Designing a Model for Predicting Corporate Bankruptcy Using Ensemble Learning Techniques
Subject Areas : Financial Mathematics
Hossein
Eghbali
1
(Department of Industrial Engineering, University of Eyvanekey, Eyvanekey, Iran)
Alimohamad
Ahmadvand
2
(Department of Industrial Engineering, University Of Eyvanekey, Eyvanekey,Iran)
Keywords: Bankruptcy , Ensemble learning Techniques, Prediction, Stacking method,
Abstract :
The bankruptcy of corporations causes huge losses for investors, managers, creditors, employees, suppliers, and customers. If someone understands the reason for the corporate's bankruptcy, then he can save the corporate from certain death with the necessary planning. Therefore, bankruptcy forecasting is the most important prerequisite for bankruptcy prevention. Due to this issue, the main aim of this article is the prediction of the economic bankrupt-cy of corporations in the Tehran Stock Exchange using group machine learn-ing algorithms. Financial ratios have been used as independent variables and healthy and bankrupt corporations as research dependent variables. The statistical population of the study is the information of financial statements of corporations on the Tehran Stock Exchange from the years 2004 to 2021. In this study, sampling is not used and corporations include two groups healthy and bankrupt. The bankrupt and non-bankrupt groups are selected based on the threshold of the Springate model. The research findings indicate that the accuracy of predicting the bankruptcy of corporations in the group learning model by stacking method is higher than other used models where the AUC and Accuracy Ratio were 0.9276 and 0.8247, respectively.
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Adv. Math. Fin. App., 2024, 9(3), P. 856- 872 | |
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Advances in Mathematical Finance & Applications www.amfa.iau-arak.ac.ir Print ISSN: 2538-5569 Online ISSN: 2645-4610
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Designing a model for predicting corporate bankruptcy using Ensemble learning techniques
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Article Info Article history: Received 2023-01-12 Accepted 2024-01-23
Keywords: Bankruptcy Ensemble learning techniques Prediction Stacking Method |
| Abstract | ||
The bankruptcy of corporations causes huge losses for investors, managers, creditors, employees, suppliers, and customers. If someone understands the reason for the corporate's bankruptcy, then he can save the corporate from certain death with the necessary planning. Therefore, bankruptcy forecasting is the most important prerequisite for bankruptcy prevention. Due to this issue, the main aim of this article is the prediction of the economic bankruptcy of corporations in the Tehran Stock Exchange using group machine learning algorithms. Financial ratios have been used as independent variables and healthy and bankrupt corporations as research dependent variables. The statistical population of the study is the information of financial statements of corporations on the Tehran Stock Exchange from the years 2004 to 2021. In this study, sampling is not used and corporations include two groups healthy and bankrupt. The bankrupt and non-bankrupt groups are selected based on the threshold of the Springate model. The research findings indicate that the accuracy of predicting the bankruptcy of corporations in the group learning model by stacking method is higher than other used models where the AUC and Accuracy Ratio were 0.9276 and 0.8247, respectively. | ||||
1 Introduction
Generally speaking, bankruptcy is a part of the foundation and natural component that modern economies are built upon [1]. It is not entirely accurate to say that bankruptcy is a natural component or foundation that modern economies are built upon. While bankruptcy is a legal process that allows companies and individuals to restructure their debts or liquidate their assets when they are unable to pay their creditors, it is not a desirable outcome for any economy. In fact, bankruptcy is often seen as a negative outcome because it represents a failure of a business or individual to meet their financial obligations. Bankruptcy can lead to job losses, creditor losses, and economic instability, which can have negative consequences for the broader economy [2]. The statement is generally true. Misclassifying firms can have significant financial consequences, particularly for bankrupt firms. If a firm is misclassified as not being at risk of bankruptcy when it actually is, then lenders and investors may continue to provide credit and investment, which can result in significant losses if the firm eventually goes bankrupt. On the other hand, if a firm is misclassified as being at risk of bankruptcy when it is actually financially stable, then the firm may face difficulties in obtaining credit and investment, which can harm its operations and growth potential. Therefore, accurate bankruptcy prediction models can be very valuable for lenders, investors, and other stakeholders in the economy [3]. By using these models to identify firms that are at risk of bankruptcy, they can take appropriate measures to reduce their exposure to risk, such as reducing