A NEURAL NETWORK APPROACH TO FINANCIAL ...

A NEURAL NETWORK APPROACH TO FINANCIAL DISTRESS ANALYSIS

Harlan Etheridge* Assistant Professor of Accounting University of Houston

and

Ram Sriram Assistant Professor of Accounting Louisiana State University

*

Send correspondence to: Ram S. Sriram Department of Accounting College of Business Louisiana State University Baton Rouge, LA 70808 The authors thank KPMG Peat Marwick for the use of the data for this study. The assistance of Tim Bell is especially appreciated.

1 This paper presents a neural network approach for identifying financial distress in commercial banks and compares how this approach improves information for decision-making in external audit situations. The study also uses two of the more traditional statistical methodologies: Logit Analysis, and Multiple Discriminant Analysis (MDA) to identify financial distress of failed commercial banks -- one year, two years, and three years prior to the actual failure. The results from the traditional statistical methodologies are compared to the neural network approach in three specific areas: classification accuracy, type I and type II errors of misclassification, and early signaling ability. Statement of Auditing Standards, SAS 59 requires auditors to actively examine on each audit, the ability of a client-firm to continue as a going concern. SAS 59 requirements, not only place auditors in the unenviable position of making judgments about an entity's future financial strength based on a limited examination of records, but also exposes auditors to legal liability. If an entity ceases to exist as a going concern within a year after receiving an audit opinion that did not express substantial doubts about the entity's ability to continue as a going concern, stockholders and other users of audited financial statements may file a lawsuit against the auditors. Even if the courts find the auditors to be non-negligent in their work or not responsible for reporting the approaching financial distress, the cost of the lawsuits to auditors can be substantial. Defending against charge of negligent audit work is often difficult. If auditors used decision support systems that improved their ability to reliably detect impending client financial distress early, then auditors could avoid some litigation and, at a minimum, defend themselves in court with greater facility. The traditional approach to evaluating financial distress uses statistical techniques such as multiple discriminant analysis (MDA) [Altman, 1968; Altman et. al,

2 1977; Ohlson, 1980; Chalos, 1985] or logit analysis [Gentry, et. al, 1985; Jones, 1987; Casey and Bartczak, 1985; and Sinkey, Jr., 1974, 1975]. 1 Logit and MDA have been widely used with reasonable success to detect financial distress in a variety of industries such as railroads [Altman, 1973]; banks [Santomero and Vinso, 1977; Pettway and Sinkey, 1980]; and insurance companies [Trieschmann and Pinches, 1973; and Pinches and Trieschmann, 1977]. MDA has by far been the most popular statistical approach and is generally used as a standard with which to compare other approaches [Coasts and Fant, 1993]. However, MDA has been criticized for serious shortcomings, in particular, its restrictive data assumptions and its requirement of linearly separable categories of data. MDA also is criticized for allowing the predictive ability of a ratio to vary in relationship to other ratios. Thus, MDA is less than efficient in analyzing the complexities of interacting and interdependent ratios [Karels and Prakash, 1987]. Logit is another technique frequently used to predict financial distress. In logit models, the dependent variable bankruptcy is treated as a dichotomous variable 2, i.e., a firm is assumed to be either bankrupt or not bankrupt. The independent variables of the models place a firm in either one of these categories. The dependent variable observations are assumed to be random and statistically independent of each other. The models assume that there is a log linear relationship between the independent

1

Studies have also used other methodologies such as probit [McFadden, 1976; Casey et. al, 1986; Pastena and Ruland, 1986], recursive partitioning [Breiman et. al, 1984; Frydman, Altman and Kao, 1985], expert systems [Elmer and Borowski, 1988], and nonparametric techniques [Barniv and Raveh, 1989]. 2

This statement reflects the traditional use of logit or probit to determine financial distress. A notable exception is Lau (1987) who used a multinomial logit model.

3 variables. If any of these assumptions are violated, then logit models will be less accurate. An artificial neural network is a suitable alternative bankruptcy prediction method that overcomes some of the shortcomings of MDA and logit. Artificial neural networks (hereafter, neural networks) are not affected by the constraining assumptions of MDA or logit. For example, neural networks do not require the data to be multivariate normal or to have equal covariance matrices, or the independent variables to have a log linear relationship. Additionally, as several recent studies demonstrate, when neural network models are used, the number of misclassification errors are smaller and the overall accuracy is at least equal to MDA or logit [Cottrel, et. al, 1987, Odom and Sharda, 1990; and Coats and Fant, 1993]. The purposes of this study are to determine: (1) whether neural networks are useful as a decision support tool for going concern situations; (2) whether neural networks are an improvement over traditional statistical techniques in the early detection of impending financial distress; and (3) whether the classification accuracy of neural networks is superior in terms of type I or type II errors compared to that of MDA and logit. This study will use MDA, logit, and neural network models to classify banks as either failed or not failed. Being able to identify failing banks early is very important to auditors, bankers, investors, managers, lending officers, portfolio managers, and many others. The remainder of this paper is organized as follows; Section 1 discusses two of the traditional statistical methodologies used in bankruptcy prediction studies -- logit and MDA and points out the statistical and application problems associated with the techniques. Section II describes the neural network approach. Section III presents the research design, sample selection, and methodology. Section IV presents results and

