OPIM 5984 ANALYTICAL CONSULTING IN FINANCIAL SERVICES SURESH NAIR, Ph.D. 1

OPIM 5984ANALYTICAL CONSULTING IN FINANCIAL SERVICES

SURESH NAIR, Ph.D.

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Financial Services Analytical Consulting 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

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Outline3

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 situations4

Known Not Obvious

Ava

ilabl

eNo need for consultants

Creative ModelingN

ot A

vaila

ble

Creative Data Gathering

Qualitative Inductive

Recommendations

Modeling/Solution TechniquesD

ata

Ava

ilabi

lity

Attributes of a good Management Consultant

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Time is of the essence6

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

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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

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Learn to work on unstructured problems Quadrant 2: Creative Modeling

Retail Bank Sweeps Credit Card solicitations

Quadrant 3: Creative Data Gathering End of life planning for a blockbuster drug going off

exclusivity Quadrant 4: Qualitative Inductive

Recommendations Impact of Comparative Effectiveness Research on

drug sales

Service Capacity and Waiting Lines (Queueing) in Financial Services

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Service Capacity And Waiting Lines 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.

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Optimizing Service

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.

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Service Configurations

Studies have shown that there are certain common service configurations.

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Poisson Arrivals, Exponential Service

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 average 10 customers/hour.

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l=1l=2

l=4

A

Single Server Model

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 (/<1, M=number of servers)

Average number in line

In general (for single and multi-server models)

Average time in line

Average system utilization

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)(

2

qL

q

q

LW

M

Example

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, m=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

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Exercise

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/dayThe 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?

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Other Models

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

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Example

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 m = 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/Mm = 36/5*10 = 72% Wq=1.055/36 = 0.029 hrs = 1.7 minutesExercise: What would happen if arrival rate=25/hrExercise: If waiting time (with arrival rate=36/hr) should be at most 1 minute, how many counters should be open?

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Analyzing the Waiting Line Formula

We can rewrite the single server total time in system formula as

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

waiting time increases rapidly Reducing variability of arrival time

and/or service time can reduce

waiting time. Reducing processing time also helps.

0.0

20.0

40.0

60.0

80.0

100.0

0 0.2 0.4 0.6 0.8 1

Utilization

Wai

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c_a=1

c_a=2

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1

1

2

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Critical Thinking

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

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Ask the Questions (Creative Brainstorming)

What What is the objective being achieved?

How Can it be done some other way? Automated? Can it be

made easier? When

Why is it done at that time? Can it be done before? After? Where

Why is this task done there? Can it be done somewhere else?

By whom Can the task be done by someone else?

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Critical Examination Worksheet

Use the worksheet

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In-class Exercise – Water Filter

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.

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Brainstorming Ground Rules

Relax Have fun Laugh Support No boundaries Completely free your mind No limits on the number of ideas Fragmented ideas OK Just keywords OK

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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”

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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

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Ground Rules

Select a moderator No dominating No interrupting No passing

Short session (20 minutes) Create ideas in silence Multiple rounds

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Critical Thinking Habits

Critical thinking is an essential component of professional accountability and apply to any discipline. These habits are show below. Confidence

Assurance of one's reasoning abilities Contextual Perspective

Consideration of the whole situation, including relationships, background, and environment, relevant to some happening

Creativity Intellectual inventiveness used to generate,

discover, or restructure ideas, imagining alternatives

Flexibility Capacity to adapt, accommodate, modify,

or change thoughts, ideas, and behaviors

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Critical Thinking Habits (contd.) Inquisitiveness

An eagerness to know by seeking knowledge and understanding through observation and thoughtful questioning in order to explore possibilities and alternatives

Intellectual Integrity Process of seeking the truth through

sincere, honest means, even if the results are contrary to one's assumptions and beliefs

Intuition Insightful sense of knowing without

conscious use of reason Open-mindedness

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

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Creativity (contd.)

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).

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Break-out Exercise – Credit Cards Consider the credit cards business

High attrition – commodity business, surfing behavior of customers

High risk of delinquency 2% interchange paid by merchants – you

buy goods for $100, merchant gets $98

Brainstorm how we pay for things. Think of a better way by demolishing the credit cards industry.

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Simulating Alternative Recommendations in Financial Services

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Simulating Alternative Recommendations in Financial ServicesA 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.

