BP Neural Network-based Commercial Loan Risk Early Warning Research
H. Zhou
College of Management and Economics, Tianjin University, China
(zh5553158@163.com)
Abstract - To establish a scientific and effective
commercial loan risk early-warning model is an important
measure to effectively prevent, defuse the risk of commercial
banks. This paper analyzes the main factors on commercial
loans risk and establishes early warning indicator system,
also uses BP neural network to build a bank commercial
loan risk early-warning model. The empirical results show
that: the neural network model can achieve higher accuracy.
Keywords - Risk warning model; commercial loans; BP
neural network
process any kind of data. By learning continuously, the
network can figure out the regular pattern from numerous
complicated data of unknown patterns. The neural
network overcomes the complexity of traditional
processing and difficulties of choosing proper model
functions. In other words, it is a natural process of no
linear modeling which does not have to distinguish which
kind of linear relation exists, thus brings great
convenience to modeling and analyzing [3-6].
2. RISK EARLY WARNING SYSTEM
1. INTRODUCTION
2.1 Principles of index design [7-10]
Building a scientific and effective risk early warning
system for commercial loans, has important practical
significance to identify the risk of loans from commercial
banks and to take timely measures to prevent spreading of
the risk. Traditional risk early warning system mainly
predicts through statistical techniques such as
multivariate statistical analysis, and logistic regression,
which has significant limitations to solve the increasingly
complex problem due to constraints of dealing with
highly nonlinear data, over-reliance on historical data,
and not having the dynamic early warning capacity. With
the development of artificial intelligence, the BP neural
network is introduced into the economic forecasting and
early warning, which provides a new research idea for the
areas of research.
Tam and Kiang (1992)[1] use the BP neural network
to train the network, provide a set of weights according to
some samples of the input to the network ,and after
training, the company of any new input can be divided
into bankruptcy and non-bankruptcy. According to the
prediction accuracy, adaptability and robustness, the
empirical results show that the neural network is a better
assessment of the bank's risk profile.
E. NurOzkan-Gunay, Mehmed Ozkan (2007) [2] use
Turkey's failed bank sample to predict the risk of using
artificial neural networks. The empirical results show that:
artificial neural networks can classify the patterns of
financial data usefully. Use this classification, most of the
banking crisis can be predicted in advance, and more
importantly, it is also able to detect potential crisis
signals.
To sum up, BP neural network has three significant
advantages of dealing economic data: First, the neural
network has advanced paralleled processing system as
well as high speed self-learning and self-adapting abilities,
with a lot of adjustable arguments which enhance the
flexibility of the system. Second, BP neural network can
First, principle of comprehensiveness. Risks of loans
involve various factors and sources, therefore
comprehensive estimate should be considered from
diverse aspects.
Second, principle of science. Science and fairness
are the principles of all systems of index. Choosing index,
determining weights of index, selecting data, calculating
and combining should be based on well-accepted
scientific theories (statistical theory, management and
decision-making theory etc.).
Third, principle of independence. Representative
index are better to be chosen when setting up indexes
since they may overlap with each other, thus indexes of
relative independence should be chosen.
Fourth, principle of measurableness. All the contents
within the index system should be measured directly
according to measuring standards and definite results can
be achieved.
Fifth, principle of operability. In terms of index
selecting and estimate, the evaluate outcome should be
comprehensive and processing procedure should be
operable.
2.2 Setting of risk recognizing index system
a) Financial Risks
Corporate financial risk is a microeconomic risk,
which is the possibility of the actual future results of
corporate financial activities deviating from the expected
results. How the performance of the organization and
management of the corporate financial activities will be
inevitably reflected in the business capital of movement
on the status and results of the performance of the
financial status and outcome. The selected financial
indicators are shown as Table 2-1:
Profitabilit
y
Operation
al capacity
Solvency
Developm
ent
capacity
Cash flow
Sales growth, profit growth rate of main
business, capital gains rate
Cash maturity debt ratio,inflow and
