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, including the CAPM, to move then to allocation methods based on Value at Risk, Expected Shortfall, as well as to techniques relying on bootstrap.
Lessons held by the instructor as well as cases study.
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.
Part IV: Advanced Asset Allocation.
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.
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.
MARINA RESTA (President)
LUCA PERSICO
Sem: II
MODERN PORTFOLIO THEORY
Written examination
Written examination plus a report, according to what stated during the lessons by the teacher
Attendance
Not mandatory.
