Financial distress prediction for portuguese SMEs

Roxana Sera Financial Distress Prediction forPortuguese SMEsOctober 2020 Uminho | 2020Roxana SeraFinancial Distress Prediction for Portuguese SMEs Universidade do MinhoEscola de Economia e Gestão Master Degree ProjectMaster in Finance Supervisor:Florinda Conceição Cerejeira Campos da Silva, PhDUniversidade do MinhoEscola de Economia e GestãoRoxana Sera Financial Distress Prediction forPortuguese SMEsOctober 2020 ii DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial-SemDerivações CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/ iii Acknowledgments I would like to thank all of those who have made possible the completion of this study. I would like to thank my advisor, Professor Florinda Silva, for always being open and eager to share her knowledge with a lot of patience and good disposition. I would also like to thank Professor Sónia Silva for her invaluable comments; allowing me to share her passion for econometrics helped increase mine. My gratitude also goes to nBanks company, for making this project possible and always being there for support. Heartfelt thanks also go to Mr. José Fernandes with additional tribute to his late wife Mrs. Alice Cracel Fernandes, who will always live in our hearts, for their enormous help and constant encouragements. In addition, I must express my very profound gratitude to my parents, Vasile and Valeria, to my spouse Mizuaki, and to my children Alexia and Ivan for providing me with unfailing support and love. You are always there for me. Finally, I thank all my family and friends for their continuous support and sympathetic ear. iv STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. v Resumo Em Portugal, as Pequenas e Médias Empresas (PMEs) representam 99.9% do número total de empresas e são um fator chave para a geração de emprego, com uma contribuição elevada para a economia geral do país. Considerando o papel estratégico desempenhado e o fato de que a maior fonte de recursos para as PMEs são as instituições financeiras, é fundamental que essas tenham tanto facilidade de acesso à instrumentos financeiros diversificados, quanto a possibilidade de apresentar a sua atividade e resultados obtidos de uma maneira adequada que lhes garante acesso a esses instrumentos. Nesse contexto, a aplicação de um modelo de previsão de insolvência baseado na análise de rácios financeiros é uma maneira de interpretar a informação disponível sobre uma empresa de uma forma clara, concisa e eficiente. A análise facilitada por tal instrumento beneficia tanto as instituições financeiras, que podem interpretar os resultados obtidos para melhor entender a situação geral da empresa, quanto os gestores da empresa, para quais facilita a detecção e prevenção de eventuais problemas financeiros. O objetivo deste estudo é identificar os principais rácios financeiros relevantes para distinguir entre empresas em dificuldades financeiras e empresas saudáveis, estimar com base neles um modelo de previsão de insolvência e utilizar os parámetros estimados para previsão de dificuldades financeiras nas PMEs portuguesas. Para obter uma amostra mais equilibrada de empresas foi aplicado o método Propensity Score Matching, com pareamentos de um-para-um e um-para-muitos. O modelo foi estimado com base nos dados financeiros de empresas insolventes de um ano antes da insolvência. Testes de validação foram feitos em amostras de um, dois e três anos antes da insolvência, amostra de um a três anos antes da falência, bem como no inteiro conjunto de empresas com dados disponíveis, até seis anos antes da insolvência. As cinco variáveis que mostraram melhor capacidade de previsão da insolvência são: Ativo Corrente/ Total do Ativo, Fluxo de Caixa Operacional/ Total do Ativo, Fluxo de Caixa Operacional/ Total do Ativo, Resultados Transitados/ Total do Ativo e Patrimônio Líquido/ Total do Passivo. A capacidade total preditiva do modelo é acima de 85%, o que leva à conclusão de que o modelo pode ser aplicado ao mercado Português, no contexto das PMEs. Palavras-chave: Insolvência, Rácios Financeiros, Modelo de Previsão de Dificuldade Financeira, Modelos Logísticos, Propensity Score Matching, Pequenas e Médias Empresas vi Abstract In Portugal, small and medium-sized enterprises (SMEs) represent 99.9% of the total number of companies and are key generators of employment and contributors to the country`s economy. Given their key role and the fact that their main source of funding comes from financial institutions, it is vital that they have easy access to diversified financing instruments as well as the capacity of presenting their activity and results in an efficient way in order to gain access to them. In this context, a way of interpreting the information available about a company in a clear, concise and efficient manner is through the application of an accounting - based financial distress model. The analysis provided by such an instrument is beneficial to both financial institutions, that can use the results in order to understand the general situation of the company, and to the company`s management, who can foresee and prevent eventual financial problems. The objective of this study is to identify the main financial ratios that are relevant in order to discriminate between financially distressed and healthy companies and estimate financial distress prediction models based on them then use the estimated parameters to predict the probability of financial distress in Portuguese SMEs. In order to obtain a more balanced data set of companies the propensity score method, with matching of one-to-one as well as one-to-many, was applied. The model estimation was made with insolvent companies` data from one year prior to insolvency. Validation tests were performed on data samples for one, two and three years before insolvency, as well as for years one to three in a joint data set and also for the entire set of insolvent companies available, up to six years prior to insolvency. The five variables found to be the best predictors of insolvency are Current Assets to Total Assets, Operating Cash Flow to Total Assets, Operating Cash Flow to Debt, Retained Earnings to Total Assets and Equity to Debt. The overall forecasting accuracy of the final model was of over 85%, by which we conclude that the model could be successfully applied to the Portuguese market, in the context of the SMEs. Keywords: Insolvency, Financial Ratios, Financial Distress Prediction Model, Propensity Score Matching, Logistic Models, Small and Medium-sized Enterprises vii Table of Contents Resumo.............................................................................................................................................. iv Abstract.............................................................................................................................................. vi List of Abbreviations ......................................................................................................................... viii List of Tables ...................................................................................................................................... ix List of Figures ...................................................................................................................................... x 1 Introduction ............................................................................................................................... 1 2 Presentation of NBanks Company ............................................................................................... 4 3 Theoretical Framework ............................................................................................................... 6 3.1 SME Definition and Insolvency ............................................................................................. 6 3.1.1 SME Definition ............................................................................................................. 6 3.1.2 Insolvency ................................................................................................................... 6 3.2 Literature Review ................................................................................................................. 9 3.2.1 Univariate Models ........................................................................................................ 9 3.2.2 Multivariate Models .................................................................................................... 10 3.2.3 Linear Probability Models ........................................................................................... 14 3.2.4 Other Models ............................................................................................................. 16 4 Methodology and Data .............................................................................................................. 18 4.1 Objectives ......................................................................................................................... 18 4.2 Methodology and Variables ................................................................................................ 18 4.3 Data Set ............................................................................................................................ 20 4.4 Descriptive Statistics ......................................................................................................... 27 4.5 Ratio Selection .................................................................................................................. 33 5 Analysis and Discussion of Results ........................................................................................... 35 5.1 Considerations on Results for Project Hosting Company nBanks ........................................ 45 6 Conclusions ............................................................................................................................. 47 References ....................................................................................................................................... 49 Appendices ...................................................................................................................................... 