## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required ## Book Description

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.

2. Preface
4. 1. Introduction
1. 1.1. PROBABILITY VS. STATISTICS
2. 1.2. OVERVIEW OF THE BOOK
5. I. Descriptive Statistics
1. 2. Basic Data Analysis
1. 2.1. DATA TYPES
2. 2.2. FREQUENCY DISTRIBUTIONS
3. 2.3. EMPIRICAL CUMULATIVE FREQUENCY DISTRIBUTION
4. 2.4. DATA CLASSES
5. 2.5. CUMULATIVE FREQUENCY DISTRIBUTIONS
6. 2.6. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
2. 3. Measures of Location and Spread
1. 3.1. Parameters vs. Statistics
2. 3.2. Center and Location
3. 3.3. Variation
4. 3.4. Measures of the Linear Transformation
5. 3.5. SUMMARY Of Measures
6. 3.6. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
3. 4. Graphical Representation of Data
4. 5. Multivariate Variables and Distributions
5. 6. Introduction to Regression Analysis
1. 6.1. THE ROLE OF CORRELATION
2. 6.2. REGRESSION MODEL: LINEAR FUNCTIONAL RELATIONSHIP BETWEEN TWO VARIABLES
3. 6.3. DISTRIBUTIONAL ASSUMPTIONS OF THE REGRESSION MODEL
4. 6.4. ESTIMATING THE REGRESSION MODEL
5. 6.5. Goodness of Fit of The Model
6. 6.6. LINEAR REGRESSION OF SOME NONLINEAR RELATIONSHIP
7. 6.7. TWO APPLICATIONS IN FINANCE
8. 6.8. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
6. 7. Introduction to Time Series Analysis
1. 7.1. WHAT IS TIME SERIES?
2. 7.2. DECOMPOSITION OF TIME SERIES
3. 7.3. REPRESENTATION OF TIME SERIES WITH DIFFERENCE EQUATIONS
4. 7.4. APPLICATION: THE PRICE PROCESS
1. 7.4.1. Random Walk
2. 7.4.2. Error Correction
5. 7.5. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
6. II. Basic Probability Theory
1. 8. Concepts of Probability Theory
1. 8.1. HISTORICAL Development of ALTERNATIVE Approaches to PROBABILITY
2. 8.2. SET OPERATIONS AND PRELIMINARIES
3. 8.3. PROBABILITY MEASURE
4. 8.4. RANDOM VARIABLE
5. 8.5. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
2. 9. Discrete Probability Distributions
1. 9.1. DISCRETE LAW
1. 9.1.1. Random Variable on the Countable Space
2. 9.1.2. Mean and Variance
2. 9.2. BERNOULLI DISTRIBUTION
3. 9.3. BINOMIAL DISTRIBUTION
4. 9.4. HYPERGEOMETRIC DISTRIBUTION
5. 9.5. MULTINOMIAL DISTRIBUTION
6. 9.6. POISSON DISTRIBUTION
7. 9.7. DISCRETE UNIFORM DISTRIBUTION
8. 9.8. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
3. 10. Continuous Probability Distributions
1. 10.1. CONTINUOUS PROBABILITY DISTRIBUTION DESCRIBED
2. 10.2. Distribution Function
3. 10.3. Density Function
4. 10.4. Continuous Random Variable
5. 10.5. Computing Probabilities from the Density Function
6. 10.6. Location Parameters
7. 10.7. Dispersion Parameters
1. 10.7.1. Moments of Higher Order
8. 10.8. Concepts Explained in this Chapter (In Order of Presentation)
4. 11. Continuous Probability Distributions with Appealing Statistical Properties
1. 11.1. NORMAL DISTRIBUTION
1. 11.1.1. Properties of the Normal Distribution
2. 11.1.2. Applications to Stock Returns
2. 11.2. CHI-SQUARE DISTRIBUTION
3. 11.3. STUDENT'S t-DISTRIBUTION
4. 11.4. F-DISTRIBUTION
5. 11.5. EXPONENTIAL DISTRIBUTION
6. 11.6. RECTANGULAR DISTRIBUTION
7. 11.7. GAMMA DISTRIBUTION
8. 11.8. BETA DISTRIBUTION
9. 11.9. LOG-NORMAL DISTRIBUTION
10. 11.10. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
5. 12. Continuous Probability Distributions Dealing with Extreme Events
6. 13. Parameters of Location and Scale of Random Variables
1. 13.1. Parameters of location
1. 13.1.1. Quantiles
2. 13.1.2. Mode
3. 13.1.3. Mean (First Moment)
2. 13.2. Parameters of scale
1. 13.2.1. Moments of Higher Order
2. 13.2.2. Variance
3. 13.2.3. Standard Deviation
4. 13.2.4. Skewness
5. 13.2.5. Kurtosis
6. 13.2.6. Kurtosis of the GE Daily Returns
3. 13.3. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
4. 13.4. APPENDIX: PARAMETERS FOR VARIOUS DISTRIBUTION FUNCTIONS
7. 14. Joint Probability Distributions
1. 14.1. Higher dimensional random variables
2. 14.2. Joint probability distribution
1. 14.2.1. Discrete Case
