# MODERN PORTFOLIO THEORY

_
iten
Codice
41605
2018/2019
CFU
6 cfu al 1° anno di 8700 ECONOMIA E ISTITUZIONI FINANZIARIE (LM-56) GENOVA
SETTORE SCIENTIFICO DISCIPLINARE
SECS-S/06
LINGUA
Inglese
SEDE
GENOVA (ECONOMIA E ISTITUZIONI FINANZIARIE )
periodo
2° Semestre
materiale didattico

PRESENTAZIONE

An introduction to mathematical methods focusing on portfolio optimization.

## OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

Starting from the model of asset allocation of Markowitz, the student will be introduced to classical portfolio theory, including the CAPM, to move then to allocation methods based on Value at Risk, Expected Shortfall, as well as to techniques relying on bootstrap.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

An introduction to mathematical methods focusing on portfolio optimization. Starting from the model of asset allocation of Markowitz, the student will be introduced to classical portfolio theory, to move to allocation methods based on Value at Risk, Expected Shortfall, as well as to techniques relying on bootstrap.

Modalità didattiche

 Modalità didattiche Lessons held by the instructor as well as cases study. The course will utilize R data analysis and statistical modeling. Presente su Aulaweb Yes   X

PROGRAMMA/CONTENUTO

Part I. Basic notations and conventions

Returns calculation. Stylized facts: lack of correlation; Quadratic Positive Correlation; Absence of Normality. Introduction to Technical Analysis.

Part II: Portfolio selection à la Markowitz

Mean-Variance Model: the case of two assets and the general case. Graphical analysis,. Implications. The separation theorem and its financial interpretation. Efficient portfolios by way of matrix algebra. The efficient frontier. The model with a risk-free asset. An outline on CAPM and market line.

Part III: Risk Measures.

A quantile-based approach. Coherent risk measures. Value-at-Risk: definition and statistical implications.  Expected Shortfall: definition and statistical implications. Some tests on VaR.

Outline of bootstrap techniques. The resampling approach by Michaud. The Black-Litterman model. Mean-variance-skewness  models of asset allocation. Portfolio optimization based on risk measures.

TESTI/BIBLIOGRAFIA

The classes material will be set in the classroom at the beginning of the lessons, as well as published on Aulaweb.

## DOCENTI E COMMISSIONI

Ricevimento: Durante il primo semestre (e fino al 22/12/2018) il ricevimento si terrà il Martedì dalle 10.40 alle 12.00. Durante il secondo semestre (18/02/2019 fino al 31/5/2019) il ricevimento si terrà il Mercoledì dalle 10.30 alle 11.30. Negli altri periodi si prega di contattare preventivamente la docente via mail all'indirizzo: marina PUNTO resta AT economia PUNTO unige PUNTO it

Commissione d'esame

MARINA RESTA (Presidente)

LUCA PERSICO

## LEZIONI

Modalità didattiche

 Modalità didattiche Lessons held by the instructor as well as cases study. The course will utilize R data analysis and statistical modeling. Presente su Aulaweb Yes   X

INIZIO LEZIONI

Sem: II

## ESAMI

Modalità d'esame

Written examination.

Modalità di accertamento

 Modalità di accertamento Written examination. The students can alternatively present and discuss a report according to the indications provided by the teacher during the lessons. Ripetizione dell’esame Three times in the first session. It is mandatory to sign for the examination through the web portal.

Calendario appelli

Data Ora Luogo Tipologia Note
10/09/2019 09:30 GENOVA Scritto

## ALTRE INFORMAZIONI

 Knowledge and understanding.  Students must acquire adequate knowledge and understanding of effective asset allocation tools. Applying knowledge and understanding. Students should be able to apply their knowledge to solv problems of optimal allocation in the presence of risk. Independent judgment capabilities. The students should know how to use the learned skills both at the conceptual and at the operational level in different application contexts. Communication skills. Students should acquire the technical language of the discipline to keep in touch, both clearly and unambiguously, with specialists. Learning skills. Students must develop proper learning skills to to independently investigate major issues of the field, withinh their operative working framework.

 The course will use R data analysis and statistical modeling. Testi di studio The classes material will be set in the classroom at the beginning of the lessons, as well as published on Aulaweb. Modalità di accertamento Esame    X scritto ☐ orale  ☐   altro: The students will present and discuss a report according to the indications provided by the teacher during the lessons. Ripetizione dell’esame Three times in the first session. It is mandatory to sign for the examination through the web portal.