key: cord-0060892-8e04ya2y
authors: Pereira, José Manuel; Ribeiro, Humberto; Silva, Amélia; Alves, Sandra Raquel
title: To Fail or Not to Fail: An Algorithm for SME Survival Prediction Using Accounting Data
date: 2020-11-14
journal: The Changing Role of SMEs in Global Business
DOI: 10.1007/978-3-030-45835-5_5
sha: 3d3d026a7ac1a37ec2bc7999abefb936105d3704
doc_id: 60892
cord_uid: 8e04ya2y

In this book chapter, the very significant negative effects of the financial crisis were examined, in particular on micro and small and medium-sized enterprises (SMEs). An algorithm that has been constructed for predicting the survival likelihood of a corporation, using financial accounting data, is proposed here. Furthermore, due to the more common fragility of SMEs, the authors consider this algorithm as a possible tool for assessing their financial condition, providing an immediate insight about their survival odds and therefore helping management to better justify their decision-making processes, namely, the critical ones, driven to avoid business failure. Overall, the results suggest that the proposed algorithm is reliable while forecasting the survival likelihood of SMEs, based on their financial accounting reported data.

The unbalanced environment that economies across the globe faced during the great recession enhanced the occurrence of the corporate insolvency phenomenon. Insolvency and bankruptcy occur on a daily basis.

helping management to support their decision-making processes, namely, the critical ones, that is, the one which may prevent business failure.

In order to test the feasibility of the proposed tool, an algorithm, which was based on an empirical study comprising a set of insolvency proceedings in Portugal involving SMEs, was subjected to a major testing process, with the research being focused on non-financial sectors only. Overall, the results suggest that the proposed algorithm is reliable while forecasting the survival likelihood of SMEs, based on their reported data on financial accounting. Therefore, the authors believe that this algorithm can be regarded as a powerful tool for SME managers to monitor the corporate performance and the outcome of their managerial decisions, particularly with regard to the survival chances of their organisations.

The main application of survival analysis in accounting research has been in the area of bankruptcy prediction and the related literature that employs this statistical technique has increased in recent years. Lane et al. (1986) were the first to employ the Cox model to predict bank failure, using a sample of 130 banks that failed between January 1978 and June 1984, and another sample of 334 non-failed banks. The survival time for each failed bank has been defined as the time (in months) since 31 December of the year considered for the calculation of financial ratios to the date of bankruptcy. Their results indicated that the overall accuracy of the Cox model was similar to the one obtained by using discriminant analysis; however, type I error was lower in the Cox model. Following these findings, many other authors contributed towards the dissemination of this technique in the field of bankruptcy. For instance, Luoma and Laitinen (1991) applied survival analysis while predicting business failure. These authors used a sample of 36 failed companies (24 from industrials and 12 retailing firms) each paired with a not failed company belonging to the same business and of similar size. The results were compared with models developed from discriminant analysis and logistic regression. The percentage of correct classifications were 61.8%, 70.6% and 72.1%, for survival analysis, discriminant analysis, and logistic regression, respectively. The authors explained the lower accuracy of the model based on survival analysis with the different failure processes found in the data.

Another reference research in this area is the one of Shumway (2001) . This author draws attention to the need to include multiple observations for each firm by using a discrete time hazard model in the prediction of financial distress and uses an accelerated failure time survival analysis model that outperformed the traditional techniques used in this strand of investigation.

Likewise, Lee (2014) used survival analysis to find the main indicators which could explain the business bankruptcy phenomenon in Taiwan. The sample employed included companies listed on the Taiwan Stock Exchange that were under financial distress between 2003 and 2009. Lee's research suggested that one does not need to use many ratios to be able to anticipate a potential business bankruptcy.

Finally, it is also noteworthy to mention Gémar et al. (2016) who used survival analysis techniques applied to the Spanish hotel industry. Their findings suggest that the hotels' survival likelihood depends on their size, location, management and opening timing (preferably in a time of prosperity).

Although some selected research was highlighted in this book chapter, it is important to note that the use of the survival technique can also be observed in many other studies that can be found in recent academic literature. Accordingly, a systematic literature review on the topic was performed in order to assess the most recent contributions in the field.

