Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
secondo semestre lauree magistrali dal Feb 25, 2019 al May 31, 2019.
The first part of the course aims to provide the student with the basic methodologies typical of the Technical Analysis aimed at studying the evolutionary characteristics of the quotations on the market in order to develop strategic and tactical actions aimed at supporting investments.
The second part of the course develops the modern portfolio selection theory with random returns, typically investments in equity securities or the production and marketing of products and / or services. The focus is on the study of models for the composition of efficient portfolios, the identification of the preferred portfolio and the analysis of the equilibrium on the capital market.
First part: Technical Analysis
The market system.
1. The study of graphs for operational purposes. Price dynamics as a function of time. Dynamics of prices and volumes as a function of time. Detection of price variations in a timeless dimension.
2. Heuristic-quantitative models. Moving averages. Oscillators. Elaboration of historical price series: RSI, DMS, MI, CCI, VHF, ADI, VI. Elaboration of time series of prices and volumes: OBV, ADL, MFI. Elaboration of time series of prices and market indices: SMEs. Elaboration of time series of quotation sets: ADI, ADR, NHNL. The logistic function.
3. Models for taking speculative positions. Trend-following techniques: systems based on moving averages, Parabolic System, Volatility System, Swing System. Indicators generated by historical series of prices and volumes: Ease of Movement Valuen (EMV). Techniques for managing positions in congested phases: TBPS, RTS, SO, Williams indicators.
4. From basic models to operating systems. Qualification of the current market phase, setting of the operating strategy, estimation of the evolutionary potential and the time horizon. Outlines of neuronal techniques and fuzzy logic.
Second part: portfolio theory and capital market equilibrium.
1. Portfolio choices. The criterion of mean-variance. Lagrangian characterization. Quadratic optimization methods. The Markowitz Model: analysis with n stocks and a certain yield security; analysis with n stocks, a security with a certain return and the possibility of borrowing at a certain cost. Single-index (Sharpe) models: Beta estimate, market model, SML, multi-index models, average correlation models and mixed models.
2. Identification of the optimal portfolio. Utility functions and investment choices. Empirical evidence of preferred alternatives.
3. International diversification. The global portfolio. Returns on investments in foreign markets. Risk on foreign securities, returns deriving from international diversification, exchange rate risk, models for the management of international portfolios.
4. Models of equilibrium of the capital market. The CAPM, non-standard forms of CAPM, the Consumption CAPM (CCAPM), the APT, Fama-French models.
5. Evaluation of the performance of a portfolio. Evaluation techniques, decomposition of the overall evaluation, evaluation of the APT multi-index and performance, analysis of the performance of mutual funds.
For the first part:
M. Pring, Technical Analysis, McGraw-Hill, NY, Fifth Edition o edizione italiana del 2003
J.J. Murphy, Analisi tecnica dei mercati finanziari, Hoepli, Milano, 2002.
For the second part:
F. Rossi, F. Mantovani, Teoria di portafoglio: diversificazione degli investimenti e controllo del profilo rendimento-rischio, Monduzzi Editore, Bologna, 2010.
Elton E.J., Gruber M.J., Brown S.J., Goetzmann W.N., Modern Portfolio Theory and Investment Analysis, J. Wiley, NY, 2003
Bodie-Kane-Marcus, Investments, Mc Graw Hill, Fifth Edition, 2003
The 54 hours of lectures are developed with applications and simulations. Interventions by professionals / experts are planned as well as tutoring activities for the preparation of the Project Work necessary to access the exam.
Under the supervision of the teacher, study groups will be formed (maximum 3 students) that will analyze some titles / indexes over time and produce a written work, Project Work (PW), to be sent to the teacher, via email, for evaluation at least one week before the exam session the students involved are interested in.
In this PW all the techniques, the models and the methods of analysis developed gradually in the course and which constitute the qualifying points of the same should be used at best.
Only after a positive evaluation of the PW (maximum 3/30 bonus points) it will be possible to enter the exam.
The PW is part of the methods of active participation of students in the course and has the following purposes:
- stimulate the student to the systematic and assiduous study of the subject as the various themes are tackled and therefore to improve the learning process, given that the methods and models proposed are the bases on which more complex methods and models are developed;
- improve skills and quality in interpersonal relationships and in particular in team work;
- improve the skills and quality of presentation / exposure using schemes and vocabulary typical of asset management.
The aforementioned elements play an important role in professional qualification and are highly considered in the labor market.
The exam consists of a written test, of two hours, on the whole program, with exercises, an open question, a question of choice, and possible interview aimed at verifying the depth and breadth of the preparation.