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QUANTITATIVE TECHNIQUES IN
FINANCE
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DECISION MAKING
Decision making is the term generally
associated with the first five steps ofthe problem solving process. Problem
solving can be defined as the process
of identifying a difference between
the actual and the desired state of affairs and then then taking action to
resolve the difference.
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PROBLEM SOLVING STEPS
Identify and define the problem
Determine the set of alternative solutions Determine the criterion or criteria that will be
issued to evaluate the alternatives
Evaluate the alternatives
choose an alternative Implement the selected alternative
Evaluate the results
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The first step of decision making is to
identify the problem and it ends withthe choosing of an alternative.
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
5
Feedback loops
at all levels!
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
6
What are the objectives?
Is the proposed problem
too narrow?
Is it too broad?
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
7
What are the available
alternatives?
How will data be
collected?
How do they differ?
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
8
What kind of model should be
used?
Is the model accurate?
Is the model too complex?
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
9
Do outputs match current
observations for current
inputs?
Are outputs reasonable?
Could the model be
erroneous?
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
10
What if there are conflicting
objectives?
Inherently the most difficult
step.
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
11
Must communicate
results in laymans terms.
System must be user
friendly!
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METHODOLOGY OF OPERATIONS RESEARCH*
THE SEVEN STEPS T O A GOOD OR ANALYSIS
SINI
12
Users must be trained on the
new system.
System must be observed
over time to ensure it works
properly.
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EXAMPLE OF DECISION
MAKING PROCESS
Assume that you are currently unemployed
Suppose that your job search from has resultedin offers from companies A, B, c, D
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ALTERNATIVES
Accept the position in A
Accept the position in B
Accept the position in C
Accept the position in D
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DETERMINE THE CRITERIA
To evaluate the four alternatives
Starting salary (for example)
Then the best alternative would be the one with
the highest salary
Single criterion decision problem.
Multi criteria decision problem
Also Consider other alternatives like location,
potential advancement etc.
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QUANTITATIVE MODELS
O.R. techniques
LPP
Integer programming
Network models
Project scheduling PERT/CPM
Inventory models
Queuing models
Simulation
Forecasting
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Q.TIN FINANCE
A course in which you learn how to apply OR andstatistical models in financial decision making.
Techniques such as
LPP
Forecasting techniques
PERT/CPM
Regression analysis
with examples financial applications
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LINEAR PROGRAMMING
MODELS
LINEAR PROGRAMMING
MODELS
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INTRODUCTION
Linear programming deals with the optimization(Maximization or minimization) of a function of variablesknown as objective function, subject to a set of linearequations and/or inequalities known as constraint. Theobjective function may be profit, cost, productioncapacity or any other measure of effectiveness, which isto be obtained in the best possible or optimal manner.
The constraint may be imposed by different resourcessuch as market demand, production process andequipment, storage capacity, raw material availability,etc.
SINI
19
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CONT
The term Linear is used to describe the
proportionate relationship of two or more
variables in a model. The given change in one
variable will always cause a resulting
proportional change in another variable.
SINI
20
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CONT
The word , Programming is used to specify
a sort of planning that involves the economic
allocation of limited resources by adopting a
particular course of action or strategy among
various alternatives strategies to achieve the
desired objective.
SINI
21
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THE GALAXY INDUSTRIES PRODUCTION
PROBLEM A PROTOTYPE EXAMPLE
Galaxy manufactures two toy doll models:
Space Ray.
Zapper.
Resources are limited to
1000 pounds of special plastic.
40 hours of production time per week.
SINI
22
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T HE G ALAXY I NDUSTRIES PRODUCTION PRO BLE M A PROTOTYPE E XAMPLE
Marketing requirement
Total production cannot exceed 700 dozens.
Number of dozens ofSpace Rays cannot exceed
number of dozens of Zappers by more than 350.
SINI
23
Technological input
Space Rays requires 2 pounds of plastic and3 minutes of labor per dozen.
Zappers requires 1 pound of plastic and
4 minutes of labor per dozen.
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THE GALAXY INDUSTRIES PRODUCTION PROBLEM A PROTOTYPE EXAMPLE
The current production plan calls for:
Producing as much as possible of the more profitable product,
Space Ray ($8 profit per dozen).
Use resources left over to produce Zappers ($5 profit
per dozen), while remaining within the marketing guidelines.
SINI
24
The current production plan consists of:
Space Rays = 450 dozenZapper = 100 dozen
Profit = $4100 per week
8(450) + 5(100)
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Management is seeking a
production schedule that willincrease the companys profit.
SINI
25
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SINI
26
A linear programming model
can provide an insight and an
intelligent solution to this problem.
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THE GALAXY LINEAR
PROGRAMMING MODEL
Decisions variables::
X1 = Weekly production level ofSpace Rays (in dozens)
X2 = Weekly production level of Zappers (in dozens).
Objective Function:
Weekly profit, to be maximized
SINI
27
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THE GALAXY LINEAR
PROGRAMMING MODEL
Max 8X1 + 5X2 (Weekly profit)
subject to
2X1 + 1X2 e 1000 (Plastic)
3X1 + 4X2 e 2400 (Production Time)
X1 + X2e
700 (Total production)X1 - X2 e 350 (Mix)
Xj> = 0, j = 1,2 (Nonnegativity)
SINI
28
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PROBLEM 1
A retired person wants to invest up to an amount
of Rs. 30,000 in fixed income securities. His broker
recommends investing in two bonds. Bond Ayielding 7% and bond B yielding 10%. After some
consideration, he decides to invest at most Rs.
12000 in bond B and at least Rs. 6000 in Bond A.
he also wants the amount invested in bond A to beat least equal to the amount invested in bond B.
what should the broker recommend if the
investor wants to maximize his return on
investment ?
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THE SERVER PROBLEM
General Description
A firm that assembles computers andcomputer equipment is about to start productionof two new Web Server models. Each type ofmodel will require assembly time, inspectiontime and storage space. The amounts of each ofthese resources that can be devoted to the
production of the servers is limited. The managerof the firm would like to determine the quantityof each model to produce in order to maximizethe profit generated by sales of these servers.
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ADDITIONAL INFORMATION
In order to develop a suitable model of the problem, themanager has met with design and manufacturing personnel.As a result of these meetings, the manager has obtained thefollowing information:
Parameter Server Type 1 Server Type 2Profit per unit USD 60 USD 50
Assembly time per unit 4 hours 10 hours
Inspection time per unit 2 hours 1 hour
Storage space per unit 3 cubic feet 3 cubic feet
The manager also has acquired information on the availability of company
resources. These daily amounts are:Resource Amount available
Assembly time 100 hours
Inspection time 22 hours
Storage space 39 cubic feet
The manager also met with the firms marketing manager and learned that
the demand for the servers was such that whatever combination of these
two models of servers is produced. All of the output can be sold.