A statistical model of fraud risk in financial statements: Case for Romania companies

Sabau, Andrada-Ioana; Mare, Codruța; Safta, Ioana Lavinia Article A statistical model of fraud risk in financial statements: Case for Romania companies Risks Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Sabau, Andrada-Ioana; Mare, Codruța; Safta, Ioana Lavinia (2021) : A statistical model of fraud risk in financial statements: Case for Romania companies, Risks, ISSN 2227-9091, MDPI, Basel, Vol. 9, Iss. 6, pp. 1-15, https://doi.org/10.3390/risks9060116 This Version is available at: https://hdl.handle.net/10419/258202 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ risks Article A Statistical Model of Fraud Risk in Financial Statements. Case for Romania Companies Andrada-Ioana Sabău (Popa) 1,*, Codrut ,a Mare 2and Ioana Lavinia Safta 2   Citation: Sabău (Popa), Andrada-Ioana, Codrut ,a Mare, and Ioana Lavinia Safta. 2021. A Statistical Model of Fraud Risk in Financial Statements. Case for Romania Companies. Risks 9: 116. https://doi.org/10.3390/risks9060116 Academic Editor: Montserrat Guillén Received: 26 April 2021 Accepted: 8 June 2021 Published: 10 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Faculty of Economics and Business Administration, Cluj-Napoca University Babes-Bolyai, 400591 Cluj-Napoca, Romania 2 Faculty of Economics and Business Management, Cluj-Napoca University Babes-Bolyai, 400591 Cluj-Napoca, Romania; codruta.mar[email protected] (C.M.); [email protected]o (I.L.S.) *Correspondence: [email protected] or [email protected] Abstract: Tax avoidance is one of the most frequent reasons for which companies tend to resort to creative accounting techniques. The purpose of the study is to identify which of the eight-variables from the Beneish influences the most or least the outcome of the final score, as a percent, by developing a statistical model. The sample was selected from the Bucharest Stock Exchange and consists of 66 companies traded on the main market, for the years 2015–2019. The results show that from the total of the eight variables, GMI (Gross Margin Index), AQI (Asset Quality Index), DEPI (Depreciation Index) and TATA (Total Accruals to Total Assets) are significantly influencing the probability to commit fraud. The developed model is validated with only 10% of the non-fraud companies being mistakenly considered as fraud based on our model and vice versa. Keywords: Beneish model; fraud; statistical model; Mann-Whitney test 1. Introduction The act of fraud has been practiced since ancient times, when it was expressed in various ways. The first definition of it was stated in Hammurabi’s Code, about 1800 years before the new era (Halilbegovic et al. 2020). In the literature it is specified that between corporate taxpayers and the taxing authorities is a continuous “war”, and that tax avoidance might be as old as the taxes itself (Ibrahim et al. 2013). Nowadays, the actions taken by companies to manipulate the financial statement continues, and the managers and accountants have gotten more and more creative in order to resort to different methods. The fraudulent action is considered to either be detected, or undetected (Mohammad et al. 2020). For this, specialists have developed and are constantly improving the models that can help identify the presence of financial fraud. Financial fraud is present and can occur in different sectors of activity. Thus, the responsibility of raising red flags is distributed to the management of the company, and to the staff who are in charge of corporate governance (Bilgin et al. 2017). Externally, the auditors should apply sufficient audit tests to be assured that financial statements are free of errors or financial manipulation. Therefore, the responsibility is not attributed only to the management or to the auditor, it is equitable distributed (Johnes 2010). The purpose of this paper is to identify which of the eight Beneish variabiles (Days Sales in Receivables Index (DSRI), Gross Margin Index (GMI), Asset Quality Index (AQI), Sales Growth Index (SGI), Depreciation Index (DEPI), Sales General and Administrative Expenses Index (SGAI), Leverage Index (LVGI), Total Accruals to Total Assets (TATA)) have a positive/negative influence on the final score for the Romanian companies traded on the main market. A similar study was conducted for companies listed on Tehran Stock Exchange and the researchers concluded that DSRI, GMI, AQI, SGI, DEPI and TATA variables have a direct significant effect on fraudulent reporting, and on the other hand SGAI and LEVI have a significant inverse effect (Mohammad et al. 2020). Risks 2021,9, 116. https://doi.org/10.3390/risks9060116 https://www.mdpi.com/journal/risks Risks 2021,9, 116 2 of 15 In