iBusiness, 2013, 5, 1-5
doi:10.4236/ib.2013.51b001 Published Online March 2013 (http://www.scirp.org/journal/ib)
1
The Logit Model Based on Owners` Equity Statement in
the Use of the Financial Risk Pre-warning
Zhaoyuan Geng, Yini Wang, Fei Shao
Department of Applied Economics, Business School of Zhejiang University City College, Hangzhou, China.
Received 2013
ABSTRACT
Under the premise that the global economic environment is in the turbulence, companies need to strive to make their
own in this environment and seek further development, which makes researches on the financial pre-warning particu-
larly important.This article stand in the point of perspective of changes in equity, through the significant difference be-
tween the U test build pre-warning indicators, the use of Logit models with owner changes in equity provided by the
establishment of early warning financial indicators model, an empirical study of listed companies. The empirical results
show that the Logit model based on owners` equity statement in the use of the financial risk pre-warning can accurately
predict the financial distress of listed companies.
Keywords: Owners` Equity Statement; Logit Model; Financial Risk Pre-warning
1. Introduction
With the constantly adjusting of the nation’s economic
structure and frame, the companies are facing to a more
fierce competition. The failure of various economic deci-
sions may lead to bankruptcy. Since the financial risk
pre-warning can be regarded as a weatherglass of the
economic function, well as a guiding light of the compa-
nies’ business, it not only has the high academic value,
but also be of great application value to do research of it
[1]. According to the new accounting standard, the own-
ers’ equity statement is added up to the audit report. So
the author thinks that the owner’s equity statement is
very important for the financial risk pre-warning and the
perfection of the financial pre-warning system appears to
be more significant [2]. This article is based on the re-
search of the use of the logit model in the financial risk
pre-warning. It adopts the average index of the financial
data quoted from the ST and non-ST companies to judge
this model can weather or not be used in the accurate
financial risk pre-warning.
2. The Basic Theory of the Financial Risk
Pre-Warning Logit Model
2.1. The Basic Theory of the Financial
Pre-Warning Logit Model can be Mainly
Divided into Two Parts
1) The basic theory of the sample selection: this article
chooses 20 listed companies which are first announced
as the ST (they are still now) between 2008 and 2010 as
the sample of the financial risk company .It matches the
ST companies and the non-ST companies in the ratio of
1:1. It also selects 21 companies as the sample of the
healthy companies. These companies have never been
announced as the ST.
2) The basic theory of the owners` equity statement
financial risk pre-warning index:
a) The profitability analysis is mainly relied on the re-
turn on equity=comprehensive income/equity and the net
return on capital=net profit/net capital.
b) The profit distribution analysis is realized by the
calculating of profit distribution rate=the distribution of
profits to shareholders/net profit.
c) The asset management capability analysis can be
divided into asset margin rate (net profit/total assets) and
capital gains rate (gain/total assets).
d) The solvency analysis can be realized by the ana-
lyzing of equity ratio (debt/equity). [3]
2.2. Sample Selection
Through the researching of many models, the author
finds that simple linear regression [4] is obviously simple
with low overall identification accuracy. So it can’t fully
reflect the overall financial characteristics. Although the
Z model and the F model [5] have a better accuracy of
the recognition, they are difficult to realize because of
the high requirement for the sample. In terms of the in-
dustry and company size, these models don’t have the

