quantitative portfolio selection for management …

Lecture 1 – Introduction to the course

Federica Ricca

MANIMP

QUANTITATIVE PORTFOLIO

SELECTION FOR MANAGEMENT:

FOUNDATIONS

General Information

QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA

Course Quantitative Portfolio Selection for management a.y. 2021-2022

Teacher

Federica Ricca [email protected]

Office: MEMOTEF Department - I floor – corridor B – room 148

Appointments for questions and explanations can be asked via email to

the teacher

General information

Prerequisites Basics of: Algebra – Set theory – Statistics – Probability.

Aim and

scope

1. Knowledge of the dynamics of the market of stocks and of the modern

Portfolio Selection Theory.

2. Familiarity with matemathical models and methods for decision aid in

Portfolio Selection and Asset Management.

3. Understanding of quantitative portfolio analyses under a risk-return

perspective.

4. Knowledge of different specialized formal models and ability of

identifying the best fitting model for any given real-life portfolio selection

problem.

5. Practical capacity of formulating and solving problems efficiently.


Course Quantitative Portfolio Selection for management a.y. 2021-2022

References

Teacher's handouts

Slides of the lectures available on the e-learning platform ‘Moodle’

Books

E. J. Elton, M. J. Gruber, Modern Portfolio Theory and investment analysis, John

Wiley and Sons, 1995 (2014)

General information

Evaluation Written test (theoretical and practical questions)

TimetableWednesday 11:00 – 13:00 room Aula Master (building RM020)

Thursday 11:00 – 13:00 room Aula Master (building RM020)

Friday 11:00 – 13:00 lab Didalab (build. RM019 first floor)


Token

At the beginning of each lecture students should confirm their presence in the

room. It is a particular type of roll call.

https://prodigit.uniroma1.it/prenotazioni/prenotaaule.nsf/home

The teacher activates a token at:

Each lecture has its own token.

This is done through a digital code (token) univocally associated to

the lecture which is generated by the teacher from Prodigit.

The one for today lecture is: 830114

Students should:

• login Prodigit

• confirm the presence using the token


E-learning platform Moodle

1. Login or create an account

https://elearning.uniroma1.it/



2. All the instructions are reported here.




Moodle is used for different tasks:

• communications and announcements by the teacher

• sharing slides and course materials

• possible Assignments

IMPORTANT: This platform has already shown to be very useful for communication with

students in case of emergency, such as possible communication about lectures

suspension or postponement, expecially when the faculty website is out of order.

Each new action or

communication by the

teacher is automathically

notified to the students

via email.

Students are kindly asked to:

• create an account in Moodle ()with their institutional email and sign up for the course

• use the institutional email for communicating with the teacher

(Please do not send electronic messages when logged whithin Moodle)


Registration key: QuantPort_21-22


Important

The course is articulated in two modules:

• FOUNDATIONS (6 CFU)

• CASES AND APPLICATIONS (3 CFU)

Frequency is high recommended, expecially in lab lessons

The FOUNDATIONS module is dedicated to the theoretical part of the course,

focusing on Portfolio analysis and related quantitative models and methods.

• Lessons will be held on Wednesday and on Thursday.

• Students should bring a USB device or their own computer.

The CASES AND APPLICATIONS module is dedicated to practical applications and

to the use of the software Excel.

• Lessons will be held in laboratory every Friday.


• masks always on

• security distances when entering and exiting the room

• starting on time and no break

CLASSROOM

Lectures can be followed both in presence and by remote.

• Course dedicated webpage:https://web.uniroma1.it/memotef/quantitative-portfolio-selection-

management-manimp-lingua-inglese-f-ricca

• Administrative and technical information:

https://www.uniroma1.it/it/pagina/informazioni-e-aiuto

GENERAL

INSTRUCTIONS

• Recording lessons is not allowed

• Microphones should be disactivated

• microphones can be switched on for asking questions

AT HOME

Lectures

Decisions and portfolio

selection


Decisions and portfolio selection

In the market of stocks, as in any other markets (goods, job, etc.), the typical

situation involves a decision maker who faces a variety of (many) possible choices

(alternatives) and has to take a decision by exploiting all the avilable information

and satisfying at best his own preferences.