order to conduct the study, the companies traded on the main market from the BVB (Bucharest Stock Exchange) were divided in two categories as follows: “FRAUD” and “NON-FRAUD”. To obtain the final number of the companies analyzed, from the total of 81 businesses, the financial institutions and companies not based in Romania were eliminated. Thus, for the remaining 66 companies, the Beneish score was applied for the period 2015–2019. An average score was made for each company. The resulting values were reported at the reference level of “ − 2.22”. The scores higher than the reference point were included in the “FRAUD” area, and those with a lower score “NON-FRAUD”. Of the companies, 44 belong to the “FRAUD” area and 22 “NON-FRAUD”. Further, to obtain the statistical model, an intermediary step was applied. The Mann-Whitney test was applied to emphasize which of the quantitative variables is significantly different from one group to the other. Then, the progressive approach was used by estimating the binary logistic regression in the sample, in univariate form, along with the ROC curve. The binary logistic regression estimates the probability of finding a fraud company, based on the factors considered. The ROC curve has a similar approach. The results show that the variables which significantly influence the probability to commit fraud are: GMI (Gross Margin Index), AQI (Asset Quality Index), DEPI (Depreciation Index) and TATA (Total Accruals to Total Assets). The developed model is validated with only 10% error. In the literature there are several models for identifying the presence of financial fraud: Beneish Model (Beneish 1999), Dechow-Dichev (Dechow and Dichev 2002), Piotroski model (Piotroski 2002), Lev-Thiagarajan model (Lev and Thiagarajan 1993), Vladu model (Vladu et al. 2016), Robu and Robu (2013), Hasan score (Hasan et al. 2017). In the current study the Beneish Model was applied, since it is the most known mathematical model for detecting earning management and financial fraud. The research question of the paper is: Research question: “What are the financial indicators that most strongly discriminate the two states: fraudulent financial statements and non-fraudulent financial statements?” Through the conducted study, we contribute to the literature, by validating the Beneish model for Romanian companies. It is important to mention that the results may vary if the sample size is larger or smaller. The outline of the paper is as follows; in Section 1we present a brief literature review regarding the financial fraud and the methods used in the literature for detecting it. For the next section we detailed the objectives and the methodology applied in order to achieve them. Section 3is dedicated to presenting the results obtained. The last part of the paper presents the main conclusion of the study and highlights the added value that was made. 2. Literature Review For a better understanding of the topic, a brief definition of the concept of financial fraud will be made, followed by the presentation of the models used in the literature, to detect fraudulent actions. Financial fraud is committed as a result of a series of intentional acts, for the purpose of gain or unjust, illegal advantage. It is an act undertaken with the intention of deceiving others, often ending in significant financial losses (Achim and Borlea 2020). Using fraudulent techniques, companies’ financial statements show discrepancies between the actual and created reality. All this creates an imbalance that should be noticed and marked with “red flags” (MacCarthy 2017). Among the many reasons for resorting to fraud, the literature also presents the situation in which a company is on the verge of bankruptcy. Thus, to present a positive image, pressure is put on managers to cosmeticize the results in order to remain attractive to stakeholders (MacCarthy 2017). The motives that grounds fraudulent actions are varied, but the most common action is to avoid paying taxes. Tax expense is an incentive for companies in accounting manipulation since income tax is perceived as an unproductive outflow of capital sources (Svabova et al. 2020). The concept of tax-fraud consists of the non-payment of the taxes, and therefore violating the law. It is an intentional act, made to reduce the tax obligation. A Risks 2021,9, 116 3 of 15 means by which a business can restore to tax avoidance is underreporting sales or income and overstating deductions. In order to reduce taxation, companies cross the line of what is allowed by the tax system, by using illegal actions to reduce the amount of taxes (Hbaieb and Omri 2019). In the literature, fraudulent actions are interpreted through the “Fraud Triangle” to outline various categories