1
OPIM 5984
ANALYTICAL CONSULTING IN
FINANCIAL SERVICES
SURESH NAIR, Ph.D.
Financial Services Analytical Consulting
2




There is increasing convergence between operations, marketing and
finance.
Nowhere is this more evident than in the financial services industry –
banking, credit cards, brokerage, insurance, mortgages, etc.
What differentiates financial services from other services

Large number of customers

Repeat nature of interactions over the customer’s lifetime,

Lots of data available for analysis and decision making, and a

Wide variety of tools and techniques are applicable – from deterministic to
stochastic modeling, from analytical methods to simulation.
There is huge potential for analytical consulting in financial services
Outline
3


Management consulting situations
Attributes of a good consultant – Lessons learnt
Time is of the essence – Quick analysis is very important
 It is far more difficult to start from a clean slate than to
improve an existing process/idea.




85% of the benefit from a good idea, however implemented.
Optimization only improves from there.
Be Rumpelstiltskin – learn to spin straw into gold. Learn to
work on unstructured problems
“Socialize” recommendations – don’t surprise client
Consulting situations
4
Available
No need for
consultants
Creative Modeling
Not Available
Data Availability
Modeling/Solution Techniques
Known
Not Obvious
Creative Data
Gathering
Qualitative
Inductive
Recommendations
5
Attributes of a good
Management Consultant
Time is of the essence
6




It is more important to be timely than perfect.
Problems are unstructured. No such thing as a perfect solution to a problem
that is hard to define.
Learn the tradeoff between time and performance
If you take too long, the problem changes by then. You have the perfect
solution to the wrong problem.
Breakthrough vs. Incremental ideas
7

It is far more difficult to start from a clean slate than to improve an existing
process/idea.

85% of the benefit from a good idea, however implemented. Optimization only
improves from there.
Be Rumpelstiltskin – spin straw into gold
8

Learn to work on unstructured problems

Quadrant 2: Creative Modeling



Quadrant 3: Creative Data Gathering


Retail Bank Sweeps
Credit Card solicitations
End of life planning for a blockbuster drug going off exclusivity
Quadrant 4: Qualitative Inductive Recommendations

Impact of Comparative Effectiveness Research on drug sales
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Service Capacity and Waiting Lines
(Queueing) in Financial Services
Service Capacity And Waiting Lines
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



The study of Waiting Lines or Queueing Theory is of utmost importance in
the design of Service Systems, e.g., capacity study of a computer network,
determining the number of servers, tellers, emergency services, size of a
restaurant, number of elevators in a building, phone lines, etc., to achieve
some level of service.
In each of these situations, there are “servers” who provide service (e.g.,
tellers, phone lines) and “customers” who require that service (e.g., bank
customers, phone calls).
If the server is busy, the customer has to wait, and forms a waiting line of
queue.
Even if there are enough servers to handle customer traffic on average,
queues will form because of the variability in customer traffic, and service
times.
Optimizing Service
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

You can add service capacity to reduce waiting, but the costs will go up.
There is a trade-off between waiting costs and capacity costs.
Usually, a service level is specified by the management, e.g, no more than 4
customers will have to wait, or an average customer will not have to wait
more than 2 minutes.
Service Configurations
12

Studies have shown that there are certain common service configurations.
Poisson Arrivals, Exponential Service
13

Studies have also shown that in many cases

Customer arrivals typically follow a Poisson Distribution


specified by a single parameter, l , called the Arrival Rate, e.g., on average 8
arrivals/hour
Service time are Exponentially distributed. Service rate is Poisson.
specified by a single parameter, m , called the Service Rate, e.g, serves on
l=1average 10 customers/hour.

l=2
A
l=4
Single Server Model
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


We evaluate various designs of service systems by analyzing the waiting
lines that would result from the designs under known traffic and service
patterns.
If the source of customers is infinite (Infinite source, the most common case)
For a SINGLE SERVER MODEL, with first come first served discipline
(l/<1, M=number of servers)
l
2

Average number in line

In general (for single and multi-server models)


Average time in line
Lq 
Wq 
Average system utilization
 (  l )
Lq
l
 
l
M
Example
15

A bank customer service rep can handle 15 calls/hour on average. Calls
come in at the rate of 10/hr. What would be the number of calls getting a
busy signal, the amount of wait, and the utilization of the rep?
Solution

l = 10, =15.

