2 Summary Motivation Literature review Research design Data description Financial ratiosModels and methodologiesResults of the analysisPrincipal component analysisCHAID decision tree modelThe logistic and the hazard modelArtificial Neural NetworkConclusions
3 MotivationThe financial crisis has already thrown many companies out of business all over the world. In Romania, for example, a study made by Coface Romania and based on the data provided by the National Trade Register Office, stated that around companies became insolvent by the end of 2008 when they were not able to pay their financial obligations due to inadequate cash flows. Looking at the above situation, we realise that only when a company can build up an efficient early warning system for financial distress and take effective actions before happening, will the company manage to keep on-going in the fierce competition. That is way, the study will focus on identifying a group of distressed and non-distressed Romanian listed companies for which financial ratios for several years will be calculated and then used to predict financial distress based on several models, such as: the Logistic and the Hazard model, the CHAID decision tree model and the Artificial Neural Network model. The study also includes a Principal Component Analysis, in order to better estimate the importance of each financial ratio included in the study.
4 Literature reviewBeaver (1966) developed a dichotomous classification test based on a simple t-test in a univariate framework and identified Cash flow/Total Debt as best predictor of bankruptcy.Altman (1968) suggested the Multivariate Discriminant Analysis (MDA) and identified five predictors: Working Capital to Total Assets, Retained Earnings to Total Assets, Earnings before Interest and Taxes to Total Assets, Market Value of Equity to Book Value of Total Debt and Sales to Total Assets.Ohlson (1980) used the Logit model and showed that size, financial structure(Total Liabilities to Total Assets), performance and current liquidity were best determinants of bankruptcy.Zmijewski’s (1984) first applied the probit model to the firm failure prediction problem.Shumway (2001) propused the hazard model for predicting bankruptcy and found that it was superior to the logit and the MDA models.Nam, Kim, Park and Lee (2008) developed a duration model with time varying covariates and a baseline hazard function incorporating macroeconomic variables.In recent years heuristic algorithms such as neural networks, hybrid neural networks and decision trees have also been applied to the distress prediction problem and several improvements were noticed for distress prediction: Zheng and Yanhui (2007) with decision tree models, Yim and Mitchell (2005) with hybrid ANN and others.
5 Research design 1. Data description For this study, public financial information for the period 2005–2008 was collected from the Bucharest Stock Exchange’s web site. The sample consisted in 100 Romanian listed companies on RASDAQ, equally divided into 50 “distressed” and 50 “non-distressed” companies, that were matched by assets size and activity field.Since there is no standard definition for a “distressed” company, I followed the same main classification criteria used in other similar studies (Zheng and Yanhui (2007), Psillaki, Tsolas and Margaritis (2008)). That is why, a company was considered “distressed” in case it had losses and outstanding payments for at least 2 consecutive years.The selection of the main set of financial ratios for each company was conditioned by those variables that appeared in most empirical work, but also restricted to the availability of the financial data.
6 Research design 2. Financial ratios: Category Code Financial ratios DefinitionProfitabilityI1Profit MarginNet Profit or Loss / Turnover *100I2Return on AssetsNet Profit or Loss / Total Assets *100I3Return on EquityNet Profit or Loss / Equity *100I4Profit per employeeNet Profit or Loss / number of employeesI5Operating Revenue per employeeOperating revenue / number of employeesSolvencyI6Current ratioCurrent assets / Current liabilitiesI7Debts on EquityTotal Debts / Equity *100I8Debts on Total AssetsTotal Debts / Total Assets *100Asset utilizationI9Working capital per employeeWorking capital / number of employeesI10Total Assets per employeeTotal Assets / number employeesGrowth abilityI11Growth rate on net profit(Net P/ L1 - Net P/L0) / Net P/L0I12Growth rate on total assets(Total Assets1 – Total Assets0) / Total Assets0I13Turnover growth(Turnover1- Turnover0) / Turnover0SizeI14Company sizeln (Total Assets)
7 Research design 3. Models and methodologies PCA involves a mathematical procedure that reduces the dimensionality of the initial data space by transforming a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components. These components are synthetic variables of maximum variance, computed as a linear combination of the original variables.CHAID decision tree model finds for each predictor the pair of values that is least significantly different with respect to the dependent variable, based on the p-value obtained from a Pearson Chi-squared test. For each selected pair, CHAID checks if p-value obtained is greater than a certain merge threshold. If the answer is positive, it merges the values and searches for an additional potential.The logistic model is a single-period classification model which uses maximum likelihood estimation to provide the conditional probability of a firm belonging to a certain category given the values of the independent variables for that firm, having the following form:where logit(pi) is the log odds of distress for the given values xi,1, xi,2,..,xi,k of the explanatory variables and βis the coefficient vector
8 Research design 3. Models and methodologies The hazard model is a multi-period logit model, which includes a baseline hazard function, which can be time-invariant or time varying, depending on its specification. It has the following form:where is the hazard function, xi,t represents the vector of explanatory variables used to forecast distress, is the baseline hazard function and β is the coefficient vector.ANN models have the ability to construct nonlinear models by scanning the data for patterns. The multilayer structure of the feed forward neural network used in this study is the following: an input layer, one hidden layer (following Jain and Nag’s study (2004)) and one output layer. The network was trained in order to learn how to classify companies as distressed and non-distressed.The hybrid ANN method includes as predictors only those variables that were highlighted as being relevant by the previous CHAID, LOGIT and HAZARD models and are marked as ANN – Ii,..Ik, where Ii,., Ik are the predictors from the previous models.