of action, to prevent the occurrence of financial fraud. The concept consists of three approaches; opportunity, which refers to the circumstance that allowed the occurrence of fraudulent action, incentives, which is also referred to as some pressure that affects the mentality of the employee and rationalization that addresses the justification of those who resort to accounting manipulation techniques (Schuchter and Levi 2013). Goldmann (2009) underlines the fact that sometimes management often lives under the impression that their organizations are immune to fraud. A series of five myths were illustrated as follows: 1. Ethics and Compliance Training “Has Us Covered” It assumes that employees are trained to detect the red flags. However, most of the time, the word “fraud” is not even included in the code of ethics. A major difference must be made in the sense that “all fraud is unethical, but not all unethical conduct is fraudulent”. 2. Our Finance Staff are Qualified to Protect Us Against Fraud In most of the companies it could be the case that “internal auditors, financial managers, accountants, treasurers, and other professionals” are not properly trained to detect the presence of financial fraud. 3. We Have Very Little Fraud Here The reality is that in most of the cases, “no organization is immune to fraud”. Some have less, some have more. 4. Fraud is a Necessary Cost of Doing Business If the organization has no policy for investigating and punishing financial fraud, then the “small” fraudulent actions can soon turn into major losses. When this happens, the outcome can do great damage to the organization and interested parties. 5. Implementing Controls and Training is Costly The most effective anti-fraud techniques include “financial controls, operational controls, physical security of inventory, employee training, audits”. (Goldmann 2009). Prevention is the key to a healthy development of a company. It comes with a cost, but the costs are lower, rather than the case when financial fraud occurs. Identifying the presence/absence of financial fraud is a topic of high importance. Therefore, we chose to approach a few of the present models in the literature as follows: the Piotroski model (F-Score), Dechow-Dichev, Lev-Thiagarajan, Hasan score, Robu&Robu, Vladu model and M-Beneish. The first model, developed by Joseph Piotroski in 2002, had as ground point assessing the financial strength of a stock to maximize an investor’s profit. The basis of Piotroski’s research allows the application of a simple, nine-step analysis that indicates scores that can reveal a possible manipulation of financial statements by defining the company’s overall financial position as “weak”/“strong”. The model can be applied to both private and state-owned companies. The calculation of the score is composed of three stages. The first stage includes profitability indicators (ROA, CFO, ACCRUAL). For the next stage, the following indicators are included: LEVER, LIQUID and EQ_OFFER. The last part includes the operational efficiency scores: MARGIN and TURN (Gimeno et al. 2019). On the same note, Dechow and Dichev (2002), in their paper, measured the level of quality of accumulations based on the cash flow from commitments and the result of Risks 2021,9, 116 4 of 15 earnings which influences the financial statements. At the same time, it is highlighted that companies with a low quality of accumulations have a higher degree of commitments that are not related to cash flows (Dechow and Dichev 2002). Another approach on measuring the level of financial manipulation was developed by Lev and Thiagarajan (1993). In the conducted study they have identified a set of 12 signals in order to measure the quality of gains and future increases. The fundamental signals analyzed are: Inventory, Accounts Receivable, Capital Expenditure, R&D (Research&Developmente), Gross Margin, Sales and Administrative Expenses (S&A), Provision for Doubtful Receivables, Effective Tax, Order Backlog, Labor Force, LIFO earnings, Audit Qualification (Lev and Thiagarajan 1993). The value of higher total positive fundamental scores suggests a high quality of earnings, while total negative fundamental scores imply a low quality of earnings. The developed score is very useful when comparing different sectors of economic activity. A relative new approach in identifying the presence of financial statement manipulation was developed by Hasan in 2017. The author established as a sample seven Asian countries (Indonesia, Thailand, Malaysia, Hong Kong, Singapore, China and Japan), with companies listed on the Malaysian Stock Exchange. In total, 4200 companies were analyzed, and the financial statements from 2008–2013 were analyzed (Hasan et al. 2017). The