outflow of cash ratio
Loans due for settlement rate, accounts
payable due for settlement rates, inventory
loan ratio
3.1 The Three-Layer three-node neural network structure
In the above system, we define the early warning as
the following three types: corresponding to normal,
attention and warning respectively. Therefore, the output
model of the network should be as follows:
(1,0,0),(0,1,0),(0,0,1). According to the experiences, the
hidden nodes should meet 2  m generally, where n is
the number of the hidden nodes.
The three-layer three-node output neural network
structure is shown as follows:
n
…
…
x
b) Non-financial risk
Non-financial factors relative to financial factors,
refer to the sum of risks which have great impact on bank
credit risk and cannot be reflected on the financial
statement analysis. They are mainly reflected in the
following areas: industry risk, business risk, management
risk and moral hazard .This paper choose the following
indicators to measure non-financial risk and these
indicator are showed in Table 2-2.
Industr
y risk
Operati
onal
risk
Manag
ement
risk
x (1)
p1
x (1)
p1
x
(1)
ph
(2)
p1
…
…
x (2)
pk
Evaluation index to quantify the
membership function
Commerci
al
reputation
Table 2-1
Sales profit margin, operating margin,
pre-tax profit margin, net margin, return on
assets
Total asset turnover, fixed asset turnover,
receivables turnover, inventory turnover
Asset-liability ratio, current ratio, quick
ratio, interest coverage ratio
w11
1
1
…
…
x (1)
ph
x
1
Ξn1
(Normal)
…
…
i
wij
j
(2)
p1
wj 2
2
ξn2
(Attention)
…
…
…
…
x (2)
pk
w11
n1
n2
wn1n2
wn2 3
3
ξn3
(Warning)
Fig. 3-1.
ˆ (1) ˆ (2)
ˆ (2)
1) In the Figure 3-1, xˆ (1)
p1 ……x ph , x p1 ……x ph are the
Table 2-2
Cost structure, industry maturity, industry
subject to periodic impact, legal and policy
environment
evaluation index attribute values of the p-th sample mode
of the domain U  {u1 , u2 ,
un } , denoted as:
(1)
(1)
(2)
(2)
Xˆ   xˆ
xˆ , xˆ
xˆ  .
Firm size, product diversity, development
stage
x ……x , x ……x(2)
are the evaluation
ph
vectors(the membership vectors) after normalizing by the
corresponding membership function, denoted as:
(2)
X p   x (1)
x (1)
x (2)
p1
ph , x ph
pk  .
Experience and quality of management layer,
management stability and financial
management capacity
p
p1
2)
ph
(1)
p1
3) Wij (i  1, 2,
ph
(1)
ph
pk
(2)
p1
, m; j  1, 2,
, n) is the connection
weight coefficient from the i-th unit of the input layer to
the j-th unit of the hidden unit layer; W j ( j  1, 2, , n) is
3. ESTABLISHING OF THE RISK EARLY WARNING
SYSTEM FOR COMMERCIAL BANKS
The feed forward Three-Layer BP(Back Propagation)
neural network is considered as the most suitable method
for simulating the approximate relationship about the
input and output. It has a wide range of applications in the
economic field and has achieved good results, such as
stock price forecasting, middle and long term forecasting
of exchange rate and so on. It is the most mature and
widely used one in the ANN, however, the research in the
early warning area, especially the risk early warning
system for commercial bank loans, is still not much.
Therefore, putting ANN into this area is a very
meaningful exploration and trial.
the connection weight coefficient from the j-th unit of the
hidden unit layer to the output layer; Y p is the output of the
p-th sample pattern.
4) Considering the general situation, we assume that
the number of the sample mode is s, and then the
evaluation index attribute values matrix and the expected
output matrix can be respectively denoted as:
Xˆ  [ Xˆ 1 , Xˆ 2 , , Xˆ s ]T  [ xˆ pi ]sxnl ,
B  [b1 , b2 , , bs ]T  [bp ]sxl .
3.2 The algorithm flow
With regard to the three-layer three-node output BP
neural network structure, Mehmet and Mclean proposed
the General Delta Rule, namely the Back Propagation(BP)
Algorithm, which is the most effective and practical
method. Its algorithm flow as shown in the Figure 3-2.
Begin to learn
The initialization of the connection
weights and thresholds
Provide learning samples
to the neural network
Adjust the connection
weight from the input
layer to the middle layer
and the output threshold
of each unit of the middle
layer
Calculate the input and output of each
unit of the middle layer
Calculate the input and output of each
unit of the output layer
Calculate the generalized error
of each unit of the output layer
N
The sample overall
error<E
Y
Stop learning
Adjust the number
of middle layer's
units
Adjust the connection
weight from the middle
layer to the output layer
and the output threshold
of each unit of the output
layer
Input new samples, test whether the
misjudgment ratio meet the discriminant
accuracy requirement
N
Y
End
Fig. 3-2
Here we still use the general delta rule, which adopts
the Sigmoid Function as the excitation function, i.e.
f ( Net pi )  1/ (1  exp( Net pi ))
(1)
Net pi  W ji o pi   j ,
(2)
j
Where i  1, 2,
, n1 ; j  1, 2,
n2


