A course on statistics for finance /

Taking a data-driven approach, A Course on Statistics for Finance presents statistical methods for financial investment analysis. The author introduces regression analysis, time series analysis, and multivariate analysis step by step using models and methods from finance. The book begins with a revi...

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Bibliographic Details
Main Author:	Sclove, Stanley L.
Corporate Author:	Taylor & Francis
Format:	eBook
Language:	English
Published:	Boca Raton, Fla. ; London : CRC Press, c2013.
Subjects:	Finance > Statistical methods. Investment analysis > Statistical methods. Finances > Méthodes statistiques. Analyse financière > Méthodes statistiques. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

I INTRODUCTORY CONCEPTS AND DEFINITIONS
1 Review of Basic Statistics
1.1 What Is Statistics?
1.1.1 Data Are Observations
1.1.2 Statistics Are Descriptions; Statistics Is Methods
1.1.3 Origins of Data
1.1.4 Philosophy of Data and Information
1.1.4.1 Data versus Information
1.1.4.2 Decisions
1.2 Characterizing Data
1.2.1 Types of Data
1.2.1.1 Modes and Ways
1.2.1.2 Types of Variables
1.2.1.3 Cross-Sectional Data versus Time Series Data
1.2.2 Raw Data versus Derived Data
1.2.2.1 Ratios
1.2.2.2 Indices
1.3 Measures of Central Tendency
1.3.1 Mode
1.3.2 Measuring the Center of a Set of Numbers
1.3.2.1 Median
1.3.2.2 Quartiles
1.3.2.3 Percentiles
1.3.2.4 Section Exercises
1.3.2.5 Mean
1.3.2.6 Other Properties of the Ordinary Arithmetic Average
1.3.2.7 Mean of a Distribution
1.3.3 Other Kinds of Averages
1.3.3.1 Root Mean Square
1.3.3.2 Other Averages
1.3.4 Section Exercises
1.4 Measures of Variability
1.4.1 Measuring Spread
1.4.1.1 Positional Measures of Spread
1.4.1.2 Range
1.4.1.3 IQR
1.4.2 Distance-Based Measures of Spread
1.4.2.1 Deviations from the Mean
1.4.2.2 Mean Absolute Deviation
1.4.2.3 Root Mean Square Deviation
1.4.2.4 Standard Deviation
1.4.2.5 Variance of a Distribution
1.5 Higher Moments
1.6 Summarizing Distributions
1.6.1 Partitioning Distributions
1.6.2 Moment-Preservation Method
1.7 Bivariate Data
1.7.1 Covariance and Correlation
1.7.1.1 Computational Formulas
1.7.1.2 Covariance, Regression Cooefficient, and Correlation Coefficient
1.7.2 Covariance of a Bivariate Distribution
1.8 Three Variables
1.8.1 Pairwise Correlations
1.8.2 Partial Correlation
1.9 Two-Way Tables
1.9.1 Two-Way Tables of Counts
1.9.2 Turnover Tables
1.9.3 Seasonal Data
1.9.3.1 Data Aggregation
1.9.3.2 Stable Seasonal Pattern
1.10 Summary
1.11 Chapter Exercises
1.11.1 Applied Exercises
1.11.2 Mathematical Exercises
1.12 Bibliography
2 Stock Price Series and Rates of Return
2.1 Introduction
2.1.1 Price Series
2.1.2 Rates of Return
2.1.2.1 Continuous ROR and Ordinary ROR
2.1.2.2 Advantages of Continuous ROR
2.1.2.3 Modeling Price Series
2.1.3 Review of Mean, Variance, and Standard Deviation
2.1.3.1 Mean
2.1.3.2 Variance
2.1.3.3 Standard Deviation
2.2 Ratios of Mean and Standard Deviation
2.2.1 Coefficient of Variation
2.2.2 Sharpe Ratio
2.3 Value-at-Risk
2.3.1 VaR for Normal Distributions
2.3.2 Conditional VaR
2.4 Distributions for RORs
2.4.1 t Distribution as a Scale-Mixture of Normals
2.4.2 Another Example of Averaging over a Population
2.4.3 Section Exercises
2.5 Summary
2.6 Chapter Exercises