author addresses the concept of “gray area”, which is defined as an “area” that has susceptibilities or elements in those financial statements with an index value higher than the benchmark of the Beneish index. To develop the model, four steps were followed as detailed: “The first stage deals with developing the indices, the second stage deals with the detection of manipulators, the third stage deals with the developing of overall manipulation index (OMI), and the fourth and final stage deals with the level of manipulation of each index” (Hasan et al. 2017). In the same vein, Vladu (Vladu et al. 2016) has developed a score applied for the Spanish companies, in the period of 2005–2012. Companies were selected which were following the rules, “good companies”, in addition to businesses which were not complying with the law. Twelve variables were developed, and the “t” symbol is used for the year in which the financial fraud has occurred. The variables developed are: Receivable index (RI), Inventories index (II), Gross margin index (GMI), Sales growth (SG), Depreciation index (DI), Discretionary expenses index (DEI), Leverage index 1 (LI1), Leverage index 2 (LI2), Asset quality (AQ), CFO index 1 (CFO1), CFO index 2 (CFO2), Sales index (SI) (Vladu et al. 2016). A model developed and applied for Romania companies was elaborated by Robu and Robu, in 2013. A series of indicators based on the Beneish model were computed. Sixtyfour companies were included in the sample, for the years 2011–2012. After computing several values, the model was established, and it is as follows: “M-FraudRisk-Beneish = − 0.383IICC + 0.039IMB − 0.325ICA + 0.448IVV + 0.273ID + 0.915IVCA + 0.478IGI − 0.153IAA”. For the developed function, three intervals were obtained: 1. The interval [ − 2.841; − 0.355]—results with a value contained in the interval is free of risk, so it is considered to be a safe zone; 2. The interval ( − 0.355; 0.313)—scores contained in this interval are part of the “grey zone”, uncertainty. In this case, additional audit procedures are expected; 3. The interval [0.313; 2.453]—any value contained in this interval, are considered to be in a zone with risk of financial fraud. (Robu and Robu 2013). Beneish Model was developed in 1999, by professor Messoud Beneish. The score measures the level of earning management of the financial situations. To compute the score, the data available from the financial statements published by the companies, are needed. The model is formed by eight variables: Days Sales in Receivables Index (DSRI), Gross Margin Index (GMI), Asset Quality Index (AQI), Sales Growth Index (SGI), Depreciation Index (DEPI), Sales General and Administrative Expenses Index (SGAI), Leverage Index (LVGI), Total Accruals to Total Assets (TATA). Risks 2021,9, 116 5 of 15 Any value of the final score higher than “ − 2.22” indicates the presence of financial fraud (Beneish 1999). In the literature, the Beneish Model is considered to be one of the most accurate and well-known models of detecting financial fraud. (Svabova et al. 2020). Halilbegovic et al. (2020), divides the Beneish variables, in two categories “manipulation signals” and “motivation signals”. In the manipulation signals are included: “Day Sales in Receivables Index (DSRI) for revenue inflation; Asset Quality Index (AQI) for expenditure capitalization; Depreciation Index (DEPI) for declining rate; and Total Accruals to Total Assets (TATA) for accounting not supported by cash”, and in the motivation signals: Gross Margin Index (GMI) for deteriorating margins; Sales Growth Index (SGI) for sustainability concerns; Selling, General, and Administrative Index (SGAI) for decreasing efficiency; and Leverage Index (LEVI) for tighter debt constraints” (Halilbegovic et al. 2020). In the literature, the way that the variables show the actual state of the company have had several approaches. Researchers have argued the probability of manipulation increases when the company’s financial statements show significant changes in accounts receivable, deteriorating gross margins, decreasing asset quality, sales growth and increasing accruals (Goldmann 2009). Beside the mathematical models presented above (and other stated in the literature), other general methods that can help detecting financial fraud are: “surprise audits, surveillance, regular internal audits, ratio analysis of the organization ’s key financial records, physical review of organization—owned supplies and asset inventory, manual review of T & E (travel&expenses) claims, manual assessment of payroll information, manual review of all vendors, have all bank reconciliations conducted by a manager outside of the accounts payable or procurement area” (Goldmann 2009). Another approach