Dynamic Early-Warning of Enterprise Financial Distress
Based on Gradient Boosting Algorithm
Ying Peng
*
, Ziyi Chen and Jingyi Wang
Business School, Jianghan University, No.8, Sanjiaohu Road, Wuhan Economic and Technological Development Zone,
China
Keywords: Enterprise Financial Distress, Gradient Boosting Algorithm, Dynamic Early-Warning.
Abstract: One of the biggest problems of users of financial statements is whether the enterprise will face financial
distress. In this study, an early-warning system model based on gradient boosting algorithm for enterprise
dynamic early-warning is presented. Sometimes special treatment (ST) is the warning of abnormal financial
or occurring other conditions in China stock exchange. We construct enterprise dynamic early-warning
model based on gradient boosting algorithm using the data of ST companies and their matching companies
before special treatment 3 years. Our model calculates the relative variable importance (RVI) of each
financial distress indicators, and get the average results of models. Through comparing with logit model, the
results show that model based on gradient boosting algorithm can get better warning results. Our paper
provides a more accurate method for enterprise dynamic early-warning, which can provide reference for
users of financial statements improve financial situation, change investment strategy and so on.
1 INTRODUCTION
An enterprise encounter financial distress is a
gradual process, not sudden. Before facing financial
distress, financial or non-financial indicators of
enterprise may appear abnormal. That is to say, we
can find indicators and use method to alert for the
probability of financial distress. Therefore, the key
to early-warning of enterprise financial distress is to
establish early-warning indicator system and find
out applicability algorithm.
About the early-warning indicator system, it has
experienced two stages. The first stage, indicators
are instructed based on financial statements; the
second stage, indicators are selected based on other
information that is also important for enterprises,
such as marketing indicators, corporate governance
indicators, and so on.
Enterprise financial distress early-warning
models can be divided into statistical methods and
machine learning methods (Alaka, Oyedele, .et al,
2018). Statistical methods have been introduced into
financial early-warning about 60 years ago. They
include z-score model, single and multiple
discriminant model, logit and probit models, and so
on (Altman, 1968; Deakin, 1972; Jones, 1987).
Machine learning methods first come into financial
distress early-warning in 1990s, and there are some
breakthroughs have been made in the financial
distress application research area. Such as genetic
algorithm, BP neural network, rand forest algorithm,
and so on (Brockeet and Cooper, 1995; Sharda and
Steiger, 1990; Breiman, 2001; Franco, 2002).
Through machine learning methods can improve
accuracy of financial distress early-warning, in spite
of the process of early warning seems in a “black
box” (Barboza and Kimura, 2017). Therefore, they
cannot provide suggestions on how to improve
performance of enterprises. However, gradient
boosting algorithm as an improved machine learning
models, which can overcome the defect of the “black
box” problem. It can not only output specific alert
results, but also output relative variable importance
of indicators, which can help users of financial
statements make decisions. In this study, we
introduce gradient boosting algorithm into the field
of financial early-warning field, which can further
expand the application scope of the method.
Peng, Y., Chen, Z. and Wang, J.
Dynamic Early-Warning of Enterprise Financial Distress Based on Gradient Boosting Algorithm.
DOI: 10.5220/0012022800003620
In Proceedings of the 4th International Conference on Economic Management and Model Engineering (ICEMME 2022), pages 17-23
ISBN: 978-989-758-636-1
Copyright
c
 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
17

2 CONSTRUCTION OF
FINANCIAL DISTRESS
EARLY-WARNING
INDICATORS SYSTEM
Gradient boosting algorithm is not affected by
collinearity and missing value of indicators, and
with the effect of alert is not monotone decreasing.
Therefore, we construct financial distress early-
warning indicators system including both financial
indicators and non-financial indicators.
