Essentials of Excel VBA, Python, and R: Volume I: Financial Statistics and Portfolio Analysis

Preface
Contents
1 Introduction
1.1 Introduction
1.2 Microsoft Excel 2019 Versus Microsoft Excel 365
1.3 Power Query
1.4 Microsoft Excel and Power Query
1.5 Microsoft Excel 64-Bit Versus Microsoft Excel 32-Bit
1.5.1 Microsoft Excel 64-Bit and Power Query
1.6 Statistical Environment of Microsoft Excel 365
1.7 Python Programming Language
1.7.1 Python Libraries for Statistics
1.7.2 Python Development Environment
1.7.2.1 Google Colaboratory
1.7.2.2 Visual Studio Code
1.8 R Programming Language
1.9 Web Scraping for Market and Financial Data
1.9.1 Microsoft Excel Power Query
1.10 Case Study, Google Study, and Active Study Approach
1.11 Structure of the Book
Bibliography
Financial Statistics
2 Data Collection, Presentation, and Yahoo! Finance
2.1 Introduction
2.2 Data Presentation
2.3 Yahoo! Finance
2.4 Market Indexes
2.4.1 Dow Jones Industrial Average
2.4.2 S&P 500
2.4.3 NASDAQ
2.5 JSON Data Format
2.5.1 Quandl Data Provider
2.5.1.1 JSON Data Format
Pretty JSON Data Format
2.5.1.2 RAW JSON Data Format
2.5.1.3 XML Data Format
2.6 Ticker Attributes
2.6.1 Yahoo! Finance API
2.6.1.1 Power Query
2.6.1.2 Power Query M Code
2.6.1.3 Microsoft Excel Ticker Attribute Template
Amazon Ticker Attributes
Johnson and Johnson Ticker Attributes
2.7 Historical Data
2.7.1 Yahoo! Finance API
2.7.2 Epoch Time
2.7.3 Power Query
2.7.3.1 Date Query
Custom Query Column
Index Column
2.7.3.2 Price Query
Index Column
2.7.3.3 Merge Query
2.7.3.4 Load Data to Microsoft Excel Worksheets
2.7.4 Python
2.7.4.1 Python Libraries
2.7.4.2 PIP Python Command to Install Libraries
2.7.4.3 Python Code
2.7.4.4 Python Output
2.8 Charting Historical Data
2.8.1 Microsoft Excel 365 Chart Wizard
2.8.2 Power Query M Code
2.9 Using Python to Graph Johnson & Johnson’s Historical Prices
2.10 Summary
Bibliography
3 Histograms, Rate of Returns, and Financial Statements
3.1 Introduction
3.2 Rate of Return
3.2.1 Power Query
3.2.1.1 Monthly Historical Prices
3.2.1.2 Ascending Date Order
3.2.1.3 Adding Index Columns
3.2.1.4 Index Column Records
3.2.1.5 Rate of Return
3.2.2 Dynamic Power Query
3.2.3 Python
3.2.3.1 Code
3.2.3.2 Output
3.3 Histograms
3.3.1 Sturge’s Rule
3.3.2 Microsoft Excel
3.3.2.1 Frequency Function
3.3.2.2 Quick Analysis
Formatting Histogram
Dynamic Chart Title
Axis
3.3.2.3 Excel Histogram Template
3.4 Using Python to Create Johnson & Johnson’s Rate of Return Histogram
3.4.1 Code
3.4.2 Output
3.5 Financial Statements
3.5.1 Power Query
3.5.1.1 Balance Sheet
2020 Balance Sheet
2019 Balance Sheet
2018 Balance Sheet
Combined Balance Sheet
3.5.1.2 Income Statement
Combined Income Statement
3.5.1.3 Cash Flow Statement
Combined Cash Flow Statement
3.5.2 Python
3.5.2.1 Code
3.5.2.2 Output
Balance Sheet
Income Statement
Cash Flow
3.6 Summary
Bibliography
4 Numerical Summary Measures on Rate of Returns of Stocks and Market Indexes
4.1 Introduction
4.1.1 Summary Measures Excel Workbook
4.1.2 Summary Worksheet
4.1.2.1 Numerical Summary Measures
4.1.2.2 Histograms of Rate of Returns
4.1.2.3 Excel Formulas
4.1.2.4 Ticker2, Ticker3 Worksheets
M Code
Yahoo! Finance API
4.1.2.5 Ticker1 Worksheets
4.1.2.6 Data Refresh All
4.2 Measure of Central Tendency
4.2.1 Arithmetic Mean (Average)
4.2.2 Annualized Monthly Returns
4.2.3 Median
4.2.4 Excel Functions
4.3 Measure of Dispersion
4.3.1 Variance