or withdrawing credit and investment. This can help to prevent losses and stabilize the economy [4]. Furthermore, the cost of misclassifying bankrupt firms can be particularly high, as these firms may have significant outstanding debts and liabilities that need to be resolved. Misclassifying a bankrupt firm as financially stable can result in significant losses for creditors and investors, as well as the potential for lengthy legal proceedings to recover their losses. Therefore, the development and expansion of accurate and well-performing models for bankruptcy prediction is important to help reduce the potential financial costs of misclassifying firms, particularly for bankrupt firms [5].During the past few years, novel approaches to machine learning techniques containing powerful data manipulation tools have been introduced which consider on a larger scale as well [4]. This issue can enhance the possibility of developing more advanced and new models. Therefore, this gives the opportunity to users to not only process more data but also not limit models due to linearity and variable selection. To the best of our knowledge and what has been reported in the open literature, there is no research study at the moment in which machine learning techniques have been tested on the management, sector, and financial statements for predicting bankruptcy [6]. Therefore, it is believed that there is great potential to develop more accurate and well-performing models, employing these approaches on a large dataset with a significant number of characteristics. The existing models are optimized to perfectly classify bankrupt firms at the expense of lower overall precision. This issue can be caused due to the high cost associated with incorrectly classifying the corporate that is actually going bankrupt. Hence, the present models are completely aligned with the point of view of the investors, banks, rating agencies, and shareholders. The obtained results from the present research study can give further life to our faith that management, sector, and financial statements are appropriate and verified data that can be used for the prediction of bankruptcy. Additionally, more complicated mathematical models such as random forest (RF) and artificial neural networks (ANN) demonstrate great potential in the prediction of bankruptcy, being able to find and handle patterns in a large dataset [7].Credit analysis and bankruptcy predictions have existed for the past decades. The earliest evidence goes back to the 1890s and is associated with the likelihood estimation [8]. Privately-owned banks mainly utilized the noted analysis to grant loans to firms according to their creditworthiness, therefore, this spreads the plan of ratio analysis. In the early 1900s, many attempts were made to standardize the structure which eventually helped to increase the credit men [8]. Later on, in 1919, the 1st ratio analysis of the federal bank in the United States was reported by the Federal Reserve to commence a public discussion on credit risk and to gain public momentum [8]. In the field of bankruptcy prediction, Beaver [9] can be introduced as one of the earliest forerunners. A univariate analysis was used by Beaver to figure out considerable differences in several specified variables for two categorical groups of non-bankrupt and bankrupt corporations. It should be mentioned that the performed analysis was carried out on a sample of 706 firms for 5 years. The sample was chosen to keep out some specified sectors, and the division between the non-bankrupt and bankrupt corporations was just about fifty percent for all the years. Thirty picked variables were also divided into five various subgroups arranged by characteristics. The noted subgroups were associated with the various sections of the firms’ financial structure, like cash flows, ratios related to acid tests, turnover, and net income. According to the obtained model, four different propositions were created for the identification of the distressed firms and appropriate thresholds for each of mentioned ratios. At the moment, the suggested thresholds are introduced and popular among scholars as rules of thumb for the aforementioned ratios. Moreover, in 1968, the trend of utilizing financial data was started by Beaver [10] to systematically rate firms by creditworthiness. In the same year, Beaver also introduced how investors view distress as well as alternative ratios from the stock market point of view [11]. Another framework to predict bankruptcy was proposed by Boyacioglu et al. [12] in 2009. In the noted research study, a ratio model was created for Turkish banks from 1988 to 2000. The main purpose to create this model was the prediction of future bank failures right after the financial crisis of 2007 and 2008. To this end, for the base case, 20 various financial ratios with 6 different characteristic groups containing management quality, asset quality, capital adequacy, liquidity, sensitivity to market risk (CAMELS), and earnings were chosen as predictor variables. With the main idea of improving the prediction performance, 4 different datasets including 22 failed and 44 non-failed banks with various features were developed. Four different approaches called