1 / 39

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.

marra
Download Presentation

Chain Merger Evaluation and Application to Banking Operations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related