4 compares the performance of the MDA, logit, and neural network models. Section V summarizes the results and discusses the limitations. TRADITIONAL BANKRUPTCY TECHNIQUES - MDA AND LOGIT ANALYSIS MDA, a multivariate technique, is widely used in bankruptcy studies [Altman, 1968; Altman, et. al, 1977; Deakin, 1972; Libby, 1975; Schipper, 1977; Ohlson, 1980; Chalos, 1985; Casey and Bartczak, 1985, and Gentry, et. al, 1985]. The technique classifies each firm in a sample as either bankrupt or non-bankrupt, using a linear combination of independent attributes. The procedure computes a composite score for observations by maximizing the between-groups to the within-groups variance and then assigns a score for each firm in a sample. If the assigned score is below the composite score, a firm is classified as bankrupt and if the assigned score is above the composite score, a firm is classified as healthy [Fisher, 1936; Welch, 1939; Altman, 1987; Jones, 1987; Barniv and Raveh, 1989]. MDA performs well when the data complies with the following statistical requirements: (1)The independent variables are multivariate normal within each group. (2) The covariance matrices of the two groups are equal. (3) The vectors of the means of the two groups, the covariance matrix and the prior probabilities are known. Often, data used in bankruptcy studies violate these assumptions. When one or more of the independent variables are dummy variables, the multivariate normal assumption is always violated [Jones, 1987]. Several studies point out that the seriousness of multivariate normal violation can be reduced by applying transformations (log, square root, etc.), to the independent variables [Altman, et. al, 1977; Barniv and Raveh, 1989]. However, the transformations do not guarantee multivariate normality.

5 Second, the variance/covariance matrices may not be equal. Once again, the severity of the problem can be reduced by using quadratic discriminant analysis instead of linear discriminant analysis [Altman, et. al, 1977; Lachenbruch, 1975; Pinches and Trieschmann, 1977; Hamer, 1983]. In general, the advantage of using linear discriminant model is its classification success, regardless of violations of some of its restrictive data assumptions [Jones, 1987]. In contrast to MDA, logit is a conditional probability technique. The technique provides the conditional probability of an observation belonging to a certain group, given the values of the independent variables for that observation [Cox, 1970; Jones, 1987]. The advantage of using logit is that, unlike MDA, it does not impose restrictive assumptions on the data such as multivariate normal or equal covariance matrices. Moreover, approaches such as maximim likelihood logit provide estimates which are asymptotically unbiased and normally distributed [McFadden, 1976; and Martin, 1977]. The maximum likelihood method sets the weight of independent variables by maximizing the joint probabilities of bankruptcy or non-bankruptcy for each observation [Jones, 1987]. The significance of the independent variables can be estimated by using a chi-square test which, similar to the standard regression technique, divides the coefficients by the standard error [Jones, 1987]. Compared to MDA, logit has both advantages and disadvantages. Logit does not suffer from some of the restrictive assumptions of MDA. However, logit may compute the probability of failure incorrectly when the proportion of failed and healthy firms in a sample are unequal. Since in most situations, the proportion of failed and non-failed firms would be unequal, the logit results may not truly reflect the population characteristics. Generally, logit has a slightly higher prediction accuracy than MDA [Collins and Green, 1982]. Given the cost of misclassifying a potential bankrupt firm as

6 non-bankrupt, the higher prediction accuracy gives logit an advantage over MDA. NEURAL NETWORKS AS DECISION SUPPORT SYSTEMS Neural networks are a type of computer-based artificial intelligence that uses special computer hardware or specifically designed software for use on conventional computers. Neural networks can be used to recognize patterns and to forecast future performances with less than complete data. The neural network technique attempts to recreate, in a much simplified manner, the basic structure of the human brain-numerous simple processing elements that are highly interconnected. Neural networks also perform in a manner that simulates the decision-making style of human experts. Cognitive scientists believe that humans use pattern association techniques to make decisions [McClelland and Rumelhart, 1988; Caudill and Butler, 1990]. 3 Neural networks use the same type of pattern association techniques to solve problems. In recent years, neural networks have been used in diverse fields ranging from medicine to finance [White, 1988]. Because neural networks are efficient in pattern recognition tasks, they should be a useful technique for recognizing approaching financial distress. Since bankruptcy is generally a pattern of deterioration in financial and other performance measures over time, use of neural networks could improve bankruptcy prediction and also allow early detection of impending financial distress. Neural networks are patterned after the human brain and process information in a parallel manner. Neural networks have an associative memory that allow them to learn and recognize patterns in a manner similar to that of the human brain [Pao, 1989].

3

Data patterns of the current situation are compared to those of previously encountered situations. The decision associated with the data pattern that most closely matches the current data pattern is used as a basis for making a decision in the current situation.