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An Example

Jack sells insurance. His records on the number of policies sold per week over a 50 week period are:

Suppose we wanted to simulate the policies Jack sells over the next 50 weeks.

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Number policies sold 0 1 2 3 4Frequency 8 15 17 7 3

Example (contd.)

It is fairly simple to evaluate different alternative order quantities quickly using simulation.

Step 1 Compute Probabilities, Cumulative Probabilities and assign

Random Numbers

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

36 Life is random Give Chance a Chance

iPod Shuffle

Number policies sold 0 1 2 3 4Frequency 8 15 17 7 3 TotalProbability 0.16 0.30 0.34 0.14 0.06 1.00Cumulative Probability 0.16 0.46 0.80 0.94 1.00Random Numbers 00-15 16-45 46-79 80-93 94-99

#Policies Simulation37

#Policies Example (contd.)

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.

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Exercise

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

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.

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Number of customers/day 0 1 2Probability 0.2 0.3 0.5

Length of car rental 1 2 3 4Probability 0.2 0.3 0.3 0.2

Break-out Exercise

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?

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Simulating Standard Distributions 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).

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Standard Distributions (contd.) 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())

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Standard Distributions (contd.)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

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Exercise: Currency Notes Requirement 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).

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Currency Notes(contd.)

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).

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Break-out Exercise (Flight Overbooking)

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:

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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.)

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?

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Optimizing Financial Services48

Financial Services Optimization 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.

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LINEAR PROGRAMMING

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?

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Example: (Minimization)

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?

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Binary (0-1) Assignment Example 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:

Who should be assigned to which task to minimize turn-around time for loan applications?

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Task John Susan David Ben Melissa

Eval and Analysis 482 444 459 370 429

Interest Rate 295 321 264 347 317

Loan Terms 379 341 384 306 397

Final Issuing 120 120 124 109 115

Non-Binary Allocation Example 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:

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.

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Needs Electricity Natural Gas

Solar Heater

Requirement /day, units

Electricity 50 20

Water heating 90 60 30 10

Space heating

80 50 40 30

Costs for Sources of

Advertising example

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

Determine the number of ads in each medium to maximize effectiveness.

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Media Effectiveness/Ad Cost/AdRadio 2.4 20,000 TV 3.2 40,000 Newspaper 1.6 30,000

Credit Card Solicitation OptimizationA 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.

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Break-out Exercise

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?

2. Do the above with the additional constraint that total $ Charge off is less than $50MM

3. Complete the following table

Objective Constraint Mai

l Siz

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# A

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ts

Pre

Tax

P

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ts

Mar

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al

NC

L R

ate

# A

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ts

Net

Cre

dit

L

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es

$ C

har

ged

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ff

Max Profits Total NCL< 4.5%, Marginal NCL < 7.5%

Max mailsizeTotal NCL< 4.5%, Marginal NCL < 7.5%

Max mailsizeTotal NCL< 4.5%, Marginal NCL < 7.5%, Total $ chargeoff < $50MM

Conjoint Analysis for New Product Development in Financial Services

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Conjoint Analysis

Conjoint Analysis is a widely used statistical Market Research technique to figure out how consumers make trade-offs in making product/service preference choices.

The product/service can be thought to be a bundle of attributes, each having different levels

For example, for a credit card, the attributes and levels may be

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Introductory rate(attribute)

Duration

0 APR(level) 3 months 3.99 APR 6 months 5.99 APR 12 months

Go to rate Rewards 9.99 APR Cash back 12.99 APR Airline Miles

Conjoint Analysis (contd.)

Prospective customers are shown a set for products and asked to rank or rate them (say from 1-100 points) Say 16 credit cards are shown, designed by

random combinations of attribute levels Card#1: 3.99 APR, 9.99 Goto, 12 month

duration, Airline Miles Card #2: 0 APR, 12.99 Goto, 3 month duration,

Cash back : Card #16: 3.99 APR, 9.99 Goto, 6 month

duration, Cash back Based on the ranks or ratings, CA tries to

tease out the value (part-worths) to each consumer for each attribute level of the product/service

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Example – Credit Cards

There are software packages available for CA. However, we will do it using Solver in Excel, using a methodology called Goal Programming

Suppose 12 products (called profiles) are shown to prospects

Check: for each profile, there is a one 1 in each attribute, others are 0

Check: A random set of designs will have evenly balances column sums for each attribute

