Corporate Bankruptcy Prediction Using the Principal Components Method

A huge number of articles and papers are devoted to the study of bankruptcy prediction problems. In attempting to solve the problem of predictive ability, many difficulties arise due to the processing of data and the necessity of choosing between appropriate models and algorithms. Efficiency is formed on the basis of three key aspects, namely tools, data quality, and algorithms. Efficiency in this regard, may also be postulated to be achieved based on the correct formulation of the problem itself.<br><br>Therefore, in this article we study the quality of methodologies for assessment of business solvency of Russian companies with a view to improving bankruptcy predicative capability. On the basis of a literature review, 35 indicators representing profitability, liquidity, business activity, capital structure, debt servicing, growth opportunities, and company size were used, and problems in relation to bankruptcy were re-evaluated using the method of neural network modelling. To do this, we propose an effective prediction algorithm, which is presented in comparison with conventional parametric methods.<br><br>With the use of the principal components method of neural networks, our results identify and contextualise key turning points that could lead to a destabilisation of the company's normal operations. It was found out that use of the principal components method does not increase the predictive power of the model in comparison to the use of the variables selected separately from each group of factors. However, we demonstrate that the model we proposed correctly classifies, on average, more than 94% of observations across the sample of small, medium, and large Russian businesses.<br><br>From a scientific point of view, this research presents a novel method for increasing the predictive power of the bankruptcy model. On the practical side, our results may be easily implemented into any effective corporate strategy. The extremely high predictive power of the model will interest investors, banks, and other creditors to foresee potential financial problems of companies with a greater accuracy. However, improvement of its predictive power might be achieved by using even more sophisticated algorithms because the methods applied in practice are invariably reduced to standard parametric methods with low predictive power. For further study of this issue, it would be interesting to consider the problem of accuracy in processing lost or missing data, by applying genetic algorithmisation and dynamic models.


Introduction
In recent years the Russian economy has been exposed to most complex stress tests, therefore the issue of corporate bankruptcy still appears relevant.It is related to many factors: high risk strategies, currency fluctuations, sanctions imposed by the USA and Western countries in order to destabilize the Russian economy and financial system, geopolitical environment in the Russian Federation.The result is that the Russian economy is subjected to serious fluctuations.In the environment of instability companies are virtually incapable of conducting their business.Sometimes even in a stable economic environment due to wrong strategies or internal problems some companies find themselves in a pre-bankruptcy state.Bankruptcy of large, strategically important industry participants may result in problems not only for directly associated economic agents, but for the economy in general.A proper tool which predicts beforehand critical states and possible bankruptcy of a company may prevent wrong resolutions of management, investors, banks and other creditors.The correct risk assessment related to financial instability of a company may prevent economic downturn in general in case of a crisis.
Warning signs of corporate bankruptcy may be formal and informal.The formal warning sign of an enterprise bankruptcy is its insolvency, that is its inability to fulfill its obligations of making payments to creditors for a long time.The informal warning signs are used mainly in order to improve the prediction accuracy.
The informal warning signs of bankruptcy comprise inefficient performance of financial services and the company information system, sharp changes in statement items, a decrease or steep increase of corporate liquid assets, lack of opportunities for growth and efficient investment, increase of the share of accounts receivable, reduction of material assets, turnover slowdown, debts to employees, shareholders, financial bodies etc.
The present paper is of relevance because it is necessary to improve the bankruptcy prediction mechanism, search for factors which influence the company financial standing.From the scientific point of view this research comprises the idea of increase of the predictive power of the bankruptcy model.But on the practical side it may be applied as one of the versions of an effective methodology.In the article the emphasis is made on small and medium companies because these groups are subjected to financial instability more than large companies.However, large companies also need control over financial stability.
In this research we used neural networks to build the bankruptcy prediction model.The sample multitude consists of Russian small, medium and large companies which conducted business or became bankrupt within 2015-2016 and which fall into the same industry and are of the same size.We use the principal components method as a means of factors dimension reduction and also verify its superiority over the standard model which comprises all considered variables.The result of the paper will be a positive influence of the offered algorithm on the predictive power of the bankruptcy model as an assessment of Russian companies' standing.The need in improvement of the predictive power is a relevant and unanswered issue because the methods applied in practice are reduced to standard parametric methods with low predictive power.