learning vector quantization, competitive learning, multi-layer perceptron, and self-organizing map were utilized in the category of neural networks. The obtained results demonstrated that learning vector quantization and multi-layer perceptron were the most accurate and successful models to predict the financial failure of banks. The Bloomberg DRSK models have been recently introduced as another well-known bankruptcy predictor within finance [13, 14]. It is noteworthy to mention that in contrast to the formerly proposed models, the Bloomberg DRSK models are more comparable to credit modeling. Besides, the Bloomberg DRSK models were established based on Merton’s Distance model. It was suggested for credit modeling in the beginning and subsequently, it was developed to be incorporated in the popular Black-Scholes model for option pricing. Frictionless trading, short selling, continuous trading, and the prices following the Brownian motion can be mentioned as the underlying assumptions of the problem [15]. The created models were unfocused and focused models, whereas the latter was purposed for financial firms [13, 14]. Furthermore, the observations were also separated based on the size, leading to the creation of four mutually collectively and exclusive exhaustive models. Depending on the out-of-sample years, an accuracy of 85.6% to 87.8% was obtained for the model proposed for non-financial private corporations. The main privilege of the Bloomberg DRSK models is the ecosystem that the models are applied in, called the Bloomberg terminal. Bloomberg terminal contains the most recent financial data existing with trailing financial statements. Additionally, Bloomberg suggests reclassified financial statements for large US corporations as well. This leads to improving the truthfulness of the financial statement as well as enhancing accuracy. The suggested models [13, 14] were established on the same assumptions as the models by Zhang et al. [16] and Crouhy et al. [17].
Furthermore, Næss et al. [18] completed the latest addition to the Norwegian markets based on Wahlstrøm and Helland’s research study [19]. The mentioned study could harmonize predictions between the Norwegian-developed SEBRA model, the famous Altman Z-score, and their own sets of variables. The models were carried out on a range of statistical techniques for each ratio set. Statistical techniques were GAM, SVM, LDA, CT, GLM, QDA, NN, and KNN. For the NN method, in addition to an approach involving reduction of the dimensionality, both backward and forward sweeps of back-propagation were implemented. Similar samples collected from corporations with financial statements from 2005 to 2014 were used to train and test each model. the logic of Bernhardsen and Larsen in Ref. [20] was followed by Wahlstrom and Helland [19] in their study in which corporations with low total assets (< 500 TNOK) were excluded. Moreover, in order to be consistent with Bernhardsen and Larsen’s research study [20] and make comparison, financial firms were also excluded in Ref. [19]. By following the logic proposed by Boyacioglu et al. [12], the distribution between the non-bankrupt corporations and bankrupt corporations was manipulated. The dataset was divided into 1/3 bankrupt corporations and 2/3 non-bankrupt corporations in which a random option was selected for the sampling of non-bankrupt corporations. On the other hand, all of the bankrupt corporations were included. This was in contrast to Berg’s study in 2007 [21]. In that research, a true distribution was utilized and a probability threshold was adjusted for classification. To create a model, it was tried to scale the financial statement to a mean of zero in order to eliminate the possibility that statistical techniques augment significance to size, rather than distance and distribution [19]. To obtain the best predictions, the hyperparameters of the models were tuned. Besides, to ensure that the obtained results have reproducibility and were not a product of random chance, the models were cross-validated. It is not an easy task to determine the exact reason or reasons for bankruptcy in any particular case. In many cases, several reasons together may lead to bankruptcy. The analysis of financial statements requires tools and techniques that enable analysts to examine current and past financial statements aimed at evaluating the performance and financial status of a corporate and estimating the possibility of future and potential risks. In this research, we proposed a model for predicting the financial bankruptcy risk of listed and OTC corporations by utilizing Ensemble learning algorithms [8]. New methods utilize machine learning, including ensemble learning techniques like bagging and boosting. The main advantage of the new machine learning methods is they provide more accurate predictions of company bankruptcy compared to previous qualitative methods. The increased prediction accuracy stems from the machine learning models' ability to capture complex patterns and relationships in data that may be hard to discern. So the main gap or difference between the old and new methods is the higher level of prediction accuracy achieved through leveraging machine learning algorithms and techniques.
