Study on financial risk prediction of enterprises based on logistic regression

Abstract

Financial risk has a great influence on the development of enterprises, and the prediction of financial risk can help enterprises to treat risks early. In order to realize the prediction of enterprise financial risk, find the risk as early as possible and make a response as soon as possible, according to the principle of predictability and reliability, this study selected 15 financial indicators from aspects of debt repayment level, profit level, operation level, growth level, and cash level, then predicted the risk by the logistic regression model, and analyzed the risk of 36 pairs of enterprises. The results showed that the model designed in this study had an accuracy rate of 91.67%, and the risk of a company was successfully predicted based on the financial situation of the company from 2018 to 2020, which verified the reliability of the method. Thus the model can effectively predict the financial risk of enterprises, and it can be further promoted and applied to ensure the long-term development of enterprises and establish a good market environment.

Keywords

Logistic regression model financial risk financial crisis financial prediction

1. Introduction

With the development of economy, the probability of financial risks in enterprises has greatly increased [1]. A minor problem will be more and more serious if it is not solved timely; eventually, the financial crisis will happen, and the enterprise will be destroyed. Financial risk prediction has been regarded as one of the important research objects in the field of corporate finance [2]. It is an important task for enterprise managers to analyze the financial situation of enterprises [3]. The financial situation of an enterprise can be controlled through financial risk prediction [4]. A scientific and effective financial risk prediction model can make a forewarning to managers in the early stage to nip the financial risk in the bud. As Basel Accords mentioned [5], not only current risks but also future risks should be identified. In the current risk assessment, there are mainly two kinds, qualitative analysis and quantitative analysis. The qualitative analysis is to find out whether an enterprise will have a financial crisis through the investigation of the actual situation and problems of the enterprise. The quantitative analysis is to establish the corresponding model based on various financial data information of an enterprise through statistics and simulation and predict the financial risk of the enterprise with the model, which is more accurate and has received extensive attention from researchers. Sun et al. [6] analyzed the low-carbon financial risk in the Green Belt and Road Initiative public-private partnership (PPP) project, determined ten risk factors that might cause project derailment, established the hierarchical structure of the low-carbon financial risk, and found that those factors had very strong correlations and establishing risk database was needed to ensure the high-efficient green investment. Li et al. [7] analyzed the financial risk of the manufacturing industry, screened out the financial indicators by principal component analysis method, then used the Back-Propagation (BP) neural network model optimized by the improved particle swarm optimization (IPSO) to predict the financial risk, and found through experiments that the method had high accuracy. Based on the unit root test and principal component analysis, Zhao et al. [8] predicted the financial risk with the least squares support vector machine (LSSVM) and found that the model had a good prediction performance. Katarina et al. [9] obtained the financial data of Slovak enterprises in 2015 and 2016 from the Amadeus database, then established a prediction model through multiple regression analysis, estimated the profitability of enterprises, and eliminated the related risks unfavorable to the financial status of the enterprises according to the results. The study selected appropriate financial indicators, excluded some indicators which were unable to reflect financial status through significance test, established the risk prediction model through logistic regression analysis, and verified the effectiveness of the model with examples. The rest of the article is organized as follows. The second chapter introduces the research methods, including the selection of financial indicators and the establishment and verification of the prediction model. The third chapter makes an instance analysis: the financial risk of an enterprise was predicted. The fourth chapter makes a discussion and analysis of the research results. The fifth chapter makes a summary of the whole paper.

2. Research methods

2.1 Overview of financial risk

With the development of economy, the risks faced by enterprises have become more and more complex. If a risk is not properly controlled, it may cause financial loss or even bankruptcy. An enterprise is an important part of the market economy, and its steady development is conducive to the stability of the market economy. Financial risk is the most common risk in the development of an enterprise. It mainly refers to the decline of enterprise earnings and the failure of capital allocation due to the improper investment and misuse of funds. Some enterprises have great payment pressures because of wrong decision-making, and the insufficient payment ability will induce financial risk. When an enterprise has financial risks, it will be unable to repay debt or bear the cost. Income and capital are important factors for the development of enterprises. If the problem in income and capital cannot be solved timely, it will be more and more serious, which will cause a lethal effect on the development of enterprises. The manifestations of financial risks include (1) decline of sales volume: the decline of sales income will reduce the profit, leading to loss of enterprise; (2) rise of the asset-liability ratio: the improvement of the ratio of liabilities to assets will weaken the debt-paying ability of enterprises; (3) capital shortage: capital is the foundation of enterprise development, and the normal operation of an enterprise is difficult to maintain if the outflow of cash flow is larger than the inflow; (4) cash flow dilemma: insufficient enterprise capital and decline of operating performance are not beneficial to the long-term development of the enterprise; (5) increase of accounts receivable: there will be bad debt if an enterprise cannot collect the account receivable, leading to cash flow difficulty.

