Program of
QUANTITATIVE PORTFOLIO SELECTION FOR MANAGEMENT
Prof. Stefano Patrì
1) Foundations (6 cfu)
Opportunities, criteria and choices: decision problems under certainty and under uncertainty – Examples
Mean-Variance Portfolio Analysis
Basic terminology, definitions and assumptions. Short-selling, Arbitrage
Characterizing the opportunity set in a market with uncertainty: expected returns, variance and standard deviation of the returns of a portfolio – Examples
Representation of portfolios and assets in the Cartesian plane St. Dev/Exp. Return. Dominance relation
General formula of the variance of the returns of a portfolio in a market with n risky assets – Diversification and effects of the diversification on portfolio risk – Equally weighted portfolio – real applications in a market with 2 risky assets
Analysis of a market with only two risky assets and different values of the correlation coefficient: 𝜌 = 1, -1,0,0.5
Quantities, prices and pay-offs and returns – assumption of linear prices – general formulas in a n risky asset market – Efficient Frontier for 3 or more risky assets
The introduction of a risk-free asset. One-Fund Separation theorem. Efficient Frontier (Efficient Line) with or without short selling: graphical analysis and mathematical models for the computation of the Efficient Line – the Sharpe optimization model for portfolio selection
Basics of optimization and mathematical programming – LP and QP models . Markowitz optimization models for portfolio selection (different variants) – Approximation of the Efficient Frontier in a market with n risky assets by the use of Markowitz models (with and without short selling) – Two-funds Separation theorem – Additional constraints: dividends, bounds on the portfolio fractions, cardinality constraints, dependencies in the asset selection – Markowitz Scalar Model – Other risk-return portfolio optimization models: MaxMin, ERPM, MAD
The Single Index model for reducing the number of estimated parameters – Formulas and application – Diversifiable and non diversifiable risk in assets and portfolios
Expected Utility theory and portfolio selection – comparing and ordering alternatives – preference functions – utility functions, the economic properties of utility functions, risk aversion and shape of the utility function. Link between mean-variance criterion and utility function: quadratic utility function and normal returns.