In the stock market the investor has to chose his preferred investment in the

different financial products, for example stocks or bonds, and he is generally

interested in future returns of the financial assets available in the market, but

there are some problems to face with…

Problem 1: one cannot know the future returns of the investments.

Problem 2:

Which are the most suitable tools to evaluate the unknown returns?

Probabilistic evaluations of the possible

decision outcomes can be done

(statistical and probabilistic tools).

Tools to manage uncertainty are needed, and they

are very usefull for exploiting at best the hystorical

information based on the returns observed in the

past to reach the best decision.

Quantitative tools can be

very useful in providing

decision support.

The decision is under uncertainty


It is necessary to identify and structure the problem under study in order to

manage the decision:

i) reduce as much as possible the set of alternative choices;

ii) base choices on ‘rational’ and ‘traceable’ criteria.

A structured and controlled decision

process is necessary to manage the

decision process at best and efficiently.

Problem 1: one cannot know the future returns of the investments.

Problem 2:

Which are the most suitable tools to evaluate the unknown returns?

Probabilistic evaluations of the possible

decisions outcomes can be done

(statistical and probabilistic tool).

The decision is under uncertainty

Quantitative tools can be

very useful in providing

decision support.


Tools to manage uncertainty are needed, and they

are very usefull for exploiting at best the hystorical

information based on the returns observed in the

past to reach the best decision.


To evaluate the future returns of a financial investment decision, we consider

the investment as a unit (portfolio) and assume that the investment’s returns

are the realizations of a random variable which we call ‘portfolio’s return’.

TOOL: Probability theory

The information about the probability distribution of the random returns is

given through the computation of characteristic indices.

TOOL: Statistics

To obtain a formal description of the entities under study (assets) and their

relations, representing the investor’s preferences and describing properly the

decision context we use mathematical functions and models.

TOOL: Mathematics and optimization

In the course we will see how all these (different) quantitative tools can be

used together (in combination) to get a powerful and efficient decision support

system.



In the course we will see how all these (different) quantitative tools can be

used together (in combination) to get a powerful and efficient decision support

system.

Surprisingly enough, in the course, we will appreciate how one can

understand and manage (even sophisticated) mathematical tools

without needing too much mathematical skill.

In the course we mainly focus on the modeling aspects of the problem

and in solution structuring and understanding.

The great availability of efficient mathematical and optimization

solvers implemented in a variety of software (among which Excel), will

make the rest:

• for a given problem, one has to learn how to select the best fitting

model and how to formulate it mathematically;

• the formal model must be then translated using an appropriate

language to be implemented in the solution software.



Quantitative tools and optimization

As soon as we will be aware of the financial market dynamics and reach a

deep knowledge of the instruments for the mean-variance Portfolio Analysis,

we will introduced advanced optimization tools which are useful tu pursue at

best the investor objectives.

For example, which kind of optimization can be done when choosing a

portfolio?

A main issue is the portfolio future return.

Optimization Problem:

MAXIMIZING THE EXPECTED PORTFOLIO RETURN.

Which other possible criterion can be considered in the optimization?

The future return is actually unknown. Therefore there is some risk when

(today) one invests in a set of assets whose return will be known only at their

(future) maturity time.

Optimization Problem:

MINIMIZING THE RISK THAT THE FUTURE RETURN

DIFFERS TOO MUCH FROM THE EXPECTED ONE.

These are the typical optimization problems we will deal with.


Modeling and solution tools

The quantitative approach to decision problems necessarily requires

the use of application software which is able to solve in short time

even large-size problems.