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Profile 0 APR 3.99 APR 5.99 APR 9.99 APR 12.99 APR 3 months 6 months 12 months Cash Back Air Miles1 0 1 0 0 1 0 0 1 0 12 1 0 0 1 0 0 1 0 0 03 0 1 0 1 0 1 0 0 1 04 1 0 0 1 0 0 0 1 0 05 0 0 1 1 0 0 1 0 0 06 0 1 0 1 0 1 0 0 1 07 0 0 1 0 1 1 0 0 1 08 1 0 0 0 1 0 1 0 0 09 0 0 1 0 1 0 0 1 0 0

10 0 1 0 0 1 0 1 0 0 111 1 0 0 0 1 1 0 0 0 112 0 0 1 1 0 0 0 1 0 1

Go to rate Duration RewardsIntroductory rate

Example – Credit Cards (contd.) There are software packages available

for CA. However, we will do it using Solver in Excel, using a methodology called Goal Programming

Suppose 12 products (called profiles) are shown to prospects



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Profile 0 APR 3.99 APR 5.99 APR 9.99 APR 12.99 APR 3 months 6 months 12 months Cash Back Air Miles1 0 1 0 0 1 0 0 1 0 12 1 0 0 1 0 0 1 0 0 03 0 1 0 1 0 1 0 0 1 04 1 0 0 1 0 0 0 1 0 05 0 0 1 1 0 0 1 0 0 06 0 1 0 1 0 1 0 0 1 07 0 0 1 0 1 1 0 0 1 08 1 0 0 0 1 0 1 0 0 09 0 0 1 0 1 0 0 1 0 0

10 0 1 0 0 1 0 1 0 0 111 1 0 0 0 1 1 0 0 0 112 0 0 1 1 0 0 0 1 0 1

Go to rate Duration RewardsIntroductory rate

Example – Credit Cards (contd.) Suppose our first prospect, Jay, is

shown the 12 profiles and asked to rate them on a scale of 1-100 as per his preference

He does this on the right Based on this, using Solver, we

can figure out that his valuation of part-worths is as follows (details in Excel)

We can similarly figure out part-worths for all the prospects in our sample.

Using this data, we can then mix and match attribute levels to design a credit card that could potentially be preferred by the most prospective consumers and they would respond to our offer of a new credit card.



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Profiles shown to prospectRel Ratings1 902 853 654 1005 706 707 108 609 35

10 6511 5012 65

0 APR 3.99 APR 5.99 APR 9.99 APR 12.99 APR 3 months 6 months 12 monthsCash Back Air Miles35.0 35.0 0.0 35.0 10.0 0.0 15.0 30.0 0.0 5.0

Introductory rate Go to rate Duration Rewards

Example – Credit Cards (contd.) Suppose the prospects have the following part-worths

Then several products could be designed and the Utility of each product to each prospect can be evaluated

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Example – Credit Cards (contd.) You can see that Jay prefers Product 1 to Product 2 Susan prefers Product 2 to Product 1 We can produce 3*3*2*2=36 different products this way

and pick the best When there are many attributes and levels, the possible

products can be in the thousands. Thousands of full products would have been difficult to ask

prospects to evaluate and rate CA allows doing this by showing only a small set of randomly

designed products (say 15-30). The fundamental assumption is that a product is a bundle of

attributes, and the part-worths are additive to give the utility of the product to a consumer.

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Break-out Exercise (Retail Bank) Suppose you have been tasked with designing the concept

for a new type of retail bank so as to beat the competition. What would be the attributes you would use? What levels for the attributes would you use? Create 12 random designs to test. Show the designs to 5 prospective customers and have them

rate the designs. (Simulate this by using fake ratings). Determine part-worths for the attribute levels and pick the best

design. Present the two designs and compare them.

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Critical Thinking (Conjoint Analysis) It is assumed that part-worths are additive. Part-worths are assumed to be compensatory,

meaning a small value in one will be compensated by a large value in another.

Too many attributes and levels complicate the data collection. It will necessitate more profiles to be shown to consumers.

Some are obvious more is better levels – use price as an attribute and eliminate infeasible combinations as explained below.

Conflicting attributes should be combined. For example, two attributes – Engine size (Big, Small) and Price (High, Low) should be combined into one attribute with 2 levels; Engine-Price(BigHigh, SmallLow)

Financial Options Valuation67

Financial Options Valuation

Financial options are popular products in the financial industry

An option give you a right (but not an obligation) to buy or sell a stock.