2.7 Bibliography
2.8 Further Reading.
3 Several Stocks and Their Rates of Return
3.1 Introduction
3.2 Review of Covariance and Correlation
3.3 Two Stocks
3.3.1 RORs of Two Stocks
3.3.2 Section Exercises
3.4 Three Stocks
3.4.1 RORs of Three Stocks
3.4.2 Section Exercises
3.5 m Stocks
3.5.1 RORs for m Stocks
3.5.2 Parameters and Statistics for m Stocks
3.6 Summary
3.7 Chapter Exercises
3.8 Bibliography
3.9 Further Reading
II REGRESSION
4 Simple Linear Regression; CAPM and Beta
4.1 Introduction
4.2 Simple Linear Regression
4.2.1 Data
4.2.2 An Introductory Example
4.3 Estimation
4.3.1 Method of Least Squares
4.3.1.1 Least Squares Criterion
4.3.1.2 Least Squares Estimator
4.3.2 Maximum Likelihood Estimator under the Assumption of Normality
4.3.3 A Heuristic Approach
4.3.3.1 Observational Equations
4.3.3.2 Method of Reduction of Observations
4.3.4 Means and Variances of Estimators
4.3.4.1 Means of Estimators
4.3.4.2 Unbiasedness
4.3.4.3 Variance of the Least Squares Estimator
4.3.4.4 Nonlinear and Biased Estimators
4.3.5 Estimating the Error Variance
4.3.5.1 Computational Formulas
4.3.5.2 Decomposition of Sum of Squares
4.4 Inference Concerning the Slope
4.4.1 Testing a Hypothesis Concerning the Slope
4.4.2 Confidence Interval
4.5 Testing Equality of Slopes of Two Lines through the Origin
4.6 Linear Parametric Functions
4.7 Variances Dependent upon X
4.8 A Financial Application: CAPM and Beta
4.8.1 CAPM
4.8.2 Beta
4.9 Slope and Intercept
4.9.1 Model with Slope and Intercept
4.9.2 CAPM with Differential Return
4.10 Appendix 4A: Optimality of the Least Squares Estimator
4.11 Summary
4.12 Chapter Exercises
4.12.1 Applied Exercises
4.12.2 Mathematical Exercises
4.13 Bibliography
4.14 Further Reading
5 Multiple Regression and Market Models
5.1 Multiple Regression Models
5.1.1 Regression Function
5.1.2 Method of Least Squares
5.1.3 Types of Explanatory Variables
5.2 Market Models
5.2.1 Fama/French Three-Factor Model
5.2.2 Four-Factor Model
5.3 Models with Numerical and Dummy Explanatory Variables
5.3.1 Two-Group Models
5.3.2 Other Market Models
5.3.2.1 Two Betas
5.3.2.2 More Advanced Models
5.4 Model Building
5.4.1 Principle of Parsimony
5.4.2 Model-Selection Criteria
5.4.2.1 Residual Mean Square
5.4.2.2 Adjusted R-Square
5.4.3 Testing a Reduced Model against a Full Model
5.4.4 Comparing Several Models
5.4.5 Combining Results from Several Models
5.5 Chapter Summary
5.6 Chapter Exercises
5.6.1 Exercises for Two Explanatory Variables
5.6.2 Mathematical Exercises: Two Explanatory Variables
5.6.3 Mathematical Exercises: Three Explanatory Variables
5.6.4 Exercises on Subset Regression
5.6.5 Mathematical Exercises: Subset Regression
5.7 Bibliography
III PORTFOLIO ANALYSIS
6 Mean-Variance Portfolio Analysis
6.1 Introduction
6.1.1 Mean-Variance Portfolio Analysis
6.1.2 Single-Criterion Analysis
6.2 Two Stocks
6.2.1 Mean
6.2.2 Variance
6.2.3 Covariance and Correlation
6.2.4 Portfolio Variance
6.2.4.1 Variance of a Sum; Variance of a Difference
6.2.4.2 Portfolio Variance
6.2.5 Minimum Variance Portfolio
6.3 Three Stocks
6.4 m Stocks
6.5 m Stocks and a Risk-Free Asset
6.5.1 Admissible Points
6.5.2 Capital Allocation Lines
6.6 Value-at-Risk
6.6.1 VaR for Normal Distributions
6.6.2 Conditional VaR
6.7 Selling Short
6.8 Market Models and Beta
6.8.1 CAPM