There are many reasons to cause financial risks. On the one hand, the changes in government policies will affect the production and the income of enterprises. When a tight policy is implemented, the cost of loaning from banks will greatly increase. Moreover, market volatility will also induce the decay of enterprises. The industry will enter the phase of decline because of poor development prospects, which will affect enterprise development in the industry. On the other hand, loose management, low economic benefits, imperfect internal control, wrong decision, aimless investment, and lack of risk awareness can all lead to the emergence of financial risks.

2.2 Selection of financial indicators

The selection of financial indicators can affect the prediction results of the model directly [10, 11]. The selection of indicators should follow the following principles:

(1)
Predictability. The selected indicators must be able to reflect the changes in the financial situation. The changes need to be recognized before the outbreak; otherwise, the selected indicators have no research significance.
(2)
Reliability. The data reflected by the selected indicators must be credible. In the process of data collection and calculation, errors should be avoided to ensure the accuracy of the predicted results.
(3)
Acuity. Indicators must be sensitive and able to reflect financial changes quickly and timely.
(4)
Integrity. Indicators must reflect the financial level of enterprises overall.

According to the principle of indicator selection, this study selected 22 indicators from five aspects: debt level, profit level, operation level, growth level, and cash level. The specific content is shown in Table 1.

Table 1
Financial indicators

Types Index code Content Index formula

Debt level K1 Current ratio Current assets/current liability

K2 Quick ratio Quick assets/current liability

K3 Asset-liability ratio Total liabilities/total assets

K4 Capitalization ratio Total equity/total liabilities

K5 Equity ratio Total liabilities/total equity of owners

Profit level K6 Return on equity Retained profits/average net asset

K7 Total asset rate Retained profits/total assets

K8 Operating profit ratio Operating profit/operating receipt

K9 Net profit margin on sales Net profit/sales revenue

K10 Earnings per share Net income/number of closing common stocks

Operation level K11 Turnover of account receivable Sales revenue/average accounts receivable

K12 Current asset turnover Main operation income/average total current assets

K13 Total assets turnover Sales revenue/total average assets

K14 Rate of stock turnover Main business cost/average stock

Growth level K15 Growth rate of operating profit Increase in operating profit in the current period/operating

profit at the beginning of the period

K16 Net profit growth rate Net profit growth of the current year/initial net profit

K17 Net asset growth rate Net asset growth of the current year/initial net asset

K18 Total asset growth rate Total asset growth of the current year/initial total assets

Cash level K19 Cash sales ratio Net operating cash flow/main operation income

K20 Asset cash recovery Net operating cash flow/total average assets

K21 Cash current liabilities ratio Net operating cash flow/flow sheet

K22 Operating cash flow per share Net operating cash flow/number of closing common stocks

