Application of Data Envelopment Analysis in Finance

ESGC6322 OPERATION RESEARCH METHODS

APPLICATION OF DATA ENVELOPMENT ANALYSIS (DEA) IN FINANCE

Prepared by:

ABANG YAZREE HAZWAN BIN ABANG YUSUF (EGE160002)

PRISEELAN A/L MUNIANDY (EGE150010)

FAUZIHASMINI BINTI FAUZI (EGE150016)

WAN MOHAMAD FARHAN BIN AB RAHMAN (EGE150020)

Copyrights Master of Applied Statistics. All Rights Reserved.

5th DECEMBER 2016

INTRODUCTION

Copyrights Master of Applied Statistics. All Rights Reserved. 1

INTR

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DEA Overall Concept

Basic model of DEA by Farrel (1957)

𝑬𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 = 𝑶𝒖𝒕𝒑𝒖𝒕

𝑰𝒏𝒑𝒖𝒕

The concept was later enhanced :

𝑬𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚

= 𝑾𝒆𝒊𝒈𝒉𝒕𝒆𝒅 𝑺𝒖𝒎 𝒐𝒇 𝑶𝒖𝒕𝒑𝒖𝒕

𝑾𝒊𝒈𝒉𝒕𝒆𝒅 𝑺𝒖𝒎 𝒐𝒇 𝑰𝒏𝒑𝒖𝒕

Restriction: 0 ≤ E ≤ 1


INTR

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Advantages and Disadvantages of DEA

(1) Can deal with multiple inputs and outputs models

(2) Does not depend on the assumption of functional form to link and relate inputs to outputs

(3) Any variables determined as inputs or outputs may have various and different measurements

(1) Extreme point generated by DEA can cause significant problems such as error from measurement

(2) Only capable to estimate relative efficiency rather than absolute efficiency, even though it will coincide slowly towards absolute

(3) Testing statistical hypothesis is difficult for DEA as it applies nonparametric technique


INTR

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Objectives of the study

To evaluate the efficiency of banks in Malaysia by using DEA

To examine the trend of the efficiency index of the banks in Malaysia by using a time series data over 10-year period

To analyze the average efficiency index of each bank in Malaysia over 10-year period

DATA AND METHODOLOGY


DA

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Data Description

Disclaimer : The data was purposely created to understand the concept of DEA in finance by using multiple inputs and outputs

Input Measures Descriptions

Number Of

Employees

Total of employees for each bank

for the particular year

Operating

Expenses

Total cost incurred from normal

business operations per year (e.g.

rent, payroll, inventory cost, etc.)

Number Of

Branches Per

50,000 Adults

The density of banks in a population

of adults per year

Output Measures Descriptions

Total Income

(RM Billions)

The total gains of the banks per year (includes

assets, dividend from investments and net profit)

Satisfaction Index

(9 Point)

1=Extremely dissatisfied; 2=Completely

dissatisfied; 3=Mostly dissatisfied; 4=Somewhat

dissatisfied; 5=Neutral; 6=Somewhat satisfied;

7=Mostly satisfied; 8=Completely satisfied;

9=Extremely satisfied

Growth Rate (%) The measure of change in market shares for a

particular year

Number of New

Deposit Accounts

Number of customers registered for new deposit

accounts per year


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Method

• Main tool : Excel Solver ; Secondary tool: Eviews

1) To calculate the minimum value of the fraction of k’s inputs available to the composite units, E where k is defined as the individual unit

2) To analyze the descriptive statistics, applying both graphical and numerical techniques

The minimum value of E is computed based on the complete model. One of the complete models is written below:

Data For 2015

Define the Decision Variables :

E = Fraction of Bank A’s input resources required by the composite bank

wA = Weight applied to Bank A’s input/output resources by the composite bank

wB = Weight applied to Bank B’s input/output resources by the composite bank

wC = Weight applied to Bank C’s input/output resources by the composite bank

wD = Weight applied to Bank D’s input/output resources by the composite bank

wE = Weight applied to Bank E’s input/output resources by the composite bank

wF = Weight applied to Bank F’s input/output resources by the composite bank

wG = Weight applied to Bank G’s input/output resources by the composite bank

Define the Objective Function: Minimize the fraction of Bank A’s input resources required by the composite bank: Minimize E


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Define the constraints:

𝑆𝑢𝑚 𝑜𝑓 𝑡𝑕𝑒 𝑤𝑒𝑖𝑔𝑕𝑡: 𝑤𝐴 + 𝑤𝐵 + 𝑤𝐶 + 𝑤𝐷 + 𝑤𝐸 + 𝑤𝐹 + 𝑤𝐺 = 1

Input Constraints:

19,457𝑤𝐴 + 20,345𝑤𝐵 + 10,876𝑤𝐶 + 8,078𝑤𝐷 + 11,769𝑤𝐸 + 15,467𝑤𝐹 + 12,768𝑤𝐺 ≤ 19,457𝐸