Corporate Bankruptcy Factors
The interest to bankruptcy prediction arose in the early 1960-ies because cases of destabilization became more frequent.The researchers Beaver [1] and E.I. Altman [2] are considered to be the ground breakers in this sphere.
The possibility to build a bankruptcy model was mentioned for the first time in the research by Beaver [1] who analyzed the indicators of corporate performance as the factors which could predict bankruptcy.In his paper the author considers a selection of 158 American companies from 38 industries which comprises two types of companies: bankrupt and functioning ones, represented in equal proportion.He chose five out of over 30 factors and eliminated all factors which have the smallest influence on the company standing.The research considers three groups of values: non-bankrupts, those which became bankrupt in one or five years.
Altman [2] applied the multiple discriminant analysis method.The selection consisted of 66 companies divided into the companies which became bankrupt in the period of 1946 and 1965, and financially sound ones as of 1966.The author included 22 factors but in the course of the research established that only five indicators were of importance.The result of his research was the Z-score indicator of a considered company.The lower this indicator the less financially sound and more prone to bankruptcy was the company.Altman defined three main groups of values of the Z-score indicator.The companies with the value less than 1.81 fall into the group of potential bankrupts.Altman called the interval of 1.81 to 2.99 an uncertainty range with a high probability of a classification error.The companies with the indicator exceeding 2.99 are considered to be financially sound ones.This method helped to predict the possibility of bankruptcy of approximately 95% of all considered companies.
Nowadays the main emphasis of papers is on improvement of the methodology of bankruptcy models building in order to obtain better predictive models.But one of important aspects is choice of factors which influence the financial standing of a company.The financial indicators such as profitability, liquidity, business activity, capital structure, debt servicing capacity, company size and its growth opportunity are of frequent occurrence in researches.In this article we consider each group of indicators as factors of corporate bankruptcy for small, medium and large companies.

Profitability
Profitability is one of the key indicators of corporate performance.The company activity is possible due to a positive amount of profit.Purchase of raw materials and supplies, administration and operating expenses, accounts payable, debt repayment is impossible without a source of funds.In case of lack of funds the company is forced to use borrowed funds which are received by creditors on the basis of the company financial indicators.In case of lack of cashflows or a security to repay the debt the company will be limited in obtaining of borrowed funds.The company profit is the source of its expansion and growth by means of reinvesting funds into companies, development of process-oriented manufacturing, scientific research or investment in profitable projects.
The company profitability has a positive impact on its status.The companies which generate profit are less prone to financial instability as they have an opportunity to mitigate or avoid the influence of instability factors on their activity.This conclusion was first studied in the pa-pers dedicated to developed [2]; [3]; [4]; [5]; [6]; [7] and emerging markets [8]; [9] (table 1).

Liquidity
Liquidity should be understood to mean the ability to pay off debts in short time.The company assets may be divided into highly liquid, low liquid and nonliquid ones, and it implies the speed of sale of an asset at a price close to the market price.The highly liquid assets comprise monetary funds and realizable securities.The low liquid assets are accounts receivable, stock of commodities and materials.Nonliquid assets are buildings, equipment and construction in progress.
The main reason for bankruptcy is the company inability to pay off its debts [12].An enterprise with liquid assets is subjected to financial instability less than companies with nonliquid assets on the balance sheet.Availability of highly liquid assets helps a company to pay its accounts payable, loans and debts, thus, reducing the likelihood of bankruptcy.It should be noted that a marginally profitable Electronic copy available at: https://ssrn.com/abstract=3638655company predeterminedly has a small amount of highly liquid assets.

Business Activity
The company business activity affords assessment of efficiency of the corporate assets use.A high turnover of reserves, accounts receivable and accounts payable is characteristic of a company with high business activity and high quality of conducting of business activity, and the speed of such activity is indicative of profitability.Consequently, one can sum up that this indicator influences negatively on the possibility of default (table 3).

Capital structure
Bankruptcy is lack of opportunity to settle with creditors and bank.Such situation may be caused by a large debt.
The management has to maintain the financial leverage.
A large amount of borrowed funds may result in financial instability and a company will be unable to settle its liabilities, its access to the borrowed funds market will be limited making it impossible to stabilize the financial standing.
From this we can deduce that the more well-balanced the financial leverage, the lower the possibility of default [1].
Empiric researches of developed markets confirmed Beaver's [1] assumption of interconnection between the capital structure and possibility of bankruptcy.This confirms a positive effect on the possibility of bankruptcy for emerging markets of Iran [13]; [20] and Brazil [8].The paper by Ciampi [26] dedicated to prediction of bankruptcy of small, medium and large companies also confirms Beaver's ideas (table 4).Electronic copy available at: https://ssrn.com/abstract=3638655

Debt servicing capacity
The ability to pay credit interest is also indicative of financial stability of a company and availability of funds to repay a credit and potential capability of raising additional borrowed funds.As long as the degree of debt servicing is directly related to the company capability to discharge its liabilities this factor has a negative influence on the degree of default.
This was shown in the research by [27] for British companies, as well as for Italian ones [26].The variable (EBIT/ IntExp) −1 was used as an indicator of debt servicing.

