Identifying distress among banks prior to a major crisis using non-oriented super-SBM

Abstract

We illustrate how data envelopment analysis (DEA) can be used as a forward-looking method to flag bank holding companies (BHCs) likely to become distressed. Various financial performance models are tested in the period leading up to the recent global financial crisis. Results generally support DEA’s discriminatory and predictive power, suggesting that it can identify distressed banks up to 2 years in advance. Robustness tests reveal that DEA has a stable efficient frontier and its discriminatory and predictive powers prevail even after data perturbations. DEA can be used as a preliminary off-site screening tool by regulators, by business managers to ascertain their standing among competitors, and by investors. Attention by regulators can be further directed at potentially distressed banks as some of them would be candidates for closer monitoring. In conclusion, DEA may be useful in making economic decisions because there is an identifiable link between inefficiency and financial distress. To the best of our knowledge, application of DEA to predict financial distress among BHCs prior to a major crisis has not been published.

Appendix 1: Primary formulae for the super slacks-based measure (super-SBM)

(See Tone 2002 for a more detailed exposition)

$$ \begin{gathered} \delta^{*} = \hbox{min} \,\delta = \frac{{\frac{1}{m}\sum\nolimits_{i = 1}^{m} {\bar{x}_{i} /x_{io} } }}{{\frac{1}{s}\sum\nolimits_{r = 1}^{s} {\bar{y}_{r} /y_{{{\text{r}}0}} } }} \hfill \\ {\text{subject \,to}} \hfill \\ \overline{x} \, \ge \,\sum\limits_{j = 1, \ne 0}^{n} {\lambda_{j} x_{j} } \hfill \\ \overline{y} \, \le \,\sum\limits_{j = 1, \ne 0}^{n} {\lambda_{j} y_{j} } \hfill \\ \overline{x} \, \ge \,x_{0} \quad {\text {and} }\quad \overline{y} \, \le \,y_{0} \hfill \\ \overline{y} \, \ge 0,\,\,\,\,\,\lambda \ge 0 \hfill \\ \end{gathered} $$

where x is the input, m the number of inputs, y the output, s the number of outputs, and n is the number of decision-making units.

In the fractional program depicted above, delta is the product of two dimensionless indices, one that captures the distance in the input space, and the other that captures the distance in the output space. Solving the optimal objective function δ ^*generates the super-SBM estimate. This estimate is units-invariant because it is independent of the units of measure as long as these units are the same for all the decision-making units.