in detecting the presence of financial fraud is data mining. It is broadly approached in the literature for detecting the presence of financial statement manipulation. A series of authors—Koh and Low, 2004; Kotsiantis, 2006; Kirkos, 2007, Hoogs, 2007; Belinna, 2009, Ravishankar, 2011 and so on applied or analyzed data mining methods to identify the presence of financial fraud (Gupta and Gill 2012). It assumes the extraction of structured data, from unstructured texts. In the process of identifying the presence of financial fraud, words or clusters of words can be used to identify the relationship with other variables (Gupta and Gill 2012). For the present case study, the application of the Beneish model was chosen to identify the degree of accounting manipulation, and the presence/absence of financial fraud, since it is the best-known model in this regard. Also, the variables developed by professor Messoud Beneish were the basis for the elaboration of numerous mathematical models to identify the risk of not complying with the law. Romania (Robu and Robu 2013), Spain (Vladu et al. 2016), Asian countries (Malaysia, Indonesia, Thailand, Hong Kong, Singapore, China, and Japan) (Sabau et al. 2020). The effectiveness of the Beneish model in detecting and preventing financial fraud was identified by Herawati (2015) and Ramírez-Orellana et al. (2017). In the approach literature, the authors did not found studies applied on the econometric model selected for the conducted study. Computing and analyzing the obtain results from the selected indexes the impact on economic environment was observed. Also, it was intended to update the results, for the computed indexes. In the following, the materials and methods will be presented, and in the end, the results and conclusion will be approached. 3. Materials and Methods To achieve the objectives, 81 companies, that trade on the main market from the Bucharest Stock Exchange (BVB) were selected. The sample was constructed from two perspectives. From the first, we have took into consideration the type of the company. Financial institutions and companies that were not based in Romania have been eliminated. The second aspect referred to the financial statement, meaning that we selected the businesses which had publish without interruption in the analyzed period, more pre- Risks 2021,9, 116 6 of 15 cisely they were not delisted in a certain year. After applying the filters mentioned above, 66 companies for the period 2015–2019 were analyzed. Next, for the selected sample, the Beneish score was calculated. An average of the score for each company was calculated, and then reported at the reference value of “ − 2.22” so the selected sample can be divided in the two categories: FRAUD and NON-FRAUD. The two categories are as follows: - 44 of the companies are restoring to illegal techniques: FRAUD - 22 present a good financial situation, do not resort to techniques that distort the current state of society: NON-FRAUD. The steps that were followed to carry out the study are: - Centralizing the data from the reports downloaded from the Bucharest Stock Exchange (BVB); - Calculation of the eight variables and finally of the Beneish score; - Calculation of the average Beneish scores for the period 2015–2019 and segmentation of companies into those of the type “FRAUD”, respectively “NON-FRAUD”; - The application of the statistical model. The detailed version of the variables that compose the Beneish score are as follows: 1. Days Sales in Receivables Index (DSRI) represents the ratio between the period of collecting receivables from one financial year to the previous one. If there are no extreme changes of the crediting policy, it is expected that this indicator has a linear structure. A value higher than 1 can be interpreted to mean that the accounts receivable is higher in the year t than in the t −1. It could signal the presence of inflated revenues (Mahama 2015). DSRI = (Net Receivablest/Salest)/(Net Receivablest−1/Salest−1) (1) 2. Gross Margin Index (GMI) is constructed to detect irregularities of financial statements by measuring the ratio of a company’s previous year’s gross margin to the present year’s gross margin (Beneish 1999). A signal that a company is engaged in result manipulation can be observed from the reduction of Gross Margi ratio in the current year, compared with the previous. A score greater than 1 indicates the deterioration of the GMI index, due to the fact that the management team was motivated to manipulate the numbers to look better than they might be otherwise. A GMI score greater than 1 is an important red flag for any auditors and accountants to show the degree of manipulation financial data (Robu and Robu 2013). An unbalanced raise in the accounts receivable compared to the revenues may indicate the presence of fictitious sales. GMI = [(Salest−1−COGSt−1)/Salest−1]/[(Salest−COGSt)/Salest] (2) where COGS is cost of goods sold (COGS) and it refers to the direct costs of producing the goods sold by a company. 