Growth opportunities
Growth is indicative of the capability to develop and reduce the chance of financial destabilization.A positive effect of growth opportunities on the possibility of bankruptcy was found out for Portuguese small, medium and large companies [28] (table 5).
On the basis of a literature review concerning corporate bankruptcy one may assume that the greatest influence on the possibility of bankruptcy is produced by the indicators of profitability, liquidity and business activity due to frequency of their use in researches.After analysis of the abovementioned articles we will define the main methods and their upgraded approaches which have been offered by the above authors.

Company size
Often in literature the company size is considered as a factor which influences the company size.Small companies are prone to financial destabilization due to limited access to the borrowed funds market.Large companies are more sensitive to high risks which may entail bankruptcy.
Researches dedicated to influence of the company size give no specific answer to the question of influence of the company size on its financial instability.One group of authors considers that as a company grows the possibility of its bankruptcy decreases [3]; [17]; [27], another group points out a positive influence of the company size on the possibility of default [25]; [18].Serrasqueiro [28] on the basis of a selection of Portuguese companies discovered a positive effect of this indicator on the probability of default (table 6).

Principal Components Method
On the basis of a literature review from the point of view of the factors of corporate financial instability 35 variables were chosen (table 1, Appendix B).These factors consist of the indicators of profitability, liquidity, business activity, capital structure, debt servicing, growth opportunities and company size.
In order to reduce dimension of bankruptcy indicators we considered the means of indicators' aggregation.One of the problems of a large number of variables is the danger of network over-training [8].It is also rather difficult to fetch out of a group of indicators precisely the factors which are most capable of bankruptcy prediction.In view of this in this paper we offer to have recourse to aggregation of input variables my means of the principal components method.
In order to check the assumption of the efficiency of use of the principal components method from the point of view of improvement of the predictive capability of the bankruptcy probability model it is necessary to verify the following hypotheses.

Hypothesis 1. Aggregation of indicators for prediction of bankruptcy probability of Russian small, medium and large companies using the principal components method has a better effect from the point of view of predictive capability of the model in comparison with use of the variables selected separately from each group of factors.
The essence of the principal components method consists in reduction of data dimension losing as little information as possible.This method implies redistribution of data in such a way that the considered variables were generalized as relating to a small number of factors (principal components) which record the maximum possible amount of information contained in the source data.This method may also be phrased as a necessity to find factors  which represent the linear dependence  ' and initial variables  which provide for the maximal variance.
Electronic copy available at: https://ssrn.com/abstract=3638655 Factor z 1 is a linear combination of initial variables x with the maximal variance.The second component contains the information not included in and not correlated to the first component.The principal components method consists in maximization of variance of the factors z = xu , which u'u=1 , or eigenvalue decomposition of the correlation matrix.
The principal components method is consigned to solution of the following equation: where R -variables correlation matrix x; λ -eigenvalue; u -eigenvector.
Eigenvalues λ are the variance of relevant factors z.The share of the variance of the initial variable x i corresponding to the first factors represents a sum of squares of factor loadings: The factor loadings are a correlation of initial variables x And components z: where D -is the diagonal matrix of components' covariants z: The method is used only if there is a correlation between the variables.After transformation z the factors do not correlate to each other.Due to a large number of considered variables it is highly probable that there is a high correlation between the indicators.This encourages application of this method.

Data
The selection of Russian companies was made using the Ruslana database created by Bureau Van Dijk.For the research we analyzed approximately 10 thousand small, medium and large companies which became bankrupt in the period of 2015-2016.The research does not consider earlier periods because financial instability of 2014 resulted in increase of bankruptcy cases in the indicated time.The economic situation in general influences greatly the company standing.Therefore, this period is to be analyzed separately within the issue of influence of political factors on corporate bankruptcy which is an exceptionally interesting issue.
Standards of Ordinance of the Russian Federation Government of July 13, 2015 No. 702 "On Threshold Values of Proceeds of Sales of Goods (Works, Services) for each Category of Small and Medium-Sized Business Entities" were used as criteria of small, medium and large business.In this paper small and medium-sized business is represented by the companies which sales proceeds from goods, works or services net of VAT vary in the range of 150 million roubles to over 2 billion roubles.
We consider two selections in the paper.The first selection touches upon the industrial sector C which comprises 6,800 companies and the second one also includes the construction sector F and comprises 10,700 companies.
In order to build the bankruptcy probability model, we used the data one year before the bankruptcy had taken place (2015-2016).The result of such model is the company predictive power for one year.We do not build models in this paper two or three years before the bankruptcy because empiric results of the papers dedicated to default probability prediction show a decrease of predictive power with increase of the time horizon between the bankruptcy fact and used data.Thus, a model built on the basis of the data related to one year before the bankruptcy can define potential bankrupts most correctly.
After calculation of the variables necessary for the research and processing of observations with missing values in the selection of bankrupts used for building of the bankruptcy probability model the offered separation and division into stacks method was applied.Division of companies into industry sectors in accordance with the Russian National Classifier of Types of Economic Activity is presented in fig. 1.The selections consider manufacturing (С -63.8%) and construction companies (F -36.21%).Electronic copy available at: https://ssrn.com/abstract=3638655 Higher School of Economics 27 Table 7 comprises descriptive characteristics of variables of manufacturing companies.

