Decision Trees

2.7.1 Decision Trees

Decision Trees (DTs) have not been as extensively used in FDP studies vis-à-vis their parametric counterparts. Some of the studies that apply DTs to FDP include: Chen (2011); Geng, Bose, and Chen (2015); Gepp, Kumar, and Bhattacharya (2010); Hung and Chen (2009); Sun and Li (2008).

Decision Trees (DTs) are models that construct a set of tree-based classification rules that recursively break down a data-set into smaller and smaller subsets (partitions).

The tree is generated in a recursive process that splits the data from a higher level to a lower level of the tree, ending with leaf nodes that characterise classification groups (distressed or successful). When applied to FDP, DTs commonly assign businesses to either the successful or distressed group. The splitting at each node is determined by comparing an expression that is assessed for each company with a cut-off point.

There are two main tasks for the algorithms that generate DTs. First, to choose the optimal splitting rule at each non-leaf node to differentiate between distressed and successful companies, and secondly, to determine the number of nodes in the decision tree (Gepp & Kumar, 2012). A sample DT can be seen in Figure 2.3 below.

DTs consist of the following:

 A root node: Topmost decision node that corresponds to the best predictor

 Non-leaf nodes (non-leaf nodes project 2 branches leading to 2 distinct nodes)

 Leaf nodes: Represents a classification or decision

 Connecting branches: connecting nodes

28 Figure 2. 3 Decision Tree

A drawback of DTs is that they do not provide precise probabilities of group membership, that is, financial distress – except for a whole node (group of businesses). However, DTs are beneficial for many reasons, including: invariance to monotonic alterations of input variables, handling outliers in the data effectively as well as mixed variables, and being able to deal with a data set that contains missing data.

There are different algorithms that can be used to generate DTs. These algorithms all create similar tree structures but selecting the correct algorithm for a particular circumstance can have a huge impact on the predictive power of the generated model.

Popular implementations of decision trees include Classification and Regression Trees (CART) and See5 (Gepp et al., 2010). In a 2005 pioneering study, Huarng, Yu, and Chen (2005) compared the accuracy of CART and See5; their results showed CART to be empirically superior to See5. However, it is crucial to note that the data-sets encompassed less than 12 businesses and five variables, that is, the sample is too small to obtain reliable results. However, Gepp et al. (2010) confirmed that CART empirically superior to See5, thus solidifying Huarng et al.’s (2005) claim.

According to Gepp et al. (2010), DTs are empirically found to be superior predictors vis-à-vis MDA when it pertains to forecasting companies’ financial distress. Studies that solidify this claim include: Chen (2011); Frydman, Altman, and Kao (1985); Kumar and Ravi (2007). When comparing DTs to LR, Chen (2011) found that DTs

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classification approach yields superior FDP accuracy in the short-run (less than one year), hence implying that ANNs are better predictors in the short-term.

Chen (2011) applied his study on 100 listed Taiwanese companies – 50 distressed vis-à-vis 50 healthy companies – using 37 financial and non-financial ratios that are common in the literature. He used Principal Component Analysis (PCA) to extract suitable variables – PCA will be explored further in Chapter 6. Three DT classification methods were used to create the FDP model; a logistic regression model was also developed for comparison purposes. Chen’s FDP model using DTs outperformed his LR model by yielded around 97% accuracy for identifying distressed firms in the short-term (two seasons prior to actual financial distress); however, the LR model marginally outperformed the DT model in the long-term (over one and a half years) by almost three percentage points (91.7% versus 88.8%). Chen concluded that Artificial Intelligence (AI) techniques are superior to traditional statistical techniques in predicting financial distress in the short-term.

Geng et al. (2015) employed data mining techniques to construct three main models for three time-periods preceding the companies’ financial distress, using DTs, neural networks, and Support Vector Machines (SVMs). Their study was based on 107 Chinese “Special Treatment” companies, that is, implying financial distress, and the same number of financially healthy companies, for the time-period 2008-2011. They incorporated 31 financial variables in all of their FDP models. Their results showed that the neural network model was the most accurate at predicting financial distress, closely followed by the DT model. ‘Net Profit Margin of Total Assets, “Return on Total Assets”, “Earnings per Share”, and “Cashflow per Share” were the financial indicators with the highest predictive capability in pointing out financial distress.

Gepp et al. (2010) provided a classic case of the Occam’s razor philosophical principle, that being, the most parsimonious models are better than more complex ones. They employed 20 financial variables and applied it on the original data-set used by Frydman et al. (1985), comprising 200 businesses, and conducted a

cross-30

sectional analysis. They devised DT models using different implementations of DT, including: CART, See5, and Recursive Partitioning Analysis (RPA). See5 yielded the best in-sample classification capability, but the poorest predictions. CART and RPA were the best overall predictors. The three DT models were compared with MDA and they outperformed it. Profitability and liquidity ratios were the most important variables at predicting financial distress.

Hung and Chen (2009) used 30 financial ratios that are common in the literature on a data-set consisting of 56 bankrupt companies and 64 healthy companies, for the time-period 1997-2001. They proposed an ensemble method of three classifiers, namely:

DTs, BNNs, and SVMs in an attempt to harness their pooled advantages, all the while mitigating the individual disadvantages of each technique. Their selective ensembles outperform weighting and voting ensembles for FDP by around 2.5 percentage points.

Sun and Li (2008) incorporated 35 financial ratios and applied them on 198 listed Chinese companies, of which 92 are financially distressed and 106 are financially healthy, for the time-period 2000-2005. They present a data mining method which includes attribute-oriented induction, information gain, and DT. Adopting entropy-based method, their model achieved a prediction accuracy rate of 95.33%.