53 4 2 Presentation of NBanks Company One important part of financial transactions is the evaluation of business performance. Financial institutions have demands that are not always easily met by businesses. In this context, fintech company nBanks aims to bridge up the gap between financial institutions and their customers, in this case SMEs from Portugal and other South European countries. The company started in officially in September of 2018 and offers products and services that penetrate and integrate areas of the financial system with the aim of changing the business landscape in the financial area. Some of the them are: - Consolidated information that comprises bank account details, transactions, business associates, administration functions, documents, etc., for easier and faster processing. This integration of all necessary information allows for faster processing and more precise analysis of company`s business performance and tax compliance and administration. This standardised processing of information is applied to all customer companies, thus creating patterns that enable a more efficient processing of this information and even getting on the brink of predicting possible future outcomes for each company. - Intelligent product search, which is a consolidated search engine that offers access to the descriptions of various financial products available on the market for the companies (such as short/ long-term loans, investments, leasing etc.), enabling the company to select the best product, contact the respective financial institution and start negotiations. - Platform integration with IRB – Índice de Risco Bancário (Bank Risk Index), where customer companiescan make a simulation of the way financial institutions evaluate their business performance based on financial statement information. - Communication hub available for interaction between the company and its accounting services, which makes possible real-time access to business partners and transactions information, eliminating the time lag needed for e-mail and other such communication that many times delays the accounting processing. Communication system with the banks, through which the financial institutions can know more about a customer company that is willing to acquire a certain financial product. For example, the bank can have access to the IRB – Bank Risk Index - and thus better understand at a glance the profile of the company, which makes the whole process faster. This helps both parties to save time and offers to the bank a more 5 independent evaluation of the customer company, once this evaluation is not done by the company itself but by nBanks. In this context, the estimation a financial distress prediction model based on recent data and on the reality of Portuguese SMEs would provide an useful tool for nBanks to apply in practice in order to attend the necessities of their customer companies. 6 3 Theoretical Framework 3.1 SME Definition and Insolvency 3.1.1 SME Definition A SME, as defined by the Decree-Law 81/2017 issued by the Portuguese Government, in accordance with the European Union Commission Recommendation 2003/361 of 6 May 20031, definition also adopted by the Portuguese Institute of Support to Small and Medium-sized Enterprises and Innovation (IAPMEI), is an enterprise that employs fewer than 250 persons, has an annual turnover not exceeding EUR 50 million and/or an annual balance sheet total not exceeding EUR 43 million. 3.1.2 Insolvency In research and in practice alike it is difficult to define insolvency and what exactly separates it from bankruptcy and many definitions of default or financial failure also exist. As mentioned by Ohlson (1980, p. 111), “there is no consensus on what constitutes `failure`”. Armour (2001, p. 3), starting from the commonly accepted sense of the word “ insolvency ” which is an inability to pay creditors, tries to establish a distinction between six different meanings of this term which are: the accounting concept of balance sheet insolvency , cash flow insolvency (or “financial distress”), economic failure (or “economic distress”), and the judicial concepts of liquidation , reorganisation and insolvency proceedings (or “bankruptcy”). The distinctions are specified by Armour (2001) as follows. Balance sheet insolvency means that the book value of its assets is exceeded by that of its liabilities. Cash flow insolvency means a firm is unable to pay its obligations as scheduled. The expression “financial distress” is commonly used to refer to a company which has difficulty in paying its creditors, while “economic distress” alludes to a lack of economic viability. The last is related to financial distress by the fact that “all firms which are economically distressed will also become financially distressed” (Armour, 2001, p. 4). The term liquidation refers to one of the possible outcomes of financial distress and means “the conversion into cash, through sale, of a firm`s assets” (Armour, 2001, p.4), and while it can also happen under administrative receivership, it is a necessary part of the closing proceedings. Insolvency is a condition, and liquidation is an event (Armour, 2001). 7 Altman (1983) sums the generic terms which refer to unsuccessful business enterprises to three: failure , insolvency and bankruptcy . Failure , “by economic criteria, means that the realized rate of return on invested capital (…) is significantly and continually lower than prevailing rates on similar investments.” (Altman, 1983, p. 6), but this does not imply the discontinuance of the entity. When the company can no longer meet the legally enforceable demands of its creditors it enters legal failure (although this may happen without formal legal action involved). Business failures (as also used by Dun & Bradstreet) include businesses that cease operation following bankruptcy or after loss to creditors after execution, foreclosure or attachment, that voluntarily compromise with creditors, or voluntarily withdraw leaving unpaid obligations. Insolvency is used technically to mean a lack of liquidity resulting in the firm not being able to meet its current obligations and indicates “a chronic rather than a temporary condition” (Altman, 1983, p. 6), and the real net worth of the firm is negative. Bankruptcy is described by Altman (1983) as being of two types: one in which the net worth of the firm is negative and another where there is a formal declaration of bankruptcy in court, together with a petition to either liquidate its assets or try recovery. Portugal`s Insolvency and Business Recovery Code (CIRE) regulates proceedings regarding insolvency and business recuperation processes. It states, in Article 3, that enterprises are considered in a state of insolvency when the book value of its liabilities surpasses the book value of its assets. It also states, in Article 7, that insolvency is not the same thing as bankruptcy since the impossibility of paying as scheduled does not automatically imply that the company is no longer economically viable or that it cannot recover from a financial point of view. This project, due to data availability, will abide by the definitions provided by the database from which the data were sourced, AMADEUS. Company status definitions are as follows. Active = the company is active. The control group companies used in this study belong to this category. Active (insolvency proceedings) – the company is declared insolvent and although remaining active it is in administration or receivership or under a scheme of arrangement, placed under the protection of the law and continues operating and repaying creditors and tries to reorganise and return to normal operating. At the end, the company will either return to normal operating or will be reorganized or will be 8 liquidated. The insolvent companies used in this study only include companies from this group that did not return to normal operating and were finally characterised as “in liquidation” at the end of the process. In liquidation = the company is in the process of liquidation and its assets are being sold. The next step will be that the company is dissolved and will no longer exist. In some cases the need for liquidation proceedings stems from the need of self-addressing creditor problems, since when an insolvent`s assets are insufficient to meet the claims of all creditors it will be in the creditor`s best interest to try and recover its claim before other creditors can do the same. The insolvency of a company has various causes. Table 1 presents some of the elements that may result in a state of insolvency, which can be divided into internal and external causes. Internal causes are related to the management of the company, such as liquidity problems, poor management, lack of quality of the product, fraud, among others. Liquidity problems due to lack of finance are closely related to the subject of this study since many SMEs face this type of problem, and this project is part of the nBanks company attempts to help with this issue by making easier for their SMEs customers to adequately present their situation to financial institutions in order to obtain the necessary funds. External causes are macroeconomic situations brought on by the environment outside the company, among which are harsher competition, economic situation difficulties, bad debt, natural disaster and so on (Kucher, Mayr, Mitter, Duller & Feldbauer-Durstmuller, 2018). Table 1: Causes of Insolvency Liquidity problems due to lack of finance Poor business-economic competences Unqualified management High cost pressure Poor quality of goods or services Conflicts between managers or owners Fraud External causes Competition increase, price fights Economic slowdown Bad debt Natural disasters Source: adapted from Kucher et al. (2018) Internal causes 9 3.2 Literature Review There is a vast literature on default prediction. Over time there have been developed several financial distress prediction models, employing different techniques. These models aim to predict the likelihood of business failure of firms, based on a selection of most relevant financial ratios that reflect the companies` financial health and probability of default. 3.2.1 Univariate Models First statistical models used univariate analysis for selected ratios, with notable contributions from Beaver, who introduced a technique that permitted classification of firms into healthy and failing, by using “financial ratios as predictors of important events – one of which is the failure of the firm” (Beaver, 1966, p. 72). Univariate models are based on the analysis of the financial ratios in isolation and comparing their values between financially distressed companies and healthy ones, in order to differentiate them. The sample used by Beaver (1966) comprised of 79 failed companies and 79 non-failed ones, with financial statements of the failed companies obtained for five years prior to failure. The data set extended between the years 1954 to 1964, 10 years. For analysis were tested 30 ratios, divided into 6 categories. From each of these categories the ratio with the highest discriminating power was selected, with the following results: - Cash flow to total debt; - Net income to total assets; - Total debt to total assets; - Working capital to total assets; - Current ratio; - No-credit interval. The ratios for the companies were classified in ascending order and an optimal cutoff point was set for each given ratio, in order to minimise incorrect predictions, then the percentage of misclassification was calculated. Beaver`s conclusion was that the strongest ability to predict failure was in the Cash Flow to Total Debt ratio, with failures of only 13% in the first year and 22% in the fifth. As further development, Beaver suggested a multi-ratio analysis that “would predict even better than the single ratios” (Beaver, 1966, p.100). 