# MODERN PORTFOLIO THEORY

_
iten
Codice
41605
2017/2018
CFU
6 cfu al 1° anno di 8700 ECONOMIA E ISTITUZIONI FINANZIARIE (LM-56) GENOVA
SETTORE SCIENTIFICO DISCIPLINARE
SECS-S/06
LINGUA
Italiano
SEDE
GENOVA (ECONOMIA E ISTITUZIONI FINANZIARIE )
periodo
2° Semestre
materiale didattico

## OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

Il corso si propone di illustrare alcuni modelli matematici che vengono utilizzati nella gestione dei portafogli finanziari.

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 referee teacher as well as cases study. The course will utilize R data analysis and statistical modeling. Presente su Aulaweb Yes   X  No ☐

PROGRAMMA/CONTENUTO

Part I: Portfolio selection à la Markowitz

Returns calculation. Stylized facts: lack of correlation; Quadratic Positive Correlation; Absence of Normality. 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 II: 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: Su appuntamento, contattando la docente via e-mail. Al rilascio del calendario delle lezioni verrà comunicato altresì un giorno (e un'orario) fisso, valido durante il periodo dell'attività didattica. Durante il secondo semestre (e fino al 31/5/2018) il ricevimento si terrà il Mercoledì dalle 10.30 alle 11.30. Dopo il 31/5/2018, si prega invece di contattare preventivamente via mail la docente.

Commissione d'esame

MARINA RESTA (Presidente)

LUCA PERSICO

## LEZIONI

Modalità didattiche

 Modalità didattiche Lessons held by the referee teacher as well as cases study. The course will utilize R data analysis and statistical modeling. Presente su Aulaweb Yes   X  No ☐

INIZIO LEZIONI

Sem: I

18 september

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

MODERN PORTFOLIO THEORY

## ESAMI

Modalità d'esame

Scritto

Modalità di accertamento

 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.

## ALTRE INFORMAZIONI

 Eventuali propedeuticità e/o pre requisiti consigliati Risultati di apprendimento previsti 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.
 Informazioni aggiuntive per gli studenti non frequentanti

 Modalità didattiche The course will utilize R data analysis and statistical modeling. Obblighi 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.