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 setting to solve portfolio choice problems. Upon successful completion of the course, students should be able to:
- understand the differences between the classical (frequentist) and the Bayesian approach
- derive posterior distributions and conduct statistical inference in analytically tractable models (e.g. models with conjugate prior distributions)
- develop code to simulate from posterior distributions for more complex models (e.g. using Gibbs sampling)
- use Bayesian methodology to solve static portfolio choice 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 is an introduction to Bayesian methodology, which has been used increasingly in Econometrics and Statistics in recent years. The Bayesian approach is then applied in a financial setting to solve portfolio choice problems. The material we will cover includes the following topics:
- A brief review of the basic elements of Probability Theory and Bayes’ rule.
- A description of the differences between the classical (frequentist) and the Bayesian approach to statistical inference, and of how the prior distribution is combined with the likelihood function to produce the posterior distribution.
- Bayesian inference for various basic statistical distributions, such as the Binomial, the Normal, the Poisson and the Negative Binomial.
- Conjugate families of prior distributions.
- Alongside these topics, we will consider the choice of prior distribution, with emphasis on the Jeffreys prior, and we will discuss different forms of inference, such as point estimators, credible intervals and hypothesis tests.
- Within the framework of the Normal distribution, we will study the simple linear regression model (with an application to the estimation of beta coefficients via shrinkage), the univariate autoregressive model, the multiple linear regression model and the vector autoregressive (VAR) model.
- As the course progresses, we will cover some Monte Carlo simulation techniques used in the computation of posterior distributions, such as the Acceptance-Rejection method and Gibbs sampling.
- Applications of the Bayesian approach to portfolio choice problems. Within the framework of the Normal distribution, we will cover the static portfolio choice problem with (a) one risky asset whose returns are independent and identically distributed (IID) random variables, (b) multiple risky assets whose returns are IID random vectors, and (c) one risky asset whose returns are predictable random variables. We will also cover the Black-Litterman model from a Bayesian perspective.
- Time permitting, we will study the dynamic portfolio choice problem with one risky asset whose returns are IID Normal random variables with unknown mean and variance.
4. Teaching and Learning Methods - Evaluation
Delivery
Use of Information and Communications Technology
- Lecture slides in PDF format.
- Distribution of the slides via the eClass platform.
- Use of the Department’s computer lab for data analysis with MatLaB, R or a similar programming language.
Teaching Methods
Activity
Semester Workload
Student Performance Evaluation
Assessment will be based on (a) a written final examination (55%) and (b) an oral final examination (45%). During the semester, ungraded practice exercises will be assigned, covering both theoretical and empirical issues. The empirical part of the exercises involves data analysis and code development in R, Python, MatLab or another 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.