A comprehensive look at how probability and statistics is applied
to the investment process

Finance has become increasingly more quantitative, drawing on
techniques in probability and statistics that many finance
practitioners have not had exposure to before. In order to keep up,
you need a firm understanding of this discipline.

Probability and Statistics for Finance addresses this issue
by showing you how to apply quantitative methods to portfolios, and
in all matter of your practices, in a clear, concise manner.
Informative and accessible, this guide starts off with the basics
and builds to an intermediate level of mastery.

• Outlines an array of topics in
  probability and statistics and how to apply them in the world of
  finance

• Includes detailed discussions of
  descriptive statistics, basic probability theory, inductive
  statistics, and multivariate analysis

• Offers real-world illustrations of the
  issues addressed throughout the text

  The authors cover a wide range of topics in this book, which can be
  used by all finance professionals as well as students aspiring to
  enter the field of finance.

  Autorentext

SVETLOZAR T. RACHEV, PhD, DSC, is Chair Professor at the University of Karlsruhe in the School of Economics and Business Engineering, and Professor Emeritus at the University of California, Santa Barbara, in the Department of Statistics and Applied Probability. He was cofounder of Bravo Risk Management Group, acquired by FinAnalytica, where he currently serves as Chief Scientist.

MARKUS HÖCHSTÖTTER, PhD, is an Assistant Professor in the Department of Econometrics and Statistics, University of Karlsruhe.

FRANK J. FABOZZI, PhD, CFA, CPA, is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of Portfolio Management. He is an Affiliated Professor at the University of Karlsruhe's Institute of Statistics, Econometrics and Mathematical Finance, and is on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University.

SERGIO M. FOCARDI, PhD, is a Professor of Finance at EDHEC Business School and founding partner of the Paris-based consulting firm Intertek Group plc.

Klappentext

The recent upheaval of the global financial system has enhanced the need for improved statistical tools for financial modeling and analysis. To fill that need, expert authors Svetlozar Rachev, Markus Höchstötter, Frank Fabozzi, and Sergio Focardi have written Probability and Statistics for Finance.

Filled with in-depth insights and practical advice, this book guides readers from the basic elements of probability and statistics to the most advanced topics. Along the way, it covers everything from the application of probability to portfolio management, asset pricing, risk management, and credit risk modeling to probability distributions that deal with extreme events and statistical measures.

This book:

• Outlines an array of topics in probability and statistics and how to apply them in the world of finance

• Offers detailed discussions of descriptive statistics, basic probability theory, inductive statistics, and multivariate analysis

• Provides real-world illustrations of the issues addressed throughout the text

• And much more

  Written with financial professionals, academics, and aspiring students in mind, Probability and Statistics for Finance has what you need to stay current and succeed in this fast-moving field.

  Zusammenfassung
  A comprehensive look at how probability and statistics is applied to the investment process

  Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before. In order to keep up, you need a firm understanding of this discipline.
  Probability and Statistics for Finance addresses this issue by showing you how to apply quantitative methods to portfolios, and in all matter of your practices, in a clear, concise manner. Informative and accessible, this guide starts off with the basics and builds to an intermediate level of mastery.
  • Outlines an array of topics in probability and statistics and how to apply them in the world of finance
  • Includes detailed discussions of descriptive statistics, basic probability theory, inductive statistics, and multivariate analysis
  • Offers real-world illustrations of the issues addressed throughout the text
  The authors cover a wide range of topics in this book, which can be used by all finance professionals as well as students aspiring to enter the field of finance.

  Inhalt

Preface xv

About the Authors xvii

Chapter 1 Introduction 1

Probability vs. Statistics 4

Overview of the Book 5

Part One Descriptive Statistics 15

Chapter 2 Basic Data Analysis 17

Data Types 17

Frequency Distributions 22

Empirical Cumulative Frequency Distribution 27

Data Classes 32

Cumulative Frequency Distributions 41

Concepts Explained in this Chapter 43

Chapter 3 Measures of Location and Spread 45

Parameters vs. Statistics 45

Center and Location 46

Variation 59

Measures of the Linear Transformation 69

Summary of Measures 71

Concepts Explained in this Chapter 73

Chapter 4 Graphical Representation of Data 75

Pie Charts 75

Bar Chart 78

Stem and Leaf Diagram 81

Frequency Histogram 82

Ogive Diagrams 89

Box Plot 91

QQ Plot 96

Concepts Explained in this Chapter 99

Chapter 5 Multivariate Variables and Distributions 101

Data Tables and Frequencies 101

Class Data and Histograms 106

Marginal Distributions 107

Graphical Representation 110

Conditional Distribution 113

Conditional Parameters and Statistics 114

Independence 117

Covariance 120

Correlation 123

Contingency Coefficient 124

Concepts Explained in this Chapter 126

Chapter 6 Introduction to Regression Analysis 129

The Role of Correlation 129

Regression Model: Linear Functional Relationship Between Two Variables 131

Distributional Assumptions of the Regression Model 133

Estimating the Regression Model 134

Goodness of Fit of the Model 138

Linear Regression of Some Nonlinear Relationship 140

Two Applications in Finance 142

Concepts Explained in this Chapter 149

Chapter 7 Introduction to Time Series Analysis 153

What Is Time Series? 153

Decomposition of Time Series 154

Representation of Time Series with Difference Equations 159

Application: The Price Process 159

Concepts Explained in this Chapter 163

Part Two Basic Probability Theory 165

Chapter 8 Concepts of Probability Theory 167

Historical Development of Alternative Approaches to Probability 167

Set Operations and Preliminaries 170

Probability Measure 177

Random Variable 179

Concepts Explained in this Chapter 185

Chapter 9 Discrete Probability Distributions 187

Discrete Law 187

Bernoulli Distribution 192

Binomial Distribution 195

Hypergeometric Distribution 204

Multinomial Distribution 211

Poisson Distribution 216

Discrete Uniform Distribution 219

Concepts Explained in this Chapter 221

Chapter 10 Continuous Probability Distributions 229

Continuous Probability Distribution Described 229

Distribution Function 230

Density Function 232

Continuous Random Variable 237

Computing Probabilities from the Density Function 238

Location Parameters 239

Dispersion Parameters 239

Concepts Explained in this Chapter 245

Chapter 11 Continuous Probability Distributions with Appealing Statistical Properties 247

Normal Distribution 247

Chi-Square Distribution 254

Student's t-Distribution 256

F-Distribution 260

Exponential Distribution 262

Rectangular Distribution 266

Gamma Distribution 268

Beta Distribution 269

Log-Normal Distribution 271 Concepts Expl…