2.1 Construction of Financial
Indicators System
There is no doubt that traditional financial indicators
still play an important role in the field of early-
warning of enterprise financial distress. They usually
include solvency indicators, profitability indicators,
operating capacity indicators and development
capacity indicators. We can use solvency indicators
to reflect mismatch of assets and debt, as the
mismatch will cause such as non-effective
investment, much bigger operational risk, which
influence negatively. The decline of profitability is
one of the important manifestations of financial
distress. Operating capacity can reflect cash that are
occupied by suppliers and customers. If there are too
much cash are occupied, that will cause companies
lack of cash for their expanded. Development
capacity can reflect the growth rate of one company,
but the growth rate too fast or too late all influences
the happening of financial distress. However, cash
flow and the degree of earnings management also
occupy a key position in determine whether one
enterprise will go bankrupt or not. Therefore, we add
cash-flow indicators and earnings management
indicators in traditional financial indicators to
improve early-warning effect.
Table 1: Financial indicators system.
Classification
of Indicators
Financial Indicators
Solvency
Indicators
Current ratio
(
x
11
)
Quick ratio
(
x
12
)
Cash ratio (x
13
)
Equity to assets ratio (x
14
)
Working capital to debt (x
15
)
Long term liabilities
to total assets (x
16
)
Fixed assets to total assets (x
17
)
Intangible assets to total assets (x
18
)
Profitabilit
y
Net
p
rofit to total assets
(
x
21
)
Indicators Net
p
rofit to ca
p
ital
(
x
22
)
Profit before interest and tax to
profit before tax + financing
expenses (x
23
)
Gross profit to sales (x
24
)
O
p
eratin
g
p
rofit to sales
(
x
25
)
Operating
Capacity
Indicators
Receivables turnover
(
x
31
)
Inventor
y
turnover
(
x
32
)
Total assets turnover (x
33
)
Working capital turnover (x
34
)
Development
Capacity
Indicators
Cumulative capital ratio (x
41
)
Earnin
g
s
p
er share
g
rowth rate
(
x
42
)
Net
p
rofit
g
rowth rate
(
x
43
)
Self-sustainable growth rate (x
44
)
Income growth rate (x
45
)
Total asset growth rate (x
46
)
Fixed assets
g
rowth rate
(
x
47
)
Intan
g
ible assets
g
rowth rate
(
x
48
)
Cash-flow
Indicators
Free cash flow
(
x
51
)
Cash flow interest
covera
g
e ratio
(
x
52
)
Cash meet investment ratio
(
x
53
)
Cash to o
p
eratin
g
income
(
x
54
)
Cash to net profit (x
55
)
Earnings
Management
Indicators
Accrued earnings
mana
g
ement de
g
ree
(
x
61
)
Real earnings
mana
g
ement de
g
ree
(
x
62
)
Absolute value of
accrued earnings management (x
63
)
Absolute value of
real earnin
g
s mana
g
ement
(
x
64
)
2.2 Construction of Non-Financial
Indicators System
As the traditional financial indicators have many
defects, which can only reflect historical information
and exist hysteresis (Brochet, Loumioti, 2015; Kraft,
Vashishtha,2018). However, non-financial indicators
that have good forward-looking and value relevance
for users of financial statements. They effectively
make up the shortage of traditional financial
indicators. Therefore, we construct non-financial
indicators system, which include marketing
indicators, corporate governance indicators and
auditors’ behaviour indicators. According to signal
transmission theory, if one company suffer financial
distress, which transfer negative signal to market,
and then it will cause negative market response.
Corporate governance is the specific of enterprise’s
internal stable environment. Good corporate
governance will effectively decline agent cost, but
bad corporate governance may cause financial
distress. Sometimes auditors cannot directly decide
one company financial risk, whose behaviour can
ICEMME 2022 - The International Conference on Economic Management and Model Engineering
18

tell us whether the corporate suffer financial distress,
such as raising audit fees, increasing audit delay,
issuing nonstandard audit opinion, and so on.