4.3.2 Annualized Monthly Variance
4.3.3 Standard Deviation
4.3.4 Annualized Monthly Standard Deviation
4.3.5 Coefficient of Variation
4.3.6 Excel Functions
4.4 Measure of Relative Position
4.4.1 Quartiles
4.4.2 Interquartile
4.4.3 Outliers
4.4.4 Z-Score
4.4.5 Excel Functions
4.5 Measure of Shape
4.5.1 Skewness
4.5.2 Kurtosis
4.5.3 Excel Functions
4.6 Measure of Linear Relationship
4.6.1 Coefficient of Correlation
4.6.2 Excel Functions
4.7 Box and Whisker Plot
4.7.1 Outliers
4.7.2 Extreme Outliers
4.7.3 Vertical Whiskers
4.7.4 Median and Mean
4.8 Excel Rate of Return Box and Whisker Workbook
4.8.1 Summary Worksheet
4.8.2 Ticker1, Ticker2, Ticker3 Worksheets
4.8.3 Ticker123 Worksheet
4.9 Creating Box and Whisker Plot in Excel
4.9.1 Single Box and Whisker Plot
4.9.2 Combined Box and Whisker Plot
4.10 Using Python to Calculate the 5-Year Numerical Measures of the Rate of Return of AAPL, MSFT, and the S&P 500
4.11 Summary
Bibliography
5 Probability Concepts and Their Analysis
5.1 Introduction
5.2 Data Presentation
5.3 Probability
5.3.1 Probability Simulation with Excel VBA
5.3.1.1 Probability Simulation Excel Workbook
5.3.1.2 Excel VBA Code
5.3.2 Probability Simulation in R
5.3.3 Probability Simulation in Python
5.3.3.1 Code
5.3.3.2 Output
5.4 Combinations
5.4.1 Combination List with Excel VBA
5.4.2 Combination List with R
5.5 Permutations
5.5.1 Permutation List with Excel VBA
5.5.2 Permutation List with R
5.6 Summary
Bibliography
6 Discrete Random Variables and Probability Distributions
6.1 Introduction and Probability Distribution
6.2 Cumulative Probability Distribution
6.3 Binomial Distribution
6.3.1 Binomial Distribution in Excel
6.3.2 Binomial Distribution in R
6.3.3 Binomial Distribution in Python
6.4 Poisson Random Variable
6.4.1 Poisson Distribution in Excel
6.4.2 Poisson Distribution in R
6.4.3 Poisson Distribution in Python
6.5 Excel 4.0 Macro Functions and Excel Names
6.6 Examples
6.6.1 Files Function
6.6.1.1 Get.CELLS Function
6.6.1.2 EVALUATE Function
6.7 Stephen Bullen’s Charting Method
6.7.1 Binomial Distribution
6.7.2 Poisson Distribution
6.8 Summary
Bibliography
7 Normal and Lognormal Distributions
7.1 Introduction
7.2 Uniform Distribution
7.2.1 Uniform Distribution in R
7.3 Normal Distribution
7.3.1 Normal Distribution in R
7.3.2 Normal Distribution in Python
7.4 Standard Normal Distribution
7.4.1 Standard Normal Distribution in R
7.4.2 Standard Normal Distribution in Excel
7.5 Lognormal Distribution
7.5.1 Lognormal Distribution in R
7.5.2 Lognormal Distribution in Python
7.6 Normal Quantile–Quantile (QQ) Plot in Excel
7.7 Normal Quantile–Quantile (QQ) Plot in Python
7.8 Summary
Bibliography
8 Sampling Distributions and Central Limit Theorem
8.1 Introduction
8.2 Sample Distribution in Excel
8.3 Mean of Sample Distribution Equals Mean of Population
8.4 Sample Distribution in Python
8.5 Central Limit Theorem
8.5.1 Uniform Distribution in R
8.5.1.1 Sample Size = 5, 300 Samples
8.5.1.2 Sample Size = 10, 300 Samples
8.5.1.3 Sample Size = 30, 300 Samples
8.5.1.4 Sample Size = 50, 300 Samples
8.5.2 Normal Distribution in R
8.5.2.1 Sample Size = 5, 300 Samples
8.5.2.2 Sample Size = 10, 300 Samples
8.5.2.3 Sample Size = 30, 300 Samples
8.5.2.4 Sample Size = 50, 300 Samples
8.5.3 Lognormal Distribution in R
8.5.3.1 Sample Size = 5, 300 Samples
8.5.3.2 Sample Size = 10, 300 Samples
8.5.3.3 Sample Size = 30, 300 Samples