10 3.2.2 Multivariate Models Default risk forecasting models thus evolved to multivariate studies, the most notable being the study by Altman (1968), in which an Multiple Discriminant Analysis (MDA) model, called the Z-Score model, was developed. MDA is “a statistical technique used to classify an observation into one of several a priori groups, dependent on the observation`s individual characteristics (…), data are collected for the objects in the groups; MDA then attempts to derive a linear combination of these characteristics which `best` discriminates between groups” (Altman, 1968, pp. 591-592). The original Z-Score model is a model aiming to forecast bankruptcy of manufacturing firms, which was developed on a sample of 66 United States companies divided into two groups of 33 failed and 33 nonfailed firms, using the estimation of a linear combination of five variables, with the final discriminant function being as follows: 𝑍 = 1.2 ∙ 𝑋+ 1.4 ∙ 𝑋+ 3.3 ∙ 𝑋+ 0.6 ∙ 𝑋+ 1.0 ∙ 𝑋 where 𝑋= Working Capital/ Total Assets 𝑋= Retained Earnings/ Total Assets 𝑋= EBIT/ Total Assets 𝑋= Market Value of Equity/ Book Value of Total Liabilities 𝑋= Sales/ Total Assets X1 – Working Capital/Total Assets measures a company`s net liquid assets relative to total capitalisation. For company having consistent losses current assets will be diminishing in relation to its total assets, and this leads to a decreasing working capital. Altman concluded that this ratio was the most valuable of the liquidity ratios evaluated. X2 – Retained Earnings/Total Assets is a measure of cumulative profitability over time and implicitly reflects the age of the firm, since a relatively young firm would not have had the time to make this kind of reserve. 11 X3 – EBIT/Total Assets is a measure of the real productivity of the assets of a company, eliminating any tax or leverage effects. This ratio is important because insolvency happens when a company`s total liabilities exceed its total assets. X4 – Market Value of Equity/Book Value of Total Debt shows how much the company`s assets can decline in value before liabilities exceed assets and the company becomes insolvent. Altman found this ratio to be a more effective predictor than the more commonly used Net Worth/Total Debt ratio. X5 – Sales/Total Assets, the capital turnover ratio, illustrates the sales generating ability of the company`s assets and measures the capability of management to deal with competition. Even though this ratio presented a very low F value, in the final model it ranked second in discriminating ability due to its relationship to the other variables in the model. Table 2 presents the results of the F test. The higher the F ratio the better the predictive ability of the respective financial ratio. Table 2: Altman`s Z-Score Model - Variable Means and Test of Significance *significant at the .001 level The interpretation of the Z-score results is as follows: a) Z > 2.99 – safe zone (non-failed company); b) 1.80 < Z < 2.99 – grey zone (uncertainty); c) Z < 1.80 – danger zone (failed company). Variable Bankrupt Group Mean Non-Bankrupt Group Mean F Ratio n = 33 n = 33 X1 -6.1% 41.4% 32.6* X2 -62.6% 35.5% 58.86* X3 -31.8% 15.3% 26.56* X4 40.1% 247.7% 33.26* X5 150.0% 190.0% 2.84 Source: Adapted from Altman (1968) 12 Table 3 shows the predictive accuracy of Altman`s initial model. Table 3: Altman`s Z-Score Model Predictive Accuracy Altman, Haldeman and Narayan (1977) developed a new model based on the Z-Score, called the ZETA model, in collaboration with Zeta Services Inc., due to which the final formula is not publicly available. This new model was adapted to the new reality that included large companies. The data set used was comprised of 53 insolvent and 58 healthy U.S. companies, from years between 1969 and 1975, and started with 27 variables. The final ratios included in the model are: - X1 – EBIT/Total Assets; - X2 – Standard error of estimate around a ten-year trend in X1; - X3 – log (EBIT/Total interest payments); - X4 – Retained Earnings/Total Assets; - X5 – Current Assets/Current Liabilities; - X6 – Common Equity/Total Capital; - X7 – log (Total Assets). The predictive capacity of this model surpassed that of the original Z-Score, with 90% hit rate for one year prior to insolvency and about 70% up to five years ahead of insolvency. The discrimination of companies into the categories of insolvent or healthy is subject to two types of errors: - Type I error is classifying an insolvent company as healthy. This is considered the costliest error, since this means that the model does not predict insolvency. Any investment based on this misclassification will be lost; - Type II error is classifying a healthy company as insolvent. This misclassification would cause a missed investment opportunity and the loss implied would be only of the possible gains not received. Years prior to insolvency Number of Observations Hits Misses Predictive accuracy 1 33 31 2 95% 2 32 23 9 72% 3 29 14 15 48% 4 28 8 20 29% 5 25 9 16 36% Source: Adapted from Altman (1968) 13 Accordingly, minimising Type I error is the most important, since this kind of misclassification is the most financially prejudicial. Altman also developed extensions of the original Z-Score model, which was originally developed for U. S. publicly traded firms, based on market data. The extensions developed are the Z`-Score model adapted for private companies, which also has five variables, and the 𝑍`` Score model, with four variables, adapted for non-manufacturers and emerging markets (Altman, 2002; Altman, Iwanicz-Drozdowska, Laitinen and Suvas, 2017). 𝑍`= 0.717 ∙ 𝑋+ 0.847 ∙ 𝑋+ 3.107 ∙ 𝑋+ 0.420 ∙ 𝑋+ 0.998 ∙ 𝑋 where 𝑋= Book Value of Equity/ Book Value of Total Liabilities and other variables the same as those in the original. The new model estimation had a small change in the cutoff value so that the interpretation of this new score is as follows: a) Z > 2.90 – safe zone (non-failed company); b) 1.23 < Z < 2.90 – grey zone (uncertainty); c) Z < 1.23 – danger zone (failed company). 𝑍`` = 3.25 + 6.56 ∙ 𝑋+ 3.26 ∙ 𝑋+ 6.72 ∙ 𝑋+ 1.05 ∙ 𝑋 The interpretation of the 𝑍``Score model is as follows: a) Z ≥ 1.10 – safe zone (non-failed company); b) Z < 1.10 – distressed condition. Altman further enhanced and improved this model, with re-estimations also considering Basel II1 environment (Altman, 2002). In an international context, Altman et al. (2017) analysed the performance of the 𝑍``Score model using a sample of firms from 31 European and three non-European countries, for private and public, 1 Basel II is a set of international regulations by the Basel Committee on Bank Supervision which introduced capital requirements for financial institutions, such as the minimum capital to be maintained in a percentage based on risk-weighted assets (see Basel, 2001). 20 to generate internal funds (Canovas & Solano, 2006). Leverage ratios are widely analysed as classic indicators of financial risk, high values increasing the probability of default (Lacerda & Moro, 2008). Activity ratios measure the effectiveness with which an asset contributes to the profitability of investment in that asset category (Butera & Faff, 2006). For each ratio category we have selected a number of financial ratios among those found relevant in most studies, as presented in Table 5, and we tested the various ratios in order to select those most potentially able to integrate the estimated model. In total, 19 ratios were selected. Table 5: Initial Ratios 4.3 Data Set Historical accounting and financial data is collected from AMADEUS, a database published by Bureau van Dijk /Moody`s Analytics, which contains financial and business information on over 21 million European companies, providing standardised annual accounts, financial ratios, sectoral activities and ownership data, with up to ten years archive. This study uses a data set for Portuguese SMEs for the last ten years available, between 2010 and 2018. X1 Current Ratio Current Assets / Current Liabilities X2 Working Capital to Total Assets Working Capital / Total Assets X3 Quick Ratio (Cash + Accounts Receivable) / Current Liabilities X4 Cash Ratio Cash / Current Liabilities X5 Current Assets to Total Assets Current Assets / Total Assets X6 EBIT to Total Assets EBIT / Total Assets X7 Operating Cash Flow to Total Assets Cash Flow / Total Assets X8 Operating Profit Margin EBIT / Operating Revenue X9 ROA Net Income / Total Assets X10 Debt to Equity Total Liabilities / Shareholders` Funds X11 Debt to EBITDA Total Liabilities / EBITDA X12 Operating Cash Flow to Debt Cash Flow / Total Liabilities X13 Retained Earnings to Total Assets (Other Shareholders`Funds + Net Income) / Total Assets X14 Debt to Asset Total Liabilities / Total Assets Solvency X15 Interest Coverage EBIT / Interest Paid X16 EBITDA to Interest Coverage EBITDA / Interest Paid X17 Equity to Debt Shareholders`Funds / Total Liabilities Activity X18 Total Assets Turnover Operating Revenue / Total Assets X19 Working Capital Turnover Operating Revenue / Working Capital Liquidity Profitability Leverage Source: Author 21 As previously stated, the financially distressed group consists of companies with the following statuses, standardized by AMADEUS: “ In liquidation” - which means the end of the firm`s activity. This category in AMADEUS includes voluntary liquidation and dissolution but there is no indication in the database to distinguish between voluntary and compulsory. “ Active (insolvency proceedings)” – from this category only companies that did not return to normal operating status and were subsequently characterized as “ in liquidation ” were selected. The control group comprises companies registered in AMADEUS as “ Active ”. From this first sample we selected only the SMEs from Portugal that comply with the following criteria: - Companies from all activity sectors except activity codes NACE 64, 65, 66, 68, corresponding to financial and real estate activities; - Unlisted companies. This initial sample comprised 281,925 Portuguese enterprises, out of which 5,479 insolvent and 276,446 active companies. Subsequently the following filters were applied, in order to select only: - Companies with year of incorporation up to and including 2016, thus ensuring a minimum of three years of activity, since during the first years of their lives young and healthy companies often show a financial structure similar to failing companies (du Jardin, 2010); - Companies with all the accounting information needed to calculate all 19 ratios considered in the first selection of independent variables for the model; - Companies attending criteria for SMEs: less than 250 employees, and less than 50 million EUR turnover/or less than 43 million EUR total assets; - In order to eliminate the very small firms, since those tend to present gaps and potential distorted values, we also eliminated companies with less than 100,000 EUR total assets (Altman, 2017, Balcaen and Ooghe, 2006); - Finally, the data were winsorized at the 1% and 99% levels to eliminate outliers. 