Insolvency Forecasting through Trend Analysis with Full Ignorance of Probabilities

17 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 INSOLVENCY FORECASTING THROUGH TREND ANALYSIS WITHFULL IGNORANCE OFPROBABILITIES1 Tomáš Poláček, Markéta Kruntorádová* Abstract The complex views of insolvency proceedings are unique, poorly known, interdisciplinary and multidimensional, even though there is a broad spectrum of different BM (Bankruptcy Models). Therefore, itisoften prohibitively difficult tomake forecasts using numerical quantifiers andtraditional statistical methods. Theleast information-intensive trend values areused: positive, increasing, zero, constant, negative, decreasing. Thesolution ofatrend model isaset ofscenarios where X istheset ofvariables quantified bythetrends. All possible transitions among thescenarios aregenerated. Anoriented transitional graph has aset ofscenarios asnodes andthetransitions asarcs. Anoriented path describes any possible future andpast time behaviour ofthebankruptcy system under study. The graph represents the complete list of forecasts based on trends. Aneight-dimensional model serves asacase study. Onthetransitional graph ofthecase study model, decision tree heuristics areused forcalculating theprobabilities oftheterminal scenarios andpossible payoffs. Keywords: forecast, insolvency, trend, qualitative, bankruptcy, transition JEL Classification: G33, G34 Introduction At this time, along with the increasing number of insolvency proceedings, efforts are being made to streamline processes and identify links between majority creditors (Mrázová and Zvirinský, 2015). These are concurrent with data mining investigations to find different ways of effectively solving insolvency proceedings in various regions of the Czech Republic (Mrázová and Zvirinský, 2014). More and more professional research is concerned with the question of why the number of insolvency proceedings for both legal and natural persons is increasing (Paseková and Crhová Kuderová, 2014). Some studies are focused on the descriptive state of the domestic market over a certain period after the introduction of the Insolvency Act (Smrčka, Schőnfeld and Ševčík, 2013) or what effect the amendments and amendments to the act itself have on the practice, which addressed some of the fundamental issues regarding powers in decision-making in insolvency proceedings (Richter, 2013). Few scientific studies deal with the recovery of claims from insolvency proceedings, for natural or legal persons, or for practical solutions to insolvency that affect various market determinants (Jakubík, 2007). 1 This paper was supported by grants FP-S-18-5074 “Development trends of the economic management of the enterprise in the European economic environment”. * Brno University of Technology, Faculty of Business and Management ([email protected]; [email protected]). 18 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 Insolvency proceedings as such are subject to the influence of many factors from the whole economic environment. Some factors (determinants) cannot be quantified and basic statistical models cannot be used (Sen, Singer, 1994). So, the use of trend research is appropriate (Vícha and Dohnal, 2008; Dohnal, 2016). This means that knowledge items of different levels of subjectivity must be taken into consideration to develop the best possible model of a unique task under study. Therefore, many bankruptcy observations are required. However, they are not available. This is the reason why information non-intensive formal tools are used more and more frequently, see e.g. fuzzy and/or rough sets (Pavláková Dočekalová and Kocmanová, 2016; Meluzín et al., 2016). 