# MODERN PORTFOLIO THEORY

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iten
Code
41605
2018/2019
CREDITS
6 credits during the 1st year of 8700 Economics and Financial Institutions (LM-56) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
SECS-S/06
LANGUAGE
English
TEACHING LOCATION
GENOVA (Economics and Financial Institutions)
semester
2° Semester
Teaching materials

OVERVIEW

 Course description An introduction to mathematical methods focusing on portfolio optimization.

## AIMS AND CONTENT

LEARNING OUTCOMES

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.

Teaching methods

Lessons held by the instructor as well as cases study.

SYLLABUS/CONTENT

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

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 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.

 Books and classes material will be available on Aulaweb.

## TEACHERS AND EXAM BOARD

Ricevimento: Office hours: up to 22 December 2018, on Tuesday 10.40-12.00 a.m.; later, please contact the instructor by mail. Office hours: in the period: 18 February 2019 up to 31 May 2019, on Wednesday 10.30-11.30 a.m.; later, 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: II

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.