22 After this second selection, the dataset comprises 65,997 companies, out of which 1,504 insolvent and 64,493 active companies. Table 6 shows the distribution of the insolvent companies by year of insolvency. Table 6: Distribution of Insolvent Companies by Year of Insolvency In face of this final sample being quite disproportional considering the number of insolvent and active companies a method was needed in order to obtain a more balanced/ homogenous sample. In order to do so this study applied the propensity score matching method (PSM), where “matching is a method of sampling from a large reservoir of potential controls to produce a control group of modest size in which the distribution of covariates is similar to the distribution in the treated group.” (Rosenbaum & Rubin, 1983, p. 48). This matching technique was developed by Rosenbaum and Rubin (1983), and its purpose is to find, for every individual in the treatment group (in our case, the insolvent companies), a statistical twin that possesses similar characteristics in the non-treated/ control group (in our case, the active companies), so that the sample can be considered randomly selected and direct comparisons be more meaningful. This is important because if the individuals of the treatment and the control group are not randomly selected the sample runs the risk of suffering from selection bias. The common support condition makes sure that the propensity scores of both groups overlap and all participants have a counterpart in the control group, which means that only firms that are sufficiently alike each other are matched. The covariates for the matching are assumed as not affected by the treatment, either pre or post treatment. The covariates used in this study are industry (NACE level 2 - division), the year of the financial statement (which in case of the insolvent companies is one year prior to insolvency) and size, for which Insolvency Year Companies 2014 68 2015 171 2016 221 2017 326 2018 336 2019 382 Total 1,504 Source: Author 23 the logarithm of total assets was used as proxy, to control for the size effect and allow comparisons of ratios (du Jardin, 2010). We performed PSM selecting the nearest neighbour with replacement, which allows for a control firm to be used more than once as a match. This helps to decrease bias since control firms similar to several treated firms can be used multiple times as needed. In order to ensure a better matching quality, we have set the maximum permitted difference between matched individuals (caliper) to 0.25 of the propensity score standard deviation, following Cochran and Rubin (2004). This also reduces the number of matches that can be performed, but it does not negatively affect this study due to the large size of the data set available. The first step in PSM is calculating the propensity score, in order to assign to each insolvent company a similar active one. For this the sample is split into five sets of intervals and tested separately to asses if the balancing properties are satisfied, which means that there are no significant statistical differences between the two groups regarding the distribution of covariates (Dehejia & Wahba, 1999). The propensity score is then calculated by a probit model: 𝑝𝑟𝑜𝑏(𝐷= 1) = 𝛼+ 𝜑𝑍; + 𝜀 where 𝐷 is a dummy variable with the value of 1 if the company is insolvent and 0 otherwise and 𝑍 the set of control variables. The one-to-one propensity score matching selects for each distressed company an active company with the nearest distance to the distressed one as indicated by the propensity score. The financial variables used for the estimation of the model, for the insolvent companies, are those from the year prior to insolvency (N-1). Appendix 1 shows the kernel density plot of the propensity score. In order to mitigate for the limitation of the propensity score matching procedure, besides one-to-one matching we also used another criterion which is one-to-many matching and performed the below tests on these matched data sets as well. The one-to-many PSM selects a specified number of active companies within the nearest distance to the insolvent one, the maximum distance (caliper) being fixed at 25% of the standard deviation of the propensity score, computed following Cochran and Rubin (2004). In this study we performed two selections: one-to-five (1 to 5) which matches 1 insolvent company to 5 active ones, and one-to-ten (1 to 10), which matches 1 insolvent company to 10 active ones. The performance of the model obtained from the 1 to 5 matching was very similar to that obtained from the 1 to 10 matching. 24 Since the results from the 1 to 10 matching data set were slightly better, this study will focus on reporting these. After the propensity score matching, the difference between the means of the proxy used for size (logarithm of Total Assets) between active and insolvent companies is reduced and no longer statistically significant, which proves that the matching was successful, as shown in Table 7. Appendix 2 shows the results for PSM 1 to 5 matched data set. Table 7: Model Estimation Data Sets - Difference in Means After PSM 1 to 1 and 1 to 10 Since the PSM method used was selecting the nearest neighbour with replacement, some of the active companies were used more than once, thus matching 1 to 1 returned 288 active companies with 289 observations, and matching 1 to 10, 2,108 active companies with 2,171 observations. Table 8 shows the composition of the data sets, in terms of number of companies and number of observations, before and after PSM 1 to 1 and PSM 1 to 10. Appendix 3 shows the composition of the data set after PSM 1 to 5. Table 8: Data Sets Composition Before and After PSM 1 to 1 and PSM 1 to 10 Table 9 shows the distribution of the matched data sets PSM 1 to 1 and PSM 1 to 10 by year. Appendix 4 shows the distribution of the PSM 1 to 5 data set by year. Treated Control t p>|t| Unmatched 13.757 13.37 29.2 5.29 0.000 Matched 1 to 1 13.757 13.697 4.5 0.54 0.589 Matched 1 to 10 13.757 13.728 2.2 0.26 0.795 Source: Author t-testMean Log (Total Assets) SampleVariable %bias Before PSM Insolvent Active Companies 1,504 64,493 Observations 3,282 235,711 After PSM 1 to 1 Insolvent Active Companies 289 288 Observations 289 289 After PSM 1 to 10 Insolvent Active Companies 289 2,108 Observations 289 2,171 Source: Author 25 Table 9: Model Estimation Data Sets - Number of Observations by Year of Financial Statement This table presents the number of observations by year of financial statement. Column Year represents the year of the financial statement. Columnt Insolvent represents the number of observations for insolvent companies at one year prior to insolvency. PSM 1 to 1 represents the number of observations for active companies matched to the insolvent by PSM 1 to 1. PSM 1 to 10 represents the number of observations for active companies matched to the insolvent by PSM 1 to 10. Table 10 shows the distribution of the matched data set by region of Portugal – NUTS II2. Insolvent companies are concentrated mainly in the North region and in Lisbon Metropolitan Area, with these two regions together with Central region accounting for over 85% of the insolvent companies (see Figure 1), which is representative of the distribution of all companies (active or not) over these regions, which is of 84%. Appendix 5 shows the distribution of the PSM 1 to 5 matched data set by region of Portugal. 2 Nomenclature of territorial units for statistics (NUTS) is a common statistical classification of territorial units for harmonised regional statistics in the European Union (EU). NUTS classification divides each Member State of EU into NUTS level I territorial units, each of which is subdivided into level II units, these again subdivided into level III units (Regulation EC 1059, 2003). Year Insolvent PSM 1 to 1 PSM 1 to 10 2013 34 62 449 2014 27 27 189 2015 48 21 220 2016 60 46 354 2017 69 67 463 2018 51 66 496 Total 289 289 2,171 Source: Author 26 Table 10: Model Estimation Data Sets - Distribution by Region This table presents the distribution of the model estimations data sets by region. Insolvent represents the number of insolvent companies per region, PSM 1 to 1 and PSM 1 to 10 represent the number of matching active companies selected by these respective methods, by region. Figure 1: Distribution of Insolvent Companies by Region According to EUROSTAT – NACE Rev. 23 statistical classification of economic activities in the European Community, the companies in the data set analysed belong to mainly the following activity divisions: G – Wholesale and retail trade; repair of motor vehicles and motorcycles, C – Manufacturing, F – Construction. 