7 The system associates input patterns with the desired output patterns and modifies the mapping from input to output as the environment changes [Wasserman and Schwartz, 1988]. The content-addressable associative memory of neural networks gives them the ability to solve complex problems rapidly and reliably (Roberts, 1988) and also produces the desired output from fragmented or partially incorrect inputs (Altman, 1987). As a classification and prediction technique, neural networks impose less restrictions on the data than traditional statistical techniques. First, neural networks do not require any assumptions about the data such as equal covariance matrices or multivariate normal distribution. Second, neural networks allow the use of all available and relevant data. However, the neural network results are not confounded by multicollinearity among the independent variables. Third, neural networks are more tolerant of noise in the input data and can operate effectively with input noise levels as high as 30 to 40 percent . The ability to operate with noisy data gives neural networks the ability to extract "ideal" output from less than ideal input [Wasserman and Schwartz, 1988]. Finally, unlike traditional statistical modelling, when using a neural network, a researcher need not start with the most appropriate model; the neural network itself develops the most appropriate model based on the underlying data. Therefore, model misspecification error is minimized. Before using neural network as a decision support system for a specific problem, the researcher must choose the appropriate network paradigm. Several types of network paradigms have been developed, each appropriate for a specific type of problem [Klimasauskas, 1988). In Appendix A, we discuss four common neural network paradigms. Generally, a network paradigm is produced by the combination of processing element neuro-dynamics and network architecture (Klimasauskas, 1988).

8 Processing element neuro-dynamics depend on (1) how the inputs are combined, (2) how the activation level is used to propagate an output, and (3) how the learning algorithm adjusts the weights associated with the processing elements (Klimasauskas, 1988). Network architecture depend on (1) the pattern and structure of the connections between processing elements, (2) the use of feedback, (3) the competition among processing elements, and (4) how the data flows through the network (Klimasauskas, 1988). As a decision support system, neural network can be used in two basic ways: as unsupervised learning networks or as supervised learning network. As an unsupervised learning network, the network is supplied with input data with no feedback regarding the correct solutions. The neural network discovers patterns in the data and structures its own relationships among the data items. In supervised learning, the user provides the neural network with feedback information (the correct network response to the input data). The network then detects data patterns and structures relationships among the variables in a manner consistent with the feedback. A neural network is trained using a training data set. A training data set should consists of data that is relevant to the decision that the network is making. Training data also must contain as many relevant data patterns as possible so that the network has no difficulty in recognizing relevant data patterns once training is complete. No data items or information that is useful in discriminating among data classes should be omitted. Once training is complete, new data patterns can be compared to data patterns that were developed with previous input. Using its associative memory, the network then determines the pattern the new data most closely resembles. Based on the strength of relationship between old and new patterns among the data, the neural

9 network generates the appropriate output.

DATA AND METHODOLOGY To apply the traditional statistical techniques multiple discriminant analysis (MDA) and logit and the non-traditional neural network technique, we used data from bankrupt and non-bankrupt commercial banks which are members of the Federal Reserve System. The focus is on identifying the financial characteristics which differentiate between failed and healthy commercial banks and comparing the classification errors of the various methodologies. The original sample of 1139 banks was split into a training sample of 911 commercial banks and a holdout sample of 228 commercial banks. According to the Federal regulatory agencies, 145 of the banks in the undivided sample had failed. The data on the 1139 banks were obtained from the records maintained by a Big Six accounting firm. Every failed bank included in the training sample was matched with approximately six healthy banks. The failed and healthy banks were matched on the basis of geographic market area, total deposits, and Federal Reserve membership. Since the two groups have similar size and structural characteristics, any differences in their financial status must be due to select financial ratios. Our approach to matching the failed and healthy banks is similar to that of Ohlson (1980) in that we tried to achieve a somewhat realistic proportion of failed to nonfailed banks while controlling for certain firm characteristics. In the real world, the proportions of failed and healthy firms in the population are never equal. Using the sample proportion of failed and healthy banks often leads to biased coefficient estimates and high classification error rates for the failed banks [Zmijewski, 1984a]. While the one-to-six ratio used in this study also does not reflect the true population proportion, we believe it will be more representative

10 of the population than a one-to-one match. Previous studies have indicated that a bank's deterioration from a healthy to a failed institution is not a sudden occurrence but a slow transition over the years [Sinkey, 1975; 1977; Martin, 1977; Stuhr and Van Wicklen, 1974]. These studies indicate that a major factor that explains bank failures is quality of management. One approach to evaluating quality of management is to evaluate select financial ratios taken from a bank's financial statements. In this study, ratios were chosen to measure a bank's performance in five important areas: liquidity, loan quality, efficiency, profitability and rates of return, and capital adequacy.Why these areas? Accordingly, this study uses ratios for three years, 1988, 1987, and 1986 (one, two and three years prior to bankruptcy), to measure performance in these five areas. The actual ratios used to construct the MDA and logit models in this study and their definitions are provided in Appendix B. The use of neural networks for data analysis and modelling is not restricted by data assumptions. Consequently, neural networks are able to construct models using many more variables than traditional modelling techniques, e.g., MDA and logit. Because of this ability, 57 independent variables were used to construct neural network models of bankruptcy. These independent variables include those used to construct the MDA and logit models and are listed in Appendix C. However, in order to better compare the bankruptcy classification ability of neural networks with that of MDA and logit, the same independent variables used with MDA and logit also were used to construct neural network models. Neural Network Methodology The neural network software package used in this study is NeuralWorks Professional II/Plus. This is a simulated neural network that is implemented in software

