# 30285 - EMPIRICAL METHODS FOR FINANCE (INTRODUCTION TO ECONOMETRICS FOR FINANCE)

Course taught in English

Only for BIEF students: the exam code 30001 Statistics is a prerequisite of the exam empirical methods for finances

The objective of this course is to introduce the main econometric methods and techniques used in empirical finance. This is an ambitious task that brings together different type of knowledge: finance theory, statistics, programming. You learn how to use software, in particular the R software, to specify, estimate and simulate model of financial data to be used for asset allocation, risk measurement and risk management. The teaching strategy is based on providing inputs to students that are supposed to active elaborate them to produce their knowledge. The choice of inputs and the mapping of inputs into knowledge is the students’ responsibility. The course is designed to give opportunities. The decision of how many opportunities to take and how to take them is left to course participants. The final assessment is designed to evaluate the solidity of the foundation in the relevant tools for financial time-series modelling achieved by the students at the end of the course.

- Lecture 1: Where are we going?
- The Econometrics of Financial Returns.
- The dimensions of the data.
- What makes Econometrics interesting.
- Econometric Modelling of Financial Returns.
- Building, Estimating, Validating and Using an Empirical Model.
- The Data.
- INPUTS.
- SLIDES.
- Notes on the Econometrics of Asset Allocation and risk Measurement, Ch.1.

- Lecture 2: Where do we stand?
- Entry Test on basic knowledge in finance, statistics, probability.
- SOLUTIONS, ANALYSIS WITH R.
- INPUTS.
- An introduction to matrix algebra, statistics and probability,(courtesy of "The master", Prof. F.Corielli).
- "A Simple derivation of the capm" by C. Deeley.

- Lecture 3-4: An introduction to R:
- Before the lecture:
- Install R and R studio on your computer and learn how to run them.
- Learn what is a package and how to install it.
- Understand what is a view.

- INPUTS.
- Singh AK and DE Allen(2017) R in Finance and Economics. A Beginners Guide, World Scientific Publishing, Ch 1.
- Torfs Brauer "A Very Short Intro to R".
- Intro R Code (from Singh and Allen).
- all R codes used in Singh and Allen are downloadle at http://www.rforresearch.com/r-in-finance-economics.
- Topics of the lecture.
- Data Objects in R (data types) and Data Structures In R (Vectors, Matrices, Arrays, Data Frames, Lists).
- Data Handling in R (Importing and Exporting data).
- Programming and Control Flow (if-else statements, using switch, loops, functions in R).
- INPUTS.
- Singh AK and DE Allen (2017) R in Finance and Economics. A Beginners Guide, World Scientific Publishing, Ch 2,3,4.
- R CODES (from Singh and Allen): Data Objects, Data Handling, Programming.
- EXERCISE 1 Write an R code that answers to all the ToDo points in P. Torfs and C. Bauer (2014) “A (very short) introduction to R”
- SOLUTION.

- Before the lecture:
- Lecture 5 Returns:
- Simple and log Returns.
- Multi-period returns and annualized returns.
- Working with Returns.
- Stock and Bond Returns.
- Stock Returns and the dynamic dividend growth model.
- Bond Returns: Yields-to-Maturity, Duration and Holding Period Returns.
- Graphical Analysis of the Data.
- Matrix Representation of the data.
- INPUTS.
- SLIDES.
- Notes on the Econometrics of Asset Allocation and risk Measurement, Ch.2.

- Lecture 6-7: Data Analysis with R.
- The Fama French and Shiller databases.
- Using R to load, transform and analyze time-series data.
- Using R Markdown to build a report with all results and comments.
- INPUTS.
- the datasets,a Rmd code, an introduction to R Markdown.
- EXERCISE 2: Learn to import, transform and graph data by answering to these questions, SOLUTION.

- Lecture 8: Modeling and Simulating Returns with R.
- Assessing Models by Simulation: Monte-Carlo and Bootstrap Methods.
- Stocks for the long run.
- INPUTS.
- SLIDES.
- a Rmd code.

- Lecture 9: Estimating Linear Models of Returns.
- Econometric Modelling of Financial Returns: a general framework.
- The Reduction Process.
- Exogeneity and Identification.
- Estimation Problem: Ordinary Least Squares.
- Derivation of the OLS estimates.
- Properties of the OLS estimates.
- Hypotheses.
- Unbiasedness, Variance and Gauss-Markov theorem.
- Residual Analysis.
- The R-squared.

- INPUTS.
- SLIDES.
- Notes on the Econometrics of Asset Allocation and risk Measurement, Ch.3.