The Logit Model Based on Owners` Equity Statement in the Use of the Financial Risk Pre-warning
2
horizontal comparability; the artificial neural networks
(ANN) model, relative flow (DRL)model, joint predic-
tion model[6] are difficult to calculate and inconvenient
to use. The advantage of the logit model is that it over-
comes the linear equation‘s limitation restrained by the
statistical hypothesis and it can be applied in a wider
range. The defect of it is the complex calculation. There
are many approximations in the progress of the calcula-
tion, which may influence the accuracy of the prediction.
China scholars, such as ChenXiao and so on find that the
debt equity ratio, accounts receivable turnover, operating
profit/total assets, retained earnings/total assets have
strong predictive power[7].
Finally, the author decides to do the research of the
company financial pre-warning in the use of logit model.
3. The Empirical Study of the Financial Risk
Pre-Warning Based on Owners` Equity
Statement
Compared with the traditional financial pre-warning
models, the empirical theory research of the Logit model
based on Owners` Equity Statement focuses on the fi-
nancial data which is provided through the Owners` Eq-
uity Statement of the financial distress of companies, and
use first-hand data and various statistical means to pre-
dict the companies’ financial state. This article is in
hopes of finding evidence to support significant of the
research.
3.1. The Thought of the Empirical Study
Firstly, compare the relevant data of the statement of
changes in owner’ s equity from the ST companies with
the non-ST companies', and analyze the significant dif-
ference of the data.
Secondly, compare the Owners' equity index changes
which are from the ST companies with the non-ST com-
panies’, and analyze the significant difference of indica-
tors rate.
Thirdly, after the significant differences of comparison
index, combining the Logit model, to construct the Logit
model on the basis of applying Excel to calculate multi-
variate return, and the accuracy of it on to the back.
3.2. The Introduction of the Research Methods
3.2.1. The Introduction of Significant Test
If the distribution of variables is unknown, it is more
suitable to adopt U inspection to choose financial va-
riables, because the U inspection is the measure to com-
pare the equality of the population medium. Domestic
and oversea literatures show that companies’ financial
ratios are not normal distribution. So this article chooses
U inspection to prove the selected variables in whether
there are significant differences between. Financial crisis
and financial normal company.
a) U inspection
U inspection supposes that two samples were from
exactly the same two overall except for the overall aver-
age in order to test whether there are significant differ-
ence between the two general of the mean value are there
significant difference.
According to the actual situation，the author gives the
assumptions in this article.
Suppose a:
Ho: there is no difference between financial normal
company’s return on capital and financial crisis.
H1: there are some differences between financial nor-
mal company’s return on capital and financial crisis.
Suppose b:
Ho: there is no difference between financial normal
company’s capital protection ratio and financial crisis.
H1: there are some differences between financial nor-
mal company’s capital protection ratio and financial cri-
sis.
Suppose c:
Ho: there is no difference between financial normal
company’s rate of capital accumulation and financial
crisis.
H1: there are some differences between financial nor-
mal company’s rate of capital accumulation and financial
crisis.
The test of the significant difference is achieved in the
test after 3 software spssl 3.0, the results in Table 1.
From the table, we can learn that the P-value of the
Return on capital, the capital protection ratio and the rate
of capital accumulation is all less than 0.05, so the null
hypothesis is rejected, which shows that they note a sig-
nificant difference in the condition in line with the re-
quirements of building a model.
But although the pair wise difference among the three
variables is significant, it is necessary to do a further test
because of the small sample size and the repeat of the
original data, so that we can exclude the 3 variables of
multicollinearity. According to this point, the author has
conducted a test of multicollinearity of the 3 variables.
b) Multicollinearity test
Generally, the domestic uses variance inflation factor
(VIF) to measure of multicollinearity
The most commonly used method for formal diagnos-
tic of multi-correlation is to use variance inflation factor.
Table 1. U test value.
Index Z-test P-value
Return on capital -6.372 0.0034
capital protection ratio -4.364 0.0052
rate of capital accumulation -7.658 0.0021
Note: all data is in the 5% level of confidence significantly.

The Logit Model Based on Owners` Equity Statement in the Use of the Financial Risk Pre-warning
opyright © 2013 SciRes. IB
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The variance inflation factor of independent variable
xj is denote as (VIF)jwhich is calculated as:


2
11
j
j
VIF R 
(1)
In the formula, 2
j
R
is the coefficient of multiple de-
terminations for other independent variable’s regression
when j
X
is the dependent variable.
The Table 2 is multicollinearity’s examination of the
picked variables in my report and 2
j
R
’s value is from
three indexes’ pair wise regression.
From the result we can see, VIF of the Owner Equity
Index including the return on capital, Capital protection
ratio, capital accumulation ratio is below 10,which means
there is no multicollinearity between those three va-
riables. Combine the result of significance test of differ-
ence with it we can know that those three variables is
well used to construct the Logit model based on owners’
equity statement.
3.2.2. The Instruction of Logit Model
The model in this report assumes that yit is the financial
situation of enterprise “i” at “t” point. For the implicit
variable y it , we can have the definition below:
When yit is equal or lesser than 0, we consider the fi-
nancial situation healthy if yitequals 0;
When yit is greater than 0, we consider the financial
situation trapped.
Since the report chose enterprises which are still being
ST while selecting samples, so the rule of assignment for
yit in this report is:
Yit equals 1 (“i” is the sample of enterprises in crisis
and “t” is the year when announced as ST)
Yit equals 0 (“i” is the sample of healthy enterpris-
es,”t” is the year before being announced as ST)
it ln 1
p
Yp




(2)
The Logit model based on owners` equity statement is
represented finally as:
it 1
it
YX



 (3)
In the formula, vector “x” is a tridimensional vector,
showed respectively as the chosen Return-on Capital(x1),
Capital Protection Ratio(x2), Capital Accumulation Ra-
tio(x3), Xit-1 is the variables of enterprises at the year of
Table 2. Multicollinearity’S examination.
variables VIF The reciprocal of VIF
return on capital 0.04 24.38
Capital protection ratio 0.05 19.45
capital accumulation ratio 0.04 25.81
t-1. ξ is the error amount, coincide the standardized nor-
mal distribution. ξ and explanatory variable Xit–1 are mu-
tual independence.
3.2.3. The Co nstruction of the Lo gi t Model Based on
Owners` Equity Statement in the Use of the
Financial Risk Pre-Warning
We can make simple data regression to calculate The
Logit Model Based on Owners’ Equity Statement quickly
using Excel.
From the data of table, we can draw a conclusion that
The Logit Model Based on Owners’ Equity Statement is:


1
23
Logit0.426649388 0.993341096
0.0126375280.004217703
yX
X
X


(4)