11 and runs on a conventional computer, in this case a 486DX PC. This software has the same capabilities and provides the same results as a true neural network (that is implemented in hardware) but is much slower because it runs on a traditional sequential computer, but costs much less than a true neural network. NeuralWorks Professional II/Plus provides over 20 neural network paradigms; however, only five of these are designed for classification problems. Consequently, only these five neural network paradigms were used in this study 4. These five paradigms are (1) Categorical Learning, (2) Counterpropagation, (3) Learning Vector Quantization, (4) Probabilistic Neural Network, and (5) Self-Organizing-Map into Categorization 5. The neural networks developed models of bankruptcy6 based on the training samples from 1986 through 1988 7. Several performance measures, including root

4

A description of these five neural network paradigms is beyond the scope of this paper. Interested readers are referred to Caudill and Butler (1990) and McClelland and Rumelhart (1988) for an introduction to various types of neural networks. 5

Previous studies investigating classification problems have used a popular type of neural network paradigm called backpropagation. However, most descriptions of backpropagation state that it is best used for forecasting. Therefore, backpropagation was not used in this study. 6

The models are defined by the strength of the connections between the individual processing elements and in how the processing elements are connected. Consequently, these bankruptcy models cannot be described conventionally. 7

A training sample encompassing data only from 1988 (one year prior to bankruptcy) also was used to train the neural networks. Use of this traning sample, while decreasing the overall error rates of most networks, increased the Type I error rates.

12 mean squared error and Pearson's coefficient, were used during the training process to ensure that the models were adequate 8. Once adequate models were obtained, the holdback sample was used to test the performance of the neural networks.

RESULTS MDA Analysis Table 1 provides descriptive information such as means and standard deviations for the ten financial ratios used in this study for the bankrupt and healthy (control) banks for the years 1986-88. Tables with descriptive statistics for (1) bankrupt banks, (2) nonbankrupt banks, (3) training sample, and (4) holdback sample? Table 2 reports the results of MDA. Univariate F-tests show that six variables are statistically significant at the 0.05 level and two variables are statistically significant at the 0.10 level in 1986. All the eight variables identified in 1986 are significant at the 0.05 level again in 1987 and in 1988 (in 1988, one of the eight variables is significant only at the 0.10 level). The degree of significance of most the variables increases over time, indicating that the rate of decline in financial condition is likely to increase for a bankrupt bank relative to a healthy bank. Move to first discussion of independent variables. Since the ratios used in this study reflect financial performance over time, it is necessary to examine the meaning of some of these significant variables. The three ratios, NLNSASST, PROVOPIN and PROVNLNS are a measure of a bank's loan volume and loan quality. The results

8

Only the Probabilistic Neural Network allowed adjustment of a priori probabilities of occurrence. Consequently, this neural network was constructed to minimize Type I error rates. Modification of certain network parameters was found to minimize Type I errors in other neural networks.

13 reported in Table 2 indicate that all three loan ratios are significant. The proportion of loan in the total asset portfolio appears to be larger for the average bankrupt bank than for the healthy bank. Similarly, a bankrupt bank appears to have greater proportion of loan losses relative to its total assets and total operating income than a healthy bank. The proportion of loan losses to total assets and total operating income increases significantly as the bank approaches bankruptcy. Now consider the ratios, OEOPINC and OPINCAST. The ratios are a measure of a bank's operating efficiency. The MDA results show that a bankrupt bank is likely to be less efficient by spending a greater portion of its operating income on operating expenses than a healthy bank. This ratio was the most important variable by rank one year prior to bankruptcy. OEOPINC, a ratio of operating income to total assets was not significant. The deterioration in operational efficiency was substantial as a bank approached the year in which it filed for bankruptcy. Another important indicator of approaching financial distress is capital adequacy (CAPADQ) obtained by dividing the total equity capital by the total assets. Comptroller of Currency often use the ratio to measure a bank's capital adequacy. Table 2 shows that a problem bank is often more starved for capital than a healthy bank. Once again, the rate of deterioration is considerable for a bankrupt bank than a healthy bank. The lack of adequate capital is most significant in the year of bankruptcy. Finally, three other variables that appear to differ significantly between a healthy and unhealthy bank are ROA, ROE and MARGIN. ROA is low for a bankrupt bank compared to a healthy bank three years prior to bankruptcy and even lower two years prior to bankruptcy. ROA and ROE were the most important variables by rank up to two year prior to bankruptcy. However, in the year prior to bankruptcy, ROE was significant only at the 0.10 level and fell to the seventh rank by order of importance. Similar to the other

14 significant variables, the profitability of bankrupt banks (MARGIN) was considerably lower than healthy banks. The rate of decline in profitability continued to grow as a bank approached bankruptcy, with the lowest profitability in the year prior to bankruptcy. The classification results reported in Table 2 show that the rate of correct classification of bankrupt banks to increase from a low of 28.3% three years prior to bankruptcy to a high of 63.3%, one year prior to bankruptcy. These classification results clearly show that a bankrupt bank is quite distinct in its financial characteristics from a healthy bank. However, the rates of misclassification ranging from a high of 61.7% to a low of 26.7% for bankrupt banks are not very encouraging. Logit Analysis The logit technique, similar to MDA, computes the conditional probability of an observation belonging to a certain class. But, unlike MDA, logit does not require the independent variables to be multivariate normally distributed [Jones, 1975; and Martin, 1977]. The logit analysis used in this study produces a set of probability estimates so that banks known to have filed for bankruptcy are assigned a higher probability score of failure and banks that are known to be healthy are assigned a very low probability of failure. The maximum likelihood estimates produced by logit analysis are asymptotically unbiased and normally distributed [McFadden, 1976] and in the case of large samples like the ones used in this study, the coefficients and estimated variance bias are small. Table 3 reports the logit results. In the year 1986, three years prior to bankruptcy, five of the nine independent variables are significant at the 0.05 level. These variables are NLNSASST (net loans to total assets) OEOPINC (operating expenses to total operating income), OPINCAST (operating income to total assets), ROE (return on equity), and ROA (return on assets). In the year 1987, two years prior