Lq = (10*10)/15(15-10)=100/75 = 1.33 calls

Wq = 1.33/10 = 0.133 hours = 8 minutes

Utilization, r = 10/(1*15)= 0.667 = 66.7%

Service time = 60/15=4 minutes

Total time = 8+4 = 12 minutes
Exercise
16
A brokerage is considering leasing one of two photocopying machines.

Mark I is capable of duplicating 20 jobs/hr at $50 per day.

Mark II is capable of duplicating 24 jobs/hr, at $80/day
The duplicating center is open 10 hours a day, with average arrivals of 18
jobs/hour.
Duplication is performed by employees from various departments whose hourly
wage is $5/hr.
Should the brokerage lease Mark I or Mark II?
Other Models
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
For a SINGLE SERVER, CONSTANT SERVICE TIME MODEL


the queue length and wait time will be half, the other formulas remain
the same.
For a MULTIPLE SERVER MODEL,



The formulas are complicated.
Use Spreadsheet, first tab.
You may use the spreadsheet even for Single Server models
Example
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In a retail bank, 5 teller counters are open. Arrivals to the counters are at the
rate of 36 per hour, service is at the rate of 10/hr per counter. What will be
the average length of queue?
Solution:

l/ = 36/10 = 3.6, M=5
From the Spreadsheet,

Lq = 1.055 and P(No one in line) = 0.023 or 2.3%.

Utilization, r = l/M = 36/5*10 = 72%

Wq=1.055/36 = 0.029 hrs = 1.7 minutes
Exercise: What would happen if arrival rate=25/hr
Exercise: If waiting time (with arrival rate=36/hr) should be at most 1 minute,
how many counters should be open?
Analyzing the Waiting Line Formula

We can rewrite the single server total time in system formula as
 ca 2  cs 2
WT  

2


 1

 1  


 t s

The above formula has three parts, the Variability part, the Utilization part, and
the service Time part. We can call this the vUt equation

CoV for Exponential times is 1

Note that an increase in any of the parts will increase the total time in the system.

Beyond 85% utilization, the

Reducing variability of arrival time
and/or service time can reduce
waiting time.

Reducing processing time also helps.
80.0
W aitin g T im e
waiting time increases rapidly
100.0
60.0
c _a= 1
40.0
c _a= 2
20.0
0.0
0
0.2
0.4
0.6
U tiliz a tio n
0.8
1
Critical Thinking
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

How do you make the tradeoff between specialization and cross training?
How do you make the tradeoff between technology improvement and head
count increase?
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Creativity, Critical Thinking and Analysis
Ask the Questions (Creative Brainstorming)
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
What


How


Why is it done at that time? Can it be done before? After?
Where


Can it be done some other way? Automated? Can it be made easier?
When


What is the objective being achieved?
Why is this task done there? Can it be done somewhere else?
By whom

Can the task be done by someone else?
Critical Examination Worksheet
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
Use the worksheet
In-class Exercise – Water Filter
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
Consider a house with well water where the water filter gets clogged very
quickly with particulate matter. Filters are expensive to replace every couple of
weeks.

Brainstorm using the worksheet to develop alternatives that will save the
homeowner money.
Brainstorming Ground Rules
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








Relax
Have fun
Laugh
Support
No boundaries
Completely free your mind
No limits on the number of ideas
Fragmented ideas OK
Just keywords OK
Brainstorming Ground Rules
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








No criticizing (during or after)
No evaluating or dismissing
No dismissing EVEN BY YOU YOURSELF
No “You must be joking” looks or comments
Explain quickly (few seconds)
No questions
Let ideas you don’t understand go
Speed is the key
Important is “Association” not “Viability”
Brainstorming Ground Rules
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
Avoid subtle evaluations
How is it going to do …
 Isn't this violating the rules
 That is an excellent idea
 How is this different than that idea

Ground Rules
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






Select a moderator
No dominating
No interrupting
No passing
Short session (20 minutes)
Create ideas in silence
Multiple rounds
Critical Thinking Habits
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Critical thinking is an essential component of professional accountability and
apply to any discipline. These habits are show below.