Separation
The stage of dividing the current revenue company and the formation of primary blocks by revenue

Formation
The stage of adding bankrupts to the formed stacks in different shares

Recovery
At this stage, data recovery occurs.Ultimately, the best recovery method is chosen

Aggregation
The stage of reducing factor dimension by the method of principal components

Education
The stage of choosing the best neural network tool

Creature
The end result is a model consisting of blocks that include stacks of the best models

The Choice
Choosing the best way to predict Electronic copy available at: https://ssrn.com/abstract=3638655 Higher School of Economics 36  Predic�ve power, % Electronic copy available at: https://ssrn.com/abstract=3638655 Higher School of Economics 37 As we see from fig. 4 for the companies from manufacturing sectors, almost at all stages the principal components method has rather big deviations for 5-15%.This result is typical at virtually all intervals of company sizes, apart from the interval of 425-430 million roubles.Fig. 5 shows for the companies of the construction sector F a more interesting situation.The principal components method affords smoothing over of sharp outlying data and, thus, during the test of the validation selection there arise outlying data, but this is true only for a small group of validation selections.

Econometric Analysis and its Results
Our selection consists of 1,200 bankrupt companies and 8,700 financially sound companies which totals to 10 thousand companies.We will use the offered method presented in fig. 3 as a forecast and try to define the influence of the method on the predictive power.
After forming the aggregate indicators we started the procedure of prediction and defining the significant factors.Analysis of interconnection between the main components and bankruptcy probability at each stack in the correlation matrix is indicative of a significant influence of two to four main components (at the 20% significance level as an assumption).Therein, the majority of correlation coefficients between the main components are of significance and do not exceed 0.5 in absolute magnitude.
The hypothesis of improvement of the predictive power applying the principal components method is rejected but it has a set of assumptions at which the hypothesis will still be accepted in case of presence in the selection of a large amount of outlying data and relevantly small validation selection.

Conclusion
A large number of articles is dedicated to improvement of quality of bankruptcy prediction.Modern methods in this sphere consist in development of complex composite hybrid models which consist not just of neural networks but of genetic algorithmization.Such models may provide the maximum predictive capability, however, this is an issue for a new research, while the offered method has an opportunity for further improvement of methodology.A high predictive power of the model helps investors, banks and other creditors to foresee potential financial problems of a company with s greater accuracy.Therefore, in this article we study the quality of methodology applied for assessment of business solvency of Russian small, medium and large companies from the point of view of the ability to predict correctly the bankruptcy probability.To do this the separation algorithm was offered.
The forecasting was done using neural simulation.35 indicators which characterize profitability, liquidity, business activity, capital structure, debt servicing, growth opportunities, company size were used.They were selected on the basis of a literature review and were aggregated applying the principal components method.It was found out that use of the principal components method does not increase the predictive power of a model in comparison to use of the variables selected separately from each group of factors.
The conclusion of this research is that it is necessary to increase accuracy of the forecast of the models which are used in practice for assessment of business solvency of Russian small, medium and large companies.It is possible to improve the methodology by means of applying advanced methodologies accompanied by complicating of models, employment of additional underlying behavioral factor, use of methods of data recovery and hybrid networks.
For further study of this issue it is interesting to consider the problem of accuracy of processing of lost or missing data applying genetic algorithmization and dynamic models.

Figure 4 .
Figure 4. Comparative analysis of the predictive power of a forecast as exemplified by the trainable, tested and validation selections for manufacturing sectors

Table 1 .
Profitability indicators used in the bankruptcy prediction models

Table 2 .
Liquidity indicators used in the bankruptcy prediction models

Table 3 .
Indicators of business activity used in the bankruptcy prediction models

Table 4 .
Indicators of capital structure used in the bankruptcy prediction models

Table 6 .
Indicators of the company size used in the bankruptcy prediction models

Table 8
comprises descriptive characteristics of variables of construction companies.As we see from table 7 and 8, 35 indicators will be used for calculation.However, it will be somewhat difficult to define the influence of each indicator and for this purpose we will use the principal components method which affords aggregation of indicators and development of the system of indicators' groups which are characteristic of each industry sector.Algorithm with added aggregation stage and analysis of effectiveness of this method Electronic copy available at: https://ssrn.com/abstract=3638655Electroniccopy available at: https://ssrn.com/abstract=3638655Figure 3.
Comparative analysis of the predictive power of a forecast as exemplified by the trainable, tested and validation selections for the construction sector