1. Alternative Decision-Making Methods intheProcess Decision-making analyses are often used to help decision-makers choose between alternatives based on the expected utility associated with the function of its consequences and potential impacts. Therefore, for example, in a study (Wang et al., 2018) a multicriteria decision model is developed. Although many successful studies have been conducted on the detection of bankruptcy, rarely have probabilistic approaches been made. In research (Antunes, Ribeiro and Pereira, 2017), a probabilistic aspect is assumed by applying Gaussian processes. Bankruptcy and reorganisation prediction models are often used in auditing large corporate transactions (mergers and acquisitions, strategic alliances, etc.), in making investment decisions and in the judiciary, where judges are final arbitrators in bankruptcy proceedings. However, all existing insolvency models are inadequate mainly because the research methods were defective. The authors merely put rigid mathematical models into bankruptcy. Models do not follow an interdisciplinary approach, do not allow optimisation and simulation to derive the best conditions for minimising financial threats. The study (Nwogugu, 2006) presents various dynamic models for insolvency decision-making and develops the framework and basis for further research into the use of dynamic systems and artificial intelligence in modelling bankruptcy decisions and legal arguments. This paper deals with bankruptcy forecasting under conditions of severe information shortages. Such bankruptcies are often described by non-numerical quantifiers, e.g. words – low, medium, high. However, the transfer of such verbal values into fuzzy sets is very subjective (Yi-Chung Hu and Tseng, 2007). 2. Trend Models There are many different interpretations of trend concepts (Kamstr and Kennedy, 1998; Stekler and Symington, 2016). The trend concepts as it is used in this paper is based on four values (Vicha and Dohnal, 2008; Bredeweg, 2009): Positive Zero Negative Any Value (1) + 0 - * An equationless trend model M is a set of w pair-wise relations M = Ps (Xi, Xj) (2) s = 1, 2, ……w 19 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 Examples/shapes of the relations P (2) are given in Figure 1: Figure 1 | Trends relationships Y X Y X Y X Y X Y X Y X 25 25 25 26 22 23 33 33 3 26 24 22 21 21 23 25 22 24 26 X Y Y Y Y Y Y X X X X X Source: Authors` own processing An algorithm, which can be used to solve the model (2), is based on the pruning of a specially generated tree of combinations. It is not the goal of this paper to describe such an algorithm, as it is a purely mathematical combinatorial task (Vicha and Dohnal, 2008). The model (2) is solved and the set of n dimensional scenarios is obtained S(n, m). There are m scenarios: S(n, m) = (X1, DX1, DDX1), (X2, DX2, DDX2),…, (Xn, DXn, DDXn)j, (3) j = 1, 2,…, m, where DX is the first and DDX is the second time trend derivatives. For example, the following three-dimensional scenario, n = 3 (3). X1 X2 X3 (4) (+ + +) (+ - 0) (+ - -). The model (2) is solved and the set of n dimensional scenarios is obtained S(n, m). There are m scenarios: 20 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 2.1 Transitional Graphs The set of scenarios S (3) is not the only result of a trend modelling. It is possible to generate transitions among the set of scenarios. Figure 2 | Atrend description ofaquantitative oscillation (+0-) (0+0) (+++) (+0+) (+--) (+-+) (0+0) (++-) Time Source: Authors` own processing The triplets given in Figure 2 describe a broad spectrum of different oscillations, e.g. dumped oscillation or irregular oscillations with randomly or deterministically changing frequencies and/or amplitudes. 3. Case Study Based on the heuristics of using trend methods, variables that have a major impact on the debt relief process have been carefully selected after discussions with insolvency experts. In the next chapter, the variables will be described with an explanation of how their existence individually affects the insolvency process. Subsequently, these variables were used to build a trend model based on time-dependent insolvency management scenarios. There are no published trend models of bankruptcies. A team of two experts was contacted and the list of case study variables was generated: SEL Selling of Assets ENJ Ensured Justice GRD Level of Greed TAX Tax Burden SAT Satisfaction of Creditors (5) SOL Solution of Debtors Assets POL Political Influence BUL Bullying of Creditors INF Inflation 21 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 Selling ofassets In principle, it is right that a secured creditor would decide on how the property of the creditor is secured. However, the practice is more complex and reflects a number of partial interests of the subjects who immediately decide