The traditional approach and present standard for predicting financial distress uses multiple discriminant analysis (MDA) to weight the relative value of information provided by a combination of fmancial ratios.1 But MDA has been sharply criticized because the validity of its results hinges on restrictive assumptions (Werbos [37], Eisenbeis [11], Altman and Eisenbeis [3], Scott [29], Tollefson and Joy [32], Sheth [31], Ohlson [26], Pinches [27], Zmijewski [41], Zavgren [39], Karels and Prakash [17], and Odom and Sharda [25]). Two assumptions are particularly problematic for ratio analysis. First, MDA requires that the decision set used to distinguish between distressed and viable firms must be linearly separable. For a single ratio, this means that a value above or below a given threshold point must always signal either distress or good health. In the instance where two ratios are considered together, the threshold separating the classification regions is a line; with more than two ratios, a plane. Second, MDA does not allow for a ratio's signal to vacillate depending on its relationship to another ratio or set of ratios. In other words, ratios are treated as completely independent. Unfortunately, these restrictions violate common sense. In practice, a ratio may signal distress both when it is higher than normal and when it is lower than normal, or a ratio's value may be considered acceptable under some conditions, yet risky under others. These problems and others (e.g., bias of extreme data points; multivariate normality assumption; and equal group covariances assumption) make MDA incompatible with the complex nature, boundaries, and interrelationships of financial ratios. The power of MDA for financial ratio analysis is compromised and the results may be erroneous (Karels and Prakash [17]). Our research is motivated by the fact that a ''neural network'' (''NN'') analysis of the same ratios used by MDA, for the same objective, is possible without any of the circumscription that binds MDA.2 Moreover, studies indicate that neural network models are at least as successful as MDA in terms of overall accuracy (Williams [38], Cottrel, Munro, and Zipser [9], Odom and Sharda [25], Webb and Lowe [36], and Utans and Moody [57]). The question asked by our study is: How successfully can neural networks discem pattems or trends in financial data and use them as early waming signals of distressful conditions in currently viable firms? Being able to form highly reliable early forecasts of the future health of firms is, of course, critically important to bank lending officers, investors, market analysts, portfolio managers, auditors, insurers and many others in the field of finance. Our approach creates NN models which glean and leam relationships in raw data from processing examples of conclusions reached by experts (auditors) who have analyzed the same data. The experts, in making their assessments, have implicitly imposed their insights and intuition cultivated over years of on-the-job experience. Our research objective is to formalize this ingrained, unaiticulated knowledge of the experts by uncovering consistencies between the experts' conclusions and the recurring pattems in the financial data. To evaluate our results, we measure our neural networks'success in using a limited number of financial ratios to duplicate the going-concem determinations rendered by auditors.3,4 The test results in this study suggest that the NN approach is more effective than MDA for the early detection of financial distress developing in firms. The NN models consistently correctly predict auditors' findings of distress at least 80% of the time over an effective lead time of up to fouryears. A statistical comparison of results shows that the neural networks are always better than the MDA models for identifying firms which eventually receive going-concem opinions. The neural network we use is a mathematical algorithm for creating a perfect mapping between the input and output values for a set of training data. The NN training process incrementally captures knowledge about the relationship between the output and the pattems in the input in order to correctly categorize the training situations. Once training is complete, the pattems found by the NN can be used to forecast situations where the outcome is unknown. MDA can be considered equivalent to a special case of NN, and the two approaches give identical results when the input variables are linearly separable. However, the NN model is not subject to MDA's constraining assumptions, such as linear separability and independence of the predictive variables. This allows a neural network to achieve better results than MDA when pattems are complex. The remainder of this paper is organized as follows. Section I provides an overview of the particular type of neural network used for our research, namely Cascade-Correlation, and details its method of training. Section II presents the research design which focuses on neural networks and MDA comparison models, and describes the collection of the data and the selection of the samples used by the neural networks and MDA models for training and testing. Section III presents the neural network results, makes comparisons with the test results for MDA models, and offers interpretations. Section IV summarizes our findings and the direction of further research.