Logitln 1
p
yp




(5)
3.2.4. The Regressi on and Judgement Collation of
Model
The Logit Model Based on Owners’ Equity Statement
uses the three Owner Equity Indexes of twenty ST com-
panies and Twenty-one non-ST companies in the year
before being announced as ST as independent variables,
pick the ST companies’ value as 1, non-ST companies’
value as 0 as independent variables to estimate. There-
fore, it’s the optimally judge point in theory when p’
value is zero point five.
Table 3. The Result of regression.
Coefficients Standardized
error t Stat
Summary output
Regression statistics
Multiple R 0.682170392
R Square 0.465356444
Adjusted R Square 0.422006966
Standardized error 0.384737061
Observed value 41
Variances analysis
df SS MS
Regression analysis 3 4.76706601 1.589022003
Residual error 37 5.476836429 0.148022606
sum 40 10.24390244
P-value Lower 95%
F Significance F
Regression analysis 10.73499545 3.23636E-05

The Logit Model Based on Owners` Equity Statement in the Use of the Financial Risk Pre-warning
4
Table 4. the regression and judgment result of logit model.
Original val-
ue Predicted value Sum Accuracy rate
0 1
0 17 4 21 80.95%
1 18 2 20 90.00%
Sum 35 6 41 85.37%
Depending on the estimate of the model to judge the
basic data, when the Predicted value is greater than zero
point five, it’s a ST company, when the Predicted value
is lesser than zero point five, it’s a non-ST company, and
the conclusion is shown in table. From the table we can
see, The Logit Model Based on Owners’ Equity State-
ment has a high accuracy in presetting companies’ finan-
cial trap.
3.2.5. The Analysis of Empirical Research Findings
Firstly, the coefficient of rate of return on capital (net
profit/average capital) is negative, and it is significant
when below 5% of the confidence level. It shows that the
influence of this variable to the financial position of the
listed company is negative, which means the higher pro-
portion of the net profit taken from the total average cap-
ital, the lower possibility to get financial difficulties.
Secondly, the coefficient of rate of capital guarantee
(the total owner’s equity in the end of the year deducted
by the objective factors/the owner’s equity in the begin-
ning of the year) is negative, and it is significant when
below 5% of the confidence level. It shows that the in-
fluence of this variable to the financial position of the
listed company is negative correlation, which means the
higher proportion of the total owner’s equity in the end
of the year deducted by the objective factors taken from
the total owner’s equity in the beginning of the year of
the enterprise, the lower possibility to get financial diffi-
culties.
Finally, the coefficient of capital accumulation rate
(the owner’s equity growth this year/the equity in the
beginning of the year) is negative, and it is significant
when below 5% of the confidence level It shows that the
influence of this variable to the financial position of the
listed company is negative correlation, which means the
higher proportion of the owner’s equity growth this year
taken from owner’s equity in the beginning of the year of
the enterprise, the lower possibility to get financial diffi-
culties.
3.3. The Enlightenment and Shortage During the
Research
3.3.1. Summa ri z ati on of the Research
First of all, to construct the cross-section data model,
which represents whether the enterprise has financial
difficulty, by combining the statement of changes in eq-
uity with Logti model, according to the possibility of the
enterprise getting financial difficulty and the quantitative
relationship of the variables chosen from the model?
Secondly, rate of return on capital and rate of capital
guarantee reflect the development and operational risk of
a company respectively, additionally; the rate of capital
accumulation measures the company’s strength. The data
above would cover the majority of the internal and eter-
nal environment of a company. The only shortage is that
these data are not sufficient enough and have a strict re-
quirement of accuracy and reliability.
3.3.2. The Problems Existing in the Model
It also has limitations to use Logit model to predict fi-
nancial distress. Firstly, china's evaluation on ST Com-
pany is not so professional. There are problems in defin-
ing the financial difficulties enterprises. Secondly, there
are insufficient variables, moreover, the neglect of ma-
croeconomic fluctuation and the influence of the policy
in equity distribution to the financial difficulties.
3.3.3. Enlightenment from the Research
After the empirical analysis, the owner’s equity index of
Chinese listed companies contains the information of
predicting financial difficulties, so it is feasible to use
related information of owner’s equity to construct a
model to predict the enterprise’s financial status. Fur-
thermore, Logit model, on the basis of the statement of
changes in equity, has a preferable accuracy on predict-
ing financial difficulties. If taking information about cap-
ital, liabilities, profit, cash flows, owner’s equity and
macroeconomic factors account, combining with the dy-
namical panel data model, we will obtain a better and
more accurate financial warning model.
4. Conclusion
From the perspective of the owner’s equity, this essay
has carried out the empirical research to listed companies
by combining statement of changes in equity and Logit
model to gain the significant difference U-test and multi-
collinearity test and construct the predict model. The
empirical results show that it is very useful to use own-
er’s equity index to predict financial status of a listed
company. And it is accurate and positively significant in
the long term. Finally, with the review of the process of
the research, this essay analyzed its limitation and points
to be improved.
5. Acknowledgment
This paper is supported by the construct program of the
key laboratory in Hangzhou.

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opyright © 2013 SciRes. IB
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