9 Results of the analysis Several distress prediction models were built in search for the model that has best out of sample performances and identifies the financial ratios that are most relevant in distress prediction problem. The following cases of initial data sets were tested:first-year data, when using the financial ratios of the year 2008 to predict financial distress one year aheadsecond-year data, when using the financial ratios of the year 2007 to predict financial distress two years aheadthird-year data, when using the financial ratios of the year 2006 to predict financial distress three years aheadcumulative three-year data, when using all the financial ratios of the years to predict financial distress one year ahead by letting the variables vary in timeFor each of the four data sets, a descriptive analysis was first conducted in order to be proper informed of any missing data, of the nature of the correlation between all 14 variables, of the differences in mean for each of the two types of companies.
10 Results of the analysis Data DescriptionFirst step consisted in identifying the financial ratios that have the highest ability to differentiate between distressed and non-distressed companies based on a mean difference t-test for each of the four data sets.
11 Results of the analysis Data DescriptionTo conclude, here are the significant mean differences in each of the 4 sets of data:first-year data set: I1, I2, I3, I4, I5, I8, I13 and I7second-year data set: I1, I2, I3, I4, I5 and I8third-year data set: I1, I2, I4, I5, I8, I9 and I11cumulative three-year data set: I1, I2, I3, I4, I5, I8, I13 and I7
12 Results of the analysis PRINCIPAL COMPONENT ANALYSISThe starting point for the PCA consisted in keeping only those variables that passed the mean differences test, while the purpose was to reduce its dimensions to a space that can allow visual interpretation of the data. The results of the PCA are presented in the following table:
13 Results of the analysis After applying the PCA for each of the 4 data sets the initial space was reduced to a 3-dimensional one, without loosing too much information. Now, it can be easily seen how the distressed companies form a separate group from the rest of the non-distressed companies, indicating that the financial information that is used in this study can be significant to classify and to predict the Romanian financial distressed companies.
14 Results of the analysis Training decision tree for PANEL 2CHAID CLASSIFICATION TREE:The initial sample of 100 companies was divided into a 70% training sample and a 30% test sample for each of the 4 data sets. In order to measure the decision tree model efficiency, the out-of-sample performances were calculated.SPSS 16.0 software was used and for each data set two decision trees resulted (one for the training sample and one for the test sample).CHAID was not only used to define the variables that can be used in the measurement of financial distress, but also to determine consistent classification rules, since a decision tree generates a rule for each of its leaves.Training decision tree for PANEL 1
15 Results of the analysis Training decision tree for PANEL 3Training decision tree for PANEL 4
16 principal components selected Results of the analysisCHAID CLASSIFICATION TREE:The results are summarized in the table below:DATA SETSprincipal components selected% in sample% out of samplePANEL 1: first-year data set188,6%93,3%PANEL 2: second-year data set1, 291,4%96,7%PANEL 3: third-year data set87,1%70,0%PANEL 4: cumulative three-year data set84,3%84,4%
17 Results of the analysis THE LOGISTIC and the HAZARD MODELS:The study was once again divided into 4 parts, by distinctly analyzing each set of data. In the first three panels, since considering only one year financial data for each company, a single-period logit model was estimated, while when using panel 4 two hazard models were estimated: first a hazard model with time invariant baseline hazard function followed by a hazard model with time varying baseline hazard function incorporating macroeconomic variables.Once again, the initial sample was divided into a 70% training sample and a 30% forecasting sampleThe following steps were taken in order to find the best logistic model for distress prediction:First a backward looking procedureThen a forward looking procedureThen, for each resulting model, each coefficient sign was checked to see if it corresponds to the economic theory and in case of a different sign, the corresponding value was dropped.Lastly, the remaining models (in case of more than just one model) were compared based on the following criteria: out-of-sample performance, McFadden value, LR value, AIC value, the goodness of fit Test (H-L Statistics) and total gain in comparison to the simple constant model.