2.3 Logistic regression model

Types	Index code	Content	Index formula
Debt level	K1	Current ratio	Current assets/current liability
	K2	Quick ratio	Quick assets/current liability
	K3	Asset-liability ratio	Total liabilities/total assets
	K4	Capitalization ratio	Total equity/total liabilities
	K5	Equity ratio	Total liabilities/total equity of owners
Profit level	K6	Return on equity	Retained profits/average net asset
	K7	Total asset rate	Retained profits/total assets
	K8	Operating profit ratio	Operating profit/operating receipt
	K9	Net profit margin on sales	Net profit/sales revenue
	K10	Earnings per share	Net income/number of closing common stocks
Operation level	K11	Turnover of account receivable	Sales revenue/average accounts receivable
	K12	Current asset turnover	Main operation income/average total current assets
	K13	Total assets turnover	Sales revenue/total average assets
	K14	Rate of stock turnover	Main business cost/average stock
Growth level	K15	Growth rate of operating profit	Increase in operating profit in the current period/operating
			profit at the beginning of the period
	K16	Net profit growth rate	Net profit growth of the current year/initial net profit
	K17	Net asset growth rate	Net asset growth of the current year/initial net asset
	K18	Total asset growth rate	Total asset growth of the current year/initial total assets
Cash level	K19	Cash sales ratio	Net operating cash flow/main operation income
	K20	Asset cash recovery	Net operating cash flow/total average assets
	K21	Cash current liabilities ratio	Net operating cash flow/flow sheet
	K22	Operating cash flow per share	Net operating cash flow/number of closing common stocks

Thirty-six real economy enterprises that implemented ST for the first time in 2017 $\sim$ 2019 were selected as the research samples, and then 36 non-ST enterprises that were the same or similar (with a difference smaller than 10%) with the real economy enterprises were selected as the paired samples. The 36 pairs of enterprises were divided into training samples and experimental samples. Relevant data that were needed by the calculation came from RESSET database.

The significance test was carried out on 15 selected indicators using SPSS 17.0, and the level of significance was 5%. The results are shown in Table 2.

Table 2
Sample significance test

Indicator code	T value	Significance
K1	$-$ 2.608	0.010
K2	$-$ 2.432	0.018
K3	$-$ 2.461	0.019
K4	0.167	0.745
K5	$-$ 1.256	0.167
K6	3.28	0.000
K7	$-$ 9.521	0.000
K8	$-$ 5.629	0.000
K9	0.132	0.114
K10	2.112	0.133
K11	$-$ 0.895	0.310
K12	$-$ 0.84	0.408
K13	$-$ 2.216	0.038
K14	$-$ 0.214	0.268
K15	0.136	0.416
K16	$-$ 3.689	0.001
K17	$-$ 4.698	0.000
K18	$-$ 2.524	0.017
K19	0.183	0.855
K20	$-$ 1.754	0.086
K21	$-$ 1.535	0.128
K22	2.336	0.159

After the significance test, the insignificant indicators were eliminated, i.e., K4, K5, K9, K10, K11, K12, K14, K15, K19, K20, K21, and K22. Finally, ten financial indicators were obtained for the subsequent modeling.

Logistic regression was performed using SPSS 17.0, and the results are shown in Table 3.

Table 3

Analysis results of logistic regression

Financial indicators	Constant term coefficient B	Standard error	Chi-square value Wals	Degree of freedom	Significance	Exp (B)
K1	$-$ 1.953	2.205	0.832	1	0.365	0.142
K2	$-$ 0.152	2.698	0.039	1	0.893	0.839
K3	0.060	0.071	0.742	1	0.382	1.057
K4	$-$ 0.035	0.471	0.003	1	0.892	0.863
K5	$-$ 0.089	0.632	0..015	1	0.873	0.908
K6	0.159	0.231	0.508	1	0.411	1.168
K7	$-$ 2.125	1.876	1.326	1	0.308	0.124
K8	0.000	0.002	0.001	1	0.892	1.001
K9	$-$ 0.029	0.030	1.015	1	0.287	0.950
K10	0.038	0.029	1.603	1	0.207	1.052
Constant quantity	$-$ 2.201	3.397	0.401	1	0.532	0.109

It was seen from Table 3 that the standard errors of the data were small, indicating that the data had good stability. It is assumed that the probability of financial risk in an enterprise is $P$ , then its logistic regression model can be expressed as:

$\displaystyle P_{m}=\frac{\exp(\alpha+\sum{\beta_{m}X_{m}+\varepsilon)}}{[{1+% \exp(\alpha+\sum{\beta_{m}X_{m}+\varepsilon)}}]},$ (1)

where $P_{m}$ represents the probability of financial risk of the company, $\alpha$ represents the intercept, and $\beta_{m}$ represents the parameter estimate. 0.05–0.95 was taken as the probability of financial risk of the enterprise, with an interval of 0.05. Then the values were substituted into the logistic regression model to calculate the change of error rate. The calculation showed that the error rate of the model was the lowest when the probability of financial risk took 0.35. Therefore, taking 0.35 as the probability of financial risk, $P>$ 0.35 indicates that the company has a high probability of financial risk and vice versa.

