Devising the Best Prospective Merger Plan for a Banking Sector Through a Hybrid DEA-Based Methodology: An Inverse DEA Perspective

Mergers & acquisitions (M&A) are strategic decisions that have long been associated with the banking sector, entailing the consolidation of assets among a group of banks through various types of financial transactions. Though a lot of research has been dedicated to the application of data envelopment analysis (DEA) to multiple aspects of M&A within this particular sector, little or even no significant attention has been paid to investigating the optimal matchings among banks, i.e., what should be the best partners of prospective bank mergers that are more likely to maximize the overall performance of the whole banking sector? To answer this question, we propose a hybrid DEA methodology that operates over two levels. The first level entails solving an inverse DEA (IDEA) model to evaluate the optimal gains that could potentially be generated out of pairwise consolidations among banks. As a result, all productive post-merger banks, i.e., those mergers that have real potential for gains’ generation, are duly discerned. In the second level, a DEA procedure integrating a standard DEA model with a greedy heuristic is devised to select the best pairs of merging banks based on the post-merger banks’ expected outcomes. Here, the best prospective merger plan is derived for the whole banking sector out of the entire sample of banks. Using data from the Office of the Superintendent of Financial Institutions (OSFI) database, the pertinence of the proposed methodology is shown by evaluating the potential merger gains of 28 Canadian banks prior to building the associated best prospective merger plan.