6.8.2 Computation of Covariances under the CAPM
6.8.3 Section Exercises
6.9 Summary
6.9.1 Rate of Return
6.9.2 Bi-Criterion Analysis
6.9.3 Market Models
6.10 Chapter Exercises
6.10.1 Exercises on Covariance and Correlation
6.10.2 Exercises on Portfolio ROR
6.10.3 Exercises on Three Stocks
6.10.4 Exercises on Correlation and Regression
6.11 Appendix 6A: Some Results in Terms of Vectors and Matrices (Optional)
6.11.1 Variates
6.11.2 Vector Differentiation
6.11.2.1 Some Rules for Vector Differentiation
6.11.2.2 Minimum-Variance Portfolio
6.11.2.3 Maximum Sharpe Ratio
6.11.3 Section Exercises
6.12 Appendix 6B: Some Results for the Family of Normal Distributions
6.12.1 Moment Generating Function; Moments
6.12.2 Section Exercises
6.13 Bibliography
6.14 Further Reading.
9 Regime Switching Models
9.1 Introduction
9.2 Bull and Bear Markets
9.2.1 Definitions of Bull and Bear Markets
9.2.2 Regressions on Bull3
9.2.2.1 Two Betas, No Alpha
9.2.2.2 Two Betas, One Alpha
9.2.2.3 Two Betas, Two Alphas
9.2.3 Other Models for Bull/Bear
9.2.3.1 Two Means and Two Variances
9.2.3.2 Mixture Model
9.2.3.3 Hidden Markov Model
9.2.4 Bull and Bear Portfolios
9.3 Summary
9.4 Chapter Exercises
9.4.1 Applied Exercises
9.4.2 Mathematical Exercises
9.5 Bibliography
9.6 Further Reading
Appendix A Vectors and Matrices
A.1 Introduction
A.2 Vectors
A.2.1 Inner Product of Two Vectors
A.2.2 Orthogonal Vectors
A.2.3 Variates
A.2.4 Section Exercises
A.3 Matrices
A.3.1 Entries of a Matrix
A.3.2 Transpose of a Matrix
A.3.3 Matrix Multiplication
A.3.4 Section Exercises 219 (1) A.3.5 Identity Matrix 220 (1) A.3.6 Inverse 220 (1) A.3.6.1 Inverse of a Matrix 220 (1) A.3.6.2 Inverse of a Product of Matrices 220 (1) A.3.7 Determinant 221 (1) A.4 Vector Differentiation 221 (1) A.5 Paths 221 (1) A.6 Quadratic Forms 222 (1) A.7 Eigensystem 222 (1) A.8 Transformation to Uncorrelated Variables 223 (2) A.8.1 Covariance Matrix of a Linear Transformation of a Random Vector 223 (1) A.8.2 Transformation to Uncorrelated Variables 224 (1) A.8.3 Transformation to Uncorrelated Variables with Variances Equal to One 224 (1) A.9 Statistical Distance 225 (1) A.10 Appendix Exercises 225 (1) A.11 Bibliography 226 (1) A.12 Further Reading 227 (2) Appendix B Normal Distributions 229 (10) B.1 Some Results for Univariate Normal Distributions 229 (2) B.1.1 Definitions 229 (1) B.1.2 Conditional Expectation 230 (1) B.1.3 Tail Probability Approximation 231 (1) B.2 Family of Multivariate Normal Distributions 231 (1) B.3 Role of D-Square 232 (1) B.4 Bivariate Normal Distributions 232 (2) B.4.1 Shape of the pagesd.f. 233 (1) B.4.2 Conditional Distribution of Y Given X 233 (1) B.4.3 Regression Function 233 (1) B.5 Other Multivariate Distributions 234 (1) B.6 Summary 234 (1) B.6.1 Concepts 235 (1) B.6.2 Mathematics 235 (1) B.7 Appendix B Exercises 235 (1) B.7.1 Applied Exercises 235 (1) B.7.2 Mathematical Exercises 236 (1) B.8 Bibliography 236 (1) B.9 Further Reading 237 (2) Appendix C Lagrange Multipliers 239 (4) C.1 Notation 239 (1) C.2 Optimization Problem 239 (1) C.3 Bibliography 240 (1) C.4 Further Reading 241 (2) Appendix D Abbreviations and Symbols 243 (4) D.1 Abbreviations 243 (1) D.1.1 Statistics 243 (1) D.1.2 General 243 (1) D.1.3 Finance 244 (1) D.2 Symbols 244 (3) D.2.1 Statistics 244 (1) D.2.2 Finance 245 (2) Index.