Course description
An introduction to mathematical methods focusing on portfolio optimization.
The course aims at providing models and methods to theoretical and practical analysis of asset allocation problems. Special attention will be devoted to classical portfolio theory and empirical studies.
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: Refer to teacher's homepage
PIERPAOLO UBERTI (President)
CRISTINA LUIGIA GOSIO
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.