15 to bankruptcy, four of these five variables are again significant at the 0.05 level. Unlike in 1986, only ROE is not significant. In the year 1988, one year prior to bankruptcy, eight of the ten variables included in the model are significant. These significant variables represent loan volume and loan quality (NLNSASST, PROVNLNS, PROVOPIN), operating efficiency and profitability (OEOPINC, OPINCAST, and MARGIN), rate of return (ROA), and capital adequacy (CAPADQ), the variable representing capital adequacy are significant at the 0.05 level. As for the classification accuracy, logit classifies 62.8% of the bankrupt banks correctly three years prior to bankruptcy. The rate of correct classification increases to 77.3% two years prior to bankruptcy and 89.2%, one year prior to bankruptcy. As for healthy banks, the classification accuracy ranges from 90.3% to 96.4%. Comparing the logit results with MDA, several observations can be made. Both approaches show that the most important indicator of bankruptcy to be loan quality and loan volume. The variables NLNSASST, PROVOPIN, PROVNLNS are significant in both approaches, although the significance of the variables vary within the different years. The next set of variables significantly associated with bankrupt banks are the variables OEOPINC, OPINCAST, and MARGIN the variables indicating operating efficiency and profitability followed by CAPADQ, indicating capital adequacy and ROA and ROE indicating rate of return. Both statistical approaches show that the significant variables increase in importance as the year of bankruptcy approaches. As for classification accuracy, logit clearly outperforms MDA in classifying bankrupt banks, in all three years prior to bankruptcy. The results are more comparable in the case of healthy banks. Our results are somewhat different in this respect compared to prior studies [Sinkey, 1975; and Martin, 1977]. A possible explanation for the difference in classification accuracy is that, unlike prior studies which matched a bankrupt firm with a

16 non-bankrupt firm on a one to one basis, the current study used a more realistic sample by matching each bankrupt bank with six non-bankrupt banks. Neural Network Analysis Tables 5, 6, and 7 report the classification accuracy of the various neural network paradigms using the 57 independent variable holdback samples for one, two, and three years prior to bankruptcy. As indicated in Table 5, the Learning Vector Quantization network had the lowest overall error rate (3.95%) one year before bankruptcy. However, the one of the objectives of this is to develop bankruptcy prediction models that minimize the Type I error rate and, therefore, the Categorical Learning and Probabilistic neural networks yield the best performance (both have a 4.00% Type I error rate) one year prior to bankruptcy. Table 6 shows that the Categorical Learning neural network still had the lowest Type I error rate (4.00%) although it also has the highest overall error rate (11.84%). Three years before bankruptcy, as indicated in Table 7, the Probablisitic neural network yields the lowest Type I error rate (12.00%) followed by the Categorical Learning neural network (16.00%). After testing the relative accuracy of the various approaches, we also tested our MDA logit? and neural network models on a holdout sample of 200 banks (25 failed and 175 healthy banks). The holdout sample was matched by the same criteria as the primary sample. Table ? compares the classification accuracy (Type I and Type II errors). A type I error is where a failed bank is incorrectly classified as healthy and type II error is where a healthy bank is incorrectly classified as a failed bank. A overall error rate refers to the total incorrect classification for the analysis. MDA generally is very successful in identifying and classifying healthy banks (a low type II error). However, it is less successful in correctly identifying and classifying

17 failed banks (a low type I error). For MDA, success in correctly identifying healthy banks over a three year horizon ranged between ? . On the other hand, success in correctly identifying failed banks over a three year horizon ranged only between ? . Certain neural network models had consistently low type I errors compared to the MDA models. Tables 8, 9, and 10 list the error rates for neural networks using the 10 independent variable holdback samples for one to three years before bankruptcy.

COST OF MISCLASSIFICATION Hopwood et al. (1989) use Type I/Type II cost ratios ranging from 1:1 to 50:1. Altman et al. (1977), Zmijewski (1984b), and Dopuch et al. (1987) also suggest that Type I error are more costly than Type II errors. We use the the same Type I/Type II cost ratios as in Hopwood et al. (1989, Zmijewski (1984), and Dopuch et al. (1987): 1:1, 10:1, 20:1, 30:1, 40:1, and 50:1. As stated in Hopwood et al. (1989, p. 36), although decision makers are unlikely to have symmetrical cost preferences, the 1:1 cost ratio is included to allow comparison with previous studies.

