# CARLO AMBROGIO FAVERO

## Teaching > Teaching materials

## 30188,30285 EMPIRICAL METHODS FOR FINANCE (INTRODUCTION TO ECONOMETRICS FOR FINANCE)

30285 - EMPIRICAL METHODS FOR FINANCE

**Carlo A. Favero- Christian Skov Jensen**

**Course Objectives: Active Learning**

The objective of this course is to introduce the main econometric methods and techniques used in empirical finance. This is an ambitious task that will bring together different type of knowledge: finance theory, statistics, programming.

You will 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 will be 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.

**The Inputs**

The main inputs provided to the students will be references, slides, notes, draft R codes and exercises designed to provide challenges that will stimulate learning. The empirical applications will be 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.

**Assessment Methods**

The level of knowledge reached by the end of the course will be assessed in a final computer based exam: In the final exam students will be required to use their knowledge to tackle empirically some variants of the empirical issues addressed during the lectures and the exercises. During the exam students will be required to modify the R codes that they have built during the course to generate answers to the questions posed in the exercises. The exam wiil be open book and it is highly recommended to prepare it via gradual learning during the course using all inputs made available. **F**inal marks will be obtained by curving the raw marks using Bocconi's distribution.

**Prerequisites**

Students are expected to have attended a core course in statistics and to be familiar with undergraduate calculus and linear algebra. Prior exposure to financial courses (financial markets and institutions, investments and corporate finance) is required to understand the applications covered in class and it is taken for granted.

**Teaching Assistant**

Federico Mainardi (federico.mainardi@studbocconi.it)

OFFICE HOURS: wednesdays 11-13 (Room 2-c3-01)

MOCK EXAM DECEMBER 2017, EXAM SEPT 2018, R CODE and DATA, SOLUTION SEPT 2018

MOCK EXAM DECEMBER 2018, R CODE

EXAM 19 DECEMBER 2018 , TEXT, SOLUTION

EXAM 23 JANUARY 2019, R CODE,DATA, SOLUTION

**Course Content Summary**

**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

RESULTS of the Entry Test

SOLUTION, an R code for Question 1

**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"

An introduction to R Markdown

Intro R Code (from Singh and Allen)

all R codes used in Singh and Allen are downloaded 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)

Dynamic Documents with R Markdown: build a report with all results and comments

**INPUTS**

Singh AK and DE Allen(2017) R in Finance and Economics. A Beginners Guide, World Scientific Publishing, Ch 2,3,4

Heiss F. (2016) Using R for introductory Econometrics http://urfie.net/read/mobile/index.html#p=4, Section 1: Introduction

Yihui Xie, Dynamic Documents with R and Knitr, Chapman and Hall

**R CODES** (from Singh and Allen) : Data Objects, Data Handling, Programming

An Illustration of R coding: the analysis of performance in the Entry Test

DATA, R CODE, R Markdown CODE

**EXERCISE 1** Write an R code that answers to all the ToDo points in Torfs P. and C. Bauer(2014) “A (very short) introduction to R” SOLUTION

**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

**INPUTS**

the datasets,

a Rmd code for the analysis of Shiller database,

a Rmd code for the analysis of the Fama-French database

Portfolio optimization with R:fPortfolio, PortfolioAnalytics

Wurtz D., Y. Calabi, W.Chen and A.Ellis(2009) "Portfolio Optimization with R/Rmetrics, Rmetrics Association & Finance Online, Zurich

Zivot A. and J.Wang (2006) "Modelling Time-Series with S-Plus", Springer

**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**

1 Econometric Modelling of Financial Returns: a general framework

2 The Reduction Process

3 Exogeneity and Identification

4 Estimation Problem: Ordinary Least Squares

4.1 Derivation of the OLS estimates

4.2 Properties of the OLS estimates

4.3 Hypotheses

4.4 Unbiasedness, Variance and Gauss-Markov theorem

4.5 Residual Analysis

4.6 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

an R code for asset allocation with a single factor model

**Lecture 11-12**: Interpreting Regression Results

5.1 Statistical significance, Relevance and Mis-specification

5.2 Inference in the Linear Regression Model

5.2.1 How to formalize the relevant hypothesis

5.2.2 How to build the Statistics

5.3 The partitioned regression model

5.4 Testing Restrictions on a subset of coefficients

5.5 Relevance of a Regression

5.5.1 The R2 as a measure of relevance

5.5.2 The Partial Regression Theorem

5.5.3 the Partial R2

**INPUTS **

SLIDES, hypotheses testing and interpreting results in R, partitioned regression in R

**Lecture 13:**

**EXERCISE 4**: on Estimation and Intepreting Regression Results

**INPUTS:**

The text of the exercise,

**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**

1. The view from the 1960:Efficient Markets and the CER

1.1 Time-Series Implications

1.2 Returns at different horizons

1.3 The cross-section of returns

1.4 The volatility of returns

1.5 Implications for Asset Allocation

2. Empirical Challenges to the traditional model

2.1 the DDG model and predictability of returns

2.2 Anomalies

2.3 the cross-section evidence

2.4 the behaviour of returns at high frequency

3. Implications of the new evidence

4. Predictive Models in Finance

**INPUTS**

SLIDES

**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, R Code to replicate SLIDES EXERCISE, Draft Rmd code

A R code for trading strategy with predictability, data

**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, R Code to replicate slides EXERCISE, Draft Rmd code

**References**

*The Econometrics of Financial Returns and Risk Measurement *, available at www.igier.unibocconi.it/favero

BROOKS C. (2002) "Introductory Econometrics for Finance", Cambridge University Press (Ch. 1-7)

CHRISTOFFERSEN P.F. (2012) "Elements of Financial Risk Management", 2nd edition,Academic Press

DIEBOLD F. *Econometrics, available at *http://www.ssc.upenn.edu/~fdiebold/Textbooks.html

SINGH AK and DE ALLEN(2017) R in Finance and Economics. A Beginners Guide, World Scientific Publishing

HEISS F. (2016) Using R for introductory Econometrics. http://www.urfie.net