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Chain Merger Evaluation and Application to Banking Operations

This paper explores the concept of chain mergers in banking operations and their efficiency using a DEA model. It also discusses leader-follower relations and incentive compatibility. The study provides a case analysis and proposes potential gains from such mergers.

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Chain Merger Evaluation and Application to Banking Operations

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  1. Chain Merger Evaluation and Application to Banking Operations Desheng Dash Wu University of Toronto, Reykjavik University[with John R. Birge, Booth School of Business, University of Chicago] Accepted and to appear at POM DSJ, 43(1) 2012

  2. Outline Introduction • Problem, Literature Background model Our model • Conceptual model, Math model • 3 main contributions • chain merger DEA model, leader-follower relations • efficiency at both chain and sub-chain levels, incentive compatible • banking intra-firm division mergers Case analysis Conclusion & Further study

  3. Outline • Introduction • Background model • Our model • Case Study • Conclusion

  4. Industry facts • New York Times, March 11, 2013: • “the dollar value of U.S. mergers and acquisitions so far this year is $233 billion, more than double last year. But there were almost 10 percent fewer deals than last year.“ • “Today's mergers and acquisitions are more about building up than cashing in.”

  5. Literature • IO: Salant (83), JOE; Deneckere and Davidson (85) RandJ;Perry and Porter (85), AER; Farrell, (90), AER; Rothschild (00) RegSci&E; Benjamin et al. (09) • merger paradox • Finance: Sapienza (02), JOF; Guerard Jr. (89); Geppert and Kamerschen(08); Houston and Ryngaert (94) JBF; Duffie (07) JFE • stock • OR: Sherman and Rupert (06), EJOR; Cummins et al.(08) JBF; Ray (04); Bogetoft (05), JPA • efficiency

  6. Our study • A model for gauging merger efficiency of supply chains • different structure • Supply chain view of banking operations • Link operations to finance • Apply the model to banking operations with DEA, considering M&A with multiple metrics • Link OR to IO/Finance

  7. Revisit Banking operations- supply chain • Question: banks or subdivisions merged, how business performance is affected considering such a banking chain? How to achieve potential gains?

  8. Outline • Introduction • Background model • Our model • Case Study • Conclusion

  9. Merger gains (Ray, 2004)2-step process: harmony effect, scale effect

  10. Mathematically • The efficiency of merger can then be measured as • denotes the harmony effect. • represents the scale effect. • potential gains from the merger of the two firms positive if > 1.

  11. Data Envelopment Analysis (DEA) What • a linear programming to measure the efficiency of multiple decision-making units (DMU) when the DMUs present a structure of multiple inputs and outputs. • Different versions: Constant return to scale (CRS), Variable return to scale (VRS) How • Define DMU, input/output variables • Define the efficiencyfrontier. • A numericalweight coefficient isgiven to eachfirm, computingits relative efficiency.

  12. Outline • Introduction • Background model • Our model • Case Study • Conclusion

  13. two-stage series-chain Conceptually the ith DMU, i=1,2…N

  14. Mathematically N : number of DMUs • : multiplier, to be solved, i=1,2…N; l=1,2 • P, Q: price vector In the lth stage, to evaluate the efficiency of the Ith DMU with 2- stage chain: • (2) Here, are the decision variables

  15. Solution approach: 6 steps • Step 1: solve the DEA model for each chain and sub-chain, and construct the efficient input-output combination for each supply chain. • Step 2: Compute the average input bundle, intermediate output/input bundle and output bundle for each supply chain and members. • Step 3:Solve the series-chain DEA problem for the average input-output supply chain

  16. Solution approach: 6 steps • Step 4: Compute the total input and output bundle of the N Series-chain models. • Step 5: Solve the merger chain DEA problem for the whole chain with input and output bundle • Step 6: Compute the sub-chain efficiency, merger efficiency for the whole chain, the harmony and scale components.

  17. Theorems • Theorem 1. full two-stage chain is efficient if and only if the sub-chain members are both efficient. • Theorem 2. Merger of the full two-stage chain is efficient if and only if the mergers of the sub-chain members are both efficient. • Similar theorems hold for the case with many sub-chain members

  18. chain with constrained resourcesHierarchical structure • Leader-follower relations Direct input Shared input Intermediate output/input Direct output Follower Leader The framework with limited resource E

  19. A Canadian bank revist… • Constrained resource, leader-follower relation

  20. Bilevel programming • Bilevel programming problem (BLP) : A hierarchical optimization problem consisting of two levels. • The upper level/ the Leader’s level/ the dominant level • The lower level/ the Follower’s level/ the submissive level • A Bilevel Linear Programming given by Bard (88) is formulated as follows:

  21. System-subsystem relation • Proposition • The system efficiency is a convex combination of both the leader and follower efficiency. • The system is efficient iff the sub-systems are efficient. • Merging of the system is efficient iff merging of the sub-systems is efficient.

  22. Incentive compatible ? • Dominant level (the Leader) gains much more potential improvement profit than what the lower level (the Follower) gains. • α -Strategy: To encourage the Follower to participate, the Leader promises to share α percentage of his profit to the Follower.

  23. Incentive compatible-example • α -Strategy: The efficiency ratio of the Leader underα strategy The efficiency ratio of the Follower under αstrategy

  24. Outline • Introduction • Background model • Our model • Case Study • Conclusion

  25. Case study: a Canadian bank… • Data from 36 branches (DMUs) for 6 variables • Mortgage banking chain input-output framework

  26. a Canadian bank… • 36 branches • efficiency analysis of the mortgage banking operations • consider mergers of the branches as a form of intra-firm re-organization. • potential savings by merging two branches at a time • 630 combinations using both the CRS and VRS DEA chain merger models

  27. Efficiency distribution

  28. Sub-chain and full chain comparison the 1st sub-chain (>100%) under CRS and VRS. full-chain (>100%) under CRS and VRS.

  29. Sub-chain VRS Harmony efficiency merger efficiency distribution. Scale efficiency

  30. Full-chain VRS VRS merger efficiency Harmony efficiency Scale efficiency

  31. Top 10 promising mergersThe computation results recommend a merger of two strong DMUs, rather than two weak ones or a weak and strong one

  32. Any incentive incompatible cases ? An example of 8 branch chains The top 10 promising mergers under CRS

  33. Incentive compatible- coordinated mergers • Coordinated effective merger Merger efficiency scores of the Leader, the Follower and the whole system are all greater than 1. The promising coordinated mergers under CRS

  34. Outline • Introduction • Background model • Our model • Case Study • Conclusion

  35. Conclusions & Further study • 3 things • Creation of chain merger DEA model • Effects captured and decomposed at both chain and sub-chain levels • a case study in banking intra-firm division merger operations • Future work • Assumptions to be validated • Breakup of firms • Comparison with other methods, e.g., game models.

  36. Thanks! • Questions?

  37. Bilevel programming efficiency analysis-optional • Model

  38. Bilevel programming efficiency analysis-optional • Model

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