Abstract
In recent years, there has been an increase in the number and value of securities class actions (SCAs), attracting the attention of various stakeholders such as investors, managers, policy makers, lawyers, etc. The present study extends the literature, by investigating for the first time the development of a classification model to forecast SCAs filed against US banks. Our results show that the proposed multicriteria decision aid model achieves a satisfactory accuracy, by classifying correct around 80 % of the banks in an out-of-sample testing. We obtain similar results when we use a walk-forward approach, instead of a tenfold cross-validation technique, for the estimation and testing of the model. Further analysis indicates that the classification accuracies can improve further by the inclusion of a corporate governance indicator that relates to executive and director compensation and ownership.
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Notes
Cornerstone Research defines the two terms as follows. “Disclosure dollar loss” is the dollar value change in the market capitalization of the defendant firm between the trading day immediately preceding the end of the class period and the trading day immediately following the end of the class period. “Maximum dollar loss” is the dollar value change in the market capitalization of the defendant firm from the trading day during the class period when its market capitalization was the highest to the trading day immediately following the end of the class period.
It should be clarified here that our models aim to forecast whether the bank will be threatened with a legal action, and not to forecast the court judgment following the SCA. Such an exercise is outside the scope of the present study.
The picture remains the same in 2009. More detailed, there were 84 class actions fillings against firms in the financial sector, out of a total of 169. The MDL was equal to $331 billion, followed by firms in the industrial sector ($96 billion), accounting for more than 50 % of the total MDL across all industries ($634 billion).
CAMEL stands for Capital, Asset quality, Management, Earnings and Liquidity. The rationale for its use in the present study lies on the fact that investors, credit agencies, researchers, and bank regulators tend to evaluate banks along the dimensions of this model. Consistent with most of the previous studies, management has not been included in the analysis due to its qualitative nature and the subjective analysis that is required.
These 120 SCAs involve 87 banks. The number of fillings is higher because some banks faced more than one SCA during the period of our study. In order for a bank to be included twice in the sample, SCAs should take place in different years.
Matching of firms is common practice when conducting classification studies in finance, (e.g. Laitinen and Kankaanpaa 1999; Neophytou and Mar Molinero 2004; Charitou et al. 2004). This approach, known as choice-based sample, has two primary advantages. First, the cost of data collection is lower than that of a strategy that is based on an unmatched sample (Zmijewski 1984; Bartley and Boardman 1990; Ireland 2003). Second, a choice-based sample provides higher information content than a random sample that is based on unequal group sizes (Cosslett 1981; Palepu 1986; Imbens 1992). The reason is that the number of firms facing an SCA is relatively small compared to non-SCA firms, which implies that an entirely random sampling will result in a dataset consisting of many non-SCA firms and only a few (if any) firms facing an SCA. From an estimating procedure perspective such a dataset is inefficient (Palepu 1986; Ireland 2003). Thus, it is essential to select the sample in a way that will ensure that SCA firms in sample represent an adequate proportion. Various researchers characterize this approach as more efficient and/or close-to-optimum (Manski and Lerman 1977; Manski and McFadden 1981; Cosslett 1981; Imbens 1992).
The use of the term “criterion” instead of “variable” originates from the MCDM literature. We use the two terms interchangeably for the rest of the paper.
A basic assumption of the UTADIS involves the monotonicity of the criteria. As this is rather the exception than the rule in real problems, the most common technique to consider such cases is to divide the range of criterion values into intervals so that preferences are monotone in each of them.
As shown in the text and discussed in more detail in Doumpos and Zopounidis (2004), the additive utility model developed through UTADIS is affected by some technical parameters (e.g. delta) involved in the solution process as well as the way that the piece-wise linear form of the marginal utility functions is considered (i.e. the way that each criterion’s range is divided into subintervals). Since there is not a general guidance for determining the parameters, this study examines the classification performance with respect to various values. As it is common practice, the final values were selected based on the classification accuracies achieved in the training sample over the tenfold cross-validation approach described in the text.
Recently, Greco et al. (2010) proposed a new method called UTADIS\(^{GMS}\). Some of the distinguishing characteristics of this method are that: (1) It makes use of a very general and flexible preference model as it considers all non-decreasing marginal value functions (rather than piecewise linear marginal value functions), (2) when computing assignments, it takes into account all value functions compatible with the assignment examples provided by the decision maker, and (3) it makes it possible to account for both the threshold- and example-based sorting procedures.
The models generated with these techniques are developed and tested following exactly the same cross-validation procedure that was used in the development of the classification model through UTADIS. As in previous studies (e.g. Pasiouras et al. 2005) the number of nearest neighbours is adjusted and the performance of the model is evaluated each time. In this study, we experiment with various values for \(k\) and we finally set it equal to 15 based on the results obtained through the cross-validation procedure. In the case of ANN, we use a feed-forward approach, and we find that a model with one hidden layer with five neurons performs slightly better than different architectures. In the case of PNN, we experiment with various values for the smoothing parameter (see e.g. Gaganis et al. 2007), which we finally set equal to 0.35. In the case of CART, we examine models with and without pruning. Finally, the highest accuracy is obtained from a model with pruning.
Many colleagues and market participants argue that the crisis started in mid-2007. Thus, it is not clear whether 2007 should be part of the pre-crisis or the crisis period. For the purposes of the present study, we include it in the pre-crisis period to ensure that we have a sufficient number of observations for the estimation of the model.
The relatively low classification accuracy in 2011 can be attributed to the very small validation sample in 2011 that consists of 6 banks, only.
See Appendix Table 7 for further details on the weights of the criteria once including the corporate governance indicators in the models.
We would like to thank an anonymous referee for suggesting this analysis.
In this case, the weights of the criteria are as follows: 13.45 % (EQAS), 10.62 % (LLR), 30.44 % (ROAA), 0.00 % (LIQ), 0.00 % (LOANS), 45.49 % (LOGTA).
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Balla, V., Gaganis, C., Pasiouras, F. et al. Multicriteria decision aid models for the prediction of securities class actions: evidence from the banking sector. OR Spectrum 36, 57–72 (2014). https://doi.org/10.1007/s00291-013-0333-8
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DOI: https://doi.org/10.1007/s00291-013-0333-8