METHODS FOR THE MANAGEMENT OF PERSONAL PORTFOLIOS

How are investment portfolios constructed? Which tools support financial decision-making under risk? How is Machine Learning changing the way investments are managed in financial markets?

This elective course, offered within the Master's Degree Programme in Economics and Finance, provides students with the knowledge and skills needed to analyse investment opportunities, assess risk, and construct financial portfolios in a rational and efficient manner. The course covers the main decision-making criteria, quantitative tools, and models used to support investment decisions in financial markets.
Particular attention is devoted to innovative methodologies currently employed in professional portfolio management. In addition to traditional portfolio management models, students will be introduced to bio-inspired optimization methods and Machine Learning algorithms for the construction and management of complex portfolios. These tools are increasingly used in the asset management industry, quantitative investment strategies, and financial advisory services.
The course combines theoretical foundations with practical applications, enabling students to understand not only the principles underlying investment decisions but also the opportunities offered by emerging technologies for addressing complex financial problems. It is particularly suitable for students interested in quantitative finance, investment analysis, and the growing role of Machine Learning in the financial industry.

1. Knowledge and understanding:
1.1. understand the quantitative tools and the mathematical methods necessary for the specification of a risky investment problem;
1.1. know the models for the selection and management of personal financial portfolios;
1.3. know the different types of risk measures and constraints on the characteristics of the portfolio.

2. Ability to apply knowledge and understanding:
2.1. formalizing a risky investment problem by specifying the risk measure and the system of constraints on the characteristics of the portfolio;
2.2. applying the quantitative tools and the mathematical methods necessary for selecting and managing personal financial portfolios;
2.3. implementing quantitative tools and mathematical methods through the use of software.

3. Judgement skill:
3.1. interpreting the results coming from the solution of a risky investment problem;
3.2. understanding virtues and drawbacks of the models for selecting and managing personal financial portfolios;
3.3. pondering on the measurement of risk on the basis of an analytical-financial method.

Keeping fresh in mind: several variable functions; matrix algebra; elements of optimization; elements of statistics.

he Modern Portfolio Theory (MPT)
- Diversification
- Classic portfolio selection models
- Limits of the MPT

Advanced portfolio selection models
- The model of Black-Litterman
- Risk-adjusted risk measures
- Coherent risk measures
- Non-standard constraints.

Metaheuristics for optimization
- Particle Swarm Optimization
- Machine Learning for MPT

Static portfolio revision
- The model of Smith
- The model of Stone and Hill

MATLAB ™ elements for portfolio selection and management
- Introduction to MATLAB™
- Free and constrained optimization with MATLAB™

- Luenberger D.G. (2013) Investment Science. Oxford University Press. [Chapters 6 (without the subsections "Solution of the Markowitz Problem" and "Solution Method".), 11 (without the subsections "Risk Aversion Coefficient" and "Certainty Equivalent")].

- Other teaching material will be indicated by the teacher during the course.

The assessment consists of three homework assignments and an oral examination.
Homework assignments:
1) must be completed in groups of two or three students;
2) are valid only for the current academic year;
3) must be submitted via Moodle no later than a specified deadline. Submission procedures and deadlines will be communicated during the course.
Oral examination:
1) must be taken individually;
2) consists of three parts: In the first part, students are required to critically present a research article using slides. Instructions on how to select the research article will be provided during the course; In the second part, students are required to present, again using slides, the results obtained by applying one or more of the methodologies learned during the course in order to replicate the findings reported in the selected research article; In the third part, students must answer one question selected by the instructor from three questions proposed by the student. The questions must concern topics covered during lectures and in the assigned course materials.
Assessment criteria:
1) each homework assignment is worth between 0 and 4 points, for a total of 0 to 12 points;
2) the oral examination is worth between 0 and 18 points.
Optionally, students may complete additional activities, which will be presented during the course, for an additional score ranging from 0 to 2 points.
The final grade is determined by the sum of the points obtained from the homework assignments, the oral examination, and any optional additional activities.

oral

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

Evaluation grid:
- 18–22: Incomplete and inaccurate completion of homework assignments; barely sufficient critical thinking skills applied to the understanding of applications, methods, models presented in the specialized literature; minimal or no ability in the development and implementation of applications, methods, and models; barely sufficient knowledge of the topics covered in class and in the assigned teaching materials.
- 23–26: Complete but not entirely accurate completion of homework assignments; fair critical thinking skills applied to the understanding of applications, methods, models presented in the specialized literature; modest ability in the development and implementation of applications, methods, and models; fair knowledge of the topics covered in class and in the assigned teaching materials.
- 27–30L: Complete and rigorous completion of homework assignments; excellent critical thinking skills applied to the understanding of applications, methods, models presented in the specialized literature; good ability in the development and implementation of applications, methods, and models; in-depth knowledge of the topics covered in class and in the assigned teaching materials.

The course is articulated into:
a) lectures in class;
b) applications of the studied tools by the use of software;
c) individual study.
Students are strongly encouraged to actively attend classes.

Site of the course on the e-learning platform Moodle.

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development