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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. Outline. Introduction Problem, Literature - PowerPoint PPT Presentation
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Chain Merger Evaluation and Application to Banking Operations
Desheng Dash WuUniversity of Toronto, Reykjavik University
[with John R. Birge, Booth School of Business, University of Chicago]
Accepted and to appear at POMDSJ, 43(1) 2012
1
2
OutlineIntroduction
Problem, LiteratureBackground modelOur model
Conceptual model, Math model3 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 analysisConclusion & Further study
3
Outlineo Introduction
o Background
model
o Our model
o Case Study
o Conclusion 4
Industry factsNew 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
LiteratureIO: Salant (83), JOE; Deneckere and
Davidson (85) RandJ;Perry and Porter (85), AER; Farrell, (90), AER; Rothschild (00) Reg Sci&E; Benjamin et al. (09)
merger paradoxFinance: Sapienza (02), JOF; Guerard Jr.
(89); Geppert and Kamerschen(08); Houston and Ryngaert (94) JBF; Duffie (07) JFE
stockOR: Sherman and Rupert (06), EJOR;
Cummins et al.(08) JBF; Ray (04); Bogetoft (05), JPA
efficiency6
Our study A model for gauging merger efficiency of
supply chainsdifferent structure
Supply chain view of banking operations Link operations to finance
Apply the model to banking operations with DEA, considering M&A with multiple metricsLink OR to IO/Finance
7
Question: banks or subdivisions merged, how business performance is affected considering such a banking chain? How to achieve potential gains?
8
Revisit Banking operations- supply chain
Borrower selection; Underwriting; Loan approval; Primary market
Securitization; Derivative Trading; Secondary market
Staff, asset
IT facility,staff
Information flow
Loans
Information flow Product flow
Sales, risks, availability, stock, customer/investor satisfaction level
Mortgage banking: a view of serial chain
Outlineo Introduction
o Background
model
o Our model
o Case Study
o Conclusion 9
Merger gains (Ray, 2004)2-step process: harmony effect, scale effect
10
Input 2
Input 1
B: (x1B, x2B)
A: (x1A, x2A)
D
G
yA
demonstration of the merger of two firms
yB
yD>1/2(yA+yB) ?
yG>(yA+yB) ?
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
Em( X A , X B )
yG
2y(
yD
y)(
yG
2yD
) H S (1)
H
yD
y
S
yG
2yD
Em
What1. 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)
How2. Define DMU, input/output variables3. Define the efficiency frontier.4. A numerical weight coefficient is given to
each firm, computing its relative efficiency.
Data Envelopment Analysis (DEA)
12
Outlineo Introduction
o Background
model
o Our model
o Case Study
o Conclusion 13
two-stage series-chain Conceptually
the ith DMU, i=1,2…N
14
MathematicallyN : 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
1 1 1 1 2 2 2 2
1, 1, 1, 2, 2, 2, 2, 1, 1,1 1 1
1 1, 1, 2 2, 2,1 1
1
( ) ( )max
. . ,
0 , 0 ,
I I I I
N N N
i i I i i I i i Ii i i
N NI I
i i i ii i
I
P f Q h P f Q h
y
y y
s t x x x x y
f f
h
1, 1, 2 2, 2,1 1
1, 2, 1, 2, 1 1 2 21 1
1 1 ,
0 , 0 ,
, , ; , , 0.
N NI
i i i ii i
N NI I I I
i i i ii i
z zh
f h f h
f1I ,h1
I , f2I ,h2
I
l ,i
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
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(xl , I
, yl , I , zl , I
)
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
Solution approach: 6 steps
, ,( )Total Total Totall l lx y z
TheoremsTheorem 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
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Leader-follower relations
Direct input Shared input Intermediate output/input Direct output
chain with constrained resources
Hierarchical structure
1DX Y
E1X 2X
2DX
1Z
Leader Follower
2Z
1DX 2DX
Y1Z
1X
The framework with limited resource E
2X
2Z19
o Constrained resource, leader-follower relation
Primary market business-leader
Secondary market business-followerOthers
IT Budget
Loans
Loan recovery
ProfitPersonal
A Canadian bank revist…
20
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:
Bilevel programming
1 1
1 1 1
2 2
2 2 2
min ( , )
. .
min ( , )
. . , 0
T T
x
T T
y
F x y p x q y
s t A x B y b
f x y p x q y
s t A x B y bx y
21
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.
System-subsystem relation
22
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.
Incentive compatible ?