3 NACE is the statistical classification of economic activities in the European Community. It consists of a hierarchical structure that contains a first level with sections identified by an alphabetical code (sections), a second level identified by a two-digit numerical code (divisions) and two more levels identifying groups and classes (Regulation (EC) 1893, 2006). In this study we use only the first two levels, sections and divisions, for identification. Region-NUTS II Insolvent PSM 1 to 1 PSM 1 to 10 PT11 - North 117 100 933 PT17 - Area Metropolitana de Lisboa 69 66 437 PT16 - Centro 61 72 536 PT18 - Alentejo 16 31 110 PT15 - Algarve 13 11 86 PT20 - Regiao Autonoma dos Acores 11 3 40 PT30 - Regiao Autonoma da Madeira 2 5 29 TOTAL 289 288 2,171 Source: Author 40% 24% 21% 6% 4% 4% 1% Insolvent Companies % by Region of Portugal PT11 - North PT17 - Area Metropolitana de Lisboa PT16 - Centro PT18 - Alentejo PT15 - Algarve PT20 - Regiao Autonoma dos Acores PT30 - Regiao Autonoma da Madeira Source: Author 27 These divisions represent over 80% of the insolvent companies. The distribution of insolvent companies per division/sections of activity is presented in Table 11. Table 11: Distribution of Insolvent Companies by Division and Section of Activity Concerning size, most of the SMEs of Portugal belongs to the micro category, with fewer than 10 employees. Micro and small enterprise categories account for around 90% of the insolvent as well as of the active companies. The distribution is shown in Table 12. Table 12: Distribution of Portuguese SMEs by Size 4.4 Descriptive Statistics Insolvent companies present lower liquidity and profitability ratios, as expected. For these companies, the ratios that have EBIT/ Operating Cash Flow/ Net Income as numerator are all negative. In terms of leverage, the Operating Cash Flow to Debt ratio, which measures creditworthiness, is high for active companies and has negative/ close to zero values for the insolvent group, while the Retained Earnings to Total Assets ratio is also negative for the insolvent companies. Total Liabilities to Total Assets ratio is higher for the insolvent companies, also as expected. As for solvency, interest coverage ratios are much NACE Rev.2 - Division Insolvent Companies % GWholesale and retail trade; repair of motor vehicles and motorcycles (45-47) 114 39% CManufacturing (10-33) 69 24% F-Construction (41-43) 54 19% H-Transportation and storage (49) 15 5% IAccommodation and food service activities (55-56) 9 3% J-Information and communication (58-63) 7 2% M-Professional, scientific and technical activities (69-75) 6 2% Others 15 5% TOTAL 289 100% Source: Author Company Size Insolvent Insolvent % Active Active % Micro (<10 employees) 137 47% 156 54% Small (<50 employees) 121 42% 106 37% Medium-sized (<250 employees) 31 11% 26 9% Total 289 100% 288 100% Source: Author 28 higher for the active companies showing better capability to meet its interest obligations from operating earnings. Table 13 shows the descriptive statistics of the initial ratios considered, for the data set after PSM 1 to 1. Appendix 6 presents the descriptive statistics for the data set without PSM. Appendices 7 and 8 show the descriptive statistics for the data set after PSM 1 to 5 and PSM 1 to 10, respectively. Table 13: Descriptive Statistics – After PSM 1 to 1 This table presents the number of observations, mean, standard deviation and median for the variables based on the sample composed of insolvent companies with data from one year prior to insolvency, and active companies matched to the insolvent by PSM 1 to 1. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. In order to see if here is a significant difference between the two groups, a t-test was applied to verify the hypothesis that the means of the independent variables (financial ratios) are not equal. Table 14 shows the results of the t-test, associated p-values and the difference between means (active minus insolvent) for the PSM 1 to 1 matched groups. Appendix 9 shows the results of the same tests applied to the data set before PSM and Appendix 10, the same for the data set PSM 1 to 5 matched groups. Obs Mean St. Dev. Median Obs Mean St. Dev. Median X1 289 3.815 6.751 1.873 289 1.686 3.003 1.013 X2 289 0.245 0.283 0.187 289 0.119 0.392 0.127 X3 289 1.868 3.343 0.943 289 0.630 0.755 0.402 X4 289 0.772 1.922 0.198 289 0.109 0.230 0.030 X5 289 0.661 0.274 0.719 289 0.682 0.266 0.754 X6 289 0.035 0.108 0.030 289 -0.172 0.305 -0.077 X7 289 0.050 0.112 0.042 289 -0.163 0.301 -0.069 X8 289 0.025 0.197 0.034 289 -0.373 0.896 -0.130 X9 289 0.015 0.100 0.014 289 -0.198 0.320 -0.096 X10 289 2.031 9.754 1.685 289 0.666 42.876 -1.450 X11 289 9.785 19.924 6.930 289 0.070 74.338 -5.347 X12 289 0.135 0.288 0.067 289 -0.117 0.192 -0.061 X13 289 0.247 0.350 0.231 289 -0.693 1.344 -0.259 X14 289 0.656 0.281 0.686 289 1.272 0.851 1.022 X15 289 108.109 648.462 4.107 289 -58.890 263.256 -5.126 X16 289 137.105 743.307 8.421 289 -28.404 112.377 -3.334 X17 289 1.047 1.595 0.459 289 -0.004 0.446 -0.021 X18 289 1.130 1.153 0.880 289 0.904 0.859 0.715 X19 289 0.425 55.267 2.945 289 -3.097 36.934 0.832 Ratios Source: Author Active Companies Insolvent Companies 29 The results shown in Table 14 show that the differences between the means of the two groups are statistically significant at the 1% level for all ratios except for the Total Liabilities to EBITDA ratio, which is significant at the 5% level, and the Total Liabilities to Shareholders` Funds and Net Income to Working Capital ratios, for which the difference in the means of the two groups is not statistically significant. Table 14: Test of Equality of Means Between Active and Insolvent Companies – After PSM 1 to 1 This table presents the test of equality of means (active minus insolvent) between the insolvent companies with data from one year prior to insolvency, and the active companies matched to the insolvent by PSM 1 to 1. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. *** p<0.01, ** p<0.05, * p<0.1 Table 15 presents the results for the PSM 1 to 10 matched groups. In this case the differences between the means of the two groups of companies are statistically significant at the 1% level for all ratios except for the Debt to Equity ratio, which is significant at the 10% level. Ratios Difference between means t value Pr(|T| > |t|) X1 2.128 4.897 0,000*** X2 0.126 4.437 0,000*** X3 1.238 6.139 0,000*** X4 0.662 5.818 0,000*** X5 -0.021 -0.922 0,357 X6 0.207 10.886 0,000*** X7 0.213 11.287 0,000*** X8 0.398 7.370 0,000*** X9 0.213 10.805 0,000*** X10 1.365 0.528 0.598 X11 9.715 2.146 0.032** X12 0.252 12.354 0,000*** X13 0.940 11.501 0,000*** X14 -0.616 -11.694 0,000*** X15 166.999 4.057 0,000*** X16 165.508 3.743 0,000*** X17 1.050 10.780 0,000*** X18 0.226 2.672 0.008*** X19 3.522 0.901 0.368 Source: Author 36 X17 = Equity to Debt. This ratio measures a company`s ability to meet its debt obligations by its shareholders` funds, and the higher the coverage the lower the probability of insolvency. Since shareholders` funds and debt are two sources of financing for a company, appealing more to debt than to shareholders` funds makes the company burdened with high interest expenses and other short-term liabilities. According to Altman (1968, p. 595), this ratio “shows how much the firm`s assets can decline in value (…) before the liabilities exceed the assets and the firm becomes insolvent”. Bellovary et al. (2007) did a comprehensive review of bankruptcy prediction studies published after 1930, and found the ratio Current Assets to Total Assets to have been used in 26 studies, Cash Flow to Total Assets in 15, Cash Flow to Total Liabilities, in 14, and Retained Earnings to Total Assets appears registered with greatest frequency being employed in 42 studies. For instance, Retained Earnings to Total Assets and Equity to Debt are two of the ratios that compose Altman`s Z Score (Altman, 1968, 1983, 2017), Cash Flow to Total Assets is one of the five ratios that compose the logistic model specific for SMEs developed by Altman and Sabato (2007). Table 18 presents the log odds coefficient estimates for logit Models 1 (estimated from the data set obtained by PSM 1 to 1) and 2 (estimated from the data set obtained by PSM 1 to 10) and the p-value associated with the z-statistic reported by the logit models. No industry dummies are included. For Model 1, all coefficients are statistically significant except X5 – Current Assets to Total Assets, which, on the other hand, is statistically significant in Model 2. In Model 2 all coefficients are statistically significant except for X13 – Retained Earnings to Total Assets. Nevertheless, substituting these ratios for correlated ones or eliminating them altogether resulted consistently in lower performance models. This could be explained by the fact that these ratios are important and add in discriminating power when combined with the other ratios present in the models. 37 Table 18: Coefficients Estimates for Model 1 and Model 2 This table contains the estimation results for the logit models .The dependent variable equals zero if the firm is not financially distressed and one otherwise. The column Model 1 contains the results of the estimation using the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1. The column Model 2 contains the results of the estimation using the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. X5, Current Assets to Total Assets; X7, Cash Flow to Total Assets; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X17, Equity to Debt. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 According to the LR-statistic, both models are significant at 1% which means they are appropriate for the study of financial distress prediction. We have also estimated two additional models, Model 3, estimated from a data sample composed of insolvent companies`data from one year prior to insolvency and active companies matched by PSM 1 to 5, and Model 4, estimated from a data sample composed of insolvent companies`data from one year prior to insolvency and a random selection of 80% of active companies` data from the same years as the insolvent companies (see appendix 23). Although Model 4, which includes the sample of insolvent companies and a control sample formed of a random selection of 80% of the active companies, presented a very high rate of accuracy, the results might be biased because of the extreme unbalance of the data set. Due to this, when using this model for validating the fit on the outof-sample test data sets, only a very small proportion of the insolvent companies can be correctly identified. Because we are trying to model failure, the expected signs of the variable coefficients are counterintuitive and thus we anticipate negative signs for the ratios whose high value means less probability of failure and vice-versa. Although negative values were expected for the coefficients of the ratios Current Assets to Total X5 0.379 4.511** (0.433) (1.972) X7 6.841*** -10.388*** (1.889) (1.985) X12 -12.285*** -0.005*** (2.188) (0.001) X13 -1.836*** -0.336 (0.538) (0.224) X17 -1.187*** -1.528*** (0.348) (0.274) Constant 0.035 -1.467*** (0.334) (0.105) Observations 578 2,474 Pseudo R-squared 0.417 0.312 Prob > chi2 0.000 0.000 VARIABLES Source: Author Model 2Model 1 38 Assets and Operating Cash Flow to Total Assets ratios, Model 1 shows positive values for these coefficients, and Model 2 shows a positive coefficient for the ratio Current Assets