Today there is a wide availability of software providing quantitative

tools for the analysis and the solution of the problems. Some examples

are:

• Excel

• R

• Matlab

• AMPL

In particular, in our course (Cases ans Applications) we will

focus on the use of the software Microsoft Excel.


Modeling and solution tools: Excel

This choice is motivated by the fact that Excel provides a variety of easy and

widely applicable tools for performing different quantitative analyses.

We can manage data and perform basic data elaborations:

• Data entry and recording

• Data manipulation and management exploiting multiple worksheets

• Computation of indices and functions

• Report printing

• Data publication on webpages

Additional operations are:

• Ordering and filtering data

• Creation of data tables and systems of related tables, pivot tables

• Graphcal representation


Modeling and solution tools: Excel

This choice is motivated by the fact that Excel provides a variety of easy and

widely applicable tools for performing different quantitative analyses.

Functions and

formulas

Advanced tools

(tendency lines,

goal seek)

Regression,

Optimization

Basic computation tools

Advanced authomated tools

Modeling tools



We are familiar with financial

operations under certainty

We are now going to face

decision under uncertainty

We deal with complex decision problems since we have:

All these elements make the problem difficult to formulate and solve, and

require powerful decision aid tools to perform the best choice.

In addition, investors’ preferences and attitudes must be taken into account,

and they must be also suitably modeled since the decision depends much on

these aspects.

Modern Portfolio TheoryH. Markowitz, Portfolio Selection,

Journal of Finance, March 1952

• multiple criteria, to be considered simultaneously in the decision process;

• huge variety of alternative decision choices;

• uncertainty on the future assets’ returns.


Portfolio Selection Theory


The problem is how to allocate a given financial resource (budget) among the

different investment possibilities (portfolio), all charatcerized by random

returns. The objective is to control both the investment’s return and risk.

The analysis is focused on the mean-variance (E-V criterion, E stands for

from ‘Expected value’ and V for ‘Variance’) which is based on the assumption

that the investor chooses her/his portfolio with the aim of maximizing the

portfolio’s returns expected value and minimizing the associated risk,

according to his system of preferences.

Basic assumption: We invest over one time period.




The possible investment choices (or

opportunities) are of different nature:

stocks or securities, bonds, currency. In the course we will

generally refer to stocks

or assets

Markowitz analysis is based on the following assumptions:





The problem is how to allocate a given financial resource (budget) among the

different investment possibilities (portfolio), all charatcerized by random

returns. The objective is to control both the investment’s return and risk.

We also may have other investment possibilities

related to business, services, industrial production.

• in the market there is a finite number of assets.

• assets are infinitely divisible.

• to simplify the analysis, we do not consider transaction costs or similar.

Formal Modeling

approach for problem

solution


Formal representation

of the decision problem

Mathematical

models

Perform a systematic evaluation

of the possible problem solutions

and find the optimal one.Algorithms

For the practical solution of

real problems and post

optimization analyses.

Application

software

Modelling approach

The most difficult step is modeling a decision problem.

Once the problem is formalized by a suitable mathematical model, algorithms and

solvers proceed automatically and find the model optimal solution.

• Model formulation must be performed carefully


Formal representation

of the decision problem

Mathematical

models

Modelling approach





MATHEMATICAL

MODEL

STRUCTURED

PROBLEM

REAL

PROBLEM

The problem must be structured in order to identify all the

relevant aspects (to be included in the model) and and all

the secondary ones (to be excluded).

The same holds for relations.

Globally, one should guarantee that the problem formally

described by the model corresponds to the decision

problem under study.


Modelling approach





MATHEMATICAL

MODEL

PRACTICAL

PROBLEMDECISIONS

Intuition

RESULTSSolution

Abstraction Interpretation

REAL WORLD

SYMBOLIC WORLD

Problem abstraction and results interpretation play a delicate role, since they must be

performed so that model solution is coherent with decision intuition.

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