It establishes a specific price, called the Strike Price, at which the contract may be Exercised, or acted on. And it has an Expiration date. When an option expires, it no longer has value and no longer exists.

Suppose today’s (Dec 1) Apple (AAPL) stock price is $388, the option prices for Dec 17 are

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There are two kinds of Options – Calls and Puts Calls give you the right to buy stock at a

price – e.g., at $400 on Dec 17 (recall the stock is at 388 today, Dec 1), and it will cost us $2.87 to buy an option today. If on Dec 17, the price is $410, we would have

$10-2.87=$7.13 of profit If on Dec 17, the price is 395, the option has

zero value Puts are the opposite of Calls. If you buy a

Put, it gives you the right to sell at a particular price.

You could also sell (called write) a Call or a Put

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Given past prices of the underlying stock, say AAPL, you can figure out the value of the Option today using simulation. Suppose the prices are as shown below (see spreadsheet)

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Simulation can give us the value of the Option.

If the value we compute is better than the market price of the option, we could purchase the option, otherwise, if the price is higher, we could write an option

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Break-out Exercise (Financial Options) Determine the value of the following financial option

AXP160115C00110000 (meaning for American Express, Call option, Jan 2016, $110 strike price)

What is the current price of the option? Would you buy it?

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Critical Thinking (Financial Options) It is assumed tomorrow’s price depends only on

today’s price. Meaning it does not matter if today’s price was

part of an increasing or decreasing trend over the past few days. It is path independent, and memoryless.

If in fact there is path dependence, then the methodology can be modified to accommodate it.

Stochastic modeling using dynamic programming

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Dynamic Programming is a technique used for sequential decision making. Typically, a large problem is broken into smaller parts and solved.

Example: (Sample Path Problem) Suppose you wanted to go from A to B. What would be the

shortest path?

DYNAMIC PROGRAMMING75

Sample Path Problem

To get from A to B, it is only necessary to know the best way to go from C to B, the best way to go from D to B, and the cost of going from A to C and D.

Further, to know the best way to go from C to B, we need only know the best way to go from E to B, the best way to go from F to B, and the cost of going from C to E and F.

and so on, until we get to the trivial case of finding the best way to go from O to B and P to B, which is 2 and 1 respectively.

These last values are called the Boundary Conditions.

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Principle of Optimality

The principle of optimality (Bellman) states that (for this example):The best path from A to B has the property that, whatever the initial decision at A, the remaining path to B, starting from the next point after A, must be the best path from that point to B.

Now that we know the minimum “cost” of going from A to B, we can go back and figure out the choices of paths at each intersection.

This is what Dynamic Programming is all about. There are no further key ideas in DP. However, there is an art in formulating DPs. This has to do with deciding what to use as a state and stage, and what to use as the value function. More on these later.

78

In co-ordinate axes

S x y

x y

a x y x y x y

a x y x y x y

S x ya x y S x y

a x y S x y

S

u

d

u

d

( , )

( , )

( , )

( , ) min( , ) ( , )

( , ) ( , )

( , )

the value of the minimum effort path

connecting ( , ) to ( , )

effort in going up from ( , ) to ( + , + )

effort in going down from ( , ) to ( + , )

and the Boundary condition is

6 0

1 1

1 1

1 1

1 1

6 0 0

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Terminology

The above equation is called the functional equation. It is a recursive relationship (it feeds on itself).

Stage: The problem is solved at different points in time, or places. These are called stages. Typically in the argument of the value function, the stage is incremented or decremented by 1 on the RHS compared to the LHS of the functional equation, (e.g., x above).

State: All other variables in the argument constitute the state, e.g., y above.

Immediate Reward: The profit (or cost) that is collected in the current state.

Policy: A predetermined plan of selecting a course of action for every circumstance. In DP we want to identify the optimal policy.

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Consider the case of a high speed solicitations mailing machine that deteriorates with age. The issue is when should one replace it, if the cost of a new machine, cost of operating an old machine, and salvage value from selling an old machine is known.

Suppose we want to solve this problem to minimize costs over an N period horizon. ci = cost of operating for one year an i year old

machine p = purchase price of a new machine si = salvage value for an i year old machine

Equipment Replacement81

Suppose

Let Sk(i) be the minimum cost of owning a machine from year k when the machine is of age i, through N.

