# CARLO AMBROGIO FAVERO

## Notes on the Econometrics of Asset Allocation and Risk Measurement

These notes, gathered over several years with the inputs of many colleaugues (Celso Brunetti,Francesco Corielli, Massimo Guidolin, Marco Giacoletti, Andrea Tamoni), are focussed on the main econometric ingredients for portfolio allocation and risk measurement: forecasting the distribution of returns of financial assets. The project is empirical and for each topic EVIEWS, R, and MATLAB programmes have been constructed to practically implement the tools introduced (with MATLAB we shall usethe Econometric Toolbox and codes on the Lesage website and download and install the spatial econometrics toolbox).

Chapter 1. The Econometrics of Financial Returns: an introduction

Chapter 2. Financial Returns

1 Returns

1.1 Simple and log Returns

1.2 Multi-period returns and annualized returns

1.3 Working with Returns

2 Stock and Bond Returns

2.1 Stock Returns and the dynamic dividend growthmodel

2.2 Bond Returns: Yields-to-Maturity, Duration and Holding Period Returns

2.2.1 Zero-Coupon Bonds

2.2.2 Coupon Bonds

2.3 A simple model of the term structure

3 Graphical Analysis of Returns

4 Matrix Representation of Returns

5 Modeling Returns

5.1 Assessing Models by Simulation: Monte-Carlo and Bootstrap Methods

5.2 Stocks for the long run

DRAFT CHAPTER MATLAB, E-VIEWS,

Chapter 3 Linear Models of Financial Returns

1 Econometric Modelling of Financial Returns: a general framework

1.1 The reduction process

1.2 Exogeneity and Identification

2 From theory to data: the CAPM

3 Graphical and Descriptive Data Analysis

4 Estimation Problem: Ordinary Least Squares

4.1 Properties of the OLS estimates

4.2 Residual Analysis

5 Interpreting Regression Results

5.1 The R2 as a measure of relevance of a regression

5.2 Inference in the Linear Regression Model

5.2.1 Elements of distribution theory

5.2.2 The conditional distribution | X

5.2.3 Hypothesis Testing

5.2.4 The Partitioned Regression Model

5.2.5 The partial regression theorem

6 The effects of mis-specification

6.1 Misspecification in the Choice of Variables

6.1.1 Under-parameterization

6.1.2 Over-parameterization

6.2 Estimation under linear constraints

6.3 Heteroscedasticity, Autocorrelation, and the GLS estimator

6.3.1 Correction for Serial Correlation (Cochrane-Orcutt)

6.3.2 Correction for Heteroscedasticity (White)

6.3.3 Correction for heteroscedasticity and serial correlation (Newey-West)

7 Econometrics in action: From the CAPM to Fama and French Factors

7.1 Fama-French Factors and the Fama-MacBeth procedure

8 References

Chapter 4 The Constant Expected Return Model

1 The Constant Expected Returns Model

1.1 Regression Model Representation

2 A Static Asset Allocation Problem with Constant Expected Returns

3 What Happens in Practice ?

3.1 The resampled optimal mean-variance portfolio

3.2 Black and Litterman’s approach

4 Going to the Data: Asset Allocation and the CER model with MATLAB

4.1 Exploratory Data Analysis

4.2 Optimal Static Asset Allocation

4.3 Testing the model

4.4 The resampled optimal portfolio and efficient frontier

4.5 Black-Litterman

DRAFT CHAPTER PART1 PART2, SLIDES, MATLAB

Chapter 5 Univariate Time-Series

1 Introduction

2 Time-Series

3 Analysing Time-Series: Fundamentals

3.1 Conditional and Unconditional Densities

3.2 Stationarity

3.3 ARMA Processes

4 Persistence: Monte-Carlo Experiment

5 AsymptoticTheory

5.1 Basic elements of asymptotic theory

5.1.1 Convergence in distribution

5.1.2 Convergence in probability

5.1.3 Central limit theorem (Lindeberg−Levy)

5.1.4 Slutsky’s Theorem

5.1.5 Cramer’s Theorem

5.1.6 Mann−Wald Theorem

5.2 Application to models for stationary time-series

6 Estimation of ARMA models. The Maximum Likelihood Method

6.1 MLE of an MA process

6.2 MLE of an AR process

7 Putting ARMA models at work

7.1 An Illustration

8 Trends

8.1 Univariate decompositions of time-series

8.1.1 Beveridge−Nelson decomposition of an IMA(1,1) process

8.1.2 Beveridge−Nelson decomposition of an ARIMA(1,1) process

8.1.3 Deriving the Beveridge−Nelson decomposition in practice

8.1.4 Assessing the Beveridge−Nelson decomposition

9 Asset Allocation with a simple TVER model: the SOP method

10 Univariate time-series analysis and portfolio allocation with TVER in

DRAFT CHAPTER, SLIDES,MATLAB,EVIEWS, DATASET COCHRANE(94)

Chapter 6 Multivariate Time Series Analysis

1 Stochastic trends and spurious regressions

2 Dynamic Models and Spurious Regressions

Chapter 7 The Term Structure of Risk: Bayesian Methods

Chapter 8 Risk Measurement with High Frequency Data

1. Introduction

2. The Evidence form High Frequency Data

2.1 Heteroscedsticity

2.2 Testing and Measuring deviations from Normality

3. GARCH variance models

3.1 a formal GARCH test

3.2 Forecasting with GARCH models

4. Maximum Likelihood Estimation of GARCH models

5. GARCH specification estimation and forecasting in MATLAB

6. From GARCH to VaR

7. Backtesting VaR

Chapter 9 Modelling Heteroscedasticity and non-normality

1 Introduction

2 Computing Measures of Risk without simulation

3 Simple Models for Volatility

3.1 Rolling window variance model

3.2 Exponential variance smoothing: the RiskMetrics model

3.3 Are GARCH(1,1) and RiskMetrics different?

4 BeyondGARCH

4.1 Asymmetric GARCH Models (with Leverage) and Predetermined Variance Factors

4.2 Exponential GARCH .

4.3 Threshold (GJR) GARCHmodel .

4.4 NAGARCHmodel

4.5 GARCH with exogenous (predetermined) factors

4.5.1 One example with VIX predicting variances

4.6 Component GARCH Models: Short- vs. Long Run Variance Dynamics

5 Modelling Non-Normality

5.1 t-Student Distributions for Asset Returns .

5.2 Estimation: method ofmoments vs. (Q)MLE

5.3 ML vs. QML estimation of models with Student t innovations

5.4 A simple numerical example.

5.5 A generalized, asymmetric version of the Student t

5.6 Cornish-Fisher Approximations to Non-Normal Distributions

5.7 A numerical example

6 Direct Estimation of Tail Risk: A Quick Introduction to Extreme Value Theory

LECTURE NOTES, DRAFT CHAPTER, MATLAB

Chapter 10: Correlation Modeling

Chapter 11: Markov and Regime Switching Models

Chapter 12: Multivariate GARCH Modeling