Table 2: Non-Financial indicators system.
Classification
of Indicators
Non-Financial Indicators
Marketing
Indicators
Price earnings ratio (x
71
)
Price to sales (x
72
)
Price to boo
k
(
x
73
)
Dividend declared ratio
(
x
74
)
Earnin
g
s
p
er share
(
x
75
)
Net asset per share (x
76
)
Corporate
Governance
Indicators
Director numbe
r
(x
81
)
Institutional investors
shareholding ratio (x
82
)
Equity concentration (x
83
)
Auditors’
Behaviour
Indicators
Abnormal audit fees (x
91
)
Audit dela
y
(
x
92
)
Nonstandard audit o
p
inion
(
x
93
)
Auditors chan
g
e
(
x
94
)
3 ESTABLISHMENT OF
EARL-WARNING MODEL AND
CALCULATION STEPS
3.1 Establishment of Enterprise
Financial Distress Model Based on
Gradient Boosting Algorithm
Gradient boosting algorithm is an ensemble learning
algorithm that can combine a series of weak
classifiers into a strong classifier. Traditional
machine learning can only establish one learning
model, but ensemble learning can establish a series
learning models and can combine all learning
models together format a committee-based learning
model. Therefore, weaker classifiers can become
strong classifier. We can use training data as
experience knowledge to establish learning model,
which can learn the relationship from input to
output. And then we can use the learning
relationship on test data.
As we all known, no matter financial indicators
or non-financial indicators can alert whether a listed
company happens financial distress or not. But
sometimes the effective of single indicator to do
early-warning is always bad, so we can define the
single indicator as a weak classifier. Therefore, we
design both financial indicators system and non-
financial indicators system, which can seem as a
strong classifier. We use the classifier to predict
whether a company facing financial distress.
Sometimes we cannot obtain the intuitiveness
and accuracy at the same time in one model.
Machine learning algorithm can enhance the
effective of early learning, but it cannot tell us how
to get the results. However, using gradient boosting
algorithm to do the dynamic prediction process
through calculating indicators relative variable
importance (RVI) and the effectiveness indicators of
early warning model. That is to say, gradient
boosting algorithm can get intuitiveness and
accuracy at the same time to some extent. The
calculations of RVI can be given in the form:
1
22
1
() [() ]
J
t
t
TiIVT
ϑ
τϑ
−
=
==

(1)
Where
2
()T
ϑ
τ
is the indicators relative variable
importance (RVI); J-1 is the number of nodes in the
decision tree;
2
[() ]
t
iIVT ϑ =
it the classification error
of indicators in i node. The bigger RVI, the better
early-warning effectivity of indicators.
We use true positive rate (TPR), false positive
rate (FPR), and accuracy rate (AR), recall rate (RR)
and precision rate (PR) to calculate the effectiveness
of early warning model. Accuracy rate can be used
to measure accuracy of the model; recall rate can be
used to calculate the probability of Type I error; and
precision rate can be used to estimate the probability
of Type II error. The formulas are shown as follow:
TP
TPR
N
=
(2)
FP
FPR
N
=
(3)
TP TN
AR
N
+
=
(4)
TP
RR
TP FN
=
+
(5)
TP
PR
TP FP
=
+
(6)
Where TP is the ST companies’ number which
is correctly classified by model; FN is the ST
companies’ number which is wrongly classified by
model; FP is the non-ST companies’ number which
is wrongly classified by model; TN is the non-ST
companies’ number which is correctly classified by
model; N is the number of the whole sample.