Data-driven machine learning models can process much larger sets of financial, operational, and macroeconomic data compared to limited qualitative assessments [7]. This enables the models to uncover more predictive insights. Ensemble techniques like random forests, gradient boosting, and stacking generalization allow for combining multiple predictive models to improve overall accuracy. This is more systematic versus subjective qualitative opinions. Machine learning can continually update predictions in real-time as new data comes in, while qualitative methods provide episodic and periodic assessments of bankruptcy risk. In summary, the automation, sophistication, and customization of modern machine learning makes it significantly more accurate than previous subjective and limited qualitative techniques for predicting company bankruptcy. The gap in accuracy continues to widen as machine learning capabilities improve [4].
In the second part, we will have a general reference to the research methodology. Then, in more detail, we first state the financial ratios for predicting the bankruptcy of companies and select those financial ratios that have the most power to predict bankruptcy using the WOE technique. After that, we define the basic prediction models. By implementing 3 basic models on the database, we get the results of each along with the accuracy of that method. Then we will implement the proposed research model, collective learning, on the results of the basic models and compare the accuracy of our method with previous similar articles.
2 Methodology
Choosing a research methodology is one of the most important researcher’s efforts since it should be determined what approach and method to adopt to help get the answers to the research questions as accurately, easily, and quickly as possible. It depends on the nature, objective, and subject matter. The research method is the way to achieve the goal and guarantees the success of the research. The research method contains a set of measures to identify the truth and achieve the designed goals. To perform this research, all corporations listed on the Tehran Stock Exchange from March 2004 to March 2021 were considered as the statistical population and the statistical sample was extracted from these corporations. The total number of year-corporate is 1652. Since the data required is in the form of year-corporate and each corporate may have been studied in a few years (from 2004 to 2021), thus, the total number of data accounted for 16984 year-corporate. The solution method in this research was set to first use the combined machine learning methods to predict the financial bankruptcy risk of listed corporations and over-the-counter corporations on the Tehran Stock Exchange. We utilized the ensemble learning method, which is one of the new areas of machine learning. Ensemble learning is a field of machine learning in which, instead of using a model to solve a problem, employs several models in combination to increase the model's output estimation power. We used the stacking technique in this research, which is one of the strongest ensemble learning techniques. In the first stage, 3 basic forecasting models, including logistic regression model, SVM model, and gradient boosting, were trained by the data. In the second stage, the final model of the education system was trained that plays the role of the final decision maker and learns in the process of learning how each model works. Due to the power of the basic models, a weight is determined and assigned for each of them to use in the decision-making process, which is the very predicting financial bankruptcy. Using this ensemble learning technique, the predictive results would be more reliable.
2.1 Research Steps
2.1.1. Review of Predictor Variables Using Previous Research
Financial ratios have been used by analysts since 1870. At the moment, financial ratios analysis is an effective tool a and strong technique for users to assess the performance of future, present, and past, and to this day, owing to the development of science, technology, and knowledge in information and computing, there have been several improvements in using financial ratios [22]. In many research papers in the field of bankruptcy prediction, financial ratios were utilized for analysis and as a consequence, a background of all used financial ratios in the existing bankruptcy models was classified and documented in Table 1 [10, 11, 23-30].
2.1.2. Choosing the Main Variables
For selecting the main features (variables) in the current research paper, the weight of evidence (WOE) algorithm was utilized as a feature selection method out of 138 technical features that have been provided as input predictor features to the system, the features that enhance the precision of bankruptcy predictions. The WOE can be calculated by 
for any feature. The predictive power of a single feature concerning its independent feature is told by WOE. In comparison to the proportion of non-events, if any of the bins/categories of a feature has a large proportion of events, a high value of WoE is gotten that in turn tells that the noted class of the feature separates the events from non-events. As mentioned above regarding the WoE value, it should be noted that the WoE value also says the predictive power of each bin of a feature. However, in the feature selection, a single value showing the whole feature’s predictive power is useful. The equation for the information value (IV) is 
where the IV is always a positive number.
