A hybrid device for the solution of sampling bias problems in the forecasting of firms’ bankruptcy

Abstract

This paper proposes a new approach to the forecasting of firms’ bankruptcy. Our proposal is a hybrid method in which sound companies are divided in clusters using Self Organized Maps (SOM) and then each cluster is replaced by a director vector which summarizes all of them. Once the companies in clusters have been replaced by director vectors, we estimate a classification model through Multivariate Adaptive Regression Splines (MARS). For the test of the model we considered a real setting of Spanish enterprises from the construction sector. With this procedure we intend to overcome the sampling-bias problems that matched-pairs models often suffer. We estimated two benchmark models: a back propagation neural network and a simple MARS model. Our results show that the proposed hybrid approach is much more accurate than the benchmark techniques for the identification of the bankrupt companies.

Introduction

Correct resource allocation decisions are critical to guarantee the survival of banks and other lenders. So, bankruptcy forecasting models are key tools to help bank managers/officers in their investment/lending decisions. From the late 1960 onwards many models have been developed and tested. During the last years the importance of such systems is even higher due to the current financial crisis, which demands an even more careful management of financial resources. Furthermore, under Basel II Accord recommendations (Bank for International Settlements (BIS), 2006), banks which choose to develop their own empirical model to quantify required capital for credit risk (internal rating-based approach) are required to maintain less capital than those using the standardized approach. So, an accurate device to estimate loan default probabilities lets a financial entity to minimize the resources held as reserves and therefore to reach a higher level of profitability.

According to Sueyoshi and Goto (2009a), research on bankruptcy-based performance assessment can be classified into three broad categories. First, those studies centered on a particular model, which test how such model performs in comparison with others. Second, research focused on the selection of an appropriate set of variables to implement a particular model. The third category comprises papers which investigate the bankruptcy process.

Among these categories, the first is the one which has received most attention by researchers. The tested models are mainly statistical methodologies (for a review of the most outstanding studies see Balcaen and Ooghe, 2006, Keasey and Watson, 1991, among others) and artificial intelligence techniques (for a review see, e.g., Aziz and Dar, 2006, Ravi Kumar and Ravi, 2007).

Ravi Kumar & Ravi (2007) discuss the models which have been most frequently used in studies focused in insolvency prediction via intelligent systems. These models are Fuzzy Logic (FL), Neural Networks (NN), Genetic Algorithms (GA), Case-Based Reasoning Systems (CBR), Rough Sets (RS), Support Vector Machines (SVM), Decision trees (DT), Data Envelopment Analysis (DEA) and Hybrid Systems (HS).

Among these, HS are the most promising. These combine two or more intelligent techniques in several forms to derive the advantages of all of them. HS have received considerable attention from researchers as they amplify the advantages of the intelligent techniques while simultaneously nullifying their disadvantages. Most HS require a considerable amount of data to reach to accurate estimations. This is not a problem nowadays, as there exist publicly available databases containing financial information of listed and unlisted firms.

However, studies using HS for bankruptcy prediction suffer from a drawback which is that the majority of them estimate the model upon the basis of a sample in which non-failed companies are underrepresented. In most cases a matched-pairs design is used. The selection of non-failed firms is arbitrary, which makes the model to achieve a high in-sample percentage of correct classifications but it is likely to be inaccurate for failure prediction in new cases drawn from a real population.

Another strategy is to consider a “real” population as the sample. That is, to consider all the companies for which we have financial information available. However, as only a very small percentage of firms enter into financial distress in a normal economic situation, such samples are very unbalanced. This causes coefficient instability and leads to poor performance ability of the models.

As an alternative to both strategies we propose a HS model where, upon the basis of a real population of firms, data are preprocessed to summarize the information of healthy firms. So, the initial unbalanced sample is transformed into a balanced one which retains the main features of the healthy firms. Self Organized Maps (SOM) is used in this stage. Then a classification device is developed upon the transformed sample, for which we use the Multivariate Adaptive Regression Splines (MARS) approach. The results are compared with benchmarks which are popular in bankruptcy prediction literature. As an important application of the combined approach, this paper applies it to the solvency assessment of Spanish construction firms.

The remainder of the paper is structured as follows. Section 2 revises prior studies on bankruptcy prediction using HS. Section 3 is devoted to build the database. Section 4 describes the algorithm and the analytical procedures we used. Section 5 comments on the main results, including the benchmark techniques applied. Finally, Section 6 is devoted to the summary and main conclusions, including also some further research avenues.