Table 11 compares the relative

cost of misclassification of the statistical and 57-variable neural network bankruptcy prediction models using the different Type I/Type II cost ratios. The relative cost of misclassification, C, is calculated as: C=

(Number of Type I errors x cost ratio) + (Number of Type II errors) 100

Table 12 shows the cost of misclassification of the statistical and 10-variable neural network bankruptcy prediction models. DISCUSSION

18 A major objective of this paper is to develop a computer-aided decision support system, neural network, that auditors can use in going concern situations. A minor objective of this paper is to compare the neural network to traditional statistical approaches such as logit and MDA in terms of their classification accuracy. If auditors are only interested in correctly classifying a healthy or failed bank and ignore the costs of misclassification, the results of this study show that neural network does not outperform MDA or logit. But, for auditors, the cost of misclassification is a major concern. Either wrongly identifying a failing bank as healthy or a healthy bank as failing can have serious consequences for auditors in terms of legal liability and reputation. If auditors consider the relative costs of misclassification for each group, then, neural network definitely outperforms MDA or logit with its low type I error rates and comparable type II error rates. Given that type I error (the cost of misclassifying a failing bank as healthy) is greater than type II error (the cost of misclassifying a healthy firm as failing), we expect neural network to improve auditor decision making and reduce the exposure to law suits.

19 APPENDIX A NEURAL NETWORK PARADIGMS Pattern Associator. In this paradigm, during the training phase the neural network is presented with pairs of patterns. The system learns the association between the pair members. Then, when one of the members of the pair is presented as input, the system produces the other member of the pair as the output. Auto Associator. In this paradigm, a set of patterns is repeatedly presented during the training phase. The system memorizes the patterns. Later, a part of an original pattern or one that closely resembles the original pattern is presented to the system. The system retrieves the original pattern and produces it as an output. Classification Builder. Prior to the training, the system developer defines a set of classes into which the patterns to be presented are to be classified. During the training phase, the patterns are presented as input along with the indication of their corresponding classes. The objective is to make the system learn to correctly classify the input patterns so that, in the future when a similar pattern is presented, the system will able to place it in the correct class. Regularity Detector. In this paradigm, the system attempts to find statistically salient features of the input patterns. Unlike the classification builder paradigm described above, there is no training, and the system operates in unsupervised learning mode (Bayle, 1988).

20 APPENDIX B DESCRIPTION OF FINANCIAL RATIOS USED IN MDA AND LOGIT MODELS CategoryVariableName 1.Liquidity Cash and due / Total Assets

CASHASST

2.Loan VolumeNet Loans / Total Assets NLNSASST 3.Loan QualityProvision for loan losses / PROVOPIN Total Operating Income 4.Loan QualityProvision for loan losses / PROVNLNS Net Loans 5.EfficiencyTotal Operating Expenses / OEOPINC Total Operating Income 6.EfficiencyTotal Operating Income/ Total Assets 7.Profitability / Total Assets

OPINCAST

Total Int. Income - Total Int. Expenses

MARGIN

8.Rate of ReturnNet Income / Average Equity Capital

ROE

9.Rate of ReturnNet Income / Total Assets

ROA

10.Capital Adequacy Total Equity Capital / Total Assets

CAPADQ

21 APPENDIX C INDEPENDENT VARIABLES USED IN NEURAL NETWORK MODELLING 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

Allowance for Loan and Lease Loss to Net Loans and Leases Yield to Breakeven Brokered Deposits to Total Deposits Capital Adequacy Cash and Due to Total Assets Commitments to Total Assets Loans and Commitments to Total Deposits Core Deposits to Total Deposits Earnings Assets to Total Assets Net Interest Income (Expense) on Federal Funds Purchased (Sold) of Total Interest Income Gross Charge-Offs to Gross Loans Gross Recoveries to Gross Loans Loans to Insiders to Net Loans Interest Bearing Deposits to Total Deposits Interest Expense to Interest Bearing Deposits Total Interest Expense to Total Operating Income Jumbo Time Deposits to Net Loans Jumbo Time Deposits to Total Deposits Large Time Deposits to Total Assets Net Interest Margin Net Charge-Offs to Gross Loans Net Loans to Total Assets Net Loans to Total Deposits Nonaccrual Loans to Gross Loans Noninterest Income to Total Operating Income Nonperforming Assets to Total Assets Nonperforming Loans to Primary Capital Nonperforming Loans to Total Assets Nonperforming Loans to Net Loans Total Nonperforming and Restructured Loans to Gross Loans Total Operating Expense to Total Operating Income Total Operating Income to Total Assets Other Real Estate Owned to Total Assets Total Overhead Expense to Total Operating Income Total Overhead Expense to Total Assets Past Due Loans to Gross Loans Personnel Expense to Total Operating Income Primary Capital to Adjusted Assets

22 APPENDIX C -- CONTINUED 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57.

Primary Capital Adequacy Provision for Loan and Lease Loss to Net Loans and Leases Provision for Loan and Lease Loss to Total Operating Income Provision for Loan and Lease Loss to Total Assets Public Deposits to Total Deposits Rate Restructured Loans to Gross Loans Return on Assets Return on Assets Adjusted for Unrealized Loss on Marketable Securities Return on Total Assets Return on Average Equity Return on Total Equity Total Securities to Total Assets Interest Rate Swaps to Total Deposits Undivided Profit and Capital Reserve to Total Assets Volatile Liability Dependence Yield Yield on Loans 3-digit ZIP code location

