Quantitative Techniques in Finance

8/3/2019 Quantitative Techniques in Finance

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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

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Feedback loops

at all levels!


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SINI

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What are the objectives?

Is the proposed problem

too narrow?

Is it too broad?


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SINI

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What are the available

alternatives?

How will data be

collected?

How do they differ?


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SINI

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What kind of model should be

used?

Is the model accurate?

Is the model too complex?


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SINI

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Do outputs match current

observations for current

inputs?

Are outputs reasonable?

Could the model be

erroneous?


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SINI

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What if there are conflicting

objectives?

Inherently the most difficult

step.


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SINI

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Must communicate

results in laymans terms.

System must be user

friendly!


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SINI

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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)

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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.

Quantitative Techniques in Finance

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