# MODERN PORTFOLIO THEORY

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iten
Code
41605
2017/2018
CREDITS
6 credits during the 1st year of 8700 Economics and Financial Institutions (LM-56) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
SECS-S/06
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Economics and Financial Institutions)
semester
2° Semester
Teaching materials

OVERVIEW

 Course description 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.

## AIMS AND CONTENT

LEARNING OUTCOMES

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, included the APT and CAPM, to move then to allocation methods based on Value at Risk, Expected Shortfall, as well as to techniques relying on bootstrap.

Teaching methods

Lessons held by the instructor as well as cases study.

SYLLABUS/CONTENT

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.

 Books and classes material will be available on Aulaweb.

## TEACHERS AND EXAM BOARD

Ricevimento: By appointment, contacting the teacher by e-mail. When the final lessons schedule is released, the instructor will also define office hours during which she can be contacted. Office hours: up to 31 May 2018, on Wednesday 10.30-11.30 a.m.; after 31 May 2018, please contact the instructor by mail.

Exam Board

MARINA RESTA (President)

LUCA PERSICO

## LESSONS

Teaching methods

Lessons held by the instructor as well as cases study.

LESSONS START

Sem: I

20 sept. - 15 dec. 2017

ORARI

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

Vedi anche:

MODERN PORTFOLIO THEORY

## EXAMS

Exam description

Written examination

Assessment methods

Written examination plus a report, according to what stated during the lessons by the teacher

## FURTHER INFORMATION

 Attendance Not mandatory.