23

TABLE 1 Descriptive Statistics for Ratios Used to Classify Failed and Healthy Banks ________________________________________________________________________________________ Failed and (Healthy) Banks ________________________________________________________________________________________ 1986 1987 1988 __________________________________________________________________________ Ratio Means Std. Dev. Means Std. Dev . Means Std. Dev. ________________________________________________________________________________________ CASHASST 0.103 0.048 0.090 0.052 0.087 0.058 (0.098)(0.076) (0.094)(0.076)(0.088) (0.067) MARGIN 0.038 0.012 0.036 0.010 0.033 (0.039)(0.010) (0.040)(0.009) (0.040) (0.008) NLNSASST 0.616 0.110 0.623 0.118 0.601 (0.500)(0.139) (0.515)(0.151)(0.523) (0.148)

0.126

OEOPINC 1.205 0.253 1.291 0.396 1.448 (0.954)(0.241) (0.914)(0.146)(0.892) (0.123)

0.429

PROVNLNS 0.036 0.023 0.042 0.042 0.062 (0.016)(0.026) (0.011)(0.017)(0.008) (0.013)

0.069

ROA-0.015 0.021 (0.006)(0.012)

-0.026 0.030 -0.043 (0.006)(0.013)(0.008) (0.012)

0.041

ROE-0.224 0.372 (0.063)(0.186)

-0.476 0.526 1.174 11.325 (0.068)(0.171)(0.084) (0.184)

PROVOPIN 0.208 0.179 0.261 0.254 0.340 (0.084)(0.137) (0.058)(0.088)(0.044) (0.074)

0.340

CAPADQ 0.076 0.037 0.055 0.033 0.012 (0.091)(0.056) (0.090)(0.047)(0.089) (0.049)

0.044

0.010

OPINCAST 0.102 0.024 0.097 0.018 0.100 0.017 (0.099)(0.035) (0.096)(0.047)(0.099) (0.051) ________________________________________________________________________________________

24 TABLE 2 Multiple Discriminant Analysis Results - 1986-88 ________________________________________________________________________________________ 1986 1987 1988 _______________________________________________________________________________________ Ratio Coeff. F Rank Coeff. F Rank Coeff. F Rank _______________________________________________________________________________________ CASHASST 0.042 0.4010 0.066 0.319 0.006 0.659 9 NLNSASST-0.384 75.74* 5 -0.229 55.95*7 PROVNLNS

0.113 54.08* 6

0.684204.10*

-0.074 30.00*

0.343386.40*4

5

PROVOPIN 0.164 77.86* 4 -0.525279.10* 4

-0.013455.90*3

OEOPINC-0.162111.00* 3

-0.243859.90*1

-0.144379.80* 3

OPINCAST-0.299 0.74 9 -0.191 0.29 10

-0.505 0.60

ROA 0.907237.50* 1 0.627414.50*

2

0.911756.10*2

ROE 0.078179.00* 2 0.870500.60*

1

0.870 7.35**

MARGIN 0.042 2.78** 8

0.088 18.60* 8

CAPADQ-0.095 7.70** 7 0.161 57.19* 6 Classification Results Bankrupt28.3%50.0% 63.3% Non-Bankrupt 97.0%97.7% 98.6%

7

0.200 76.67* 0.307254.10*5

10

8 6

25 TABLE 3 Logit Results - 1986-88 ________________________________________________________________________________________ 1986 1987 1988 ______________________________________________________________________________ RatioBeta Chi-Sq.p-Value Beta Chi-Sq. p-value BetaChi-Sq.p-value ________________________________________________________________________________________ CASHASST 0.07 0.00

0.97

4.23

NLNSASST- 6.7431.200.00 PROVNLNS

- 4.78

- 8.50 0.470.49

2.43

0.11

11.04

0.00

43.73

PROVOPIN 4.03 2.46

0.11

- 5.75

OEOPINC- 1.91 3.80

0.05

1.67

2.71

0.50 0.47 - 7.57

0.09

10.38

-77.18

0.00 5.14 0.02

0.25

17.70

6.94

0.00

1.11

0.29

-5.81

2.00

0.15

OPINCAST-13.0011.350.00 -21.60 15.23 ROE- 2.13 3.89 0.04 1.19 1.400.23

0.00 -0.40

-17.30 1.79

1.27 0.18

41.01

1.00

0.31

ROA 89.4221.99

0.00 96.83

MARGIN 19.38 2.09 0.14 CAPADQ 3.51 0.73 0.39 Classification Results Bankrupt63.8%75.00%

12.43

1.30

2.57

0.00

50.86 8.520.00 10.68 3.740.05

89.2%

Non-Bankrupt 90.3%92.8% 96.4%

-52.00 57.80

2.73 0.09 36.86 0.00

0.25

26 TABLE 3 Multiple Discriminant Analysis Results - Holdout Sample _____________________________________________________________________________________________ 1986 1987 1988 _________________________________________________________________________ RatioCoeff. F pCoeff. F pCoeff. F p ______________________________________________________________________________________________ CASHASST-0.007 0.770.37 0.054 0.310.57 0.101 0.250.87 NLNSASST-0.83525.52*0.00-0.37821.410.00-0.195 10.16 0.00 PROVNLNS -0.837 5.490.00-0.12230.250.00-0.203158.70

0.00

PROVOPIN 1.089 6.180.01-0.05719.590.00 0.448170.20 0.00 OEOPINC 0.290 6.830.00 0.8797.810.00-0.185289.50 0.00 OPINCAST-0.471 0.860.35 0.1841.090.29-0.004 1.08

