20191 - FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE - MODULE 1 / FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE - MODULE 1
Per la lingua del corso verificare le informazioni sulle classi/
For the instruction language of the course see class group/s below
Classe/i impartita/e in lingua italiana
Fornire agli studenti conoscenze di base nelle tecniche per la costruzione di modelli probabilistici e nelle tecniche di analisi statistica inferenziale comunemente utilizzate in ambito finanziario per descrivere ed analizzare processi di valutazione, prendere decisioni tra alternative di investimento e controllare il rischio di mercato. Illustrare tali tecniche con esempi tratti dalla pratica finanziaria.
Esame esclusivamente in forma scritta, a libri chiusi, uguale per frequentanti e non frequentati.
Non e’ prevista prova parziale.
Tutte le prove passate sono disponibili in rete con relative soluzioni.
- Dispense corredate da fogli excel e programmi MATLAB
- D. Ruppert, “Statistics and Finance” , Springer 2004.
- Prove d'esame passate e relative soluzioni
- Una scelta di articoli a cura del docente e disponibili in rete tra i quali:
- Fisher, Statman (1999) "A Behavioral framework for time diversification".
- Litterman Winkelmann (1988) "Estimating covariance matrices"
- Sharpe (1992) Asset allocation: management style and performance measurement.
- He, Litterman (1999) The Intuition Behind Black-Litterman Model Portfolios.
- Bevan Winkelmann (1998) Using the Black Litterman Global Asset allocation Model: Three Years of Practical Experience.
Class group/s taught in English
Provide the students with basic techniques for probabilistic modelling and statistical inference commonly applied in the field of finance in order to describe and analyze valuation processes, choose between investments and control market risk. The techniques presented in the course shall be illustrated with examples drawn from actual financial practice.
- An introduction to statistical problems in finance. Data and data transforms. Returns, different definitions and aggregation properties w.r.t. security portfolios and time.
- Probability models for return distributions: gaussian or non gaussian? Dependence or independence?
- Univariate problems: risk premium and its estimation, volatility estimation. VaR estimation, confidence intervals for the VaR.
- Multivariate problems. Matrix algebra and Statistics. Concepts of dependence. Measures of dependence.
- Factor models in finance. The linear model. Inference for the linear model. The least squares method and its properties under several hypothetical settings. Prediction. How to read the results of a linear model .
- Style analysis and its use for fund management performance evaluation.
- Estimations methods for the covariance matrix. Principal components method. Its applications to risk management.
- The Markowitz model, its main properties and its limits in applications. Bayesian methods and portfolio selection. The Black and Litterman model.
- (note: while dealing with points 1 to 4, the basic concepts of probability and statistics required as a prerequisite of the course shall be recalled and re-examined)
Written, closed books, exam, Identical for both participants and non participants in the course.
No midterm exam.
All past exams are available in the Internet together with solutions.
(See the detailed program of the course)
Handouts available on e-learning Excel and Matlab examples
D. Ruppert, Statistics and Finance, Springer, 2004
Past exams: questions (and answers)
and a selection of papers available on e-learning:
Fisher, Statman (1999) "A Behavioral framework for time diversification".
Litterman Winkelmann (1988) "Estimating covariance matrices"
Sharpe (1992) Asset allocation: management style and performance measurement.
He, Litterman (1999) The Intuition Behind Black-Litterman Model Portfolios.
Bevan Winkelmann (1998) Using the Black Litterman Global Asset allocation Model: Three Years of Practical Experience.
- Probability: definition of event, algebra of events, definition of probability, conditional probability. Basic results: probability of a non disjoint union, decomposition of the probability of an event into conditional and marginal probability, Bayes theorem. Random variable, distribution function, models for distribution functions (Bernoulli, Binomial, Geometric, Poisson, Gaussian, Negative exponential, Chi square, Student’s T). Function of a random variable. Moments, quantiles and other summaries of the properties of a distribution. Two dimensional random vector, conditional distributions, conditional expectation and conditional variance: definitions and properties. N dimensional random Vector: joint, marginal and conditional distributions, mixed moments. Random sequence, convergence in Law and in square mean.
- Statistical inference: Sample and sample functions, sampling variability. Point estimate, interval estimate. Unbiased, efficient and consistent estimates. Method of moments and maximum likelihood method. Testing statistical hypothesis. Multiple regressor linear model.
- Matrix algebra: Concept of matrix and vector, basic operations (matrix sums, products, transpose etc.), rank of a matrix, determinant, inverse, product rule for the inverse. Quadratic forms and their classification. Eigenvalues and eigenvectors of a (semi) positive definite matrix and the spectral theorem.