The terminal condition (reward) is

Data

)1(:

)1(:min)(

1

10

iScKeep

ScspBuyiS

ki

kik

)()( isiSN

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0,0,0,8,17,25

100,100,70,40,20,13,10

50

5

654321

6543210

ssscss

ccccccc

p

N

Solution

In the above example, k is the stage, and i is the state. The formulation is complete when the recursion and the boundary condition is given. This can then be solved using a simple computer program.

Age 0 1 2 3 4 51 76 48 24 -4 -252 115 63 35 12 -173 97 45 24 -84 79 30 05 56 0

Time period

Age 0 1 2 3 4 51 Keep Keep Buy Keep Keep2 Buy Buy Buy Keep Keep3 Buy Buy Buy Keep4 Buy Buy Keep5 Buy Keep

Time period

83

84

Break-out Exercise (Sales force planning) An insurance company has 5 sales representatives

available for assignment to 3 sales districts. The sales in each district during the current year depend on the number of sales reps assigned. Use dynamic programming to determine an assignment of sales reps to districts that maximizes the expected sales.

Hint: Let stage 1 be North, stage 2 be Central and stage 3 be South

Reps Assigned North Central South

0 1 2 31 2 5 62 3 6 83 5 9 11

Elementary VBA Coding85



Real Options in Financial Services

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Real Options in Financial Services Real Options, are like financial options,

only for real items or property. Usage, risk, profitability, cash flows, etc.,

may be uncertain (stochastic) over a time horizon. Several possible actions may be available at any time (give credit line increase, do not give credit line increase; reprice the product, do not reprice; sweep funds, do not sweep funds, etc.). Given that these actions are taken, customer behavior may change (increased use of line, customer attrition, etc.)

In a sense this is a richer, more complex environment than financial options

Dynamic Programming is a good tool to use for this

89

90

Example: Bank Sweep Programs Monetary Control Act (1980) authorized

Fed Reserve to require banks to hold 10% of transaction deposits as reserves. No reserve requirement for time deposits

(savings, money market) Reserves earn no interest for bank

Banks had an incentive to keep deposits as Savings rather than Checking deposits

90

Background of Sweep Programs In 1994 one bank came up with a neat

idea. The bank would maintain two accounts for

every customer [a Bank Transaction Account (BTA) and a Money Market Deposit Account (MMDA)]

By sweeping funds frequently from BTA into MMDA, banks can keep checking deposits to a minimum Win-win for both banks and customers Banks reserve requirements reduce Customers get higher interest in MMDA accounts

These sweep accounts are transparent to customer

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Background of Sweep Programs There are limitations to sweep

programs Debits only serviced from transaction

accounts – need some BTA balance to cover check writing, etc.

Regulation D limits the number of withdrawals from savings accounts to 6 per month.

6th transfer requires full dump to BTA

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Existing Sweep Method - Cushion

Min Transfer Actual TransferDay MMDA BTA Withdrawal MMDA to BTA Cushion MMDA to BTA Comments

1 50,000 - 1,000 1,000 1,000 2,000 Transfer #12 48,000 1,000 - 3 48,000 1,000 - :6 48,000 1,000 7,000 6,000 2,000 8,000 Transfer #27 40,000 2,000 - :

10 40,000 2,000 3,000 1,000 3,000 4,000 Transfer #311 36,000 3,000 -

:15 36,000 3,000 4,000 1,000 4,000 5,000 Transfer #416 31,000 4,000 -

:18 31,000 4,000 6,000 2,000 5,000 7,000 Transfer #519 24,000 7,000 - 20 24,000 7,000 8,000 1,000 Dump 24,000 MMDA Dumped21 - 23,000

:30 - 23,000

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Motivation for Model0

1

2

3

456

7

89

Game Show: Look who is counting

Opponent 1 Opponent 2

5 5

Whoever gets the larger 5 digit number wins!!

94

95

Motivation for Model

Source: Puterman, MDP, 1994

This model can be solved using stochastic dynamic programming

01

2

3

456

7

89

Game Show: Look who is counting

Opponent 1 Opponent 2

5 5

Whoever gets the larger 5 digit number wins!!