23
α -Strategy:
Incentive compatible-example
00.0
10.0
20.0
30.0
40.0
5
0.060
00000
00000
001 0.07
0.080
00000
00000
001 0.09 0.1
80%90%
100%110%120%130%
DMU1
DMU2
DMU3
DMU4
DMU5
DMU6
DMU7
DMU8
Efficiency ra-tio
α
00.0
10.0
20.0
30.0
40.0
50.0
60.0
7
0.0800
0000
000000
01 0.09 0.1
90%100%110%120%130%140%
DMU1DMU2DMU3DMU4DMU5DMU6DMU7DMU8
Efficiency ratio
α
adjusted optimized profitEfficiency ratioobserved profit
The efficiency ratio of the Leader under α strategy
The efficiency ratio of the Follower under α strategy
24
Outlineo Introduction
o Background
model
o Our model
o Case Study
o 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
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435360
0.2
0.4
0.6
0.8
1
1.2
sub-chain CRSchain CRSsub-chain VRSchain VRS
Sub-chain and full chain comparison
29
the 1st sub-chain (>100%) under CRS and
VRS.
full-chain (>100%) under CRS and VRS.
Sub-chain VRS
30
merger efficiency distribution. Harmony efficiency
Scale efficiency
31
VRS merger efficiencyFull-chain VRS
Harmony efficiency
Scale efficiency
Top 10 promising mergers The computation results recommend a merger of two strong DMUs, rather than two weak ones or a weak and strong one
32
Code Merger ME Scale
D1 5 29 1.4943 0.95031
D2 5 28 1.4677 0.93631
D3 5 23 1.4453 0.93501
D4 5 30 1.3427 0.91358
D5 5 35 1.3309 0.87452
D6 5 31 1.3308 0.91817
D7 23 28 1.3155 0.95172
D8 4 5 1.3137 0.93138
D9 23 29 1.3095 0.94289
D10 5 17 1.3057 0.92251
Any incentive incompatible cases ? An example of 8 branch chains
Merger leader follower system4,5 1.125 0.99 1.0923,4 1.098 0.99 1.0725,8 1.09 1.001 1.0674,7 1.081 1.001 1.0593,8 1.06 1.001 1.0451,4 1.059 0.9 1.0421,8 1.057 0.99 1.0417,8 1.047 0.99 1.0355,6 1.042 0.99 1.0314,6 1.035 1.001 1.027
The top 10 promising mergers under CRS
33
Coordinated effective merger Merger efficiency scores of the Leader, the
Follower and the whole system are all greater than 1.
Incentive compatible- coordinated mergers
Merger leader follower system5,8 1.09 1.001 1.0674,7 1.081 1.001 1.0593,8 1.06 1.001 1.0454,6 1.035 1.001 1.0276,8 1.023 1.001 1.0182,8 1.014 1.001 1.011
The promising coordinated mergers under CRS
34
Outlineo Introduction
o Background
model
o Our model
o Case Study
o Conclusion 35
Conclusions & Further study3 things
Creation of chain merger DEA modelEffects captured and decomposed at
both chain and sub-chain levelsa case study in banking intra-firm
division merger operationsFuture work
Assumptions to be validatedBreakup of firmsComparison with other methods, e.g.,
game models.36
Thanks!
Questions?
37
Model
Bilevel programming efficiency analysis-optional
1 1 1 1
1 1 2 1 1 1 2 1
, , , ,
1 2 1 2
1 1
1 1
1
1 1
1
( 1) max ( ) ( )
. ,
,
,
T T T T
DJ J J J
DJ J J J
X X Y Z
n n
J J j j j jj j
nD DJ j j
j
n
J j jj
J
P Q Z Q Y P X P X
s t X X X X
X X
Z Z
Y
1
1
1 2
1 1
1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
,
( .),
,
( ) ( ) ( ) ( )T T T T T T T T
n
j jj
J J
D DJ J
D DJ J J J J J J J
Y
X X E const
X X
Q Z Q Y P X P X Q Z Q Y P X P X
38
Bilevel programming efficiency analysis-optional
2 2 2 2
3 2 1 2 3 2 2 2
, , , ,
2 2
1
2
1
( 2) max ( )
. ,
,
T T T T
DJ J J J
DJ J J J
X X Y Z
nD DJ j j
j
n
J j jj
J
P Q Z P X P X Q Y
s t X X
Y Y
Z
2 2
1
2 2
2 1
3 2 1 2 3 2 2 2 3 2 1 2 3 2 2 2
1 2 1 2 1
,
,
,
( ) ( )
, , , , ,
T T T T T T T T
n
j jj
D DJ J
J J
D DJ J J J J J J J
D DJ J J J J
Z
X X
Y Y
Q Z P X P X Q Y Q Z P X P X Q Y
X X X X Y Y
2 1 2, , , , 0J J JZ Z
Model
39