o pi  1
 W ji o pi   j   1
 Net , (3)
1  exp  
1  e pi
 j

where  j is the threshold of the unit U j .
For this kind of excitation function
o pj
 o pj (1  o pj ) ,
Net pj
with regard to the output layer unit,
o pj
(5)
 o pj (1  o pj ) ,
Net pj
with regard to the hidden layer unit,
 pj  ( jp  o pj )o pj (1  o pj )( j  1, 2,3) . (6)
(4)
In order to make the learning rate large enough and
difficult to produce concussion, it is still necessary to add
“trend items” to the Delta Rule, namely
W ji (t  1)   pj pi  W ji (t ) .
(7)
Where  is a constant, which determines the
influence degree of the past weight changes on the current
weight changes.
The following algorithm assumes that the network is
the Forward Multi-layer Network, the Excitation Function
adopts the Sigmoid Function and threshold makes the
same training.
4. EMPIRICAL TEST OF RISK EARLY WARNING
MODEL FOR COMMERCIAL BANKS
As a test, this paper selects 15 of the financial risk
early warning indicators to establish the BP network. 15
financial indicators means that there are 15 input nodes in
the BP network and each input nodes corresponds to a
financial indicators. The System’s input has defined 3
nodes: (1,0,0), (0,1,0), (0,0,1) corresponds to normal,
attention and warning, 3 different warning level.
Based on the experience, the hidden nodes need to
satisfy r>m. Since the sample of this paper is 30/r, so n=5
and that is there are 5 nodes in the hidden layer.
Because the inputs are continuous variable and the
outputs are Boolean discrete vector, the inputs need to be
normalized. The values of 15 indicators are calculated
according to the enterprise and the actual inputs are got
from the formula: actual inputs= weighs + (actual value ÷
standard value).
This paper used 15×5×3 network topology and
neuron function was Sigmoid characteristic function.30
sample data form the risk management of the Bank of
Communications were selected as learning samples.
Based on BP algorithm training 15×5×3 network
topology by error of 0.001 and   0.3 ，   0.3 , the
weight matrix initial value of 15×5 matrix and 5×3
matrix .Their Element is subject to the normal distribution
N (0,1) random number. The initial weight matrix as
follows:
 0.2427
 0.0901

 0.5822

 0.4744
 0.3779

 0.2813
 0.5744

W ji   0.5807

 0.1050
 0.2017

 0.2799
 0.0899

 0.3810
 0.2628

 0.0145
0.2413
0.2081
0.1830
0.1048 0.2811
0.1314
0.3793 0.7520 0.1062
0.6353 0.3661 0.1845
0.1617
0.0515
0.1249
0.2614
0.7770
0.4042
0.6788 0.6617 0.4776
0.2216 0.0054 0.3411
0.3261
0.6540
0.0330
0.2862
0.2691
0.1881
0.3858
0.3980
0.3844
0.5024
0.0665 0.0466
0.4057
0.3596 0.1064
0.6725 0.0637 0.0069
0.1619
 0.2600
 0.7522