3.2 Establishment of Enterprise
Financial Distress Calculation
Steps
The aim of gradient boosting algorithm is to train a
strong classifier, which can improve the effect of
early-warning of enterprise financial distress. The
Dynamic Early-Warning of Enterprise Financial Distress Based on Gradient Boosting Algorithm
19

strong classifier is combine with many weak
classifiers. Therefore, how to train a strong classifier
is a problem. The steps are as follow:
Step 1: input training data set;
Step 2: assign the weight of sample point as 1/n;
Step 3: assume there are m financial distress
indicators in total:
 Use the training set that was assigned
weight, and get the basic classifier:
{
}
(): 1,1
m
Gxx→−
(7)
 Calculate the classification error rate
of G
m
(x) in the training set:
m
e(())
mii
PG x y=≠
(8)
 Calculate the coefficient of G
m
:
1
1
log
2
m
m
m
e
a
e
−
=
(9)
 Update the weight distribution of
training data set:
m1 1,1 1,2 1,
(, ,, )
mm mn
Dww w
+++ +
= 
(10)
,
1,
exp( ( ))
mi
mi mim i
m
w
wayGx
Z
+
=−
(11)
m,
1
exp( ( ))
n
mi m i m i
i
Z
wayGx
=
=−

(12)
Where D
m+1
is the updated weight of training
data set.
Step 4: get a linear combination of weak
classifiers:
1
f( ) ( )
M
mm
m
x
aG x
=
=

(13)
Repeat the above process, finally we can get the
linear combination f(x) of weaker classifier, which is
our strong classifier trained by gradient boosting
algorithm. Using this strong classifier to judge
whether the listed company will have financial crisis
can greatly improve the warning effect.
4 AN ILLUSTRATIVE EXAMPLE
4.1 Data and Sample Selection
Our sample data includes all public listed companies
in the Chinese market between 2007 and 2017. 2007
is the start year because it is the year that newly
Chinese Accounting Standard issued. The relevant
financial data of sample firms are collected from the
China Stock Market and Accounting Research
(CSMAR) database. In order to test the indicators’
differences between ST companies and normal
companies, we select out 404 publicly listed
companies which are the first time to be ST. We
removed financial industry samples and with a large
number of missing data samples. Finally, it keeps
266 publicly listed companies that are the first time
to be ST.
We paired matching companies of the first time
to be ST companies at a ratio of 1:1. The principles
for selecting matching samples are as follows: first,
matching companies and ST companies are in the
same industry; second, the matching companies
always be listed throughout the sample range from
2007 to 2017; third, the matching companies have
never been ST in the entire sample range; fourth,
when it meet the above three conditions, selecting
the companies that closest to the total assets of the
ST company as the matching samples.
4.2 Descriptive Statistics
In order to analyse how to predict operational risks,
we start with the descriptive analysis on showing the
distribution characteristics of indicators, and the
results are presented in Table 3.
Table 3: Descriptive statistics.
Index Mean1 Med1 Mean2 Med2 Mean3 Med3
x11 1.06 0.78 1.22 0.93 1.42 1.10
x12 0.74 0.50 0.84 0.59 0.99 0.71
x13 0.26 0.13 0.28 0.14 0.38 0.16
x14 -3.61 1.96 2.31 1.60 1.68 1.30
x15 0.55 -0.37 0.71 -0.15 1.97 0.06
x16 0.08 0.02 0.08 0.03 0.07 0.03
x17 0.34 0.35 0.34 0.33 0.31 0.31
x18 0.06 0.04 0.05 0.03 0.05 0.03
x21 -0.13 -0.09 -0.07 -0.06 0.01 0.01
x22 -0.19 -0.10 -0.07 -0.05 0.03 0.03
x23 -0.66 -0.08 -0.25 -0.01 0.13 0.12
x24 0.08 0.07 0.95 1.00 0.67 0.78
x25 -0.86 -0.20 -0.40 -0.11 -0.02 0.01
x31
332.77 5.82 181.96 5.76 403.51 6.29
x32
103.17 3.73 10.71 3.83 26.37 4.13
ICEMME 2022 - The International Conference on Economic Management and Model Engineering
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x33 0.51 0.43 0.56 0.47 0.63 0.52
x34
0.91 -0.98 -13.76 -0.58 0.48 0.62
x41 -0.35 -0.25 -0.14 -0.12 -0.03 0.02
x42 0.21 0.40 -16.90 -7.31 -0.64 -0.76
x43 -0.12 0.32 -20.11 -6.35 -0.72 -0.65
x44 -0.34 -0.23 -0.16 -0.13 0.03 0.01
x45 -0.07 -0.07 0.13 -0.09 3.35 0.06
x46 -0.07 -0.07 0.00 -0.02 1.22 0.04
x47 -0.03 -0.06 0.26 -0.02 2.75 -0.01
x48 14.77 -0.03 0.74 -0.02 2.29 -0.02
Table 3: Descriptive statistics.