0.0031𝑤𝐴 + 0.0027𝑤𝐵 + 0.0022𝑤𝐶 + 0.0016𝑤𝐷 + 0.0025𝑤𝐸 + 0.0089𝑤𝐹 + 0.0084𝑤 ≤ 0.0031𝐸

19𝑤𝐴 + 20𝑤𝐵 + 14𝑤𝐶 + 11𝑤𝐷 + 15𝑤𝐸 + 17𝑤𝐹 + 15𝑤𝐺 ≤ 19𝐸

Output Constraints: 0.474𝑤𝐴 + 5.892𝑤𝐵 + 8.603𝑤𝐶 + 8.134𝑤𝐷 + 6.867𝑤𝐸 + 10.066𝑤𝐹 + 8.337𝑤𝐺 ≥ 8.134

2𝑤𝐴 + 4𝑤𝐵 + 6𝑤𝐶 + 6𝑤𝐷 + 4𝑤𝐸 + 8𝑤𝐹 + 5𝑤𝐺 ≥ 6

−20.8𝑤𝐴 + 30.3𝑤𝐵 + 49.7𝑤𝐶 + 74.2𝑤𝐷 + 59.1𝑤𝐸 + 30.9𝑤𝐹 + 80.4𝑤𝐺 ≥ 74.2 103,044𝑤𝐴 + 100,582𝑤𝐵 + 132,508𝑤𝐶 + 146,971𝑤𝐷 + 117,908𝑤𝐸 + 125,169𝑤𝐹 + 145,988𝑤𝐺 ≥ 146,971

Non-negativity of variables: E, wA, wB, wC, wD, wE, wF, wG ≥ 0

RESULTS AND DISCUSSION


Summary of efficiency index, E of banks in Malaysia

Years A B C D E F G

2006 1 0.700 1 1 0.698 1 0.739

2007 0.551 1 1 1 1 1 0.762

2008 0.561 1 1 1 1 1 0.767

2009 0.551 1 1 1 1 1 0.939

2010 0.526 0.707 1 1 0.667 1 1

2011 1 1 0.873 1 1 1 1

2012 0.868 0.997 0.853 1 1 1 0.768

2013 1 1 1 1 1 1 1

2014 0.710 0.818 1 1 0.854 1 1

2015 0.579 0.593 1 1 0.733 1 1

1st Objective: To evaluate the efficiency of banks in Malaysia by using DEA

RESU

LTS A

ND

DIS

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SSIO

N


BANKS A B C D E F G

Input Measure

Number of employees 18,856 12,432 11,023 8,789 16,433 9,897 11,655

Operating expenses (RM’ billions) 0.0056 0.0088 0.0016 0.0021 0.0067 0.0014 0.0045

Number of branches per 50,000

adults per day 19 20 12 11 15 10 18

Output Measure

Total Income (RM’ billions) 2.56 3.44 3.02 6.94 3.24 6.11 4.34

Satisfaction Index (scale of 1 - 9) 4 1 4 5 4 5 6

Growth rate (%) 24.5 -20.3 11.2 14.6 21.6 45.7 21.3

Number of new deposit accounts 112,727 122,092 155,865 122,327 100,342 115,468 142,766

