Quantitative Methods for Finance

The course opens with the presentation of some types of data used in finance and the problems associated with them. After studying the cross-section and temporal aggregation properties of returns, the topic of estimating the variance-covariance matrix of returns as well as the empirical risk and return characteristics of the main financial asset classes will be addressed.

Subsequently, decision theory and in particular expected utility theory will be presented, followed by the study of the mean-variance optimization model, the properties of frontier portfolios and the Capital Asset Pricing Model (CAPM). Finally, after some references to aspects related to portfolio and investment fund management, the lognormal model of prices and some Value-at-Risk calculation techniques will be discussed.

The course sets the following three objectives:

• identify and discuss the properties and characteristics of temporal and cross-section aggregation of returns;
• analyze quantitative models for asset allocation and portfolio risk management, using expected utility theory as the theoretical framework of reference for justifying optimal investment choices;
• empirical implementation of theoretical models through the analysis of real market data, with particular attention to the risk-return characteristics of the main asset classes and the practical applications of the underlying mathematical tools.

In presenza

The course combines theoretical aspects and practical applications, addressing concrete topics such as the acquisition and processing of financial data, the critical interpretation of mean-variance optimization results and the analysis of their limitations. The R statistical software will be used systematically to implement examples with real data and conduct guided practical exercises.

The exam will be held in oral or written form depending on the number of enrolled students.