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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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)
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
E-learning platform Moodle
1. Login or create an account
https://elearning.uniroma1.it/
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
E-learning platform Moodle
2. All the instructions are reported here.
https://elearning.uniroma1.it/
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
E-learning platform Moodle
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)
https://elearning.uniroma1.it/
Registration key: QuantPort_21-22
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
• 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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
Decisions and portfolio selection
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 PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
Decisions and portfolio selection
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
Decisions and portfolio selection
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
Decisions and portfolio selection
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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
Portfolio Selection Theory
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.
Modern Portfolio TheoryH. Markowitz, Portfolio Selection,
Journal of Finance, March 1952
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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:
Modern Portfolio TheoryH. Markowitz, Portfolio Selection,
Journal of Finance, March 1952
Portfolio Selection Theory
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.
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
Formal representation
of the decision problem
Mathematical
models
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
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.
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT: FOUNDATIONS – FEDERICA RICCA
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
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.