Bank inputs and outputs in 2010

RESU

LTS A

ND

DIS

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SSIO

N


Cell Name Final

Value

Reduced

Cost

Objective

Coefficient

$C$12 wA 0 0.473684211 0

$D$12 wB 0 0.526315789 0

$E$12 wC 0 0.105263158 0

$F$12 wD 0 0.052631579 0

$G$12 wE 0 0.263157895 0

$H$12 wF 1 0 0

$I$12 wG 0 0.421052632 0

$J$12 E 0.526315789 0 1

Cell Name Final

Value

Shadow

Price

Constraint

R.H. Side

$M$2 Weightage 1 0.526315789 1

$M$3 Number of employees -27.21052632 0 0

$M$4 Operating expenses (RM’ billions) -0.001547368 0 0

$M$5 Number of branches per 50,000

adults 0 -0.052631579 0

$M$6 Total Income (RM’ billions) 6.112 0 2.564

$M$7 Satisfaction Index (scale of 1 - 9) 5 0 4

$M$8 Growth rate (%) 45.65 0 24.5

$M$9 Number of new deposit accounts 115468 0 112727

Sensitivity report of Bank A in 2010

RESU

LTS A

ND

DIS

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N


BANKS A B C D E F G

Input Measure




adults per day 20 21 16 13 16 19 21

Output Measure



Growth rate (%) 24.8 23.4 18.2 12.1 33.3 19.2 18.9



RESU

LTS A

ND

DIS

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SSIO

N


Cell Name Final

Value

Reduced

Cost

Objective

Coefficient

$C$40 wA 0.020783354 0 0

$D$40 wB 0 0.042937568 0

$E$40 wC 0 0.126791262 0

$F$40 wD 0.703931202 0 0

$G$40 wE 0.275285443 0 0

$H$40 wF 0 0.226226105 0

$I$40 wG 0 0.085388296 0

$J$40 E 0.873208738 0 1

Cell Name Final

Value

Shadow

Price

Constraint

R.H. Side

$M$30 Weightage 1 0.791239994 1

$M$31 Number of employees 0 -5.31984E-05 0

$M$32 Operating expenses (RM’ billions) -7.8696E-05 0 0


Adults 0 -0.017959643 0


$M$35 Satisfaction Index (scale of 1 - 9) 6.662364494 0 5

$M$36 Growth rate (%) 18.2 0.004503777 18.2

$M$37 Number of new deposit accounts 160778.2101 0 144232

Sensitivity report of Bank C in 2011

RESU

LTS A

ND

DIS

CU

SSIO

N


BANKS A B C D E F G

Input Measure




adults per day 19 20 14 11 15 17 15

Output Measure



Growth rate (%) -20.8 30.3 49.7 74.2 59.1 30.9 80.4



RESU

LTS A

ND

DIS

CU

SSIO

N


Cell Name Final

Value

Reduced

Cost

Objective

Coefficient

$C$14 wA 0 0.9375 0

$D$14 wB 0 0.6875 0

$E$14 wC 0 0.375 0

$F$14 wD 1 0 0

$G$14 wE 0 0.5625 0

$H$14 wF 0 4.5625 0

$I$14 wG 0 4.25 0

$J$14 E 1 0 1

Cell Name Final

Value

Shadow

Price

Constraint

R.H. Side

$K$4 Weightage 1 1 1

$K$5 Number of employees 0 0 0

$K$6 Operating expenses (RM’ billions) 0 -625 0

$K$7 Number of branches per 50,000

adults 0 0 0

$K$8 Total Income (RM’ billions) 8.134 0 8.134

$K$9 Satisfaction Index (scale of 1 - 9) 6 0 6

$K$10 Growth rate (%) 74.2 0 74.2

$K$11 Number of new deposit accounts 146971 0 146971

Sensitivity report of Bank D in 2015

RESU

LTS A

ND

DIS

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SSIO

N


RESU

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DIS

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SSIO

N

2nd Objective: To examine the trend of the efficiency index of the banks in Malaysia

by using a time series data over 10-year period

0.5

0.6

0.7

0.8

0.9

1.0

06 07 08 09 10 11 12 13 14 15

Bank A

0.5

0.6

0.7

0.8

0.9

1.0

06 07 08 09 10 11 12 13 14 15

Bank B

0.72

0.76

0.80

0.84

0.88

0.92

0.96

1.00

06 07 08 09 10 11 12 13 14 15

Bank G


RESU

LTS A

ND

DIS

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SSIO

N

0

1

2

06 07 08 09 10 11 12 13 14 15

Bank D

0.5

0.6

0.7

0.8

0.9

1.0

06 07 08 09 10 11 12 13 14 15

Bank B

0

1

2

06 07 08 09 10 11 12 13 14 15

Bank F

0.6

0.7

0.8

0.9

1.0

06 07 08 09 10 11 12 13 14 15

Bank E


BANKS A B C D E F G

Input Measure




adults per day 19 20 13 12 15 16 16

Output Measure



Growth rate (%) 13.9 27.7 32.0 38.3 33.5 34.7 35.1


3rd Objective: To analyze the average efficiency index of each bank

in Malaysia over 10-year period

RESU

LTS A

ND

DIS

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SSIO

N


Bank E

A 0.63222829

B 0.65778558

C 0.89031798

D 1

E 0.76357951

F 1

G 0.72806837

RESU

LTS A

ND

DIS

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SSIO

N

10 years average efficiency index of each bank in Malaysia

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

A B C D E F G

Effi

cie

ncy

Ind

ex, E

Banks


Sensitivity report of Bank A for average of 10 years

Cell Name Final

Value

Reduced

Cost

Objective

Coefficient

$C$13 wA 0 0.367771708 0

$D$13 wB 0 0.328918185 0

$E$13 wC 0 0.129290045 0

$F$13 wD 1 0 0

$G$13 wE 0 0.388565256 0

$H$13 wF 0 1.564587332 0

$I$13 wG 0 1.238854699 0

$J$13 E 0.632228292 0 1

Cell Name Final

Value

Shadow

Price

Constraint

R.H. Side

$M$3 Weightage 1 0.632228292 1

$M$4 Number of employees -2178.235099 0 0

$M$5 Operating expenses (RM’ billions) 0 -286.7683472 0


adults -0.171064103 0 0


$M$8 Satisfaction Index (scale of 1 - 9) 6.4 0 2.5

$M$9 Growth rate (%) 38.26 0 13.85

$M$10 Number of new deposit accounts 143371.6372 0 103308.5931 RESU

LTS A

ND

DIS

CU

SSIO

N

Application of Data Envelopment Analysis in Finance

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