COURSE OUTLINE
Bayesian Econometrics with applications to Portfolio Choice
1. General
School
Academic Unit
Level of Studies
Course code
Semester
Course Title
Idependent Teaching Activities
Weekly Teaching Hours
Credits
Course Type
Prerequite Courses
Language of Instruction and Examinations
Is the course offered to Erasmus Students?
Url (Eclass)
2. Learning Outcomes
Learning Outcomes
The aim of the course is to introduce students to the Bayesian approach to statistical inference and to apply it in a Financial Economics context to solve portfolio selection problems. Upon successful completion of the course, students should be able to:
- understand the differences between the classical (frequentist) and Bayesian approaches to statistical inference
- derive posterior distributions and conduct statistical inference in analytically tractable models (e.g., models with conjugate priors)
- develop code to simulate from posterior distributions in more complex models (using, e.g., Gibbs sampling)
- apply Bayesian methodology to solve static portfolio selection problems with one or multiple risky assets
General Competences
- Search for, analysis and synthesis of data and information, with the use of the necessary technology
- Adapting to new situations
- Decision-making
- Working independently
- Team work
- Working in an interdisciplinary environment
- Production of new research ideas
3. Syllabus
The course offers an introduction to the Bayesian methodology employed in econometrics and statistics with increasing popularity in recent years. The Bayesian approach is applied in a Financial Economics context to tackle portfolio choice problems. We will cover the following topics.
- Brief review of Probability Theory basics and Bayes’ rule.
- Discussion of the contrast between the classical (frequentist) and Bayesian approaches to statistical inference and how the prior distribution combines with the likelihood to generate the posterior distribution.
- Bayesian inference for several standard statistical distributions, such as Binomial, Normal, Poisson, and Negative-Binomial.
- Conjugate families of prior distributions.
- Along the way, we will address the choice of prior, with emphasis on Jeffreys’ prior, and discuss different modes of inference, that is, point estimation, interval estimation, and hypothesis testing.
- Within the Gaussian framework, we will cover univariate linear regression models (with an application to beta estimation through shrinkage), univariate autoregressive models, multivariate linear regression models, and Vector AutoRegression models.
- As we proceed, the course will also cover Monte Carlo simulation techniques that are used in posterior calculations, such as Acceptance-Rejection method and Gibbs sampling.
- Applications of the Bayesian approach to portfolio choice problems. Within the Gaussian framework, we will cover the static portfolio choice problem with (a) a single risky asset and IID returns, (b) multiple risky assets and IID normal returns, (c) a single risky asset and predictable returns. Further, we will cover the Black-Litterman model from the Bayesian perspective.
- Time permitting, we will discuss the dynamic portfolio choice problem with a single risky asset with Νormal IID returns and unknown mean and variance.
4. Teaching and Learning Methods - Evaluation
Delivery
Use of Information and Communications Technology
- Presentation slides in PDF format.
- Distribution of slides through the E-class
Teaching Methods
Activity
Semester Workload
Student Performance Evaluation
Assessment will be based on (a) a written final exam (55%) and (b) an oral final exam (45%). Ungraded practice exercises covering both theoretical and empirical topics will be assigned throughout the semester. The empirical part of the exercises involves data analysis and coding in R, Python, MatLab, or a similar programming language. In addition, active participation in class will be rewarded with a bonus to the final grade.
5. Attached Bibliography
Suggested Bibliography
- Albert, J. and J. Hu (2020), Probability and Bayesian Modeling, CRC Press.
- Bolstad, W.M. and J.M. Curran (2016), Introduction to Bayesian Statistics, Wiley.
- Gelman, A., J.B. Carlin, H. S. Stern, D.B. Dunson, A. Vehtari, and D. B. Rubin (2013), Bayesian Data Analysis, CRC Press.
- Geweke, J. (2005), Contemporary Bayesian Econometrics and Statistics, Wiley.
- Gill, J. (2015), Bayesian Methods, A Social and Behavioral Sciences Approach, CRC Press.
- Greenberg, E. (2007), Introduction to Bayesian Econometrics, Cambridge University Press.
- Hoff, P. D. (2009), A First Course in Bayesian Statistical Methods, Springer.
- Johnson, A. A., M.Q. Ott, and M. Dogucu (2022), Bayes Rules! An Introduction to Applied Bayesian Modeling, CRC Press.
- Reich, B.J. and S.K. Ghosh (2019), Bayesian Statistical Methods, CRC Press.
- Robert, C. P. (2007), The Bayesian Choice, From Decision-Theoretic Foundations to Computational Implementation, Springer.