on the method of monetisation and, in this sense, they instruct the insolvency administrator. Although the insolvency trustee may refuse the orders of the hedged creditor if they consider that the object of the hedge can be monetised more advantageously. Ensured justice It is a variable that represents the moral and fair behaviour of the insolvency court, which should perform a catalytic and independent role in the insolvency process. The insolvency court is the regional court where the debtor`s insolvency proceedings are conducted. If it is a legal entity, it is a regional court in the region where the debtor is based. In the case of a natural person, it is the court where the debtor resides. Level ofgreed The level of greed is a variable understood in trend modelling as the irrational behaviour of the debtor, which pushes against other variables for amortisation of the debt and the satisfaction of the creditor`s requirements. It has been selected as an important factor in the entire insolvency process and is also a suitable variable for trend modelling in terms of its vagueness and difficulty in quantifying. Tax burden For trend modelling purposes, the tax load variable is applied as a contradictory constant (depending on the type of debtor/creditor and the case to which the insolvency proceedings are dedicated). Unlike other process variables, it is of a sharp nature. Satisfaction ofcreditors Satisfaction of creditors is the first of the variables that are perceived in the model as target variables to represent the best possible state for the question under investigation. It is a fair payment of debts to creditors from debtors where, based on the court`s decision, the creditor(s) and creditor committees are split into secured and unsecured. Solution ofdebtor assets In the trend decision model, this variable is seen as one of the goals that should be as costeffective as possible for the subject, so that the creditor`s claim and the economic and social status of the debtor are maintained. Political influence It is not possible to analyse the country`s economy by only taking into account market factors (Radu, 2015). Every economic system must be integrated and harmonized with the country`s continuing development, a trend that reflects technological change and innovation as well as political conflicts that lead to the representation and changing of different interests and institutions. Therefore, it is important to include political factors to analyse the economic process (Boyer, 2011) 22 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 Bullying ofcreditors Being bullied by a creditor is against the law. Although creditors have many options to claim their right to repayment of the debt, which is considered legal, there are also many practices that are widely used that are not lawful (Kirwan, 2018). The initiation of insolvency proceedings not only has negative legal consequences (e.g. limiting the alleged debtor in relation to the handling of his property) but also has non-legal consequences (damage to the alleged debtor`s reputation, doubt of his credibility and economic situation). Inflation Simple inflation refers to an increase in the price level. In everyday life, an increase in inflation may mean that consumers pay more at a grocery store or, for example, at a petrol station (Vicki, 2017). Increased inflation also affects services and their providers. These traders need to adjust their service prices adequately to inflationary developments because their rising costs are dependent on increasing suppliers` prices and can have a direct effect on the entire debtor/creditor system. 