8.5.3.4 Sample Size = 50, 300 Samples
8.5.4 Binomial Distribution in R
8.5.4.1 Sample Size = 5, 300 Samples
8.5.4.2 Sample Size = 10, 300 Samples
8.5.4.3 Sample Size = 30, 300 Samples
8.5.4.4 Sample Size = 50, 300 Samples
8.5.5 Poisson Distribution in R
8.5.5.1 Sample Size = 5, 300 Samples
8.5.5.2 Sample Size = 10, 300 Samples
8.5.5.3 Sample Size = 30, 300 Samples
8.5.5.4 Sample Size = 50, 300 Samples
8.6 Summary
Bibliography
9 Other Continuous Distributions
9.1 Introduction
9.2 t-Distribution
9.2.1 t-Distribution in R
9.2.2 t-Distribution in Python
9.2.3 Student’s t-Distribution in Excel
9.3 Chi-Square (χ2) Distribution
9.3.1 Chi-Square (χ2) Distribution in R
9.3.2 Chi-Square (χ2) Distribution in Python
9.3.3 Chi-Square (χ2) Distribution in Excel
9.4 F-Distribution
9.4.1 F-Distribution in R
9.4.2 F-Distribution in Python
9.4.3 F-Distribution in Excel
9.5 Exponential Distribution
9.5.1 Exponential Probability Density Function in Excel
9.5.2 Exponential Cumulative Density Function in Excel
9.6 Summary
Bibliography
10 Estimation
10.1 Introduction
10.2 Confidence Interval Simulation in Python
10.2.1 Python Code
10.2.2 Confidence Interval Simulation Data
10.3 Interval Estimates for μ When σ2 is Known
10.3.1 Z Confidence Intervals
10.3.1.1 Example A
10.3.1.2 Example B
10.3.1.3 Example C
10.3.1.4 Example D
10.4 Confidence Intervals for μ When σ2 is Unknown
10.4.1 T Confidence Intervals
10.4.1.1 Example E
10.4.1.2 Example F
10.5 Confidence Intervals for the Population Proportion
10.5.1 Example G
10.5.2 Example H
10.5.3 Example I
10.5.4 Example J
10.6 Confidence Intervals for the Variance
10.6.1 Example K
10.7 Summary
Bibliography
11 Hypothesis Testing
11.1 Introduction
11.2 One-Tailed Tests of Mean for Large Samples
11.2.1 Example 11.1
11.3 Z-Test
11.4 Hypothesis Testing and the p-Value
11.4.1 Example 11.2
11.5 One-Tailed Tests of Mean for Large Samples: Two-Sample Test of Means
11.5.1 Example 11.3
11.6 Two-Tailed Tests of Mean for Large Samples
11.6.1 Example 11.4
11.6.2 Example 11.5
11.7 One-Tailed Tests of Mean for Small Samples
11.7.1 Example 11.6
11.8 Hypothesis Testing for a Population Proportion
11.8.1 Example 11.7
11.9 The Power of a Test and Power Function
11.9.1 Example 11.8
11.10 Power and Sample Size
11.11 Power and Alpha Size
11.12 Comparing the Average EPS of AAPL and MSFT in Python
11.13 Summary
Bibliography
12 Analysis of Variance and Chi-Square Tests
12.1 Introduction
12.2 One-Way Analysis of Variance
12.2.1 Example 12.1
12.2.1.1 Box Plot
12.2.1.2 One-Way Analysis of Variance
12.2.1.3 95% Confidence Interval for Mean
12.2.2 Example 12.2
12.2.2.1 Box Plot
12.2.2.2 One-Way Analysis of Variance
12.2.2.3 95% Confidence Interval for Mean
12.3 Two-Way Analysis of Variance
12.3.1 Example 12.3
12.3.1.1 Two-Way Analysis of Variance
12.4 Chi-Square Test
12.5 Goodness of Fit
12.5.1 Example 12.4
12.6 Test of Independence
12.6.1 Example 12.5
12.7 Using the Chi-Square Test and Python to Determine if the Rate of Return of Apple Inc. Is a Normal Distribution
12.8 Summary
Bibliography
13 Simple Linear Regression and the Correlation Coefficient
13.1 Introduction
13.2 Regression Analysis
13.3 Retrieving Data Using Power Query
13.4 Combining Power Query Data Sets
13.5 Scatter Chart
13.6 Deterministic Relationship and Stochastic Relationship
13.7 Least Square Method
13.8 Standard Assumptions for Linear Regression