18 Results of the analysis PANEL 1: first- year data setPANEL 2: second- year data setDependent Variable: TIPMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/22/09 Time: 12:41Sample: 1 70Included observations: 70Convergence achieved after 6 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb. C0.0005I30.0373I50.0003I80.0076Mean dependent var S.D. dependent varS.E. of regression Akaike info criterionSum squared resid Schwarz criterionLog likelihood Hannan-Quinn criter.Restr. log likelihood Avg. log likelihoodLR statistic (3 df) McFadden R-squaredProbability(LR stat)8.05E-08Obs with Dep=035 Total obs70Obs with Dep=1Dependent Variable: TIPMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/19/09 Time: 07:59Sample: 1 70Included observations: 70Convergence achieved after 10 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb. C0.0183I10.0029Mean dependent var S.D. dependent varS.E. of regression Akaike info criterionSum squared resid Schwarz criterionLog likelihood Hannan-Quinn criter.Restr. log likelihood Avg. log likelihoodLR statistic (1 df) McFadden R-squaredProbability(LR stat)Obs with Dep=035 Total obs70Obs with Dep=1
19 Results of the analysis PANEL 4: cumulative three-year data setHazard model with time-invariant baseline functionPANEL 3: third- year data setDependent Variable: TIPMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/23/09 Time: 02:42Sample: 1 70Included observations: 70Convergence achieved after 6 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb. C0.0216I50.0209I20.0068Mean dependent var S.D. dependent varS.E. of regression Akaike info criterionSum squared resid Schwarz criterionLog likelihood Hannan-Quinn criter.Restr. log likelihood Avg. log likelihoodLR statistic (2 df) McFadden R-squaredProbability(LR stat)2.62E-09Obs with Dep=035 Total obs70Obs with Dep=1Dependent Variable: TIPMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/23/09 Time: 04:12Sample: 1 210Included observations: 210Convergence achieved after 7 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb. C0.0000I20.0057I48.15E-050.0002Mean dependent var S.D. dependent varS.E. of regression Akaike info criterionSum squared resid Schwarz criterionLog likelihood Hannan-Quinn criter.Restr. log likelihood Avg. log likelihoodLR statistic (2 df) McFadden R-squaredProbability(LR stat)Obs with Dep=0126 Total obs210Obs with Dep=184
20 Results of the analysis PANEL 4: cumulative three-year data setHazard model with time-varying baseline functionDependent Variable: TIPMethod: ML - Binary Logit (Quadratic hill climbing)Date: 06/23/09 Time: 05:07Sample: 1 210Included observations: 210Convergence achieved after 8 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb. CHANGE_EUR0.0067C0.0000I20.0022I48.67E-050.0002Mean dependent var S.D. dependent varS.E. of regression Akaike info criterionSum squared resid Schwarz criterionLog likelihood Hannan-Quinn criter.Restr. log likelihood Avg. log likelihoodLR statistic (3 df) McFadden R-squaredProbability(LR stat)Obs with Dep=0126 Total obs210Obs with Dep=184
21 principal components selected Results of the analysisDATA SETSprincipal components selected% in sample% out of samplePANEL 1: first-year data set1, 390.0%PANEL 2: second-year data set1, 294,3%96,7%PANEL 3: third-year data setno valid modelPANEL 4: cumulative three-year data set187,1%86,7%THE LOGISTIC and the HAZARD MODELS :
22 Initial set of variables for ANN Results of the analysisFirst, the four data sets were transformed as follows: all the positive values of each predictor were scaled to the interval [0,1], while all the negative values of each predictor were scaled to the interval [-1,0]. A program using a feed forward backpropagation network was then implemented in MATLAB.THE ANN:THE HYBRID ANN:DATA SETSInitial set of variables for ANNno. neurons% in sample% out of samplePANEL 1: first-year data setall 141100,0%90,0%PANEL 2: second-year data setPANEL 3: third-year data set66,7%PANEL 4: cumulative three-year data set98,6%88,9%DATA SETStype of hybrid ANNno. neurons% in sample% out of samplePANEL 1: first-year data setANN - I1198,6%100,0%PANEL 2: second-year data setANN - I3, I591,4%PANEL 3: third-year data setANN - I1, I1187,1%73,3%ANN - I2, I585,7%76,7%PANEL 4: cumulative three-year data setANN - I2, I493,3%91,1%ANN - I2, I390,5%90,0%
23 ConclusionsPanel 1: Best financial distress predictor: I1 (profitability ratio)Best prediction models: single-period logit model and ANN – I1Panel 2: Best financial distress predictors: all 14 (profitability, solvency, asset utilization, growth and size ratios)Best prediction model: ANNPanel 3: Best financial distress predictors: (I1, I11), (I2, I5) (profitability and growth )Best prediction models: single-period logistic model, CHAID model, ANN –I1,I11 and ANN – I2,I5Panel 4: Best financial distress predictors: (I2, I4, exchange rate) (profitability ratios and macroeconomic variable)Best prediction model: hazard model with time varying baseline hazard function incorporating macroeconomic variables
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