After discussing the basic method of discriminant analysis in the class today, let us all have a look into the application of discriminant analysis to predict bankruptcy.

Bankruptcy prediction has been one of the most challenging tasks in accounting. Two main approaches in bankruptcy prediction studies can be distinguished: the first and most often used approach has been the empirical search for the predictors (financial ratios) that lead to lowest misclassification rates. The second approach has concentrated on the search for statistical methods that would also lead to improved prediction accuracy.

At the beginning of the research period of failure prediction, the values of failed and nonfailed firms were compared with each other and it was found that they were poorer for failed firms. In 1966 the pioneering study of Beaver presented the univariate approach of discriminant analysis and in 1968 Altman expanded this analysis to multivariate analysis. Until 1980's discriminant analysis was the dominant method in failure prediction. However, it suffered from assumptions that were violated very often. The assumption of normality of the financial ratio distributions was problematic, particularly for the failing firms. During the 1980's the method was replaced by logistic analysis which until last years has been the most used statistical method for failure prediction purposes.

Most failure prediction studies (done before 1980's) applied an empirical approach, i.e., they aimed at improved prediction accuracy by appropriate selection of financial ratios for the analysis. Naturally, these financial ratios have been selected according to their ability to increase prediction accuracy.

**Discriminant analysis** tries to derive the linear combination of two or more independent variables that will discriminate best between a priori defined groups, which in our case are failing and non-failing companies.

The discriminant analysis derives the linear combinations from an equation that takes the following form:

Z = w1x1+ w2x2+...+wnxn where

Z = discriminant score

wi (i=1, 2, ... ,n) = discriminant weights

xi (i=1, 2, ... ,n ) = independent variables, the financial ratios

Thus, each firm receives a single composite discriminant score which is then compared to a cut-off value, which determines to which group the company belongs to.

This study shows that the use of DA, logit analysis or genetic algorithm all lead to different failure prediction models. The amount of variables included in the models varies.

Also, different methods lead to the selection of different financial ratios. Despite of the selection method used, liquidity seems to be very important factor in failure prediction. Two reasons for this were discussed. First, the liquidity failure is the more general failure type in Finland which stresses the importance of this factor in the models. Second, the variables in our original sample were mostly factors describing liquidity.

Three conclusions can be made. First, the differences between alternative model selection methods affect the number of independent variables to be selected. Second, not only the number of variables but also the information content of the models varies due to the variables that are measuring different economic dimensions of a firm. Finally, connected with alternative failure prediction methods, also the prediction accuracy varies.

References: Choosing Bankruptcy Predictors Using Discriminant Analysis, Logit Analysis, and Genetic algorithms ( Barbro Back)

Author: Surya Narayana Adiga

Group: Finance - 2

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