13.9 Standard Error of Estimate
13.10 The Coefficient of Determination
13.11 Correlation Coefficient
13.12 Regression Analysis in Excel
13.12.1 Correlation and Coefficient of Determination
13.12.2 Regression Line
13.12.3 Residuals of the Regression Line
13.12.4 Fit Plot of the Data Set
13.13 INTERCEPT and SLOPE Excel Functions
13.14 Oil and Gasoline Regression Analysis in Python
13.15 Summary
Bibliography
14 Simple Linear Regression and Correlation: Analyses and Applications
14.1 Introduction
14.2 Standard Error of Estimate
14.3 Two-Tailed t-Test for β
14.4 Two-Tailed t-Test for α
14.5 Confidence Interval of β
14.6 F Test
14.7 The Relationship Between the F-Test and the t-Test
14.8 Market Model
14.9 Yahoo! Finance Beta Screener
14.10 Historical Monthly Data from Yahoo! Finance
14.10.1 Excel’s Import Text Wizard
14.11 Market Model of Apple Inc. in Excel
14.11.1 Data Analysis and Regression Report
14.11.2 Yahoo! Finance Beta and Power Query
14.11.3 Yahoo! Finance Ticker Historical Data
14.11.4 Yahoo! Finance S&P500 Historical Data
14.11.5 Calculating Rate of Return
14.11.5.1 Dynamic Arrays
14.11.6 Date, Time, and Epoch Time
14.11.6.1 Epoch Unix Time
14.11.6.2 New York Time and UTC Offset
14.11.7 Converting to and from Epoch Time
14.11.7.1 Converting to Epoch Time
14.11.7.2 Converting from Epoch Time
14.11.8 Other Power Queries
14.11.8.1 TickerSummary1
14.11.8.2 TickerDescription
14.11.8.3 SP500Description
14.11.8.4 Sectors and Industry
14.12 Market Model of the Clorox Company in Excel
14.12.1 Regression Report
14.12.2 Yahoo! Finance Beta and the Market Model
14.12.3 Sectors and Industry
14.13 Market Model in Python
14.14 Summary
Bibliography
15 Multiple Linear Regression
15.1 Introduction
15.2 R-Square
15.3 F-Test
15.4 Confidence Interval of Β
15.5 t-Test
15.6 Analyzing the Determination of Price Per Share
15.6.1 Regression Analysis
15.6.2 Workbook Sources
15.6.3 Data Source
15.6.3.1 Dow 30 Components
Power Query
15.6.3.2 Stock Prices
15.6.3.3 Dividends
Power Query
15.6.3.4 Earnings Per Share
Power Query
15.7 Power Query Resource Issue
15.8 Excel 365 and OneDrive
15.9 Using R to Predict
15.10 Summary
Bibliography
16 Residual and Regression Assumption Analysis
16.1 Introduction
16.2 Regression Analysis
16.3 Linearity
16.4 The Expected Value of the Residual Term is Zero
16.5 The Variance of the Error Term is Constant
16.6 Autocorrelation Durbin–Watson Test
16.6.1 VBA Code
16.6.2 Durbin–Watson 1% Table
16.7 Autocorrelation Walmart’s Dividend and EPS from 2019 to 2000
16.7.1 Data Source
16.7.1.1 Earnings Per Share
16.7.1.2 Dividends Per Share
16.8 Using VBA to Retrieve a Ticker’s Name
16.9 Durbin–Watson Test Market Model Python Code
16.10 The Independent Variables Are Uncorrelated: Multicollinearity
16.11 Variance Inflationary Factor (VIF)
16.12 Summary
Bibliography
17 Nonparametric Statistics
17.1 Introduction
17.2 Mann–Whitney U Test
17.2.1 Calculation in Microsoft Excel
17.2.1.1 Boxplot
17.2.2 Calculation in R
17.3 Kruskal–Wallis Test
17.3.1 Calculation in Microsoft Excel
17.3.1.1 Boxplot
17.3.2 Calculation in R
17.3.3 Calculation in Python
17.4 Spearman’s Rank Correlation Test
17.4.1 Calculation in R
17.4.2 Calculation in Python
17.5 Using Python to Test the Randomness of the Rate of Return of JNJ
17.6 Using Python to Test the Randomness of the Rate of Return of MSFT
17.7 Summary
Bibliography
18 Time Series: Analysis, Model, and Forecasting
