity(ROE), total assets increase and
operating cash flow per share to forecast the enterprise finance with totally twenty quarterly data of
Zhongwugaoxin Co. Ltd. According to the change randomcity of financial index , Markov is used to
analyze the change rule of financial index empirically in this paper to forecast the risk of company
finance. The result of empirical study may forecast promptly the business finance risk. Besides this, it
urges the enterprise to adopt the rectification measures immediately and avoids the enterprise moving
toward the bankrupt settlement. But time and quantities of samples are limited in the quarterly reports,
so the results may be not accurately highly.
References
＆
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York,1993:16-18
[2] Mark E. Zmijewski .Methodological Issues Related to the Estimation of Financial Distress
Prediction Models. [J].Journal of Accounting Research
，1984（22):59～82
[3]Wang Hongbo, Song Guoling. System of Risk Early Warning, [M]. Beijing: Economic and Scientific
Press, 2002:35~52(in Chinese)
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