BP Neural Network-based Commercial Loan Risk Early Warning Research
H. Zhou
College of Management and Economics, Tianjin University, China
()
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
1. INTRODUCTION
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 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
2.1 Principles of index design [7-10]
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:
Table 2-1
Profitability / Sales profit margin, operating margin, pre-tax profit margin, net margin, return on assetsOperational capacity / Total asset turnover, fixed asset turnover, receivables turnover, inventory turnover
Solvency / Asset-liability ratio, current ratio, quick ratio, interest coverage ratio
Development capacity / Sales growth, profit growth rate of main business, capital gains rate
Cash flow / Cash maturity debt ratio,inflow and outflow of cash ratio
Commercial reputation / Loans due for settlement rate, accounts payable due for settlement rates, inventory loan ratio
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.
Table 2-2
Industry risk / Cost structure, industry maturity, industry subject to periodic impact, legal and policy environmentOperational risk / Firm size, product diversity, development stage
Management risk / Experience and quality of management layer, management stability and financial management capacity
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.
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 generally, where n is the number of the hidden nodes.
The three-layer three-node output neural network structure is shown as follows:
Fig. 3-1.
1) In the Figure 3-1, are the evaluation index attribute values of the p-th sample mode of the domain , denoted as: .
2) are the evaluation vectors(the membership vectors) after normalizing by the corresponding membership function, denoted as:
.
3) is the connection weight coefficient from the i-th unit of the input layer to the j-th unit of the hidden unit layer;is the connection weight coefficient from the j-th unit of the hidden unit layer to the output layer;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:
,
.
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.
Fig. 3-2
Here we still use the general delta rule, which adopts the Sigmoid Function as the excitation function, i.e.
(1)
, (2)
Where
, (3)
where is the threshold of the unit.
For this kind of excitation function
, (4)
with regard to the output layer unit,
, (5)
with regard to the hidden layer unit,
. (6)
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
. (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 ，, 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:
(8)
(9)
The PC training took about 8 minutes and after 9065 times, it meets the requirement. The final value of weights matrix are and . Noticing that different 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%.
(10)
(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
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 layer / Output layer / Output layer / Output layer / Output layer / Output layer / Output layer / Output layer / Output layer--node1 / --node2 / --node3 / Actual output
--node1 / Actual output
--node2 / Actual output
--node3 / Error
--node1 / Error
--node2 / Error
--node3
1 / 0 / 0 / 0.9966 / 0.0016 / 0 / 0.0034 / 0.0016 / 0
1 / 0 / 0 / 0.9312 / 0.006 / 0 / 0.0688 / 0.0060 / 0
1 / 0 / 0 / 0.9621 / 0.0006 / 0 / 0.0379 / 0.0006 / 0
1 / 0 / 0 / 0.9598 / 0.0077 / 0 / 0.0402 / 0.0077 / 0
1 / 0 / 0 / 0.9876 / 0.0014 / 0 / 0.0124 / 0.0014 / 0
0 / 1 / 0 / 0 / 0.999 / 0.0021 / 0 / 0.0010 / 0.0021
0 / 1 / 0 / 0 / 1 / 0 / 0 / 0 / 0
0 / 1 / 0 / 0 / 0.9998 / 0 / 0 / 0.0002 / 0
0 / 1 / 0 / 0 / 0.9944 / 0.3233 / 0 / 0.0056 / 0.3233
0 / 1 / 0 / 0 / 0.9991 / 0.0006 / 0 / 0.0009 / 0.0006
0 / 0 / 1 / 0.0035 / 0.0006 / 0.9841 / 0.0035 / 0.0006 / 0.0159
0 / 0 / 1 / 0 / 0 / 1 / 0 / 0 / 0
0 / 0 / 1 / 0 / 0 / 1 / 0 / 0 / 0
0 / 0 / 1 / 0 / 0 / 1 / 0 / 0 / 0
0 / 0 / 1 / 0 / 0.0001 / 0.9999 / 0 / 0.0001 / 0.0001
REFERENCES
[1] Tam, Kar-Yan, Melody Y Kiang. Managerial Applications of Neural Network: The Case of Bank Failure Prediction[J]. Manent Science, 1992, 38: 927~ 938.
[2] E. Nur Ozkan-Gunay, Mehmed Ozkan. Prediction of Bank Failures in Emerging Financial Markets: an ANN Approach[J]. The Journal of Risk Finance, 2007, 8(5):465~ 480.
[3] E. Philip Davis, Dilruba Karim. Comparing Early Warning Systems for Banking Crises[J]. Journal of Financial Stability, 2008, 4(2):89~120.
[4] E. Nur Ozkan~Gunay Meluned Ozkam. Prediction of Bank Failures in Emerging Financial Markets:an ANN Approach[J]，The Journal of Prisk Finance 2007，8 (5):465~480.