18.1 Introduction
18.2 Moving Averages
18.2.1 Moving Averages in Excel
18.2.1.1 Data Analysis
18.2.1.2 Moving Average Trend Chart
18.2.2 Moving Averages in R
18.2.3 Moving Averages in Python
18.2.4 Data Source
18.2.4.1 https://www.alphavantage.co/
18.3 Linear Trend
18.3.1 Linear Trend Analysis in Excel
18.3.1.1 Excel TREND Function
18.3.1.2 Excel Linear Trend Graph
18.3.1.3 Data Source
https://carsalesbase.com/
18.3.2 Linear Trend Analysis in R
18.3.2.1 Ford’s Sales Linear Trend Analysis in R
18.3.2.2 BMW’s Sales Linear Trend Analysis in R
18.3.2.3 Lexus’ Sales Linear Trend Analysis in R
18.3.3 Linear Trend Analysis in Python
18.3.3.1 Ford’s Sales Linear Trend Analysis in Python
18.3.3.2 BMW’s Sales Linear Trend Analysis in Python
18.3.3.3 Lexus’ Sales Linear Trend Analysis in Python
18.4 Exponential Smoothing
18.4.1 Exponential Smoothing in Excel
18.4.1.1 Exponential Smoothing Ford’s Sales
18.4.2 Exponential Smoothing in Python
18.4.2.1 Exponential Smoothing Ford’s Sales
18.5 Summary
Bibliography
19 Index Numbers and Stock Market Indexes
19.1 Introduction
19.2 Simple Price Index
19.2.1 Example 19.1
19.3 Laspeyres Price Index
19.4 Paasche Price Index
19.5 Fisher’s Ideal Price Index
19.6 Stock Indexes: S&P500 Index and NASDAQ Composite Index
19.7 Stock Indexes: Dow Jones Industrial Average (DJIA)
19.8 Components of the Dow Jones Industrial Average (DJIA)
19.8.1 Using Power Query to Retrieve the Dow 30 Components
19.9 Components of the S&P 500 Index
19.9.1 Using Power Query to Retrieve the S&P 500 Components
19.10 Components of the NASDAQ Composite Index
19.10.1 Using Power Query to Retrieve the NASDAQ Composite Components
19.11 Using Python to Calculate the Four Statistical Moments of the Rate of Returns of Every Component in the S&P 500
19.12 Summary
Bibliography
20 Sampling Surveys: Methods and Applications
20.1 Introduction
20.2 Random Number Tables
20.2.1 Excel VBA
20.2.2 Python Code
20.3 Confidence Interval for the Population Mean
20.3.1 Example 20.1
20.3.1.1 Python Code
20.4 Confidence Interval for the Population Proportion
20.4.1 Example 20.2
20.4.1.1 Python Code
20.5 Determining Sample Size
20.5.1 Example 20.3
20.5.1.1 Python Code
20.6 Summary
Bibliography
21 Statistical Decision Theory
21.1 Introduction
21.2 Decision Trees and Expected Monetary Values
21.3 NPV and IRR Method for Capital Budgeting Decision Under Certainty
21.4 The Statistical Distribution Method
21.4.1 Methodology
21.4.2 Excel and VBA Application
21.5 Summary
Bibliography
Portfolio Analysis
22 Risk Classification, Estimation, and Diversification
22.1 Introduction
22.2 Risk Classification
22.2.1 Business Risk
22.2.2 Financial Risk
22.2.3 Total Risk
22.3 Portfolio Analysis and Application
22.3.1 Expected Rate of Return on a Portfolio
22.3.1.1 Variance and Standard Deviation of a Portfolio
22.3.2 The Two-Asset Case
22.3.3 The N-asset Case
22.3.4 The Efficient Portfolios
22.3.5 Corporate Application of Diversification
22.4 Determination of Commercial Lending Rates
22.5 The Dominance Principle and Performance EVALUATION
22.6 Summary
Appendix 22A: The Normal Distribution
Appendix 22B: Minimum-Variance Approach to Derive Optimal Weight
Appendix 22C: Sharpe Performance Approach to Derive Optimal Weight
Appendix 22D: Beta Coefficients, Sharpe Performance Measures, and Optimal Portfolio Weights for Five Companies
Bibliography