Index Mean1 Med1 Mean1 Med2 Mean3 Med3
x51
4.1E+07 3.6E+6 1.1E+8 1.8E+7 -9.2E+7 8.3E+6
x52 261.19 0.75 3.57 0.73 -1.25 1.48
x53 0.24 0.25 0.28 0.25 0.68 0.24
x54 1.35 1.03 1.06 1.03 1.05 1.03
x55 -1.49 -0.11 -0.05 -0.09 7.54 1.55
x61 -0.09 -0.08 -0.05 -0.04 0.00 0.00
x62 0.06 0.06 0.08 0.07 0.06 0.05
x63 0.11 0.09 0.07 0.06 0.06 0.04
x64 0.12 0.09 0.13 0.10 0.14 0.10
x71 -60.42 -11.72 -33.73 -14.90 174.14 106.03
x72 19.38 3.02 15.00 2.10 7.88 1.99
x73 1.81 4.25 5.51 2.82 3.32 2.30
x74 0.00 0.00 -0.01 0.00 0.18 0.00
x75 -0.78 -0.50 -0.43 -0.33 0.09 0.04
x76 1.67 1.53 2.56 2.22 3.17 2.62
x81 8.82 9.00 9.13 9.00 9.22 9.00
x82 3.40 1.70 3.46 1.97 3.51 2.09
x83 43.37 41.83 45.22 43.69 47.45 46.29
x91 0.01 0.00 -0.04 -0.07 -0.02 -0.03
x92 98.50 108.00 101.26 107.00 92.02 98.00
x93 0.30 0.00 0.18 0.00 0.08 0.00
x94 0.26 0.00 0.19 0.00 0.19 0.00
Where Mean1 is the mean value before one year
of companies’ special treated year; Med1 is the
median value before one year of companies’ special
treated year. From Table 3, it can be seen that the
mean value is smaller than its median value in major
development capacity indicators (x41, x42, …, x48).
That is to say, companies went through negative
growth. Accrued earnings management indicators
are negative, but real earnings management
indicators are positive. Because the cost of accrued
earnings management is lower than real earnings
management. At the beginning of enterprises suffer
financial deteriorate, they tend to pay low cost to do
earnings management. But they have to do the real
earnings management to manipulate the surplus,
which shows the two types of earnings management
methods have a certain substitution effect.
About the value of all non-financial indicators
are go bad from t-3 year to t-1 year. The increase
value of abnormal audit fees, audit delay and
nonstandard audit opinion with the time goes by,
which means that auditors have the demand of
reducing risk.
4.3 Analysis of Indicators Relative
Variable Importance (RVI)
Relative variable importance (RVI) can provide a
reference for executives to improve corporate
performance and avoid financial distress. As we all
known, financial distress is a gradual process, and
different early warning indicators play different
roles before companies’ special treated 3 years.
Therefore, we estimated average score of RVI
respectively, and compared the average score of RVI
in different years. The results of each classification
of indicators are presented in Table 4.