Table 1: Financial Ratios
Commercial and non-commercial | x70 | Operating Profit | x1 |
Accounts and documents of commercial | x71 | Net other operating income and expenses | x2 |
Cost ratio | x72 | Financial costs | x3 |
Working capital | x73 | Net cash inflow (outflow) of investment activities | x4 |
Debt ratio | x74 | Cash balance at the beginning of the year | x5 |
Ownership ratio | x75 | Legal reserve | x6 |
Debt service | x76 | Tangible fixed assets | x7 |
Current debt ratio | x77 | Total liabilities and equity | x8 |
Financial to operating profit | x78 | Cash balance at the end of the year | x9 |
Accumulated profits to equity | x79 | Inventories | x10 |
Accumulated profit to total debts | x80 | Taxes paid | x11 |
Retained earnings on total assets | x81 | Total debt | x12 |
Receipts to total assets | x82 | Net cash inflows and outflows of | x13 |
Operating profit to current assets | x83 | Saved end-of-staff service | x14 |
Net profit to total assets | x84 | Fund | x15 |
Net profit to sell | x85 | Net cash inflows and outflows for tax purposes | x16 |
Special interest before interest and | x86 | Equities | x17 |
Net profit to equity | x87 | income tax | x18 |
Operating profit to sell | x88 | Intangible assets | x19 |
Interest cost coverage ratio | x89 | Gross profit | x20 |
Special interest on interest and taxes | x90 | Total current liabilities | x21 |
Frequency of inventory turnover | x91 | Sales, administrative and general expenses | x22 |
Inventory turnover period | x92 | Net cash inflows (outflows) from | x23 |
Sell to inventory | x93 | Net increase (decrease) in cash | x24 |
Working capital to total debts | x94 | Net profit | x25 |
Working capital to total assets | x95 | Received financial facilities | x26 |
Sales to total assets | x96 | Total current assets | x27 |
Relative to the current | x97 | Total non-current liabilities | x28 |
Instant ratio | x98 | Profit (loss) accumulated at the | x29 |
Inventory to working capital | x99 | Profit before tax | x30 |
Current assets to total assets | x100 | Net other non-operating income | x31 |
Financial costs to total debt | x101 | Orders and prepayments | x32 |
Financial to net sales | x102 | Net cash inflows (outflows) from the | x33 |
Cash inventory to total assets | x103 | Accumulated profit (loss) | x34 |
Table 1: continue | |||
Short-term cash balance | x104 | Accounts and documents of commercial | x35 |
Inventory to current assets | x105 | Definable profit | x36 |
Short-term operating costs | x106 | Total Non-Current Assets | x37 |
Total operating costs | x107 | Cash balance and fund bank | x38 |
Total costs to total sales | x108 | Total assets | x39 |
Sale or return on fixed assets | x109 | Net sales or operating income | x40 |
Sales or revenue to accounts receivable | x110 | Cost of | x41 |
Short-term sales or revenue | x111 | Annual adjustments | x42 |
Net sales to working capital | x112 | Commercial and non-commercial | x43 |
Gross profit on sales or revenue | x113 | Long-term financial facilities received | x44 |
Gross profit to total assets | x114 | Total receipts received | x45 |
Gross profit for the short term | x115 | Average of total assets | x46 |
Total Cash - Cash Inventory} Sales | x116 | Profit before tax on total assets | x47 |
Sales or revenue to inventory | x117 | Profit before tax on total debt | x48 |
From interest and taxes to profits | x118 | Income or sales on total debt | x49 |
Net profit to warehouse | x119 | Total current assets | x50 |
Equity-equity to total assets} | x120 | Equity to fixed assets | x51 |
Working capital to fixed assets | x121 | Equity of long-term assets | x52 |
Fixed assets to total assets | x122 | Accounts paid on sales revenue | x53 |
Receipts to total debts | x123 | Cash flow sold or earned | x54 |
Financial cost to receive | x124 | Cash flow to assets | x55 |
Financial costs to current debt | x125 | Cash flow to equity | x56 |
Cash flow to current debt | x126 | Cash flow to total debt | x57 |
Cash flow to working capital | x127 | Long-term amount to total assets | x58 |
Financial to net profit | x128 | Short-term net sales facility | x59 |
Net income logarithm | x129 | Short-term facility to current debt | x60 |