to Total Assets as well. This could be explained by the fact that, for Current Assets, the difference in the means of the two groups is very small and statistically nonsignificant. It could also be due to the fact that insolvent companies may have high levels of inventory or customers`due payments incorrectly recorded accounts. The positive coefficient of the ratio Operating Cash Flow to Total Assets in Model 1 could be explained by the fact that the sample contains companies from all business sectors of Portugal which can have very different Operating Cash Flow profiles, due to which this ratio may also reflect their business characteristics. Model 2 as well as Model 3 estimated from PSM 1 to 10 and PSM 1 to 5, respectively, show the expected sign for the coefficient of this ratio which may be due to a larger sample. In both Models 1 and 2, the ratios Operating Cash Flow to Total Assets and Shareholders` Equity to Total Liabilities are statistically significant, which indicates that these ratios are the better predictors. In Model 1, the ratio Retained Earnings to Total Assets is also statistically significant. The ratio Current Assets to Total Assets is also statistically significant in Model 2. Overall, the coefficients show that the ratio that has the best predictive power in both models is X7 - Operating Cash Flow to Total Assets ratio. This was found to be an important ratio also by Beaver (1966), who reported its significant relationship with the probability of insolvency, as well as by Vieira (2013). Following Agarwal and Taffler (2008) and Altman et al. (2017) among others, we assessed the classification performance of the models by the Area Under Curve (AUC) extracted from the ROC (Receiver Operating Characteristic) curve. If a model is incapable of discriminating between insolvent and active companies, the ROC curve will be a 45 degree line; the greater the predictive power of the model the more bowed the ROC curve will be (Charalambakis, E. C., Garrett, I., 2018). AUC is closely connected to the Accuracy Ratio (AR), since AR = 2 x AUC -1. The larger the AUC the better the model is at predicting financial distress. Figures 2 and 3 show the AUC for Models 1 and 2. For Model 1, AR = 79.50% and for model 2, AR = 76.22%, the accuracy of Model 1 being slightly better. 39 Figure 2: Area Under Curve – Model 1 (PSM 1 to 1) This figure shows the ROC curve and the Area Under Curve for Model 1 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1. Figure 3: Area Under Curve – Model 1 (PSM 1 to 10) This figure shows the ROC curve and the Area Under Curve for Model 2 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. We have applied goodness-of-fit (GOF) tests based on covariate patterns - Pearson`s Chi-square test, and based on estimated probabilities - Hosmer-Lemeshow test (Hosmer and Lemeshow, 1989). The results, presented in Tables 19 and 20, respectively, show a better fit of Model 1 with both tests showing no statistical significance for this model. 40 Table 19: GOF - Pearson`s Chi-square Test This table presents the results of Pearson`s Chi-square tests for for Model 1 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1 and for Model 2, estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. Table 20: GOF - Hosmer-Lemeshow Test This table presents the results of Pearson`s Chi-square tests for for Model 1 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1 and for Model 2, estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. Financial distress prediction models assess the ability to predict by counting the total errors, and there are two types of errors that occur when classifying companies, which are: Type I, which is to classify a financially distressed company as healthy, and Type II, which classifies a healthy company as financially distressed (Altman, 1968). A company is classified as financially distressed if its probability of default score is above the cutoff point, and as healthy if the score is below the cutoff point. According to Weiss (1996), Type I errors have the consequence of loss from lending to firms that end up as insolvent while type II errors incur the opportunity cost of not lending to firms that do not end up as insolvent but continue healthy. According to du Jardin (2010), most models correctly predict healthy firms at a rate higher than that at which they predict failing firms, and this is a common result in the financial literature regardless of the modelling technique. For those who may use the model as a decision tool, du Jardin (2010, p. 2051) finds that “the cost of having a failing company classified as healthy (Type I error) is far greater than the cost of a healthy company classified as failing (Type II error). A Type I error involves the loss of an investment or debt that will not be reimbursed as result of bankruptcy, while a Type II error involves the loss of a potential bargain. Thus, models should avoid above all Type I errors”. For example, Altman et al. (1977) find the cost for Type I errors is 70% of the amount lent while for Type Model 1 Observations 578 Covariate patterns 578 Pearson chi2 (572) 560.9 Pearson chi2 (2468) 2,751.33 Prob > chi2 0.622 Model 2 2,474 2,474 0.000 Source: Author Model 1 Model 2 Observations 578 2474 Groups 10 10 Hosmer-Lemeshow chi2 (8) 14.6 26.96 Prob > chi2 0.068 0.001 Source: Author 41 II errors is 2% of the amount that could have been lent, but this estimation does not take into account the size of the company or the loan amount. The results of predictive ability of Models 1 and 2 are tabulated at first on the basis of a cutoff point of .5. The output of the estimation of a logit model gives results in terms of sensitivity, which (in the terms of this study) is the probability that the test result will be positive for an insolvent company, a true positive rate, and specificity, which again in the terms of this study is the probability that the test result will be negative for a healthy company, a true negative rate. When a higher value of the cutoff is selected, false positives decrease, with increased specificity, but at the same time true positives and sensitivity decreases. When a lower cutoff value is chosen, true positives and sensitivity increase but at the detriment of true negatives and specificity which will decrease (Jackson & Wood, 2013). In order to account for the unbalance in insolvent and active companies in the data sets, another cutoff was estimated for each model, this time in order to minimize the sum of the errors. The sensitivity/specificity versus probability cutoff graphs, illustrating the optimal cutoff points at the crossing of sensitivity and specificity lines, are shown in Figure 4 for Model 1 and Figure 5 for Model 2. Figure 4: Model 1 (PSM 1 to 1) Estimation – Sensitivity and Specificity vs Probability Cutoff This figure presents the sensitivity line (positive result for an insolvent company, true positive) and the specificity line (negative result for a healthy company, true negative), and the encounter of these lines at the cutoff point, for Model 1 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1. 42 Figure 5: Model 2 (PSM 1 to 10) Estimation – Sensitivity and Specificity vs Probability Cutoff This figure presents the sensitivity line (positive result for an insolvent company, true positive) and the specificity line (negative result for a healthy company, true negative), and the encounter of these lines at the cutoff point, for Model 1 estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. The predictive accuracy of the two models is presented in Table 21. Table 21: Predictive Accuracy This table presents the predictive accuracy for Model 1, estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 1, and Model 2, estimated from the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 10. True Status Distressed Active MODEL 1 Distressed 82.01 17.99 Active 17.65 82.35 Cutoff = .5 Accuracy Distressed 79.93 20.07 Active 14.53 85.47 Cutoff = .521 Accuracy MODEL 2 Distressed 33.00 67.00 Active 2.03 97.97 Cutoff = .5 Accuracy Distressed 77.56 22.44 Active 14.00 86.00 Cutoff = .134 Accuracy 84.96 Source: Author 82.18 82.70 90.02 43 For model 1, the cutoff setting to minimise the sum of errors slightly increases the overall predictive ability of the model but increases the Type I error, therefore if using this model as a decision tool, keeping the cutoff of .5 might help to avoid the costs associated with this type of error. For Model 2, the optimal cutoff is the one that minimises the sum of errors and also greatly reduces the Type I error. This is due to the fact that the sample is unbalanced in the sense that the number of active companies is about 7 times larger (the PSM method was not able to find 10 counterparts for each of all the insolvent companies). After estimation, the models were tested on the following validation samples: for insolvent companies, data from year N-1 (one year before insolvency), year N-2 (two years before insolvency), year N-3 (three years before insolvency) and for N-1&2&3 = years one, two and three before insolvency, all together; for the corresponding active companies was used the total available sample, respecting the same years of financial data as the insolvent companies in each group. Another testing was done with all data available for insolvent companies, up to 6 years prior to insolvency, and active companies data from the same years. Table 22 presents the number of observations used for testing estimated models`forecast accuracy. Table 22: Number of Observations/ Companies Used for Testing Forecast Accuracy This table presents the composition of the data sets used for testing of the estimated models, Model 1 and Model 2. N-1 is a data set made up of insolvent companies`data one year prior to insolvency (same insolvent companies used for models estimation). N-2 contains insolvent companies`data from two years prior to insolvency and active companies`data from the same respective years. N-3 contains insolvent companies`data from three years prior to insolvency and active companies`data from the same respective years. N-1&2&3 contains insolvent companies`data from 1, 2 and 3 years prior to insolvency, all together, and active companies`data from the same respective years. N-1to6 contains all insolvent companies`data available for this study, up to 6 years prior to insolvency and active companies`data from the same respective years. N-1 , N-1&2&3 and N-1to6 all contain data for insolvent companies used for models estimation (for year N1, one year prior to insolvency). N-2 and N-3 are out-of-sample data sets. Period Distressed Active Distressed Active Distressed