23 Asset Allocation and Markowitz Portfolio-Selection Model
23.1 Introduction
23.2 Utility Theory, Utility Functions, and Indifference Curves
23.2.1 Utility Theory
23.2.2 Utility Functions
23.2.2.1 Linear Utility Function and Risk
23.2.2.2 Concave Utility Function and Risk
23.2.3 Risk Aversion and Asset Allocation
23.2.4 Indifference Curves
23.3 Efficient Portfolios
23.3.1 Portfolio Combinations
23.3.2 Short Selling
23.4 Techniques for Calculating the Efficient Frontier with Short Selling
23.4.1 The Normal Distribution
23.4.2 The Log-Normal Distribution
23.4.3 Mathematical Method to Calculate Efficient Frontier
23.4.4 Portfolio Determination with Specific Adjustment for Short Selling
23.4.5 Portfolio Determination Without Short Selling
23.5 Summary
Appendix 23A: Excel Program to Calculate the Optimal Weight For Johnson & Johnson, IBM, and Caterpillar
Appendix 23B: Graphical Analysis in Markowitz Portfolio-Selection Model: Three-Security Empirical Solution
Bibliogrphy
24 Capm, Beta Estimation, and Forecasting
24.1 Introduction
24.2 A Graphical Approach to the Derivation of the Capm
24.2.1 The Lending, Borrowing, and Market Portfolios
24.2.2 The Capital Market Line
24.2.3 The Security Market Line—The Capital Asset Pricing Model
24.3 Mathematical Approach to the Derivation of the Capm
24.4 The Market Model and Risk Decomposition
24.4.1 The Market Model
24.4.2 Risk Decomposition
24.4.3 Why Beta is Important for Security Analysis
24.4.4 Determination of Systematic Risk
24.5 Growth Rates, Accounting Betas, and Variance in Ebit
24.5.1 Sustainable Growth Rates
24.5.2 Accounting Beta
24.5.3 Variance in EBIT
24.5.4 Capital–Labor Ratio
24.5.5 Fixed Costs and Variable Costs
24.5.6 Beta Forecasting
24.5.7 Market-Based Versus Accounting-Based Beta Forecasting
24.6 Some Applications and Implications of the Capm
24.7 Summary
Appendix 24A: Empirical Evidence for the Risk–Return Relationship
Anomalies in the Semi-Strong Efficient-Market Hypothesis
Appendix 24B: Composite Forecasting Method
Bibliography
25 Portfolio Selection Methods: Theory and Application
25.1 Introduction
25.2 The Single-Index Model
25.2.1 Deriving the Single-Index Model
25.2.1.1 Expected Return of a Portfolio
25.2.1.2 Variance of a Portfolio
25.2.2 Portfolio Analysis and the Single-Index Model  lessthan S2 greaterthan  
25.2.3 The Market Model and Beta
25.3 Multiple Indexes and the Multiple-Index Model
25.4 Summary
Appendix 25A: A Linear-Programming Approach to Portfolio Analysis Models
Appendix 25B: Expected Return, Variance, and Covariance for a Multiple-Index Model
Appendix 25C: Using Microsoft Excel to Calculate Optimal Weights of a Portfolio
Bibliography
26 Investment Performance Approach to Portfolio Selection
26.1 Introduction
26.2 Sharpe Performance-Measure Approach with Short Sales Allowed
26.3 Sharpe Performance-Measure Approach with Short Sales and Upper Bound Constraints
26.4 Treynor-Measure Approach with Short Sales Allowed
26.5 Treynor-Measure Approach with Short Sales not Allowed
26.6 Impact of Short Sales on Optimal-Weight Determination
26.7 Economic Rationale of the Treynor Performance-Measure Method
26.8 Summary
Appendix 26A: Derivation of Eq. (26.6a)
Appendix 26B: Derivation of Eq. (26.10)
Appendix 26C: Derivation of Eq. (26.15)
Appendix 26D: Quadratic Programming and Kuhn–Tucker Conditions
Appendix 26E: Portfolio Optimization with Short Selling Constraints
Bibliography