Confidence


Contextual Perspective


Consideration of the whole situation, including relationships, background, and
environment, relevant to some happening
Creativity


Assurance of one's reasoning abilities
Intellectual inventiveness used to generate, discover, or restructure ideas,
imagining alternatives
Flexibility

Capacity to adapt, accommodate, modify, or change thoughts, ideas, and
behaviors
Critical Thinking Habits (contd.)
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
Inquisitiveness


Intellectual Integrity


Insightful sense of knowing without conscious use of reason
Open-mindedness


Process of seeking the truth through sincere, honest means, even if the results are
contrary to one's assumptions and beliefs
Intuition


An eagerness to know by seeking knowledge and understanding through
observation and thoughtful questioning in order to explore possibilities and
alternatives
A viewpoint characterized by being receptive to divergent views and sensitive
to one's biases
Perseverance

Pursuit of a course with determination to overcome obstacles
Creativity (contd.)
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
Reflection

Contemplation of a subject, especially one's assumptions and thinking, for the
purposes of deeper understanding and self-evaluation
Adapted from R. W. Paul, Critical Thinking (Santa Rosa, Calif.: Foundation for
Critical Thinking, 1992).
Break-out Exercise
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Brainstorm on how you would make the payment part of this product easier? Use
the worksheet. I am keen that you fill it out completely and methodically brainstorm
www.koffeekarousel.com
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Simulating Alternative Recommendations
in Financial Services
Simulating Alternative
Recommendations in Financial Services
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A Simulation is an experiment in which we attempt to understand how some
process will behave in reality by imitating its behavior in an artificial
environment that approximates reality as closely as possible.
Simulation is typically used when



No formulae or good solution methods exist because assumptions in existing
formulae/methods are violated.
Data does not follow standard probability distributions
Most importantly, to evaluate alternatives (e.g..., designs, systems, methods
of providing service, etc.)
Examples include valuing options, evaluating overbooking policies for
airplanes, evaluating work schedules, maintenance policies, financial portfolios,
real estate salesperson planning, etc.
An Example
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Jack sells insurance. His records on the number of policies sold per week over a
50 week period are:
Number policies sold
Frequency

0
8
1
15
2
17
3
7
4
3
Suppose we wanted to simulate the policies Jack sells over the next 50
weeks.
Example (contd.)
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
Life is random
Give Chance a Chance
iPod Shuffle
It is fairly simple to evaluate different alternative order quantities quickly
using simulation.
Step 1

Compute Probabilities, Cumulative Probabilities and assign Random
Numbers
Number policies sold
Frequency
Probability
Cumulative Probability
Random Numbers
0
8
0.16
0.16
00-15
1
15
0.30
0.46
16-45
2
17
0.34
0.80
46-79
3
7
0.14
0.94
80-93
4
3 Total
0.06
1.00
1.00
94-99
The trick for assigning random numbers is easy. Compute the cumulative
probability, start from 00 to 1 less than the cum frequency. For the next row,
start from the next random number to 1 less than the cum prob., etc.
Step 2

Simulate the next 50 orders
#Policies Simulation
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#Policies Example (contd.)
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

Suppose 30% of the policies are Life and 70% are
Supplemental, simulate the type of policies for the next 50
weeks.
Suppose 25% of the Life policies are for $100K, 50% for
$250K, and 25% for $500K, simulate the value of the policies
for the next 50 weeks.
Exercise
39


You want to start a small car rental firm and would like to lease cars that
you will rent out. You want to decide how many cars to lease.
You do some market research and obtain the following information
Number of customers/day
Probability
Length of car rental
Probability


0
0.2
1
0.3
1
0.2
2
0.5
2
0.3
3
0.3
4
0.2
Lease costs are $10 per day, and net profits (exclusive of lease costs) is
$20/day.
Simulate the process for 15 days if you had chosen to lease 3 cars.
Break-out Exercise
40
For the Credit Cards data file on the website, please simulate the following
for the next 24 months for a customer:

Current Balance

Payment

Purchase + Cash advance
What are the assumptions you made?
What else would you have done in modeling future behavior, if you had more
time?
Simulating Standard Distributions
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

In Excel, use \Data\Data Analysis and then select Random Number
Generation. This tool can simulate the following distributions:

Normal

Uniform

Binomial

Poisson

Discrete
The random numbers generated do not change when F9 is pressed (that is,
once generated, they stay fixed).
Standard Distributions (contd.)
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
Random numbers following certain distributions can be generated to change with
every press of F9. This can be very useful in practice.
Generating Normally distributed random numbers:

Suppose you wanted to generate Normal random numbers with a mean of 50 and
standard deviation of 5.