Optimal Policy

Placement in unoccupied cellNumberon wheel 1 2 3 4 5

0 5 4 3 2 11 5 4 3 2 12 5 4 3 2 13 4 4 2 2 14 3 3 2 1 15 3 2 1 1 16 2 2 1 1 17 1 1 1 1 18 1 1 1 1 19 1 1 1 1 1

Spin Number

96

Modeling Customer Behavior

Divide the population into various segments Divide withdrawals and deposits into “transaction

intervals.” For example, Large withdrawal (<-$1500), Small withdrawal (-$1 to -$1499), no transaction (0), Small deposit ($1-$750) and Large deposit (>$751).

For each segment create a transition matrix showing the chance of withdrawal and amount of withdrawal every day.

Current day 1 2 3 4 5 Avg Amt1 11% 44% 32% 8% 5% -22002 5% 49% 35% 8% 3% -1503 3% 28% 54% 8% 6% 04 4% 47% 37% 8% 4% 3255 15% 50% 30% 2% 3% 4100

Next day

96

97

Modeling Customer Behavior

Divide the population into various segments Divide withdrawals and deposits into “transaction

intervals.” For example, Large withdrawal (<-$1500), Small withdrawal (-$1 to -$1499), no transaction (0), Small deposit ($1-$750) and Large deposit (>$751).

For each segment create a transition matrix showing the chance of withdrawal and amount of withdrawal every day.

Current day 1 2 3 4 5 Avg Amt1 11% 44% 32% 8% 5% -22002 5% 49% 35% 8% 3% -1503 3% 28% 54% 8% 6% 04 4% 47% 37% 8% 4% 3255 15% 50% 30% 2% 3% 4100

Next day

97

Stochastic DP Model

The state of the system may be defined as (m,b,i,x), where m is the balance in MMDA, b is the balance in BTA, i is the transaction interval, and x is the transfer count (x<6).

Suppose rmb is the reward from having a balance of m in MMDA and b in BTA, then

Where d is the % reserve requirement, and r is the return for the bank on funds invested.

98

)]1[( bmrrmb

The functional equation of our model will be

Where b is the one period discount factor and p the transition matrix.

The functional equation changes a bit for specific conditions (e.g., x=6).

Stochastic DP Model - Cushion

)]1,,0,([:0

)]1,,,([:

)]1,,,([:

max),,,(

1

1111

1

,...,0

xjsbmfpCushion

xjccsbmfpcCushion

xjccsbmfpcCushion

rxibmf

iTt

jij

iTt

jij

zziTt

jijz

ccmb

Tt

z

99

100

Sample Results - Cushion

Dayof Month 1 2 3 4 5 1 2 3 4 5

1 500 5002 500 500 500 7503 500 500 1000 500 750 10004 250 500 1000 1500 500 500 1000 22505 250 500 750 1500 3250 500 500 1000 2250 37506 250 500 750 1250 3250 250 500 1000 2000 37507 250 500 750 1250 3250 250 500 750 2000 37508 250 500 750 1250 3250 250 500 750 2000 37509 250 500 750 1000 3250 250 500 750 2000 3750

10 250 250 500 1000 3000 250 500 750 2000 375011 250 250 500 1000 3000 250 250 750 2000 375012 250 250 500 1000 3000 250 250 500 2000 350013 0 250 500 750 2750 250 250 500 2000 350014 0 250 500 750 2750 0 250 500 2000 325015 0 250 250 750 2500 0 250 500 2000 325016 0 250 250 500 2500 0 250 500 2000 325017 0 0 250 500 2250 0 0 250 2000 300018 0 0 250 500 2000 0 0 250 2000 300019 0 0 250 500 1750 0 0 250 2000 275020 0 0 0 250 1750 0 0 250 2000 275021 0 0 0 250 1250 0 0 250 2000 250022 0 0 0 250 1000 0 0 250 2000 250023 0 0 0 0 500 0 0 0 2000 200024 0 0 0 0 250 0 0 0 1750 175025 0 0 0 0 0 0 0 0 0 0

Transfer #, x Transfer #, xMMDA+BTA: 25,000 MMDA+BTA: 50,000

100

101

Impact of Model

The model is scheduled to be implemented in a mid size bank.

Savings are expected to be about $3 million per year.

In simulations, reduced BTA balances from 13% to 26% over existing methodology

Documents

OPIM 5984 ANALYTICAL CONSULTING IN FINANCIAL SERVICES SURESH NAIR, Ph.D. 1