- Lecture 10: CAPM estimation and simulation with R.
- Estimation, simulation and VaR with a more articulated model.
- INPUTS.
- EXERCISE 3, SOLUTION.

- Lecture 11-12: Interpreting Regression Results.
- Statistical significance, Relevance and Mis-specification.
- Inference in the Linear Regression Model.
- How to formalize the relevant hypothesis.
- How to build the Statistics.

- The partitioned regression model.
- Testing Restrictions on a subset of coefficients.
- Relevance of a Regression.
- The R2 as a measure of relevance.
- The Partial Regression Theorem.
- The Partial R2.

- INPUTS.
- SLIDES, partitioned regression in R.

- Lecture 13:
- EXERCISE 4: on Estimation and Intepreting Regression Results.
- INPUTS.
- The text of the exercise, a draft RMD code.

- Lecture 14-16:Model Mis-Specification.
- Mis-specification in the choice of variables.
- Under-parameterization.
- Over-parameterization.
- Mis-specification in omitting parameters constraints.
- Estimation under linear constraints.
- Misspecification of residuals' behaviour.
- INPUTS.
- SLIDES.
- EXERCISE 5: Model Mis-Specification.
- a draft Rmd code.

- Lecture 17 : Testing the CAPM.
- Fama MacBeth and the cross section of returns.
- Multi-Factor Models.
- INPUTS.
- SLIDES.
- EXERCISE 6, a draft Rmd code.

- Lecture 18: An Historycal Perspective.
- The view from the 1960:Efficient Markets and the CER.
- Time-Series Implications.
- Returns at different horizons.
- The cross-section of returns.
- The volatility of returns.
- Implications for Asset Allocation.

- Empirical Challenges to the traditional model.
- The DDG model and predictability of returns.
- Anomalies.
- The cross-section evidence.
- The behaviour of returns at high frequency.

- Implications of the new evidence.
- Predictive Models in Finance.
- INPUTS.
- SLIDES.

- The view from the 1960:Efficient Markets and the CER.
- Lecture 19-21: Univariate Time-Series.
- Analysing Time-Series: Fundamentals.
- Conditional and Unconditional Densities.
- Stationarity.
- ARMA Processes.
- Persistence: A Monte Carlo Experiment.
- Estimation of ARMA models. The Maximum Likelihood Method.
- Putting ARMA models at work.
- INPUTS.
- SLIDES, EXERCISE, Draft Rmd code.

- Lectures 22-24. Modelling Heteroscedasticity.
- A look at the data: Correlation and non-normality.
- GARCH Modelling.
- Representation.
- Testing for GARCH.
- Maximum Likelihood Estimation.
- Forecasting.
- Beyond GARCH: threshold models.
- Simulation.
- VaR with GARCH.
- Backtesting VaR.
- INPUTS.
- SLIDES, EXERCISE, Draft Rmd code.

The objective of this course is to introduce the main econometric methods and techniques used in empirical finance. This is an ambitious task that brings together different type of knowledge: finance theory, statistics, programming. You learn how to use software, in particular the R software, to specify, estimate and simulate model of financial data to be used for asset allocation, risk measurement and risk management. The teaching strategy is based on providing inputs to students that are supposed to active elaborate them to produce their knowledge. The choice of inputs and the mapping of inputs into knowledge is the students’ responsibility. The course is designed to give opportunities. The decision of how many opportunities to take and how to take them is left to course participants.

- Apply econometric techniques to assset allocation and risk measurement.

- Face-to-face lectures
- Exercises (exercises, database, software etc.)

The main inputs provided to the students are references, slides, notes, draft R codes and exercises designed to provide challenges that stimulate learning. The empirical applications are based on databases freely available on the web. Students are expected to download and install the R and Rstudio packages on their PC at the beginning of the course.

Continuous assessment | Partial exams | General exam | |
---|---|---|---|

x |

The final grade depends entirely on the performance at the written individual exam.

- T
*he Econometrics of Financial Returns and Risk Measurement*, available at www.igier.unibocconi.it/favero. - C. BROOKS,
*Introductory Econometrics for Finance*, Cambridge University Press, 2002 (Ch. 1-7). - P.F. CHRISTOFFERSEN,
*Elements of Financial Risk Management*, Academic Press , 2012, 2nd edition. - F. DIEBOLD,
*Econometrics*, available at http://www.ssc.upenn.edu/~fdiebold/Textbooks.html. - A.K. SINGH, DE ALLEN,
*R in Finance and Economics. A Beginners Guide*, World Scientific Publishing, 2017.