As for the outset, one should be aware that the medical sciences were the first to develop a systematic literature review, based on the survival methodology used to predict the likelihood of patient survival. Due to the necessity to integrate clinical evidences from different studies, that is, Evidence Based Medicine, meta-analysis became very popular in medicine. More recently, this methodological approach has been increasingly applied to the social sciences. Regardless of the required adaptations, this methodology allows the grouping of a huge volume of literature and the integration of the different contributions in a field of knowledge. The Clarivate's Web of Science search engine was selected to perform this review. The following research query was applied:

• Topic: ("survival analysis") AND Topic: (bankruptcy) • Publication years: OR 2010 OR 2018 OR 2017 OR 2012 • Document types: (ARTICLE)

The search was performed on 30 November 2019, with 32 papers being gathered initially. In order to assess the relevance of each paper, the title and the abstract of each of these papers were examined. From the 32 papers, only one paper was excluded because it dealt with personal bankruptcy and was related to the physical conditions of the individual. The remaining 31 papers were included in the sample and were distributed by years as shown in Fig. 5 .1.

In Table 5 .1, we summarise the goal of each paper reviewed, ranked by year of publication.

It is interesting to note that, despite the novelty of the introduction of new variables in some studies, most papers use accounting-driven ratios as predictor variables. In the selected sample of collected papers, one could find studies from many different countries around the globe. 

-Show that the reduced-form entrepreneurial equilibrium and profit-maximisation entrepreneurial equilibrium, as defined by Magill and Quinzii (1996) , are equivalent. In addition, we find an inverse relationship between the economy real interest rate and the probability of default -Propose a Cox proportional hazards model with time-dependent covariates for a sample of sole proprietorships' unsecured credit operations in the Brazilian economy 2013 Mokarami and Motefares

-Propose a Cox regression Criteria used for corporate governance are size of Board of Directors, percentage of non-Executive Directors, Chief Executive Officer (CEO) change and major ownership -Develop a cure model for analysing default time data where two groups of companies are supposed to coexist: those which could eventually experience a default (uncured) and those which could not develop an endpoint (cured) -The probability of being uncured is estimated with a binary logit regression, whereas a discrete time version of a Cox's proportional hazards approach is used to model the time distribution of defaults, accomplished by replacing the discrete time baseline function with an appropriate time-varying system level covariate, able to capture the underlying macroeconomic cycle 2015 Alves and Dias (2015) -Score the credit risk of a financial institution's clients -General framework of survival mixture models (SMMs) that addresses the unobserved heterogeneity of the credit risk of a financial institution's clients, containing specific cases of aggregate and immune fraction models 2015 Kim and Partington (2015) -Investigate dynamic probability forecasts use of time-varying variables in forecasts from a Cox model -Forecast accuracy is evaluated using receiver operating characteristics curves and the Brier Score 2016

Lado-Sestayo, Vivel-Búa and Otero-González

-Assess the determinants of survival of Spanish hotel firms (2019) -Test the different definitions of "book-value distance to default" (BVDD) to assess whether using downward assets volatility provides some advantage to the index performance or produces adverse impacts on its effectiveness -Develop a Cox semi-parametric hazards model where the BVDD is built as a function of a parameter theta, which indicates the percentage of upward assets volatility incorporated in its calculation so as to compare its success in predicting banks' distress over different levels of theta 2019

Djeundje and Crook (2019) -Discuss how survival analysis can be enhanced using generalised additive models (GAMs) -Show how GAMs can be used to improve not only the application, behavioural and macroeconomic components of survival models for credit risk data at the individual account level, but also the accuracy of predictions -Propose parametrised GAMs for credit risk data in terms of penalised splines, outline the implementation via frequentist and Bayesian MCMC methods, apply them to a large portfolio of credit card accounts 2019

Gémar, Soler and Guzman-Parra (2019) -Examine variables influencing resort hotels' survival in Spain which had not been analysed previously. In this country, determining whether the reasons resort hotels close are different from why other hotels close could be imperative to resort hotels' survival -Develop Cox's semi-parametric proportional hazards regression to determine which variables influence hotel closure and how much each variable increases risk of closure 2019

Ivanović, Kufenko, Begović, Stanišić and Geloso (2019) -Demonstrate that the design of the privatisation process in Serbia allowed rent-seekers to conserve their privileges through asset-stripping, which explains the failure -Analyse the determinants of liquidation, merger and bankruptcy of privatised firms (continued) However, the majority were from European countries. One evidence coming from this literature review is that a sound theoretical approach that may explain corporate bankruptcy broadly is still under development. Figure 5 .2 summarises, in the form of keywords, the content of the abstracts of the 31 articles analysed, using a Word Cloud Generator software.

