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
1 Introduction
2 Predicting the distribution of future returns: The Econometric Modelling
Process
3 The Challenges of Financial Econometrics
4 Prof Wald and the missing bullet holes: identification matters
5 The Traditional Model
5.1 The view from the 1960s: EfficientMarkets and CER
5.1.1 Time-Series Implications
5.1.2 Returns at different horizons
5.1.3 The Cross-Section of Returns
5.1.4 The Volatility of Returns
5.1.5 Implications for Asset Allocation
6 Empirical Challenges to the traditional model
6.1 The time-series evidence on expected returns
6.2 Anomalies
6.3 The Cross-section Evidence on Expected Returns
6.4 The behaviour of returns at high-frequency: non-normality and heteroscedasticity
7 The Implications of the new evidence
7.1 Asset Pricing with Predictable Returns
8 Quantitative Risk Management and the behaviour of returns at high frequency
9 The Plan of the book. Predictive Models in Finance
9.1 Appendix: The Data
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
2.1 Non Stationary Time-Series, Cointegration and Error Correction Models
2.2 Static Regressions and Dynamic Models .
3 Spurious Regressions and the predictability of returns at different frequencies
4 Cointegration with Multiple Cointegrating Vectors
4.1 The Johansen procedure
4.2 Identification of multiple cointegrating vectors
4.3 Hypothesis testing with multiple cointegrating vectors
5 Using VAR Models
6 Identification of VAR
7 Description of VAR models
8 From VAR innovations to structural shocks
8.1 Choleski decomposition
8.2 CVAR and Identification of shocks
8.3 Sign Restrictions
8.4 GIRF
9 Cointegration and Present Value Models
9.1 Cointegration and multivariate trend-shocks decompositions
9.2 Forecasting froma Cointegrating VAR
9.3 VECM and common trends representations
10 An Application: Cointegration, Noise and Information
in Stock Market Returns
11 Risk, Returns and Portfolio Allocation with Cointegrated VARs
11.1 Inspecting the mechanism: a bivariate case
11.2 A VAR with many assets and predictors
11.3 Mean-Variance Analysis with a VAR model
12 Multivariate Time-Series with Matlab
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
LECTURE NOTES, DRAFT CHAPTER,MATLAB
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
LECTURE NOTES
Chapter 11: Markov and Regime Switching Models
LECTURE NOTES
Chapter 12: Multivariate GARCH Modeling
LECTURE NOTES