Ateneo - UPO

The first part of the course introduces the main notions regarding the classical theory of Portfolio (Model Media-Variance, CAPM).
In the second half, the focus is on market risk, focusing in particular on VaR calculation and regulatory requirements. The main and most significant results are derived analytically and commented on. Matlab and Excel are used for the practical implementation of the studied models.

Portfolio Theory: materials provided by the teacher and published on DIR.
A useful reference textbook is

C. Huang, R. H. Litzenberger. Foundations for Financial Economics. Prentice Hall. 1988

For the market risk part:

Jorion P., (2007). Value at Risk, 3rd ed.

Christoffersen, P., (2012). Elements of Financial Risk Management, Academic Press, 2nd edition.

Additional materials provided by the teacher.

At the end of the module, the Student will have acquired an adequate knowledge of the main models of Portfolio Theory, and will be able to implement them independently. They will also recognize the critical issues related to the calculation of returns and the measurement of market risk, with particular reference to the VaR as a risk measure.

Basic knowledge of mathematics and statistics. Minimum knowledge of Excel and Matlab

Lectures and exercises.

Attendance of the lecture class is not compulsory but is strongly recommended.

A compulsory oral exam during which the student will also be asked to solve some problems on the course topics.

Brief review of random variables, distributions, expected utility theory, and decisions under risk conditions. Construction of a portfolio of risky assets, with and without the presence of a risk-free security, according to the criterion medium-variance (Markowitz). Efficient frontier construction. Sharpe index. CAPM. Returns calculation methods: linear returns vs logarithmic returns. Main characteristics, properties and implications for the calculation of the performance of a portfolio. Introduction to the main types of financial risks. Market risk: critical issues, regulatory requirements and calculation of Value at Risk for individual assets and for a portfolio of risky assets.
All problems are discussed from a theoretical point of view, with attention to quantitative implications, and implememented as an example and as an exercise in Matlab and/or Excel.

At the end of the course, the student will have acquired an adequate knowledge of the main aspects of Portfolio Theory. They will also be able assess the risk of their portfolio. In addition, they will be able to independently implement the models studied, providing a critical interpretation of the results.