3. Asset Quality Index (AQI) For measuring the quality of the company (AQI) in a given year, computing the ratio of non-current assets (except property, plants and equipment) will show the company’s actual condition (Beneish 1999). A greater value than 1 of the AQI variable can signal the presence of financial fraud. The cases in which the AQI has a higher value is when the accountant professional resort to revaluation techniques of assets/fixed assets, the research and development and advertising costs are capitalized as intangible assets (Ibadin and Ehigie 2019). The outcome of the last techniques might be to increase the assets while the profitability of the company is preserved by using the manipulation techniques (Ibadin and Ehigie 2019). Shortly, a high value of the variable indicates the presence of creative accounting/fraud by using excessive capitalization of expenditure (Ibadin and Ehigie 2019). AQI = [1 −(Current Assetst+ PP&Et+ Securitiest)/Total Assetst]/ [1 −((Current Assetst−1+ PP&Et−1+ Securitiest−1)/Total Assetst−1)] (3) Risks 2021,9, 116 7 of 15 where PP&Erepresents property plant and equipment (PPE). 4. Sales Growth Index (SGI) measures the probability in manipulating the financial statement through the ratio of current sales to previous sales. If it is a case of a high value of the index, then it may be a case of manipulation of financial statements (Mahama 2015). SGI = Salest/Salest−1(4) 5. Depreciation Index (DEPI) Depreciation index represents the ratio of depreciation expenses and gross value (Mahama 2015). The tendency of this index is to manipulate the revenues for the current year (Mahama 2015). A value greater than 1 shows that the rate at which assets are depreciated has slowed down (Beneish 1999). DEPI measures the depreciation expenses of tangible assets and equipment. So, the red flags could be raised when the revenues are increasing and the expenses with depreciation are decreasing (Ibadin and Ehigie 2019). Another case in which the DEPI index has a higher value than 1 could be when the accountants, together with the management, hide the receivables resulting from fictitious sales; this fact can be observed by changing the value of the depreciation. DEPI = (Depreciationt−1/(PP&Et−1+ Depreciationt−1))/(Depreciationt/(PP&Et+ Depreciationt)) (5) 6. Sales General and Administrative Expenses Index (SGAI) compares the ratio of a company’s sales, general and administrative expenses to sales (Ibadin and Ehigie 2019). The index could include a series of incentives or bonuses for the managers. A correlation is expected between SGAI and sales. So, a disproportionate increase of the sales in relation to general and administrative expenses could signal the presence of red flags. SGAI = (SG&A Expenset/Salest)/(SG&A Expenset−1/Salest−1) (6) 7. Leverage Index (LVGI) measures the ratio between the total debt of an enterprise and the total assets. A value higher than 1 may suggest the possibility of the company being involved in financial fraud (Ibadin and Ehigie 2019). LVGI = [(Current Liabilitiest+ Total Long Term Debtt)/Total Assetst]/ [(Current Liabilitiest−1+ Total Long Term Debtt−1)/Total Assetst−1](7) 8. Total Accruals to Total Assets (TATA) is a qualitative indicator of cash flows for the company. It shows the extent to which cash sales are made. The red flags in case of this index can be raised if the degree of accruals as part of the total assets increases. Also, an increase in revenue or decrease in expenses, within the framework of accruals, indicate the presence of manipulation of financial information (Aghghaleh et al. 2016). TATA = (Income from Continuing Operationst−Cash Flows from Operationst)/ Total Assets (8) The M-Beneish equation is as follows: M = − 4.84 + 0.92 × DSRI + 0.528 × GMI + 0.404 × AQI + 0.892 × SGI + 0.115 × DEPI −0.172 ×SGAI + 4.679 ×TATA −0.327 ×LVGI (Beneish 1999). The first step in the research was the descriptive analysis of the variables—mean, median, standard deviation, minimum and maximum were computed and interpreted. As the goal is to discriminate between fraudulent and non-fraudulent companies, the next step was to apply comparison tests for this—we have used the non-parametric approach given by the Mann-Whitney test. This choice is based on two reasons: (1) we have evaluated normality of the distributions of the variables on the two groups and in most cases, they turned out not to be normal; (2) the previous result was expected as we have relatively