Wkj   0.6554

 0.6005
 0.5545
0.1098
0.4591
0.0147 
0.5624 
0.2693 

0.5756 
0.2876  (8)

0.1909 
0.1127 

0.4825 

0.0116 
0.1298 

0.7337 
0.0082 

0.1235 
0.2094 

0.4392 
0.3673 0.0131 
0.3582 0.4839 
0.0651 0.4563

0.1832 0.3781
0.2828 0.2891 
(9)
The PC training took about 8 minutes and after 9065
times, it meets the requirement. The final value of
weights matrix are Wkj and Wkj . Noticing that different
 1.5447
 11.2659

 5.7659

 23.1046
 5.2303

 7.0783
 19.5395

W jh   29.1984

 5.9162
 17.3507

 7.7016
 19.1718

 4.7370
 2.3017

 18.5184
1.6211
0.7020
3.7252
3.5588
0.7725
1.3400
3.4426 24.4115
2.2591 4.1776
2.9613 10.2205
1.1361 4.2272
0.7366 13.8896
3.5135 16.7223
3.7378
1.1523
4.7926 8.30098
0.3578
19.5454
0.0494
8.6073
2.4674 16.6633
0.3945 10.7106
2.3729
2.2117 
21.3867 18.2992 
4.0820
2.0921 

19.4779 11.5019 
6.2449 4.2933 

18.7865 13.5627 
9.2150 11.2725

7.1715 0.9966 

32.8327 27.8172 
23.9371 22.0060 

33.5136 30.0967 
6.2621 1.3512 

0.4380
1.5085 
24.4167 19.3385 

0.7802
3.2665 
 14.1739 23.7384 17.9570 
 4.0861 4.4634 1.7070 


Whi   24.6918 23.3329 3.5381 


 11.2089 26.5356 29.5935
 7.3141 17.3059 25.1014 
Output
layer
Output
layer
--node1
--node2
--node3
1
1
1
1
0
0
0
0
0
0
0
0
(11)
In the learning process, for overlearning will
introduce much noisy signal into the weights set,
prediction results are not necessarily the better when the
control errors of learning termination are smaller. We
should pay attention to it.
From the Table 4-1 we know that, the actual output
is very close to our expected output except some specific
sample.
5. OUTCOMES AND PROSPECTS
initial value can be trained into different final value, but
this will not affect the final warning output. The coincide
rate of the original input-output data is 95%.
Output
layer
(10)
Commercial loan risk early warning index system is
built in this paper, on which a BP neural network loan risk
early warning model based on multi-output is established.
Artificial neural network structure of 3-level, 3-node and
algorithm process are introduced. In the end, existing data
of the Bank of Communications are used to verify the
validity of the system, and the results show that the
system meets the requirements of the risk warning.
Further researches on refining risk early warning
standard of commercial bank loan and expansion and
integration of candidate sets are needed, which will attach
great significance to clarify the boundary of the pattern
space of all loans, and then solve the distribution problem
of learning samples.
Table 4-1
Test Result
Output Output Output Output Output Output
layer
layer
layer
layer
layer
layer
Actual
output
--node1
0.9966
0.9312
0.9621
0.9598
Actual
output
--node2
0.0016
0.006
0.0006
0.0077
Actual
output
--node3
0
0
0
0
Error
--node1
Error
--node2
Error
--node3
0.0034
0.0688
0.0379
0.0402
0.0016
0.0060
0.0006
0.0077
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0.9876
0
0
0
0
0
0.0035
0
0
0
0
0.0014
0.999
1
0.9998
0.9944
0.9991
0.0006
0
0
0
0.0001
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0
0.0021
0
0
0.3233
0.0006
0.9841
1
1
1
0.9999
0.0124
0
0
0
0
0
0.0035
0
0
0
0
0.0014
0.0010
0
0.0002
0.0056
0.0009
0.0006
0
0
0
0.0001
0
0.0021
0
0
0.3233
0.0006
0.0159
0
0
0
0.0001