The Basics of Financial Econometrics Tools, Concepts, and Asset Management Applications Frank J. Fabozzi Series

As finance and financial products have become more complex, financial econometrics has emerged as a fast-growing field and necessary foundation for anyone involved in quantitative finance. The techniques of financial econometrics facilitate the development and management of new financial instruments by providing models for pricing and risk assessment. In short, financial econometrics is an indispensable component to modern finance.

The Basics of Financial Econometrics covers the commonly used techniques in the field without using unnecessary mathematical/statistical analysis. It focuses on foundational ideas and how they are applied. Topics covered include: regression models, factor analysis, volatility estimations, and time series techniques.

• Covers the basics of financial econometrics?an important topic in quantitative finance
• Contains several chapters on topics typically not covered even in basic books on econometrics such as model selection, model risk, and mitigating model risk

Geared towards both practitioners and finance students who need to understand this dynamic discipline, but may not have advanced mathematical training, this book is a valuable resource on a topic of growing importance.

Acknowledgments xvii

About the Authors xix

Chapter 1 Introduction 1

Financial Econometrics at Work 2

The Data Generating Process 5

Applications of Financial Econometrics to Investment Management 6

Key Points 10

Chapter 2 Simple Linear Regression 13

The Role of Correlation 13

Regression Model: Linear Functional Relationship between Two Variables 14

Distributional Assumptions of the Regression Model 16

Estimating the Regression Model 18

Goodness-of-Fit of the Model 22

Two Applications in Finance 25

Linear Regression of a Nonlinear Relationship 36

Key Points 38

CHAPTER 3 Multiple Linear Regression 41

The Multiple Linear Regression Model 42

Assumptions of the Multiple Linear Regression Model 43

Estimation of the Model Parameters 43

Designing the Model 45

Diagnostic Check and Model Significance 46

Applications to Finance 51

Key Points 79

chapter 4 Building and Testing a Multiple Linear Regression Model 81

The Problem of Multicollinearity 81

Model Building Techniques 84

Testing the Assumptions of the Multiple Linear Regression Model 88

Key Points 100

CHAPTER 5 Introduction to Time Series Analysis 103

What Is a Time Series? 103

Decomposition of Time Series 104

Representation of Time Series with Difference Equations 108

Application: The Price Process 109

Key Points 113

chapter 6 Regression Models with Categorical Variables 115

Independent Categorical Variables 116

Dependent Categorical Variables 137

Key Points 140

Chapter 7 Quantile Regressions 143

Limitations of Classical Regression Analysis 144

Parameter Estimation 144

Quantile Regression Process 146

Applications of Quantile Regressions in Finance 148

Key Points 155

CHAPTER 8 Robust Regressions 157

Robust Estimators of Regressions 158

Illustration: Robustness of the

Corporate Bond Yield Spread Model 161

Robust Estimation of Covariance and Correlation Matrices 166

Applications 168

Key Points 170

Chapter 9 Autoregressive Moving Average Models 171

Autoregressive Models 172

Moving Average Models 176

Autoregressive Moving Average Models 178

ARMA Modeling to Forecast S&P 500 Weekly Index Returns 181

Vector Autoregressive Models 188

Key Points 189

Chapter 10 Cointegration 191

Stationary and Nonstationary Variables and Cointegration 192

Testing for Cointegration 196

Key Points 211

chapter 11 Autoregressive Heteroscedasticity Model and Its Variants 213

Estimating and Forecasting Volatility 214

ARCH Behavior 215

GARCH Model 223

What Do ARCH/GARCH Models Represent? 226

Univariate Extensions of GARCH Modeling 226

Estimates of ARCH/GARCH Models 229

Application of GARCH Models to Option Pricing 230

Multivariate Extensions of ARCH/GARCH Modeling 231

Key Points 233

Chapter 12 Factor Analysis and Principal Components Analysis 235

Assumptions of Linear Regression 236

Basic Concepts of Factor Models 237

Assumptions and Categorization of Factor Models 240

Similarities and Differences between Factor Models and Linear Regression 241

Properties of Factor Models 242

Estimation of Factor Models 244

Principal Components Analysis 251

Differences between Factor Analysis and PCA 259

Approximate (Large) Factor Models 261

Approximate Factor Models and PCA 263

Key Points 264

Chapter 13 Model Estimation 265

Statistical Estimation and Testing 265

Estimation Methods 267

Least-Squares Estimation Method 268

The Maximum Likelihood Estimation Method 278

Instrumental Variables 283

Method of Moments 284

The M-Estimation Method and M-Estimators 289

Key Points 289

CHAPTER 14 Model Selection 291

Physics and Economics: Two Ways of Making Science 291

Model Complexity and Sample Size 293

Data Snooping 296

Survivorship Biases and Other Sample Defects 297

Model Risk 300

Model Selection in a Nutshell 301

Key Points 303

Chapter 15 Formulating and Implementing Investment Strategies Using Financial Econometrics 305

The Quantitative Research Process 307

Investment Strategy Process 314

Key Points 318

Appendix A Descriptive Statistics 321

Basic Data Analysis 321

Measures of Location and Spread 328

Multivariate Variables and Distributions 332

Appendix B Continuous Probability Distributions Commonly Used in Financial Econometrics 343

Normal Distribution 344

Chi-Square Distribution 347

Student’s t-Distribution 349

F-Distribution 352

α-Stable Distribution 353

Appendix C Inferential Statistics 359

Point Estimators 359

Confidence Intervals 369

Hypothesis Testing 372

Appendix D Fundamentals of Matrix Algebra 385

Vectors and Matrices Defined 385

Square Matrices 387

Determinants 388

Systems of Linear Equations 389

Linear Independence and Rank 391

Vector and Matrix Operations 391

Eigenvalues and Eigenvectors 396

APPENDIX E Model Selection Criterion: AIC and BIC 399

Akaike Information Criterion 400

Bayesian Information Criterion 402

Appendix F Robust Statistics 405

Robust Statistics Defined 405

Qualitative and Quantitative Robustness 406

Resistant Estimators 406

M-Estimators 408

The Least Median of Squares Estimator 408

The Least Trimmed of Squares Estimator 409

Robust Estimators of the Center 409

Robust Estimators of the Spread 410

Illustration of Robust Statistics 410

Index 413

FRANK J. FABOZZI is Professor of Finance at EDHEC Business School and Editor of the Journal of Portfolio Management.

SERGIO M. FOCARDI is Visiting Professor of Finance at Stony Brook University and a founding partner of the Paris-based consulting firm The Intertek Group.

SVETLOZAR T. RACHEV is Professor of Finance, College of Business and Center for Finance, Stony Brook University, and Chief-Scientist with FinAnalytica.

BALA G. ARSHANAPALLI is the Gallagher-Mills Chair of Business and Economics at Indiana University Northwest.