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First Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[11/83]  ECONOMICS, FINANCE AND PUBLIC POLICY [83/20 - Ord. 2017]  Economia e Mercati Finanziari 6 36


The course aims to provide students with the basics of asset allocation methods to be applied in portfolio management in order to better understand the effectiveness of such methods in solving real life problems related to the asset management. At the end of the course, students will be able to better understand the basics of advanced statistical methods used for that purpose, and to assess their importance for the decision making process typical of asset allocation.

In line with the Dublin Descriptors, the learning skills acquired at the end of the course can be classified as follows:
1) Knowledge and understanding. The course permits to study the multivariate statistical models utilized for decision-making processes in modern (multinational) financial companies, and understand the effects they produce on asset management actions.
2) Applying knowledge and understanding. The methods being studied are applied during case-studies classes, where students can learn the basics of the R software for statistical computing and understand how it can be used to solve real problems related to portfolio asset management.
3) Making judgements. During classes, students are asked for problem solving and decision making as if they where a asset managers that need to take a decision in order to improve profitability of their investments.
4) Communication skills. Students are called during classes to discuss on the appropriateness of suggested methods in different management scenarios.
5) Learning skills. Classes, lecture notes, and case-study analyses allow to maximize the students overall learning skills in the statistics and asset management field.


Students attending the course are expected to have acquired the basic notions in univariate and bivariate descriptive statistics, probability distribution and statistical inference (“important”) and some basic notions of Mathematics (“useful”).


1. Introduction to the course; Intro to R, Intro to measurements, Descriptive Statistics (4 hours)
2. R functions and financial functions to manipulate assets (4 hours)
Manipulating financial time series
Price and index series
Return and cumulated return series
Drawdowns and Duration series
Estimates of covariance matrices
Quantile and related risk measures
3. Robust estimation of mean and covariance of financial assets (4 hours)
Robust covariance estimator
Nearest-Neighbour covariance estimator
Shrinkage and Bagging estimator
4. Exploratory data analysis of assets (4 hours)
Graphical representation of prices and returns
Testing asset returns of normality
Selecting similar or dissimilar assets
Comparing multivariate return and risk statistics
Pairwise dependencies of assets
5. Specifying portfolios and their constraints in R (4 hours)
6. Mean-Variance portfolios (4 hours)
Markowitz portfolio theory
Minimum-risk mean-variance portfolios
Efficient frontier
Robust portfolios
7. Mean-CVaR Portfolios (4 hours)
Long-only portfolio frontier
Unlimited short portfolio frontier
Box-Constrained portfolio frontier
Group-Constrained portfolio frontier
8. Portfolio Backtesting (2 hours)
9. Issues in asset management of financial portfolios (6 hours)
Adaptive asset allocation
Mean-Gini Portfolios
Portfolio shrinkage
Resampled efficient frontier
Omega portfolios
Rebalancing strategies
Performance attribution
130/30 management strategy

Teaching Methods

The course is scheduled in 6 Lecture hours per week.
Some classes (of 2 hours each) are given to analyse case studies and apply all acquired knowledge to understand how using the R software to solve real problems in portfolio management.

Verification of learning

Students preparation is verified through a two-hours written exam where students are asked to answer 7 questions related to the theoretical foundations of the statistical methods as well as to the interpretation of the results of a statistical analysis. Ability in mathematical formalization, graphical representation and appropriate statistical language are also evaluated.
All classes and additional material, along with notes and reference books, are necessarily needed for the full completion of the exam.
In line with the Dublin Descriptors, the evaluation process aims also to verify:
1) the ability to identify the statistical method to be applied in order to analyse a specific dataset (evaluation of knowledge and understanding).
2) the ability in the interpretation of the results of a statistical analysis (evaluation of applying knowledge and understanding).
3) the capacity to use properly the R statistical software in order to apply the most appropriate method for a specific dataset (evaluation of making judgements).
4) the capacity of synthesizing the results of a statistical analysis and to represent them both with mathematical formulations and rigorous graphic representation (evaluation of communication skills).
5) the theoretical knowledge of multivariate statistical methods (evaluation of learning skills).

Final mark is expressed through a 30-point scale.
A passing mark ranges from:
- 18/30: if the student shows a sufficient level of knowledge, that is he is able to at least identify the scenario in the analysis of a real dataset, knows the basic elements to draw the appropriate graphics and tables, and expresses comments with an elementary technical language.
- to 30/30, eventually cum laude, if the student is able to schematize in a logic and coherent way the statistical knowledge acquired during the course, namely all the theoretical issues characterizing statistical methods, and is able to apply these methods in a proper way.


Lecturer will not follow any textbook.

Notes and reference papers are made available through the personal homepage.

More Information

Additional material, further readings, and past exams, along with every additional information on the course and its credits, will be provided at request.

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