2.1 Model ofInsolvency Proceedings Build variables (5), which play an important role in the decision-making process, and form a complete set of scenarios, were selected after discussions with experts on insolvency. The very nature of the variables used suggests that it is very difficult to quantify, see, for example, GRD. Therefore, the use of trend models is justified. See e.g. Figure 1 Trends relationship 1, (1) X Y 1 + SEL ENJ 2 25 SEL GRD 3 21 SEL SAT 4 24 SEL SOL 5 23 ENJ TAX (6) 6 - ENJ BUL 7 + TAX POL 8 - SAT BUL 9 + POL INF 23 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 There are 23 scenarios, m = 23(6). # SEL ENJ GRD TAX SAT SOL POL BUL INF V V V V G G O O O 1 +++ +++ +-- +++ +++ +-+ +++ +-- +++ 2 +++ +++ +-- +++ +++ +-0 +++ +-- +++ 3 +++ +++ +-- +++ +++ +-- +++ +-- +++ 4 +++ +++ +-- ++0 +++ +-+ ++0 +-- ++0 5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0 6 +++ +++ +-- ++0 +++ +-- ++0 +-- ++0 7 +++ +++ +-- ++- +++ +-+ ++- +-- ++- 8 +++ +++ +-- ++- +++ +-0 ++- +-- ++- 9 +++ +++ +-- ++- +++ +-- ++- +-- ++- 10 ++- ++- +-+ ++- ++- +-+ ++- +-+ ++- 11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+ 12 +00 +00 +00 +00 +00 +00 +00 +00 +00 (7) 13 +0- +0- +0+ +0- +0- +0+ +0- +0+ +014 +-+ +-+ ++- +-+ +-+ +++ +-+ ++- +-+ 15 +-+ +-+ ++- +-+ +-+ ++0 +-+ ++- +-+ 16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+ 17 +-+ +-+ ++- +-0 +-+ +++ +-0 ++- +-0 18 +-+ +-+ ++- +-0 +-+ ++0 +-0 ++- +-0 19 +-+ +-+ ++- +-0 +-+ ++- +-0 ++- +-0 20 +-+ +-+ ++- +-- +-+ +++ +-- ++- +-- 21 +-+ +-+ ++- +-- +-+ ++0 +-- ++- +-- 22 +-+ +-+ ++- +-- +-+ ++- +-- ++- +-- 23 +-- +-- +++ +-- +-- +++ +-- +++ +-- Figure 3 | Transition graph based onaset of23 scenarios (7) 10 13 23 12 16 15 11 19 22 21 20 17 18 14 7 4 8 3 9 6 2 5 1 Source: Authors` own processing 24 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 Any forecasting is heavily predetermined by interpretations of variables (5). The choice of the sets V, O, G, is of crucial importance and is based on the current point of view. Any forecasting/decision-making will be based on an n-dimensional model M(X). A set X of n variables is a union of Decision variables V, Goals variables G and Off-control variables O (8). SEL V Selling of Assets ENJ V Ensured Justice GRD V Level of Greed TAX O Tax SAT G Satisfaction of the Creditors (8) SOL G Solution of Debtor`s Assets POL O Political Influence BUL V Bullying of Creditors INF O Inflation O = [POL, INF, TAX] G = [SAT, SOL] (9) V = [SEL, ENJ, GRD, BUL] A simple common-sense analysis indicates that there is one view and forecast from the creditor`s point of view: Figure 4 | Creditor`s view – where t represents avariable time SAT SOL t t Source: Authors` own processing The best trend description of the creditor`s view: SAT Increase more and more rapidly DSAT = + DDSAT = + SOL Decreasing more and more slowly DSOL = - DDSOL = + (10) The worst trend description of the creditor`s view: SAT Decreasing more and more slowly DSAT = - DDSAT = + SOL Increase more and more rapidly DSOL = + DDSOL = + (11) 25 Acta Oeconomica Pragensia, 2019, 27(3–4), 17–30, https://doi.org/10.18267/j.aop.625 The best scenario is S7 (7). The shortest path is the path leading from the worst scenario S16 to the target scenario S7 (see Figure 3): S16 →S11 →S3 →S5 →S7 (12) Figure 5 | Asimplified transition graph based onaset of23 scenarios (7) 16 3 5 711 Source: Authors` own processing The sequence of scenarios is, see (23): No. SEL ENJ GRD TAX SAT SOL POL BUL INF V V V V G G O O O 16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+ 11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+ (13) 3 +++ +++ +-- +++ +++ +-- +++ +-- +++ 5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0 7 +++ +++ +-- ++- +++ +-+ ++- +-- ++- A decision-maker has no free choice to change the variables (5). Some variables are not under his/her control (8). Therefore, there are variables selected by O as out of control. This means that any forecast is partially based on available descriptions of O variables (13) e.g. probability distributions. 3.2 Probability Distributions Based on the transitional graph from the case study in Figure 5, the path from the worst kind of scenario to the best kind of scenario according to the creditor´s point of view was used. The transition graph in Figure 3 has been transformed into a decision tree where some of the decision-making heuristics can be used for obtaining the probabilities and to determinate the forecast. The resulting terminal scenarios, which also reflect the positive status for creditors, were designated as termination points. Where S16 was designated as the root node and S7 was the termination node (with the others S1, S8 and S9). Where the termination scenarios have slightly different outputs. Figure 6 | Thetransition graph has been transformed into adecision tree (7) 2 16 1 7 89 5 4 3 11 6 Source: Authors` own processing