From Table 4, we can get the contribution of
each early-warning indicators through calculating
average score of RVI. Among all early-warning
indicators, profitability indicators contribute most in
gradient boosting algorithm, which also play an
important role in other financial early-warning
models. However, development capacity indicators
and marketing indicators have also made great
Dynamic Early-Warning of Enterprise Financial Distress Based on Gradient Boosting Algorithm
21

contributions in early-warning indicators system,
which usually ignored by a large number of studies.
Table 4: Average score of RVI.
Classification of Indicators t-1 t-2 t-3
Solvency Indicators 5.03 9.65 15.32
Profitabilit
y
Indicators 31.26 14.59 32.98
Operating Capacity
Indicators
11.50 12.27 18.43
Development Capacity
Indicators
23.14 22.22 31.65
Cash-flow Indicators 10.07 10.50 5.99
Earnings Management
Indicators
1.51 4.03 8.58
Marketing Indicators 20.34 21.75 37.09
Corporate Governance
Indicators
6.30 11.43 14.27
Auditors’ Behaviour
Indicators
3.05 4.85 4.85
Besides, the importance of indicators changes
with the time goes by. The importance of some
indicators reduced, such as solvency indicators,
operating capacity indicators, earnings management
indicators, marketing indicators and corporate
governance indicators; however, the importance of
other indicators enhanced, such as cash-flow
indicators.
4.4 Empirical Results
(1) Average results based on gradient boosting
algorithm
We get the results of early-warning from
indicators, such as true positive rate, false positive
rate, accuracy rate, recall rate and precision rate.
From Table 5, we can get the average effectiveness
of early warning model, which estimated by the
percentage of training samples and test samples as
7:3, 8:2 and 9:1. It can be seen accuracy rate
increased with the time near special treatment year.
Each recall rate is higher than accuracy rate and
precision rate, that is to say, the probability of Type
I error is smaller than Type II error in our model
based on gradient boosting algorithm. As we all
known, the cost of Type I error is higher than Type
II error (Lian, 2017). Therefore, the dynamic early-
warning model of enterprise financial distress can
better identify enterprises from all sample
companies, which can help investors, managers and
other enterprise stakeholders to make decisions.
Table 5: Average results based on gradient boosting
algorithm.
Indicators t-1 t-2 t-3 Average
True Positive Rate 0.507 0.510 0.484 0.500
False Positive Rate 0.026 0.049 0.089 0.055
Accuracy Rate 0.900 0.885 0.756 0.847
Recall Rate 0.952 0.913 0.847 0.904
Precision Rate 0.872 0.886 0.758 0.839
(2) Average results based on logit
For further verification early-warning effectivity
of gradient boosting algorithm, we construct a
comparing model based on logit. From Table 6, we
can see all the indicators results in logit model are
lower than gradient boosting algorithm. The result
shows that effectiveness of gradient boosting model
significantly better than logit model. But also the
RVI that reported by gradient boosting can provide
suggestions for improving management.
Table 6: Average results based on logit.
Indicators t-1 t-2 t-3 Average
True Positive Rate 0.431 0.427 0.433 0.430
False Positive Rate 0.154 0.176 0.189 0.173
Accuracy Rate 0.788 0.724 0.680 0.731
Recall Rate 0.797 0.741 0.691 0.743
Precision Rate 0.732 0.715 0.659 0.724
5 CONCLUSIONS
This paper constructs enterprise dynamic early-
warning model based on gradient boosting algorithm
using the data of ST companies and their matching
companies before special treatment 3 years. The
model calculates the relative variable importance
(RVI) of each financial distress indicators, and get
the average results of models. Through comparing
with logit model, the results show that model based
on gradient boosting algorithm can get better
ICEMME 2022 - The International Conference on Economic Management and Model Engineering
22

warning results. This study provides a more accurate
method for enterprise dynamic early-warning, which
can provide reference for users of financial
statements improve financial situation, change
investment strategy and so on.
ACKNOWLEDGEMENTS
Supported by the Discipline Group of "Urban Circle
Economy and Industrial Integration Management" of
Jianghan University.
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