Active Distressed Active Distressed Active Observations 304 235,711 713 200,456 793 159,376 1,810 235,711 3,282 235,711 Companies 304 64,493 713 64,415 793 64,142 1,032 64,493 1,504 64,493 Years Source: Author N-1to6 2013-2018 N-1 N-2 N-3 N-1&2&3 2013-20182013-20162013-20172013-2018 Table 23 presents the forecast accuracy of Model 1 and Model 2, with both 0.5 cutoff and re-estimated cutoffs. Table 23: Forecast Accuracy for Models 1 and 2 (%) This table presents the composition of the data sets used for testing of the estimated models, Model 1 and Model 2. N-1 is a data set made up of insolvent companies`data one year prior to insolvency (same insolvent companies used for models estimation). N-2 contains insolvent companies`data from two years prior to insolvency and active companies`data from the same respective years. N-3 contains insolvent companies`data from three years prior to insolvency and active companies`data from the same respective years. N-1&2&3 contains insolvent companies`data from 1, 2 and 3 years prior to insolvency, all together, and active companies`data from the same respective years. N-1to6 contains all insolvent companies`data available for this study, up to 6 years prior to insolvency and active companies`data from the same respective years. N-1 , N-1&2&3 and N-1to6 all contain data for insolvent companies used for models estimation (for year N-1, one year prior to insolvency). N-2 and N-3 are out-of-sample data sets. True Status Distressed Active Distressed Active Distressed Active Distressed Active Distressed Active MODEL 1 Distressed 78.62 21.38 58.77 41.23 51.32 48.68 59.28 40.72 56.31 43.69 Active 19.53 80.47 20.21 79.79 21.27 78.73 19.53 80.47 19.51 80.49 Cutoff = .5 Accuracy Distressed 75.99 24.01 56.10 43.90 48.30 51.70 56.63 43.37 53.84 46.16 Active 19.53 80.47 20.21 79.79 21.27 78.73 19.53 80.47 19.51 80.49 Cutoff = .52 Accuracy MODEL 2 Distressed 72.70 27.30 54.98 45.02 50.32 49.68 64.09 35.91 81.29 18.71 Active 2.01 97.99 2.09 97.91 2.21 97.79 2.02 97.98 2.47 97.53 Cutoff = .5 Accuracy Distressed 97.37 2.63 94.67 5.33 93.06 6.94 95.08 4.92 96.19 3.81 Active 13.44 86.56 13.96 86.04 14.68 85.32 13.45 86.55 13.53 86.47 Cutoff = .13 Accuracy N-1 N-2 N-3 N-1&2&3 N-1to6 80.46 79.72 78.60 80.30 80.16 80.46 79.71 78.58 80.29 80.12 97.96 97.76 97.56 97.72 97.31 Source: Author 86.57 86.07 85.36 86.62 86.61 Despite the fact that the goodness-of-fit statistics showed a good fit only for Model 1, the testing results suggest that Model 2 is able to predict with better overall accuracy and also with lower Type I errors than Model 1. Overall predictive accuracy of Model 1 is almost identical with either of the cuttofs, .5 and optimal calculated of .52. Model 1 with the cutoff of .05 performs slightly better than same Model 1 with the cutoff calculated at .52, being able to correctly classify over 50% of the insolvent companies across all data sets. Model 1 with .52 cutoff can classify only 48% of the insolvent companies at year N-3. Overall predictive accuracy of Model 2 with the cutoff set at .5 is higher than at the optimal calculated cutoff of .13 but, at .13 cutoff Model 2 correctly classifies over 93% of the insolvent companies across all data sets, as opposed to only over 50% across all data sets with the cutoff set at .5. Model 2 with with the cutoff of .5 performs better than Model 1 for all data sets of Portuguese companies, being able to correctly classify over 50% of the insolvent companies across all data sets, as well as better classify the active companies at over 97%, compared to Model 1 which classifies active companies with an accuracy of 80% for year N-1, 79% for year N-2 and 78% for year N-3. We can conclude that most appropriate cutoffs are .5 for Model 1 and .13 for Model 2. For each one of them, the overall forecast accuracy level is quite similar through all the periods analysed (years N-1, N-2, N-3, N-1&2&3, and N-1 to 6), of around 80% for Model 1 and 86% for Model 2. However, Type II errors increase the further in time we go from the time of insolvency, as expected. For Model 1, for all periods besides N-1, Type II errors are over 40%. With the adjusted cutoff, Type II errors are very small for Model 2 with the adjusted cutoff of .13, which could be explained by the larger total number of observations used. 5.1 Considerations on Results for Project Hosting Company nBanks Considering the above, we conclude that the combination of variables presented in this study, which are Current Assets to Total Assets, Operating Cash Flow to Total Assets, Operating Cash Flow to Debt, Retained Earnings to Total Assets and Equity to Debt, can be used in order to timely detect a possible insolvency situation for Portuguese SMEs, or to assess the risk of insolvency of a SME at a specific point in time. 52 Taffler, R. J. (1984). Empirical Models for the Monitoring of UK Corporations. Journal of Banking and Finance , 8, 199-227. Vieira, E. S., Pinho, C., Correia, C. (2013). Insolvency Prediction in the Portuguese Construction Industry. Marmara Journal of European Studies , 21(2), 143-164. Zavgren, C. V. (1985). Assessing the Vulnerability to Failure of American Industrial Firms: a Logistic Analysis. Journal of Business Finance & Accounting, 12(1), 19–45. Zmijweski, M. E. (1984). Methodological Issues Related to the Estimation of Financial Distress Prediction Models. Journal of Accounting Research , 22, 59–82. Weiss, L. A. (1996). The Impact of Incorporating the Cost Errors Into Bankruptcy Prediction Models. INSEAD Working Paper Series , 2. 53 Appendices Appendix 1: Kernel Density Plot of the Propensity Score Appendix 2: Difference in Means After PSM 1 to 5 Appendix 3: Data Set Composition After PSM 1 to 5 Appendix 4: Data Set Composition by Year of Financial Statement After PSM 1 to 5 This table presents the number of observations by year of financial statement. Column Year represents the year of the financial statement. Columnt Insolvent represents the number of observations for insolvent companies at one year prior to insolvency. PSM 1 to 5 represents number of observations for active companies matched to the insolvent by PSM 1 to 5. Treated Control t p>|t| Unmatched 13.757 13.37 29.2 5.29 0.000 Matched 13.757 13.732 1.9 0/23 0.821 Log (Total Assets) Source: Author Variable Sample Mean %bias t-test After PSM 1 to 5 Insolvent Active Companies 289 1,083 Observations 289 1,100 Source: Author Year Insolvent PSM 1 to 5 2013 34 228 2014 27 99 2015 48 110 2016 60 179 2017 69 233 2018 51 251 Total 289 1,100 Source: Author 54 Appendix 5: Model Estimation Data Sets - Distribution by Region (PSM 1 to 5) This table presents the distribution of the model estimations data sets by region. Insolvent represents the number of insolvent companies per region, PSM 1 to 5 represents the number of matching active companies selected by this matching method, by region. Appendix 6: Descriptive Statistics for the Financial Ratios before PSM This table presents the number of observations, mean, standard deviation and median for the variables, for the initial sample composed of insolvent companies and active companies. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. Region-NUTS II Insolvent PSM 1 to 5 PT11 - North 117 472 PT17 - Area Metropolitana de Lisboa 69 211 PT16 - Centro 61 278 PT18 - Alentejo 16 56 PT15 - Algarve 13 48 PT20 - Regiao Autonoma dos Acores 11 19 PT30 - Regiao Autonoma da Madeira 2 16 TOTAL 289 1100 Source: Author Obs Mean St. Dev. Median Obs Mean St. Dev. Median X1 235,711 3.415 5.417 1.823 3,282 1.974 3.442 1.256 X2 235,711 0.233 0.258 0.201 3,282 0.214 0.289 0.202 X3 235,711 1.728 2.670 0.958 3,282 0.881 1.402 0.553 X4 235,711 0.739 1.701 0.188 3,282 0.215 0.704 0.040 X5 235,711 0.046 0.101 0.038 3,282 0.544 0.152 0.630 X6 235,711 0.087 0.106 0.076 3,282 -0.035 0.117 0.003 X7 235,711 0.064 0.097 0.056 3,282 -0.032 0.119 0.004 X8 235,711 0.027 0.192 0.038 3,282 -0.117 0.314 0.005 X9 235,711 0.022 0.088 0.018 3,282 -0.063 0.121 -0.015 X10 235,711 3.073 9.735 1.612 3,282 4.162 14.979 2.513 X11 235,711 8.098 27.311 6.039 3,282 5.787 41.981 6.606 X12 235,711 12.342 37.914 7.205 3,282 -0.033 0.249 0.005 X13 235,711 0.231 0.385 0.248 3,282 -0.171 0.512 -0.013 X14 235,711 0.679 0.305 0.674 3,282 0.960 0.373 0.882 X15 235,711 78.045 451.215 4.138 3,282 -3.953 189.776 0.198 X16 235,711 141.205 740.875 9.030 3,282 12.926 256.511 1.249 X17 235,711 0.947 1.503 0.483 3,282 0.209 0.579 0.134 X18 235,711 1.173 0.899 0.972 3,282 1.029 0.847 0.821 X19 235,711 1.175 51.191 2.965 3,282 0.315 40.735 1.867 Source: Author Active Companies Insolvent Companies Ratios 55 Appendix 7: Descriptive Statistics for the Financial Ratios After PSM 1 to 5 This table presents the number of observations, mean, standard deviation and median for the variables, for the data set after PSM 1 to 5. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. Obs Mean St. Dev. Median Obs Mean St. Dev. Median X1 303 2.861 4.032 1.719 1,100 1.736 3.189 1.018 X2 303 0.261 0.260 0.241 1,100 0.132 0.360 0.127 X3 303 1.365 1.506 0.968 1,100 0.679 0.969 0.411 X4 303 0.473 0.861 0.151 1,100 0.122 0.310 0.029 X5 303 0.040 0.110 0.038 1,100 -0.150 0.233 -0.073 X6 303 0.080 0.116 0.075 1,100 -0.115 0.222 -0.042 X7 303 0.059 0.112 0.055 1,100 -0.139 0.226 -0.064 X8 303 0.019 0.249 0.036 1,100 -0.296 0.507 -0.129 X9 303 0.018 0.105 0.020 1,100 -0.173 0.236 -0.093 X10 303 3.487 12.170 1.667 1,100 1.727 20.361 -1.374 X11 303 11.009 40.376 6.174 1,100 -1.209 62.727 -4.959 X12 303 12.744 37.489 7.450 1,100 -7.793 62.263 -5.948 X13 303 0.217 0.422 0.246 1,100 -0.567 0.843 -0.258 X14 303 0.685 0.320 0.670 1,100 1.201 0.591 1.021 X15 303 61.350 413.009 4.213 1,100 -44.975 184.872 -4.549 X16 303 104.254 518.921 9.480 1,100 -18.108 85.313 -3.085 X17 303 0.806 1.028 0.492 1,100 0.009 0.458 -0.020 X18 303 1.203 0.880 1.048 1,100 0.897 0.848 0.715 X19 303 4.645 39.377 3.220 1,100 -1.685 31.340 0.970 Ratios Active Companies Insolvent Companies Source: Author 56 Appendix 8: Descriptive Statistics for the Financial Ratios After PSM 1 to 10 This table presents the number of observations, mean, standard deviation and median for the variables, for the data set after PSM 1 to 10. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. Obs Mean St. Dev. Median Obs Mean St. Dev. Median X1 303 2.861 4.032 1.719 2,171 1.736 3.189 1.018 X2 303 0.261 0.260 0.241 2,171 0.132 0.360 0.127 X3 303 1.365 1.506 0.968 2,171 0.679 0.969 0.411 X4 303 0.473 0.861 0.151 2,171 0.122 0.310 0.029 X5 303 0.040 0.110 0.038 2,171 -0.150 0.233 -0.073 X6 303 0.080 0.116 0.075 2,171 -0.115 0.222 -0.042 X7 303 0.059 0.112 0.055 2,171 -0.139 0.226 -0.064 X8 303 0.019 0.249 0.036 2,171 -0.296 0.507 -0.129 X9 303 0.018 0.105 0.020 2,171 -0.173 0.236 -0.093 X10 303 3.487 12.170 1.667 2,171 1.727 20.361 -1.374 X11 303 11.009 40.376 6.174 2,171 -1.209 62.727 -4.959 X12 303 12.744 37.489 7.450 2,171 -7.793 62.263 -5.948 X13 303 0.217 0.422 0.246 2,171 -0.567 0.843 -0.258 X14 303 0.685 0.320 0.670 2,171 1.201 0.591 1.021 X15 303 61.350 413.009 4.213 2,171 -44.975 184.872 -4.549 X16 303 104.254 518.921 9.480 2,171 -18.108 85.313 -3.085 X17 303 0.806 1.028 0.492 2,171 0.009 0.458 -0.020 X18 303 1.203 0.880 1.048 2,171 0.897 0.848 0.715 X19 303 4.645 39.377 3.220 2,171 -1.685 31.340 0.970 Ratios Active Companies Insolvent Companies Source: Author 57 Appendix 9: Test of Equality of Means Between Active and Insolvent Companies - Before PSM This table presents the number of observations, mean, standard deviation and median for the variables, for the initial sample composed of insolvent companies and active companies. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. *** p<0.01, ** p<0.05, * p<0.1 58 Appendix 10: Test of Equality of Means Between Active and Insolvent Companies - After PSM 1 to 5 This table presents the number of observations, mean, standard deviation and median for the variables, for the data set after PSM 1 to 5. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. *** p<0.01, ** p<0.05, * p<0.1 Ratios Difference between means t value Pr(|T| > |t|) X1 -1.442 8.773 0,000*** X2 -0.019 6.195 0,000*** X3 -0.847 11.482 0,000*** X4 -0.524 10.591 0,000*** X5 0.498 -320.000 0,000*** X6 -0.122 67.668 0,000*** X7 -0.095 62.425 0,000*** X8 -0.144 22.190 0,000*** X9 -0.085 60.521 0,000*** X10 1.089 -2.899 0,003*** X11 -2.312 1.718 0,085* X12 -12.374 7.127 0,000*** X13 -0.402 59.042 0,000*** X14 0.281 -51.662 0,000*** X15 -81.998 6.049 0,000*** X16 -128.280 6.112 0,000*** X17 -0.738 21.403 0,000*** X18 -0.144 8.442 0,000*** X19 -0.861 0.821 0.007*** Source: Author Appendix 11: Pearson`s Correlation Coefficients for the Financial Ratios - Before PSM This table presents Pearson`s correlation coefficients for the initial sample composed of insolvent companies and active companies. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. * denotes statistical significance at 5% or inferior. Before PSM X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X16 X17 X18 X19 X20 X1 1.0000 X2 0.1605* 1.0000 X3 0.7677* 0.1295* 1.0000 X4 0.6686* -0.0984* 0.8365* 1.0000 X5 0.0167* 0.0148* 0.0824* 0.0925* 1.0000 X6 0.0104* -0.0752* 0.1129* 0.1328* 0.7101* 1.0000 X7 0.0172* -0.0763* 0.1182* 0.1358* 0.6997* 0.9853* 1.0000 X8 0.0411* 0.0113* 0.1050* 0.1082* 0.5021* 0.6045* 0.6062* 1.0000 X9 0.0509* 0.0311* 0.1271* 0.1332* 0.7622* 0.9020* 0.9116* 0.6691* 1.0000 X10 -0.0520* -0.0089* -0.0670* -0.0606* -0.0142* -0.0276* -0.0252* 0.0107* -0.0176* 1.0000 X11 -0.0229* 0.0405* -0.0408* -0.0470* 0.0180* -0.0043* 0.0114* 0.1483* 0.0565* 0.0813* 1.0000 X12 -0.0214* 0.0738* -0.0468* -0.0577* -0.0092* -0.0365* -0.0270* 0.1198* 0.0371* 0.0911* 0.4417* 1.0000 X13 0.2118* 0.1083* 0.2820* 0.2667* 0.4284* 0.5356* 0.5564* 0.4689* 0.6289* -0.0588* 0.0011 -0.0115* 1.0000 X14 -0.2792* -0.1332* -0.3397* -0.3035* -0.2546* -0.3466* -0.3737* -0.3330* -0.4202* 0.1033* 0.0344* 0.0473* -0.8646* 1.0000 X16 0.0631* -0.0004 0.0943* 0.1144* 0.1779* 0.1913* 0.1945* 0.1550* 0.2210* -0.0236* -0.0022 -0.0141* 0.1733* -0.1384* 1.0000 X17 0.0629* -0.0132* 0.0895* 0.1090* 0.1246* 0.1491* 0.1579* 0.1072* 0.1636* -0.0220* -0.0002 -0.0141* 0.1363* -0.1159* 0.9378* 1.0000 X18 0.4553* 0.0264* 0.4829* 0.4749* 0.1301* 0.1634* 0.1799* 0.1827* 0.2140* -0.1299* -0.0735* -0.0849* 0.5555* -0.6990* 0.1694* 0.1562* 1.0000 X19 -0.1370* -0.0416* -0.0705* -0.0537* 0.1920* 0.2558* 0.2303* 0.0801* 0.1956* 0.0069* -0.0243* -0.0313* 0.0322* 0.0395* 0.0478* 0.0299* -0.1050* 1.0000 X20 -0.0152* 0.0688* 0.0009 -0.0234* 0.0038 0.0010 0.0020 -0.0063* 0.0076* -0.0016 0.0001 0.0027 0.0067* -0.0101* -0.0006 -0.0024 -0.0145* 0.0465* 1.0000 Source: Author 60 Appendix 12: Pearson`s Correlation Coefficients for the Financial Ratios After PSM 1 to 5 This table presents Pearson`s correlation coefficients for the data set composed of the insolvent companies with data from one year prior to insolvency, and the active companies matched to these insolvent companies by PSM 1 to 5. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. * denotes statistical significance at 5% or inferio PSM 1 to 5 wX1 wX2 wX3 wX4 wX5 wX6 wX7 wX8 wX9 wX10 wX11 wX12 wX13 wX14 X15 X16 X17 X18 X19 X1 1.0000 X2 0.2784* 1.0000 X3 0.5650* 0.2031* 1.0000 X4 0.4876* -0.0533* 0.7500* 1.0000 X5 0.1293* 0.2202* 0.2117* 0.1760* 1.0000 X6 0.0992* 0.1550* 0.2172* 0.1887* 0.9643* 1.0000 X7 0.1074* 0.1624* 0.2155* 0.1845* 0.9603* 0.9930* 1.0000 X8 0.1459* 0.1305* 0.1704* 0.1387* 0.5984* 0.5824* 0.5730* 1.0000 X9 0.1371* 0.2284* 0.2092* 0.1706* 0.9924* 0.9544* 0.9648* 0.5879* 1.0000 X10 -0.0391 0.0077 -0.0544* -0.0419 0.0388 0.0434 0.0463 0.0575* 0.0420 1.0000 X11 0.0823* 0.0814* -0.0295 -0.0120 0.0782* 0.0634* 0.0710* 0.1472* 0.0862* 0.1106* 1.0000 X12 0.0520 0.1485* 0.0037 -0.0085 0.1044* 0.0807* 0.0899* 0.1478* 0.1141* 0.0832* 0.2880* 1.0000 X13 0.2218* 0.3305* 0.3274* 0.2777* 0.7040* 0.6697* 0.6891* 0.4923* 0.7224* 0.0390 0.0410 0.1359* 1.0000 X14 -0.2676* -0.3348* -0.3525* -0.2948* -0.5228* -0.4998* -0.5219* -0.3870* -0.5444* -0.0231 -0.0195 -0.1131* -0.9138* 1.0000 X15 0.0584* 0.0248 0.1345* 0.1347* 0.2441* 0.2250* 0.2140* 0.1673* 0.2320* 0.0076 0.0570* 0.0372 0.1784* -0.1316* 1.0000 X16 0.0552* -0.0183 0.1206* 0.1397* 0.1825* 0.1754* 0.1684* 0.1289* 0.1748* 0.0002 0.0412 0.0226 0.1367* -0.1086* 0.8806* 1.0000 X17 0.4464* 0.1732* 0.4889* 0.4680* 0.3235* 0.3111* 0.3204* 0.2730* 0.3317* -0.0693* -0.0160 0.0194 0.5772* -0.6793* 0.1586* 0.1617* 1.0000 X18 -0.1685* -0.1285* -0.0207 0.0164 0.1165* 0.1491* 0.1157* 0.1793* 0.0822* 0.0125 -0.0392 -0.0213 0.0226 0.0522 0.0054 0.0162 -0.0697* 1.0000 X19 -0.0129 0.0336 0.0376 0.0152 0.0904* 0.1030* 0.0991* 0.0281 0.0867* -0.0219 -0.0271 0.0114 0.0824* -0.0507 0.0138 -0.0193 0.0334 0.1048* 1.0000 Source: Author Appendix 13: LDA - Ranking of the Standardised Coefficients This table presents the LDA standardised coefficients in absolute values for the data sets composed as follows: PSM 1 to 1 = insolvent companies with data from one year prior to insolvency and corresponding active companies matched to them by PSM 1 to 1; PSM 1 to 5 = insolvent companies with data from one year prior to insolvency and corresponding active companies matched to them by PSM 1 to 5; PSM 1 to 10 = insolvent companies with data from one year prior to insolvency and corresponding active companies matched to them by PSM 1 to 10; Without PSM – random 80% of active companies = insolvent companies with data from one year prior to insolvency and randomly selected 80% of the active companies from the same years as the insolvent. X1, Current Ratio; X2, Working Capital to Total Assets; X3, Quick Ratio; X4, Cash Ratio; X5, Current Assets to Total Assets; X6, EBIT to Total Assets; X7, Cash Flow to Total Assets; X8, Operating Profit Margin; X9, ROA; X10, Debt to Equity; X11, Debt to EBITDA; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X14, Debt to Asset;; X15, Interest Coverage; X16, EBITDA to Interest Coverage; X17, Equity to Debt; X18, Total Assets Turnover; X19, Working Capital Turnover. Rank PSM 1 to 1 Standardised Coefficients (absolute values) PSM 1 to 5 Standardised Coefficients (absolute values) PSM 1 to 10 Standardised Coefficients (absolute values) Without PSM - random 80% of active companies Standardised Coefficients (absolute values) 1 X9 0.6173 X7 1.5629 X5 2.3057 X6 3.2732 2 X7 0.5320 X6 0.7632 X9 2.1858 X7 2.9294 3 X14 0.5184 X9 0.4128 X6 0.9968 X5 2.2761 4 X12 0.3952 X14 0.3854 X7 0.3840 X9 1.7331 5 X16 0.3897 X18 0.2635 X14 0.3771 X2 0.0784 6 X15 0.3072 X12 0.2230 X18 0.2022 X17 0.0463 7 X18 0.2667 X2 0.1378 X2 0.1761 X12 0.0387 8 X6 0.2371 X8 0.1284 X8 0.1664 X4 0.0368 9 X17 0.2095 X4 0.1220 X12 0.1401 X18 0.0362 10 X8 0.1569 X16 0.1220 X15 0.1263 X16 0.0268 11 X13 0.1270 X17 0.1171 X16 0.1196 X14 0.0265 12 X4 0.1135 X15 0.1013 X13 0.1004 X3 0.0257 13 X5 0.1041 X11 0.0958 X4 0.0986 X8 0.0239 14 X2 0.1013 X13 0.0642 X3 0.0740 X13 0.0212 15 X11 0.0933 X5 0.0610 X11 0.0702 X10 0.0175 16 X3 0.0823 X1 0.0584 X10 0.0568 X1 0.0135 17 X1 0.0691 X3 0.0447 X17 0.0468 X11 0.0069 18 X19 0.0493 X10 0.0330 X19 0.0316 X15 0.0042 19 X10 0.0031 X19 0.0249 X1 0.0303 X19 0.0005 Source: Author 68 Appendix 21: Probit regression - Marginal Effects PSM 1 to 1 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 VARIABLES Marginal effects X1 -0.003 (0.006) X2 -0.136 (0.103) X3 -0.010 (0.017) X4 -0.217** (0.090) X5 0.265** (0.118) X6 0.752 (1.372) X7 2.690*** (0.977) X8 0.012 (0.048) X9 -1.947 (1.643) X10 0.000 (0.001) X11 -0.000 (0.000) X12 -2.435*** (0.402) X13 -0.252 (0.170) X14 0.145 (0.229) X15 0.000 (0.000) X16 -0.001** (0.000) X17 -0.189*** (0.065) X18 -0.094*** (0.036) X19 -0.001 (0.000) Observations 578 69 Appendix 22: Probit regression - Marginal Effects PSM 1 to 10 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 VARIABLES Marginal effects X1 -0.000 (0.002) X2 -0.051*** (0.018) X3 0.003 (0.005) X4 -0.027* (0.015) X5 0.527 (3.901) X6 -0.005 (3.925) X7 -0.436 (3.898) X8 -0.009 (0.016) X9 -0.352 (3.886) X10 -0.000 (0.000) X11 -0.000 (0.000) X12 -0.000** (0.000) X13 -0.024 (0.019) X14 -0.008 (0.033) X15 0.000 (0.000) X16 -0.000 (0.000) X17 -0.062*** (0.017) X18 -0.026*** (0.007) X19 -0.000 (0.000) Observations 2,474 70 Appendix 23: Coefficient Estimates for Model 3 and Model 4 This table contains the estimation results for the logit Models 3 and 4 .The dependent variable equals zero if the firm is not financially distressed and one otherwise. The column Model 3 contains the results of the estimation using the data set composed by insolvent companies with data one year prior to insolvency and active companies matched to the insolvent ones by PSM 1 to 5. The column Model 4 contains the results of the estimation using the data set composed by insolvent companies with data one year prior to insolvency and a random selection of 80% of all active companies from the same years as the insolvent ones. X5, Current Assets to Total Assets; X7, Cash Flow to Total Assets; X12, Cash Flow to Debt; X13, Retained Earnings to Total Assets; X17, Equity to Debt. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 X5 3.632 43.515*** (2.251) (2.409) X7 -9.365*** -34.257*** (2.256) (2.263) X12 -0.006*** -0.021*** (0.002) (0.006) X13 -0.358 -0.851 (0.240) (0.541) X18 -1.646*** -0.889 (0.300) (0.543) Constant -0.771*** -10.417*** (0.116) (0.526) Observations 1,403 188,896 Pseudo R-squared 0.335 0.948 Prob > chi2 0.000 0.000 Model 3 Model 4 Source: Author VARIABLES