Logarithm of total assets | x130 | Short-term debt to total expenses | x61 |
Debt to banks | x131 | Current debt to net sales | x62 |
Inventory of materials and goods * 365 | x132 | Current liabilities to total assets | x63 |
Receivables * 365 Sold or earned | x133 | Current debt of special value | x64 |
Short term * 365 sold or earned | x134 | Debtors or accounts receivable to total assets | x65 |
Short term * 365 at the cost of goods sold | x135 | Gross profit plus sales or revenue | x66 |
Operational operations to tangible assets | x136 | Gross profit in addition to the benefit of | x67 |
Operations on intangible assets | x137 | Net profit plus interest expense on total assets | x68 |
Inventories | x138 | Current assets - Inventory Long-term assets} | x69 |
Table 2: Fixed Rule IV
Information Value | Predictive power |
<0.02 | Useless |
0.02 to 0.1 | Weak predictors |
0.1 to 0.3 | Medium Predictors |
0.3 to 0.5 | Strong predictors |
> 0.5 | Suspicious |
The final variables of this research (72 pcs) were extracted using the WOE method to predict the bankruptcy of corporations Index in Table 3:
Table 3: The Final Variables to Predict the Bankruptcy
Accounts and documents of commercial | x71 | Operating Profit | x1 |
Cost ratio | x72 | Net other operating income and expenses | x2 |
Working capital | x73 | financial costs | x3 |
Current debt ratio | x77 | Legal reserve | x6 |
Cash balance at the end of the year | x9 | Tangible fixed assets | x7 |
Accumulated profits to equity | x79 | Inventories | x10 |
Receipts to total assets | x82 | Taxes paid | x11 |
Operating profit to sell | x88 | Total debt | x12 |
Operating profit to current assets | x83 | Saved end-of-staff service | x14 |
Net profit to total assets | x84 | Fund | x15 |
Net profit to sell | x85 | Net cash inflows and outflows for tax purposes | x16 |
Special interest before interest and | x86 | Equities | x17 |
Net profit to equity | x87 | income tax | x18 |
Frequency of inventory turnover | x91 | Sales, administrative and general expenses | x22 |
Working capital to total debts | x94 | Net profit | x25 |
Relative to the current | x97 | Total non-current liabilities | x28 |
Instant ratio | x98 | Profit (loss) accumulated at the | x29 |
Financial to net sales | x102 | Profit before tax | x30 |
Cash inventory to total assets | x103 | Net other non-operating income | x31 |
Short-term cash balance | x104 | Orders and prepayments | x32 |
Sales or revenue to accounts receivable | x110 | Net cash inflows (outflows) from the | x33 |
Short-term sales or revenue | x111 | Accumulated profit (loss) | x34 |
Total operating costs | x107 | Cash balance and fund bank | x38 |
Sales or revenue to accounts receivable | x110 | Cost of | x41 |
Short-term sales or revenue | x111 | Annual adjustments | x42 |
Net sales to working capital | x112 | Commercial and non-commercial | x43 |
Gross profit on sales or revenue | x113 | Long-term financial facilities received | x44 |
Table 3: continue | |||
Working capital to fixed assets | x121 | Equity of long-term assets | x52 |
Fixed assets to total assets | x122 | Accounts paid on sales revenue | x53 |
Receipts to total debts | x123 | Cash flow sold or earned | x54 |
Financial cost to receive | x124 | Cash flow to total debt | x57 |
Financial costs to current debt | x125 | Long-term amount to total assets | x58 |
Logarithm of total assets | x130 | Short-term debt to total expenses | x61 |
Debt to banks | x131 | Current debt to net sales | x62 |
Inventory of materials and goods * 365 | x132 | Current liabilities to total assets | x63 |
Inventories | x138 | Current assets - Inventory Long-term assets} | x69 |
2.2 Logistic Regression Model