=NORMINV(RAND(),50,5)
Generating Uniformly distributed random numbers:

Suppose you wanted to generate sales per day that were Uniformly distributed
between 6 and 12 (inclusive).

=RANDBETWEEN(6,12)
Generating Exponentially distributed random numbers:

Suppose you want to simulate the next breakdown of a machine that fails
exponentially with a mean of 5 hours (i.e., l=0.2), then use

= – 5*LN(RAND())
Standard Distributions (contd.)
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Generating Poisson distributed random numbers:

You need the average for the Poisson distribution.

Use Random Number Generator under
\Data\Data Analysis
Generating Discrete distributed random numbers:

Use Random Number Generator
Exercise: Currency Notes Requirement
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

John Bender, a bank manager, needs to figure out the number of currency
notes of a particular denomination to stock in his branch. If he has unused
notes at the end of the day, that costs float. If he is short notes, that turns
off customers. The costs are:

Float cost of unused notes, per unused note
$1

Penalty cost for note shortage/note
$2
Customers traffic depends on how many customers came in the previous
day. From past year’s data, the relationship is
Customers(Wed)= 372+ 0.7091 Customers(Tues)

(1)
Which has a residual error of 59 (more on this later). He figures 65-85%
of customers will need to withdraw cash, and they will need a mean of 10
currency notes of this denomination (Poisson distributed).
Currency Notes(contd.)
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
The number of customers Tuesday was 215. How many currency notes of
this denomination should the manager carry on Wednesday to minimize the
sum of excess and shortage costs?
Solution:

Plugging 215 into (1) we get an expected customers today 525. Therefore
the attendance is going to follow a Normal distribution with mean of 525
and standard deviation of 59 (the residual error stated above).
Break-out Exercise (Flight Overbooking)
46
This example will focus on a very successful, regional carrier (Midwest Express Airlines). Midwest
Express is headquartered in Milwaukee, Wisconsin, and was started by the large consumer
products company Kimberly Clark, which has large operations in nearby Appleton, Wisconsin.
Laura Sorensen is the manager of Revenue (or Yield) Management. She has been reviewing the
historical data on the percentage of no-shows for many of Midwest Express' flights. She is
particularly interested in Flight 227 from Milwaukee to San Francisco. She has found that the
average no-show rate on this flight is 15% (Binomial, use p=0.15, number of trials, n =
reservations accepted; use the function CRITBINOM(n,p,rand()) ). The aircraft (MD88) has a
capacity of 112 seats in a single cabin. There is no First Class/Coach cabin distinction at Midwest
Express. All service is considered to be premium service. You would believe that if you could smell
the chocolate chip cookies baking as you fly along.
The question Laura wants to answer is to what level should she overbook the aircraft.
Demand is strong on this primarily business route. The actual demand distribution is as follows:
Demand
100
105
110
115
120
125
130
135
140
145
Probability
0.03
0.05
0.08
0.12
0.18
0.19
0.12
0.10
0.08
0.05
Break-out Exercise (contd.)
47
The average fare charged on this flight is $400. If Laura accepts only 112
reservations on this flight, it is almost certain to go out with empty seats because of the no-shows
that represent an opportunity cost for Midwest Express as it could have filled each seat with
another customer and made an additional $400. On the other hand, if she accepts more
reservations than seats, she runs the risk that even after accounting for the no-shows, more
customers will show up than she has seats available. The normal procedure in the event that a
customer must be denied boarding is to put the "extra" customers on the next available flight,
provide them some compensation toward a flight in the future and possibly a voucher for a free
meal and a hotel. This is all done to mitigate the potential ill will of the "bumped" customer. Laura
figures this compensation usually costs Midwest Express around $600 on average.
How many reservations should Laura accept? What is the profit for this policy?
48
Optimizing Financial Services
Financial Services Optimization
49



In most business situations, managers have to achieve objectives while
working within several resource constraints. For example, maximizing sales
within an advertising budget, improving production with existing capacity,
reducing costs while maintaining service metrics, etc.
Mathematical modeling can help in such situations. Linear Programming (LP)
is the most important of these techniques.
It is used in a wide array of applications, such as


Determining the credit card acquisitions, risk management, optimal product mix,
advertising and media planning, investment decisions, branch/ATM location
siting, assignment of people to tasks, etc.
We will learn about how LP helps decision making by considering several of
these applications.
LINEAR PROGRAMMING
50
Example: (Maximization)