The data in Table 3 are substituted, then

$\displaystyle P=\frac{{\begin{array}[]{l}\exp(-1.953K1-0.152K2+0.060K3-0.035K4% -0.089K5\\ {}+0.159K6-2.125K7+0.000K8-0.029K9+0.038K10-2.201)\\ \end{array}}}{\left[{\begin{array}[]{l}1+\exp(-1.953K1-0.152K2+0.060K3-0.035K4% -0.089K5\\ {}+0.159K6-2.125K7+0.000K8-0.029K9+0.038K10-2.201)\\ \end{array}}\right]}$ (2)

The data of 18 pairs of experimental samples were substituted into the risk prediction model to compare the performance of the model designed in this study and the model designed by Sun et al. [6], and the results are shown in Table 4.

Table 4

The sample judgment results

	ST		Non-ST		Total
	The model designed by Sun et al.	The model designed in this study	The model designed by Sun et al.	The model designed in this study	The model designed by Sun et al.	The model designed in this study
Predicted value
ST	16	17	4	2	20	19
Non-ST	2	1	14	16	16	17
Accuracy rate	88.89%	94.44%	77.78%	88.89%	83.33%	91.67%

It was seen from Table 4 that the model designed by Sun et al. made misjudgment on 2 cases in the judgment of ST enterprises and made misjudgment on 4 cases in the judgment of non-ST enterprises, and the comprehensive accuracy rate was 83.33%; the model misjudged 1 case in the judgment of ST enterprises and 2 cases in the judgment of non-ST enterprises, and the comprehensive accuracy rate was 91.67%, which was significantly higher than that of the model designed by Sun et al. It showed that this model had good accuracy and practicability in the prediction of financial risks.

3. Empirical analysis

The financial situation of a company from 2018 to 2020 was analyzed by the model designed in this study, and the relevant financial data come from RESSET database.

The ten financial indicators selected and processed above were calculated based on the data from the database, and the results are shown in Table 5.

Table 5
The calculation results of financial indicators

	2018	2019	2020
K1 current ratio	2.04	1.31	1.34
K2 quick ratio	2.24	1.27	1.31
K3 debt-to-assets ratio	0.64	0.63	0.64
K4 net assets income rate	0.84	1.04	1.03
K5 total asset rate	0.03	0.05	0.04
K6 operating profit ratio	0.94	0.94	0.94
K7 total assets turnover	0.10	0.10	0.09
K8 net profit growth rate	1.01	1.07	$-$ 0.28
K9 net asset growth rate	1.03	1.05	$-$ 0.62
K10 total asset growth rate	1.09	1.10	$-$ 0.36

The data in Table 5 were substituted into the Logistics regression model, and the following model was obtained:

The probability of financial risk of 2018 $\sim$ 2020 was calculated, and the financial risk of 2021 was predicted:

$\displaystyle P_{2018}=0.012$ (4) $\displaystyle P_{2019}=0.057$ (5) $\displaystyle P_{2020}=0.055$ (6) $\displaystyle P_{2021}=0.061$ (7)

$P>$ 0.35 indicates that the company has a high probability of financial risk and vice versa. It was found that the financial situation of the company between 2018 and 2020 was normal. Through prediction, the probability of financial risk in 2021 was 0.061, which indicated that the financial condition of the enterprise was normal, and the probability of financial risk was very small. In conclusion, the model which was designed in this study could predict the financial risk of enterprises and help them to avoid risks better.

4. Discussion

As market competition becomes more and more competitive, the difficulty of enterprise survival also increases greatly. The occurrence of risks is usually premonitory, and financial risk prediction can help enterprises reach the source of the risks; decision-makers take steps timely, prevent the risks from getting worse, and restrain the financial crisis. Duca et al. [12] judged the financial position of a company with multiple logit models and found out that the model could make accurate predictions of the crisis through experiments. Deng et al. [13] constructed the FREW model for financial risks in colleges based on SVM and found that the model provided the early prediction for colleges. Ma [14] selected seven indicators that might affect the financial situation of companies to establish a risk prediction model based on the improved probabilistic neural network (PNN), and analyzed the effectiveness of the model.