small samples. Risks 2021,9, 116 8 of 15 The Mann-Whitney test was an intermediary step intended to emphasize which of the quantitative variables is significantly different from one group to the other. By using a progressive approach, we have then estimated the binary logistic regression in the sample, univariate form, along with the ROC curve. The binary logistic regression estimates the probability to find a fraud company, based on the factors considered. The ROC curve has a similar approach. The AUROC and p-value are presented in the results part. The construction of the final estimation model is based on previous results, in the sense that dimensions that turned out to be significant in the univariate estimations were included in a multiple binary logistic regression model. The function returns a score (z), which is then transformed in the probability (using the exponential function—exp) based on the following formula: P=exp(β0+β1GMI +β2AQI +β3DEPI +β4TATA) 1+exp(β0+β1GMI +β2AQI +β3DEPI +β4TATA) that can be reduced at: P=1 1+exp−z A series of estimation and post-estimation tests were applied to evaluate the model’s quality. They all validate the model. One of these procedures is given by the classification scheme which compares the real group with the one estimated through the model. Another such procedure is, again, related to the ROC curve. Probabilities computed based on the model were used in the construction of the ROC curve and, once again, the goodness-of-fit was assessed based on the AUROC and the probability attached. Additionally, this method allows for evaluating different thresholds and the sensitivity and specificity related to the model. 4. Results and Discussions In the following, the results of the applied method are presented. The descriptive analysis (Table 1) conducted on the groups of fraud (fraud and nonfraud) clearly emphasize that the non-fraud group has lower scores for all eight dimensions that are considered in the Beneish score. This is valid for both the average and the median value. In the mentioned above table, GMI index for the companies committing fraud has the minimum value of 0.574, the maximum 34.535, the average 3.627 and the standard deviation 6.164. While the non-fraud companies have the minimum value of − 26.727, and the maximum 1.865, the average − 1.274 and standard deviation 6.368. In case of the companies who commit fraud, the minimum for AQI is 0.750, while the maximum is 39.623. The average has the value of 2.704 and the standard deviation 6.053. For the non-fraud companies the minimum is 0.608, the maximum 1.846, the average 1.059 and the standard deviation 0.269. DEPI, for the fraud companies has a minimum 0.844, maximum 32.262, average 3.639 and standard deviation 5.310. The non-fraud companies have minimum for DEPI 0.905, maximum 4.782, average 1.437 and standard deviation 0.839. For TATA variable the minimum for fraud companies is − 0.663, the maximum 0.195, average − 0.009 and standard deviation 0.129. The non-fraud businesses have the minimum − 0.485, the maximum 0.227, the average − 0.085 and standard deviation 0.136. The results clearly underline the differences between the fraud companies, compared to the non-fraud. For all the components of the test (mean, median, std. deviation, minimum, maximum) in the case of the fraud category the values are higher than in the case of non-fraud, where the results are lower. So, it is very clear that in the case of the mean, just as stated above, the average and the median scores for all these variables are significantly lower for the non-fraud companies. Risks 2021,9, 116 15 of 15 Sabau, Andrada Ioana, Ioana Lavinia Safta, Gabriela Monica Miron, and Monica Violeta Achim. 2020. Manipulation of Financial Information through Creative Accounting: Case Study at Companies listed on the Romanian Stock Exchange. Paper presented at the 18th RSEP International Economics, Finance & Business Conference, Istanbul, Turkey, August 26–27; pp. 64–80. Available online: https://www.researchgate.net/publication/346927731_Manipulation_of_Financial_Information_through_Creative_ Accounting_Case_Study_at_Companies_listed_on_the_Romanian_Stock_Exchange (accessed on 20 March 2021). Schuchter, Alexander, and Michael Levi. 2013. The Fraud Triangle revisited. Security Journal 29: 107–21. [CrossRef] Svabova, Lucia, Katarina Kramarova, Jan Chutka, and Lenka Strakova. 2020. Detecting earnings manipulation and fraudulent financial reporting in Slovakia. Oeconomia Copernicana 11: 485–508. [CrossRef] Vladu, Alina Beattrice, Oriol Amat, and Dan Dacian Cuzdriorean. 2016. Truthfulness in Accounting: How to Discriminate Accounting Manipulators from Non-manipulators. Journal of Business Ethics 140: 633–48. [CrossRef]