A insurance broker sells 2 kinds of products, Homeowners Insurance (H) and
Life Insurance (L). The profit from H is $300, and the profit from L is $250.
The limitations are



Direct personnel: It takes 2 hours to effort for sale of H, and 1 hour of
effort for every sale of L. There are only 40 hours in a week.
Support staff: It takes 1 hour support work for each H and 3 hours for L.
There are only 45 support staff hours in a week.
Marketing: The broker determines she cannot sell more than 12 units of H
per week.
How many of H&L should she aim to sell each week to maximize profits?
Example: (Minimization)
51
A credit card company wishes to have a balance of balance carrying and
monthly usage customers in its portfolio of new accounts. It is required that the
portfolio have a usage rating of at least 300 units, and a monthly balance
carrying level of at least 250 units. These can be produced by two types of
accounts, Revolvers and Transactors.

Both revolvers and transactors provide 1 unit of monthly usage per account.

Only revolvers carry balance, of 3 units per account.

Acquiring revolvers costs $45 and acquiring transactors costs $12/account.
How many revolvers and transactors should the credit card company acquire to
minimize costs while achieving its portfolio profile?
Binary (0-1) Assignment Example
52

A manager Global Financial Corp, a commercial loan firm, wishes to
minimize turn around time for loan processing. He has 5 associates and the
task requires 4 steps. He needs to pick the best 4 associates depending on
their time for each of the tasks. The average times (in minutes) for each of
task was recorded as below:
Task
Eval and Analysis

John
482
Susan
444
David
459
Ben
370
Melissa
429
Interest Rate
295
321
264
347
317
Loan Terms
379
341
384
306
397
Final Issuing
120
120
124
109
115
Who should be assigned to which task to minimize turn-around time for loan
applications?
Non-Binary Allocation Example
53

A bank wishes to achieve Leadership in Energy and Environmental Design
(LEED) rating for its new corporate office. The energy needs in the building
fall into 3 categories (1) electricity (2) heating water, and (3) heating space
in the building. The costs and daily requirements are shown below:
Needs

Costs for Sources of
Electricity Natural Solar Requirement
Gas
Heater /day, units
Electricity
Water heating
50
90
60
30
20
10
Space
heating
80
50
40
30
The size of the roof limits the largest possible solar heater to 30 units/day.
There is no limitation of electricity and natural gas. However, electricity
needs can only be met by purchasing electricity. Find the plan that
minimizes the cost of meeting energy needs.
Advertising example
54
An Investment Bank often uses Linear Programming to determine an optimal
allocation of advertising budgets. Recently they wanted to develop a plan that
would allocate $1,200,000 among radio, TV and newspaper advertisements
with the stipulation that no more than 40% of the budget be allocated to any
one medium. They wanted to maximize effectiveness (# eyeballs) of the ads.
After some research, the following data was gathered
Media
Radio
TV
Newspaper
Effectiveness/Ad Cost/Ad
2.4
20,000
3.2
40,000
1.6
30,000
Determine the number of ads in each medium to maximize effectiveness.
Credit Card Solicitation Optimization
55
A credit card company wishes to optimize it direct mail campaign for profitability and
risk. It divides the mailbase into 90 segments by risk, response and balance scores. Use
data file provided

The company wishes to maximize pre-tax profits

It wishes to pick segments to mail or not mail

Each segment’s marginal risk for charge-off should be below 7.5%

The total risk of charge-offs should be less than 4.5% over all segments being
mailed.
Break-out Exercise
56
Using the Credit Card data file do the following:
Identify the optimal segments to mail for the following scenario
1.
Maximize size of mailing (same constraints as before – Total Net Credit Losses
< 4.5%, Marginal Net Credit Losses < 7.5%)

What is the % increase in mailing from the classroom solution? What is the reduction in
profit?
Max mailsizeTotal NCL< 4.5%, Marginal NCL < 7.5%
Max mailsizeTotal NCL< 4.5%, Marginal NCL < 7.5%,
Total $ chargeoff < $50MM
$ Charged
off
Constraint
# Accounts
Net Credit
Losses
Objective
Max Profits Total NCL< 4.5%, Marginal NCL < 7.5%
Marginal
NCL Rate
Complete the following table
Pre Tax
Profits
3.
# Accounts
Do the above with the additional constraint that total $ Charge off is less than
$50MM
Mail Size
2.