This study found that the established financial prediction model had a good performance in financial risk prediction and could accurately distinguish ST and non-ST enterprises, and it had high accuracy than that method proposed by Sun et al. Then, a company was taken as the research subject, and the financial situation of the enterprise in 2018 $\sim$ 2020 was analyzed using the model designed in this study. It was found that there was no financial risk in the company from 2018 to 2020. $P$ -value was still within the range of financial risks, although it increased slightly. From the perspective of data, the current assets and quick assets decreased in the past three years, and the total liabilities increased slightly, but the operating revenue maintained a good upward trend, the net profit increased year by year, and the total assets rose slowly. It showed that the strategy and policies formulated by the company were correct in the three years, which brought great profits to the enterprise. The prediction result of 2021 suggested that the $P$ -value was 0.061, showing a little increase, i.e., the financial condition of the enterprise will have a small amplitude of change, but controllable. Facing with the increase of $P$ -value, the company should be more vigilant. The company should take measures to reduce corporate debt, improve corporate income, or make appropriate efforts to innovate to open up new situations for the development of companies.

5. Conclusion

Predicting financial risks is necessary. In this study, proper financial indicators were selected to reflect the financial situation of an enterprise and further processed, and the financial risk prediction model was established based on the final indicators. It was found through verification that the accuracy rate of the model proposed in this paper reached 91.67%. Then, the financial situation of a company between 2018 and 2020 was analyzed by the model, and $P$ -value was smaller than 0.5, which meant that the company had a good financial situation. The result showed that the model based on logistic regression could predict the financial risk of enterprises, truly reflect the probability of financial risk, and provide a direction for the future development of enterprises. But this study also has some shortcomings, for example, the selection of indicators lacks reliable bases, and the research samples have some limitations, which need to be improved in future research.

References

Wei

, Establishing Financial Crisis Early Warning Models for Listed Companies, in: International Conference of Information Technology, Computer Engineering and Management Sciences, IEEE Computer Society, 2011, pp. 195–198.

Zhao

D.D.

Ding

J.C.

and Chai

S.C.

, Systemic financial risk prediction using least squares support vector machines, Modern Physics Letters B 32 (2018), 1850183.

Wang

Business

S.O.

et al., Effect study of the indicator selection method on the accuracy rate of financial early warning, Journal of Wuhan University of Technology 39(3) (2017), 348–352.

Kotane

, Evaluating the importance of financial and non-financial indicators for the evaluation of company’s performance, Applications of Fibonacci Numbers 37(1) (2015), 80–94.

Deng

and Han

Y.Q.

, Financial crisis early warning model for universities based on support vector machine, Journal of Nanjing University of Science & Technology 36(3) (2012), 551–556.

Duca

M.L.

and Fratzscher

, A global early warning system of financial crises, Journal of International Money & Finance 25(6) (2010), 953–973.

Kou

Peng

and Heyde

C.C.

, External risk measures and basel accords, Mathematics of Operations Research 38(3) (2013), 393–417.

and Quan

, Financial risk prediction for listed companies using IPSO-BP neural network, International Journal of Performability Engineering 15(4) (2019), 1209–1219.

Stone

S.B.

Singla

Comeaux

et al., A comparison of financial indicators: the case of detroit, Public Budgeting & Finance 35(4) (2016), 90–111.

10.

S.Y.

, Improvement of financial crisis early-warning model based on PNN, Business Economy 0(24) (2014), 31–36.

11.

Katarina

Tomas

Lucia

et al., Financial risk measurement and prediction modelling for sustainable development of business entities using regression analysis, Sustainability 10(7) (2018), 2144.

12.

Rong

, Study on financial risk prediction of listed companies based on logistic regression model, Boletin Tecnico/technical Bulletin 55(20) (2017), 107–114.

13.

Sun

Chen

Sun

H.P.

and Taghizadeh-Hesary

, Low-carbon financial risk factor correlation in the belt and road PPP project, Finance Research Letters 35 (2020).

14.