The correlation coefficient is often used to express the intensity of the linear relationship between two quantitative variables. The regression model is also employed to display the relationship model between the two. In the meantime, a model is created to predict the dependent variable (Y) based on the independent variable (X) [31]. However, it should be noted that both independent and dependent variables in the created model are quantitative. In addition, the condition of correlation of these values lies in the regression method. However, scholars may be interested in measuring the relationship between an independent variable (with continuous values) and a dependent variable with qualitative values. In this case, the normal linear regression method will not work out and it is compulsory to use the “logistic regression” method. The logistic regression model can be seen as a specific case of the general linear and linear regression model. The logistic regression model is based on quite different hypotheses (about the relationship between dependent and independent variables) of the linear regression. An important difference between these two models can be attributed to the two features of logistic regression. First, the conditional distribution y|
is a Bernoulli distribution instead of a Gaussian distribution since the dependent variable is a binary one. Second, the prediction values are probabilistic and limited to the range between zero and one and they can be obtained using the logistic distribution function. The logistic regression predicts the odds of an outcome. It is known that linear regression refers to creating a parametric linear relationship to represent the relationship between an independent variable and a dependent variable. The form of a simple linear regression model is as follows:
Y=β0+β1X+ϵ | (1) |
As can be seen, this relation is the equation of a line to which the error sentence or “i” is added. The parameters of this linear model are the “y-intercept” (β0) and the gradient of the line (β1). In this case, if “
” is the estimated value for the dependent variable, it can be considered as the mean of observations for the dependent variable for the constant value of the independent variable. So if we replace the mean with the expected value, assuming that the mean of the error sentence is also zero, we will have:
| (2) | |||||
| (3) | |||||
| (4) | |||||
Class | Precision | Recall |
0 | 0.77 | 0.76 |
1 | 0.86 | 0.82 |
AVG/TOTAL | 0.81 | 0.81 |
Table 5: Confusion Matrix
Actual/Prediction | 0 | 1 |
0 | 1579 | 285 |
1 | 520 | 1381 |
AUC: 0. 7396
Accuracy Ratio :0.7897
· Results with logistic regression
Table 6. Evaluation of Test Data Using the Lr Model
Class | Precision | Recall |
0 | 0.81 | 0.86 |
1 | 0.87 | 0.79 |
AVG/TOTAL | 0.83 | 0.83 |
Table 7: Confusion Matrix
Actual/Prediction | 0 | 1 |
0 | 1560 | 300 |
1 | 439 | 1466 |
AUC: 0.8097
Accuracy Ratio: 0.6837
· Results with XGBoost
Table 8: Evaluation of test data using XGBoost model
Precision | Recall | |
0 | 0.74 | 0.76 |
1 | 0.81 | 0.83 |
AVG/TOTAL | 0.78 | 0.78 |
Table 9: Confusion Matrix
0 | 1 | |
0 | 1557 | 307 |
1 | 487 | 1414 |
AUC: 0.8890
Accuracy Ratio: 0.7267
· Results with Ensemble learning
The evaluation of the ensemble learning (stacking) model on the test data using the features selected by each of the basic models is as follows.
Table 10. Evaluation of Test Data Using Stacking Model
Class | Precision | Recall |
0 | 0.86 | 0.87 |
1 | 0.85 | 0.86 |
AVG/TOTAL | 0.86 | 0.86 |
Table 11: Confusion Matrix
Actual/Prediction | 0 | 1 |
0 | 1565 | 299 |
1 | 289 | 1612 |
AUC: 0.9276
Accuracy Ratio: 0.8247
As it was observed in this research, the combined stacking method has achieved a much better result. The stacking technique is a kind of improved version of the voting technique. In this technique, each model has a different share in the decision-making process and this share in the training process is determined by the decision-making model. The prediction accuracy of a ensemble learning model compared to other machine learning models depends on several factors, such as the size and complexity of the dataset, the quality of the data, and the hyperparameters of the models. However, in general, collective learning models have been shown to improve prediction accuracy when compared to single models in several studies. One reason for the improved accuracy of collective learning models is that they can reduce overfitting, which is a common problem in machine learning. The ensemble of models is able to generalize better by reducing the variance of the predictions. Additionally, collective learning models can capture different aspects of the data, which can improve the overall accuracy of the predictions.