0.00

ROE 0.27423.500.00 0.386 5.620.01 0.054 1.70

0.19

MARGIN 0.103 0.300.86-0.0160.630.80 0.117 9.79

0.00

CAPADQ-0.471 1.790.18-0.2396.810.00-0.253 30.26

0.00

Classification Results Bankrupt40.0% 48.0% Non-Bankrupt

79.2% 97.7%

96.6%

99.4%

27 TABLE 4 Type I and Type II Error Rates for MDA and Logit Holdout Sample - 200 firms ____________________________________________________________________________________ MDALogit _______________________________________________________________________________ YearType IType IIOverallType IType IIOverall ____________________________________________________________________________________ 1986 60% 2.3%

1987 52% 3.4%

1988 21% 0.6% ____________________________________________________________________________________ _

28

TABLE 5 Neural Network Results 57 Independent Variables 1 Year Prior to Bankruptcy Neural Network Type

Overall

Type I

Type II

Categorical Learning

10.96

4.00

11.82

Counterpropagation

9.65

56.00

3.94

Learning Vector Quantization

3.95

28.00

0.99

Probabilistic Neural Network

10.96

4.00

11.82

Self-Organizing-Map into Categorization

4.39

24.00

1.97

29

TABLE 6 Neural Network Results 57 Independent Variables 2 Years Prior to Bankruptcy Neural Network Type

Overall

Type I

Type II


11.84

4.00

12.81

Counterpropagation

10.09

64.00

3.45


6.14

32.00

2.96


10.96

16.00

10.96


9.65

60.00

3.45

30


Overall

Type I

Type II


10.53

16

9.85

Counterpropagation

10.09

52

4.93


8.77

48

3.94


16.23

12

16.75


12.72

64

6.40

31

TABLE 8 Neural Network Results 10 Independent Variables 1 Year Prior to Bankruptcy Neural Network Type

Overall

Type I

Type II


9.65

16.00

8.87

Probabilistic Neural Network 1

14.47

12..00

14.78


40.35

4.00

44.82

32


Overall

Type I

Type II


11.84

44.00

7.88


15.79

24.00

7.88


39.03

4.00

43.35

33


Overall

Type I

Type II


19.74

52.00

15.76


22.81

16.00

23.65


48.68

0.00

54.68

34

TABLE 11 Relative Costs of Misclassification Statistical Models and 57-variable Neural Network Models Year

Cost Ratio

Y-1

1:1

Y-1

MDA

Logit


Counterpropatatio n

Learning Vector Quantizati on

Probablisit ic Neural Network

SOM into Categoriza tion

.07

.25

.22

.09

.25

.10

10:1

.52

.34

1.48

.72

.34

.64

Y-1

20:1

1.02

.44

2.88

1.42

.44

1.24

Y-1

30:1

1.52

.54

4.28

2.12

.54

1.84

Y-1

40:1

2.02

.64

5.68

2.82

.64

2.44

Y-1

50:1

2.52

.74

7.08

3.52

.74

3.04

Y-2

1:1

.21

.27

.23

.14

.25

.22

Y-2

10:1

1.47

.36

1.67

.86

.61

1.57

Y-2

20:1

2.87

.46

3.27

1.66

1.01

3.07

Y-2

30:1

4.27

.56

4.87

2.46

1.41

4.57

Y-2

40:1

5.67

.66

6.47

3.26

1.81

6.07

35 Y-2

50:1

7.07

.76

8.07

4.06

2.21

7.57

Y-3

1:1

.25

.24

.23

.20

.37

.29

Y-3

10:1

1.78

.60

1.40

1.28

.64

1.73

Y-3

20:1

3.48

1.00

2.70

2.48

.94

3.33

Y-3

30:1

5.18

1.40

4.00

3.68

1.24

4.93

Y-3

40:1

6.88

1.80

5.30

4.88

1.54

6.53

Y-3

50:1

8.58

2.20

6.60

6.08

1.84

8.13

36

TABLE 12 Relative Costs of Misclassification Statistical Models and 10-variable Neural Network Models Year

Cost Ratio

Y-1

1:1

Y-1

MDA

Logit


Probabilisti c Neural Network 1

Probablilisti c Neural Network 2

.07

.22

.33

.92

10:1

.52

.58

.60

1.01

Y-1

20:1

1.02

.98

.90

1.11

Y-1

30:1

1.52

1.38

1.20

1.21

Y-1

40:1

2.02

1.78

1.50

1.31

Y-1

50:1

2.52

2.18

1.80

1.41

Y-2

1:1

.21

.27

.36

.89

Y-2

10:1

1.47

1.26

.90

.98

Y-2

20:1

2.87

2.36

1.50

1.08

Y-2

30:1

4.27

3.46

2.10

1.18

Y-2

40:1

5.67

4.56

2.70

1.28

37 Y-2

50:1

7.07

5.66

3.30

1.38

Y-3

1:1

.25

.45

.52

1.11

Y-3

10:1

1.78

1.62

.88

1.11

Y-3

20:1

3.48

2.92

1.28

1.11

Y-3

30:1

5.18

4.22

1.68

1.11

Y-3

40:1

6.88

5.52

2.08

1.11

Y-3

50:1

8.58

6.82

2.48

1.11

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