Despite the limitations that this analysis model may present, one can, nevertheless, highlight the predominance of the empirical approach, rather than the use of a theoretical approach to explain the bankruptcy phenomenon. -Investigate the symptoms of failure in public corporations with multiple hospitality businesses and examine whether a new case-based deep-layer predictive analysis methodology is more appropriate than conventional approaches to failure analysis -A case-based deep-layer predictive analysis of multi-business hospitality failures was conducted using an independently incremental process, a dependent retrieval process, a pre-early-warning process and an early-warning process 

According to Collett (1994) , the current survival time of an individual t can be regarded as the realisation of a random variable T, which may assume any given non-negative value. Therefore, T indicates the time to failure of a firm. T is thus associated with survival time and follows a given probability distribution. T being a continuous probability distribution, and assuming f as the underlying probability density function, the function of distribution is then given by

which represents the probability of the survival time being inferior to a given value of t. The survival function S(t) is defined as the probability that a firm will survive longer than t times units, being equal or higher than t, and assumes the following notation: S t P T t F t t 1 .

(5.

2)

The survival function may therefore represent the probability of the survival time of an individual to exceed a given value of t.

The hazard function describes the evolution over time of the immediate rate of "death" of a firm. To obtain the hazard function, we assume the probability that the random variable associated with a survival time T is between t and t + δt, subject to a T value greater than or equal to t, which can be shown as

The hazard function h(t) is then the limit of that probability divided by the interval of time δt, with δt tending to zero as we can verify below:

The hazard h(t) is the probability of failure in the next period, given that the firm was alive at time t (Lane et al. 1986 ).

The survival function, S(t), can be obtained from the following equation:

The function H(t) is called the cumulative hazard function.

The model that can be used as a base for application in this book chapter is the proportional hazards model proposed by Cox (1972) , which is also known as the Cox regression model.

The definition of the model is as follows. Assuming that the hazard of "failure" for a given time period depends on the values x 1 , x 2 , …, x p of p explanatory variables X 1 , X 2 , …, X P , the set of values of explanatory variables in the proportional hazard model will be represented by the vector x, so x = (x 1 , x 2 , …, x p ) ′ .

We designate h 0 (t) as the hazard function of a company for which the values of all variables that make the vector x is zero. The function h 0 (t) is called baseline hazard function. The hazard function for i companies can then be written as:

where ψ(x i ) is the function of the values of the vector of explanatory variables for i companies. The function ψ(x i ) can be interpreted as the risk over time t for a company whose vector of explanatory variables is x i on the risk for a company whose x = 0.

Since the relative risk ψ(x i ) cannot be negative it should be written as exp(η i ), where η i is a linear combination of p explanatory variables in x i . Therefore

which is equivalent to

where β is the vector of coefficients of the x 1 , x 2 , …, x p explanatory variables in the model.

The quantity η i is called the linear component of the model, also known as risk score or prognostic index for i firms. The proportional hazard model can generally be expressed as follows:

Taking into consideration the models offered by the literature, but also employing a specific set of variables that the authors of this book chapter find appropriate to test using a survival function, the proposal of a predictive model of corporate failure follows below.

In this research, several economic and financial indicators were used to construct a set of independent variables. Similarly to the procedure used in diverse studies devoted to predicting business failure, the selection of the independent variables was based on its popularity, measured by its use in previous studies. The 22 selected indicators that were collected from the balance sheet and from the income statement of the companies included in the sample are listed below:

X1 (Current assets − current liabilities)/Total liabilities X2 Current assets/Current liabilities X3 Equity/Total assets X4 Equity/Liabilities X5 Cash flow/Current liabilities X6 Cash flow/Liabilities X7 Financing charge/Operating gains X8 Cash/Total assets X9 Cash/Current liabilities X10 Bills payable/Total assets X11 Working capital/Total assets X12 Operating gains/Current assets X13 Operating gains/Operating costs X14 (Net profit before tax + depreciation expense + provisions)/ Financing charge X15 Net profit/Total assets X16 Net profit/Equity X17 Net profit/Liabilities X18 Net profit/Operating gains X19 Net profit/Sales X20 Sales/Cash X21 (Net profit before tax + financing charge)/Sales X22 Net profit before tax/(Net profit before tax + financing charge)

In order to adjust the model, it was necessary to collect a sample of companies where the event of insolvency occurred. Based on the information provided by insolvency administrators it was possible to obtain a sample of 14 companies, whose survival times were known and which could therefore be classified as belonging to the group of failed companies. The survival times for the 14 companies were as follows: 2 companies with 3 months, 1 company with 4 months, 4 companies with 5 months, 2 companies with 6 months, 4 companies with 8 months and 1 company with 10 months. Concurrently, we obtained a sample of 14 companies that did not fail, with survival times obtained from SABI, a database from Bureau Van Dijk, a Moody's Analytics company.