Overall, collective learning models have been shown to be effective at improving prediction accuracy compared to single models in several studies. However, the specific performance of these models compared to other machine learning models depends on the specific characteristics of the dataset and the task at hand. The comparison of previous researches on corporate bankruptcy prediction based on accuracy is presented in Table 12.
Table 12: Comparison of previous researches on corporate bankruptcy prediction | ||||||
Reference Year Data set Method Accuracy (%) Country number of corporate Features | ||||||
[35] | 2019 | Greece | 100 | 20 | Deep neural networks | 73 |
[36] | 2019 | French | 2150 | 50 | Boosting | 75 |
[37] | 2018 | Polish | 1000 | 15 | Jordan recurrent neural | 81 |
[38] | 2018 | Polish | 10503 | 64 | ANN | 88 |
[39] | 2018 | Colombia | 1000 | 15 | Decision tree | 91 |
[40] | 2017 | American and Canadian | 998 | 11 | Random forest | 87 |
[41] | 2016 | Taiwan | 480 | 190 | KNN | 82 |
4 Conclusions
One of the main objectives of the current research paper is to utilize ensemble methods in bankruptcy prediction instead of just using a classification method. In the field of finance, bankruptcy forecasting can be considered one of the most momentous research because the possibility of correct bankruptcy can be used and done in a location that can reduce the high costs of bankruptcy. Reputable rating agencies and banks typically utilize this model to assign ratings and make credit decisions. Predicting bankruptcy and subsequently rooting out the problem and having a solution for that can engender very satisfying results. Looking at various types of financial processes and methods that concentrate on historical information is one way to perform financial analysis. Due to the fact that the financial ratios are from the loss and profit statement of the business unit and the items in the balance sheet, therefore, some financial ratios from the unification of the historical financial statements are significantly different from the historical items. The accuracy rate of models can be considerably improved as confirmed by research findings. Machine learning techniques are shown remarkably advanced prediction ability in different scientific fields like the financial sector. Identification of the pertinent characteristics that drives this prediction and improves explanation ability is a challenging task in this domain. In the current research, an attempt was made to design the bankruptcy forecasting model by employing all the financial ratios utilized in various models in financial bankruptcy forecasting. Thus, according to the prediction methods used in this research, the WOE method is used to identify the most important prediction variables. The lowest error rate was given by the results obtained from the confusion matrix with a similar subset of any vote. This demonstrates that the single approach to feature election can restrict machine learning algorithms in achieving optimal decision-making process and also can enhance the error level in the study. In addition, it can be seen that the XGboost algorithm achieves the highest AUC scores among the three used basic predictor models which makes it a cost-effective and efficient algorithm. Besides, it was shown that the ensemble approach to bankruptcy forecasting outperformed the single learning. This can be considered supportive proof for the available hypothesis that ensemble methods produce much higher performance in comparison to single learners. In the general form, all the experiments have given a great performance compared to existing studies in the open literature in this domain. The results confirm the high accuracy of the Stacking hybrid model in predicting the financial bankruptcy risk of listed and OTC corporations. The stacking technique, which is one of the most powerful techniques of collective learning, shows great success in such issues. Regarding the high power of the produced model and also stated research findings in this study, it can be concluded that the model can be successfully used by investors in choosing the optimal portfolio and as creditors to help prevent lending to corporations with high bankruptcy risk. Generally speaking, it can be said that by using the results of this study as a first step and also performing preventive actions, corporations can be prevented from bankruptcy and future losses can be reduced.
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* Corresponding author. Tel.: 09012797836 E-mail address: alimohammadahmadvand@yahoo.com
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