Financial ratio selection for business failure prediction using soft set theory
Introduction
Business failure prediction (BFP) is one of the most essential problems in the field of economics and finance. It has been a subject of great interest to practitioners and researchers over decades. Being able to forecast potential failure provides an early warning system so that timely decisions are allowed to be made and appropriate adjustment in resource allocation can be taken place. There are three major tasks involved in the process of BFP, as shown in Fig. 1.
First, researchers need to determine their research objects [13]. Business failure prediction is a broad subject. Specific fields such as bank failure prediction, tourism failure prediction, small business failure prediction may take different approaches. Here we are interested in the failure prediction of Chinese listed firms from the Shenzhen Stock Exchange and Shanghai Stock Exchange.
Second, researchers need to select variables for BFP. Since the operational business environment changes quickly, BFP must be done in a timely fashion to provide early warnings. It has been shown that financial ratios have more forecasting power than other types of variables in such dynamic settings [20]. Hence we focus on financial ratio variables. Available ratios could not be used indiscriminately because some ratios could prove to be more powerful in their predictive ability than others. Predictive ability presents in two aspects. One is the forecasting accuracy (ACC). The other is the forecasting stability. If a forecasting system includes too many nonsignificant financial ratios, it will produce results low in forecasting accuracy and stability [10]. The goal of this paper is to select important financial ratios for BFP.
Third, researchers need to select forecasting models for BFP. The forecasting method, in particular the forecasting classifier used for a qualitative response, has a significant impact on the forecasting performance. Since the early empirical work on methods adopted by large USA banks, there has been a large number of literatures on the forecasting methods. Those methods include discriminant analysis [2], logistic regression (LR) [28], neural networks (NN) [3], probit method [35], rough set theory (RS) [11], support vector machine (SVM) [25], case-based reasoning [17], combination methods [7], [20], [34] and others. For a detailed review, one can refer to Dimitras et al. [10] and Zopounidis [36]. In this paper, we will use LR, SVM and NN to evaluate performance of variable selection methods rather than to study the selection of those forecasting models.
Differing from the development on prediction models, not much progresses have been made in variable selection for BFP. Beaver [4] selected six financial ratios including debt ratios. Altman [2] employed five financial ratios including sales to total assets. Deakin [8] made an attempt to identify variables useful in BFP. Ohlson [28] adopted nine different features. Recently, scholars [12], [21], [26], [31], [34] proposed additional financial ratios for BFP. Most popular financial ratios adopted in the prior literatures are summarized in Table 1. However, most of those financial ratios are selected either by the expert system method or by statistical approaches. Expert system relies heavily on users’ knowledge and ability, which imposes difficulty to make it widely used. Statistical approaches have disadvantages for variable selection on their stringent model assumptions, which are often not met in practice. Small departures from the assumed model may make the statistical methods yielding unreliable even unacceptable results.
On the other hand, as we mentioned before, BFP must to be done in a dynamic setting. We shall include more factors or variables in the model such that information loss on the nature of firms in a dynamic operational environment is minimal. Inevitably we deal with BFP problem based on high-dimensional data. Soft set theory (SS), initiated by Molodtsov [27], has advantages to deal with high-dimension data sets. It also has been proved theoretically to be an effective tool for dimension reduction [9]. We expect SS a good performance on financial ratio selection for BFP. However, the prior literatures on SS are either purely theoretical or applied only on simple situations [24], [6], [16], [37], [14], [30], [23], [1]. The available algorithms are rarely useful to be applied directly to the BFP problem. This motivates us to develop a novel method based on SS (NSS) to select financial ratios for BFP.
We first propose a general way to transfer the complex real-life data to 0–1 data frame so that SS or RS methods can be applied. Using LR, the importance of each variable is measured by its influence on predicting whether the firm will fail or not. A critical parameter involved in this step is determined optimally by a cross-validation procedure. Then the uni-int decision making on the SS is employed to obtain an optimal set of significant financial ratios. In such a way, our method utilizes the flexibility and efficiency of soft set theory and in the same time takes advantages of the statistical method without worrying about justifications of the underlying assumptions.
For comparison, principle component analysis (PCA) [15], traditional soft set (TSS) [16], rough set (RS) [29] are reduction methods included in the study of real data sets from Chinese listed firms along with evaluations of the financial ratio set proposed in previous literatures. TSS and RS use the same tabular representation data as NSS. Comparing with TSS, the uni-int decision making method is developed based on the redefined operations that exploits available tabular information more fully.
The remainder of this paper is organized as follows. Section 2 reviews the classical SS theory and introduces the proposed parameter reduction method. Section 3 describes the application to a real data set. In Section 4, we present the empirical results and compare performance of the proposed method with other methods. We conclude and discuss possible future work in Section 5.
Section snippets
Soft set oriented parameter reduction methods
Originated by Molodtsov [27], soft set theory deals with uncertainty in a non-parametric manner. It has been extended to effectively select parameters [16]. In this section, we first review soft set theory, the uni-int decision making method and the traditional reduction method proposed, then propose our novel method.
Sample and data
According to the benchmark of China Securities Supervision and Management Committee (CSSMC), listed firms are categorized into two classes: Specially Treated firms (ST) and Not Specially Treated firms (NST). The criteria are either negative net profits in recent consecutive two years or announcement on purpose about serious financial misstatements. Here, we consider ST companies as firms that have had negative net profits in recent two years.
We use real financial data sets from Chinese listed
Experiment results and discussion
Matlab software package (2012) and Statistical Product and Service Solutions (IBM SPSS 20) are employed to obtain the result of financial ratios selection and forecasting performance of different forecasting models.
Conclusion
In this paper, we extended research of financial ratios for BFP by proposing a novel parameters reduction method based on soft set theory. It constructs a tabular representation of SS from LR, then uses optimal decision on SS to select significant financial ratio variables. It inherits advantages and in the same time avoids disadvantages of both methods. From PLFRS and FASCS, NSS chooses nine financial ratios for BFP. Among them, four financial ratios are the first time to be selected as
Acknowledgements
The authors are highly grateful to referees and editors for their valuable comments and suggestions that helped in improving this paper.
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Support by the National Science Foundation of China (Grant No. 71171209) and support by Major Consulting Research Project of Chinese Academy of Engineering (Grant No. 2012-ZD-12).