Taking into consideration the survival times, it was possible to split each company into three sets of observations, which resulted in a group of failed companies with 42 observations, and a group of companies that did not fail with 42 observations as well. Each observation is regarded as a company. To illustrate this situation, one can consider the data from a company that was active until six months after the latest year for which we have data records. Since we collected data for three consecutive years, it was possible to have data for 6, 18 and 30 months prior to the time of business closure. This procedure was repeated for every 28 companies included in the testing sample. The selection method of the explanatory variables followed Collett's (1994) procedure, and the testing was performed using SPSS software.

The explanatory variables that contributed significantly to the reduction of statistics −2log L  are shown in Table 5 .2. 

In Table 5 .3 are shown the values of the survival function relative to the average of the variables' values.

The survival analysis provides quantitative information about the probability of a company failing at the end of a time period t and not only whether it will, or will not, fail. The compiled data, shown in Table 5 .3, made it possible to develop an algorithm using Matlab, which allows to deliver a company's performance forecast and a survival function value for the time considered. The time period considered for the study was 12 months. The values of the survival function, for each firm, were based on the respective figure for the nearest time frame obtained in the survival model developed earlier (ten months). In order to calculate the forecast for each company, a cut-off point of 0.5 was used, that is, the model considers 1 for a company when the likelihood to survive is greater than 0.5, and 0 otherwise. The combination of these criteria and data allowed to produce the algorithm, which is show below in italic. As the authors had the information for the last year before the failure of 72 companies in the sample, another sample of 72 non-failed companies was collected from the SABI database.

With the sample of failed companies, it was verified that the survival function value for the considered time was higher than expected (type I error) in four situations. With the sample of non-failed companies, the survival function value was less than expected in two cases (type II error). Based on these results the type I error was 5.55%, and the type II error was 2.86%.

An extract of the algorithm output can be seen below, showing the algorithm running commands and output for a number of selected companies in italic. According to the algorithm, using this selected sample, only six companies were forecast to survive. 

Small and medium-sized enterprises are the bulk of any economy. Nevertheless, they are mostly vulnerable and are prone to face several constraints that often result in some relevant issues that may even lead to insolvency proceedings. Besides being more susceptible to the surrounding environment, SMEs often lack control and quality information, which could eventually prevent them from being involved in dramatic failure processes. In this book chapter, the very significant negative effects of the financial crisis were examined, in particular on micro and small and medium-sized enterprises (SMEs). The issue of corporate bankruptcy has been, and keeps being, a topic of significant interest for a broad set of economic agents. Accordingly, an algorithm that has been constructed for predicting the survival likelihood of a corporation, with a particular focus on SMEs, was proposed here.

On the one hand, this chapter focused on examining SME data in order to perceive whether a sample of these companies could be facing serious financial difficulties, but, on the other, it focused on trying to understand whether they could have benefited from an early diagnosis in order to try preventing business failures with proper monitoring, together with some other eventual support. Taking into account recent data, this research examined insolvency processes, involving SMEs, that have taken place recently in Portugal. A specific tool was constructed and proposed: a survival algorithm that was based on financial accounting data from a set of SMEs. The reliability of this tool was subject to testing, while employing an empirical study comprising a set of insolvency proceedings.

Overall, the results of this research suggest that the proposed algorithm is reliable while forecasting the survival likelihood of SME, based on financial accounting data. Decisions need to be based on reliable information and sound forecasting tools. Therefore, the authors believe that this algorithm can be regarded as a powerful tool for SME managers to monitor both the corporate performance and the outcome of their managerial decisions, particularly with regard to the assessment of the survival chances of their organisations.

Current economic conditions, driven by the Covid-19 pandemic containment measures and uncertainty, are certainly very challenging for corporations. SMEs, as usual, continue to be the main victims of the negative economic cycles. Despite the massive support that is being offered by governments and monetary authorities to ensure the survival of corporations, the fact of the matter is that, in general, SMEs are not attractive enough or financially sound to be able to capture such support, as financial institutions often prefer backing large companies.

As many SMEs will likely be forced to continue to manage their financial issues on their own during the Covid-19 pandemic period, it is believed that the tool presented in this chapter may effectively help managers, while supporting their decision-making processes, particularly with regard to critical decisions that may, ultimately, result in the future success or failure of the organisation. SMEs cannot fully rely on bailouts from governments and financial institutions. They lack size and mediatic importance, so they can be easily disregarded, forgotten even. They are "too small to save". Survival is a matter of fate. Not a matter of faith. To fail, or not to fail: another Shakespearean drama that perhaps can be unveiled with an algorithm.

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