2. 14.2.2. Continuous Case
3. 14.3. Marginal distributions
4. 14.4. Dependence
5. 14.5. Covariance and correlation
1. 14.5.1. Discrete Case
2. 14.5.2. Continuous Case
3. 14.5.3. Aspects of the Covariance and Covariance Matrix
4. 14.5.4. Correlation
5. 14.5.5. Criticism of the Correlation and Covariance as a Measure of Joint Randomness
6. 14.6. Selection of multivariate distributions
1. 14.6.1. Multivariate Normal Distribution
2. 14.6.2. Multivariate t-Distribution
3. 14.6.3. Elliptical Distributions
7. 14.7. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
8. 15. Conditional Probability and Bayes' Rule
1. 15.1. Conditional Probability
1. 15.1.1. Formula for Conditional Probability
2. 15.2. Independent Events
3. 15.3. Multiplicative Rule of Probability
4. 15.4. Bayes' Rule
5. 15.5. Conditional Parameters
6. 15.6. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
9. 16. Copula and Dependence Measures
1. 16.1. Copula
1. 16.1.1. Construction of the Copula
2. 16.1.2. Specifications of the Copula
3. 16.1.3. Properties of the Copula
4. 16.1.4. Simulation of Financial Returns Using the Copula
5. 16.1.5. The Copula for Two Dimensions
6. 16.1.6. Simulation with the Gaussian Copula (d = 2)
2. 16.2. Alternative dependence measures
1. 16.2.1. Rank Correlation Measures
2. 16.2.2. Tail Dependence
3. 16.3. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
7. III. Inductive Statistics
1. 17. Point Estimators
1. 17.1. SAMPLE, STATISTIC, AND ESTIMATOR
2. 17.2. QUALITY CRITERIA OF ESTIMATORS
3. 17.3. LARGE SAMPLE CRITERIA
4. 17.4. MAXIMUM LIKEHOOD ESTIMATOR
5. 17.5. Exponential family and sufficiency
6. 17.6. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
2. 18. Confidence Intervals
3. 19. Hypothesis Testing
1. 19.1. Hypotheses
1. 19.1.1. Setting Up the Hypotheses
2. 19.1.2. Decision Rule
2. 19.2. Error Types
3. 19.3. Quality criteria of a test
1. 19.3.1. Power of a Test
2. 19.3.2. Unbiased Test
3. 19.3.3. Consistent Test
4. 19.4. Examples
5. 19.5. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
8. IV. Multivariate Linear Regression Analysis
1. 20. Estimates and Diagnostics for Multivariate Linear Regression Analysis
1. 20.1. THE MULTIVARIATE LINEAR REGRESSION MODEL
2. 20.2. ASSUMPTIONS OF THE Multivariate LINEAR REGRESSION MODEL
3. 20.3. ESTIMATION OF THE MODEL PARAMETERS
4. 20.4. DESIGNING THE MODEL
5. 20.5. DIAGNOSTIC CHECK AND MODEL SIGNIFICANCE
6. 20.6. APPLICATIONS TO FINANCE
7. 20.7. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
2. 21. Designing and Building a Multivariate Linear Regression Model
1. 21.1. THE PROBLEM OF MULTICOLLINEARITY
2. 21.2. INCORPORATING DUMMY VARIABLES AS INDEPENDENT VARIABLES
3. 21.3. MODEL BUILDING TECHNIQUES
4. 21.4. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
3. 22. Testing the Assumptions of the Multivariate Linear Regression Model
1. 22.1. TESTS FOR LINEARITY
2. 22.2. ASSUMED STATISTICAL PROPERTIES ABOUT THE ERROR TERM
3. 22.3. TESTS FOR THE RESIDUALS BEING NORMALLY DISTRIBUTED
4. 22.4. TESTS FOR CONSTANT VARIANCE OF THE ERROR TERM (HOMOSKEDASTICITY)
1. 22.4.1. Modeling to Account for Heteroskedasticity
5. 22.5. ABSENCE OF AUTOCORRELATION OF THE RESIDUALS
6. 22.6. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
9. A. Important Functions and Their Features
1. A.1. CONTINUOUS FUNCTION
2. A.2. INDICATOR FUNCTION
3. A.3. DERIVATIVES
4. A.4. MONOTONIC FUNCTION
5. A.5. INTEGRAL
1. A.5.1. Approximation of the Area through Rectangles
2. A.5.2. Relationship Between Integral and Derivative
6. A.6. SOME FUNCTIONS
10. B. Fundamentals of Matrix Operations and Concepts
1. B.1. THE NOTION OF VECTOR AND MATRIX
2. B.2. MATRIX MULTIPLICATION
3. B.3. PARTICULAR MATRICES
4. B.4. POSITIVE SEMIDEFINITE MATRICES
11. C. Binomial and Multinomial Coefficients
1. C.1. Binomial Coefficient
1. C.1.1. Derivation of the Binomial Coefficient
2. C.2. Multinomial Coefficient
12. D. Application of the Log-Normal Distribution to the Pricing of Call Options
13. References