The support vector machine (SVM) has been applied to the problem of bankruptcy prediction, and proved to be superior to competing methods such as the neural network, the linear multiple discriminant approaches and logistic regression. However, the conventional SVM employs the structural risk minimization principle, thus empirical risk of misclassification may be high, especially when a point to be classified is close to the hyperplane. This paper develops an integrated binary discriminant rule (IBDR) for corporate financial distress prediction. The described approach decreases the empirical risk of SVM outputs by interpreting and modifying the outputs of the SVM classifiers according to the result of logistic regression analysis. That is, depending on the vector’s relative distance from the hyperplane, if result of logistic regression supports the output of the SVM classifier with a high probability, then IBDR will accept the output of the SVM classifier; otherwise, IBDR will modify the output of the SVM classifier. Our experimentation results demonstrate that IBDR outperforms the conventional SVM.
Corporate financial distress forecasting is an important and widely studied topic since it has significant impact on lending decisions and profitability of financial institutions. Therefore, accurate bankruptcy prediction models are of critical importance to various stakeholders (i.e., management, investors, employees, shareholders and other interested parties) as it provides them with timely warnings. From a managerial perspective, financial failure forecasting tools allow to take timely strategic actions such that financial distress can be avoided. For stakeholders, efficient and automated credit rating tools allow to detect clients that are to default their obligations at an early stage.
Financial failure occurs when the firm has chronic and serious losses and/or when the firm becomes insolvent with liabilities that are disproportionate to assets. Widely identified causes and symptoms of financial failure include poor management, autocratic leadership and difficulties in operating successfully in the market. The common assumption underlying bankruptcy prediction is that a firm’s financial statements appropriately reflect all these characteristics. Several classification techniques have been suggested to predict financial distress using ratios and data originating from these statements, e.g., univariate approaches (Beaver, 1966), multivariate approaches, linear multiple discriminant approaches (MDA) (Altman, 1968 and Altman et al., 1977), multiple regression (Meyer & Pifer, 1970), and logistic regression (Dimitras et al., 1996, Ohlson, 1980 and Pantalone and Platt, 1987). However strict assumptions of traditional statistics such as the linearity, normality, independence among predictor variables and pre-existing functional form relating the criterion variable and the predictor variable limit application in the real world.
To develop a more accurate and generally applicable prediction approach, data mining and machine learning techniques including decision trees, neural networks (NNs), fuzzy logic, genetic algorithm (GA), support vector machine (SVM), etc., have been successfully applied in corporate financial distress forecasting. Developed by Vapnik (1995), SVM is gaining popularity due to many attractive features and excellent generalization performance on a wide range of problems. Also, SVM embodies the structural risk minimization principle (SRM), which has been shown to be superior to traditional empirical risk minimization principle (ERM) employed by conventional neural networks. SRM minimizes an upper bound of generalization error as opposed to ERM that minimizes the error on training data. It has been shown by Min and Lee (2005) that SVM outperforms NNs, MDA and logistic regression in corporate bankruptcy prediction. However, the SRM embodied in SVM implies that the empirical risk of misclassification may be high, especially when a point to be classified is close to the hyperplane.
The purpose of this paper is to develop a new financial distress prediction approach to improve its prediction accuracy. The described approach provides an integrated binary discriminant rule (IBDR) by interpreting and modifying the outputs of the SVM classifiers. Since logistic regression analysis has also been used to investigate the relationship between binary response probability and explanatory variables, it can be integrated into the modifying process to decrease the empirical risk of the SVM outputs. That is, depending on the vector’s relative distance from the hyperplane, if result of logistic regression supports the output of the SVM classifier, then IBDR will accept it; otherwise, modify it. The validity of IBDR has been verified by numerical results on several benchmark data sets, and tested on the prediction of financial distress of companies listed in Shanghai Stock Exchange (China) by comparing its accuracy with that of the conventional SVM.
The rest of this paper is organized as follows. The following section presents a brief review of SVM for binary classification. Section 3 describes the proposed IBDR approach. Sections 4 and 5 explain the experimental design and the results of the evaluation experiment. The final section ends the paper with some conclusion remarks.
The conventional SVM employs the structural risk minimization principle, thus empirical risk of misclassification may be high, especially when a point to be classified is close to the hyperplane. This paper develops a new financial distress prediction approach to improve its prediction accuracy. The described approach (IBDR) decreases the empirical risk of SVM outputs by interpreting and modifying the outputs of the SVM classifiers according to the result of logistic regression analysis. Our experimentation results demonstrate that IBDR is significantly better than the conventional SVM when they are applied to the prediction of corporate financial distress. We also investigate the effect of various values of the regularization parameter C.
Our study has the following limitations that need further research. First, the method of modifying the output of the SVM classifier has an important impact on the performance of the resulting approach. Alternative methods of modifying output of SVM are possible and interesting. For example, we can try to find a method that will minimize the empirical risk of misclassification. The second issue for future research relates to a structured method of selecting an optimal value of parameters in IBDR and SVM for the best prediction performance.
