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Preface xv

Acknowledgments xvii

About the CFA Institute Investment Series xix

Chapter 1 The Time Value of Money 1

Learning Outcomes 1

1. Introduction 1

2. Interest Rates: Interpretation 2

3. The Future Value of a Single Cash Flow 4

3.1. The Frequency of Compounding 9

3.2. Continuous Compounding 11

3.3. Stated and Effective Rates 12

4. The Future Value of a Series of Cash Flows 13

4.1. Equal Cash Flows-Ordinary Annuity 14

4.2. Unequal Cash Flows 15

5. The Present Value of a Single Cash Flow 16

5.1. Finding the Present Value of a Single Cash Flow 16

5.2. The Frequency of Compounding 18

6. The Present Value of a Series of Cash Flows 20

6.1. The Present Value of a Series of Equal Cash Flows 20

6.2. The Present Value of an Infinite Series of Equal Cash Flows-Perpetuity 24

6.3. Present Values Indexed at Times Other than t = 0 25

6.4. The Present Value of a Series of Unequal Cash Flows 27

7. Solving for Rates, Number of Periods, or Size of Annuity Payments 27

7.1. Solving for Interest Rates and Growth Rates 28

7.2. Solving for the Number of Periods 30

7.3. Solving for the Size of Annuity Payments 31

7.4. Review of Present and Future Value Equivalence 35

7.5. The Cash Flow Additivity Principle 37

8. Summary 38

Practice Problems 39

Chapter 2 Organizing, Visualizing, and Describing Data 45

Learning Outcomes 45

1. Introduction 45

2. Data Types 46

2.1. Numerical versus Categorical Data 46

2.2. Cross-Sectional versus Time-Series versus Panel Data 49

2.3. Structured versus Unstructured Data 50

3. Data Summarization 54

3.1. Organizing Data for Quantitative Analysis 54

3.2. Summarizing Data Using Frequency Distributions 57

3.3. Summarizing Data Using a Contingency Table 63

4. Data Visualization 68

4.1. Histogram and Frequency Polygon 68

4.2. Bar Chart 69

4.3. Tree-Map 73

4.4. Word Cloud 73

4.5. Line Chart 75

4.6. Scatter Plot 77

4.7. Heat Map 81

4.8. Guide to Selecting among Visualization Types 82

5. Measures of Central Tendency 85

5.1. The Arithmetic Mean 85

5.2. The Median 90

5.3. The Mode 92

5.4. Other Concepts of Mean 92

6. Other Measures of Location: Quantiles 102

6.1. Quartiles, Quintiles, Deciles, and Percentiles 103

6.2. Quantiles in Investment Practice 108

7. Measures of Dispersion 109

7.1. The Range 109

7.2. The Mean Absolute Deviation 109

7.3. Sample Variance and Sample Standard Deviation 111

7.4. Target Downside Deviation 114

7.5. Coefficient of Variation 117

8. The Shape of the Distributions: Skewness 119

9. The Shape of the Distributions: Kurtosis 121

10. Correlation between Two Variables 125

10.1. Properties of Correlation 126

10.2. Limitations of Correlation Analysis 129

11. Summary 132

Practice Problems 135

Chapter 3 Probability Concepts 147

Learning Outcomes 147

1. Introduction 148

2. Probability, Expected Value, and Variance 148

3. Portfolio Expected Return and Variance of Return 171

4. Topics in Probability 180

4.1. Bayes' Formula 180

4.2. Principles of Counting 184

5. Summary 188

References 190

Practice Problem 190

Chapter 4 Common Probability Distributions 195

Learning Outcomes 195

1. Introduction to Common Probability Distributions 196

2. Discrete Random Variables 196

2.1. The Discrete Uniform Distribution 198

2.2. The Binomial Distribution 200

3. Continuous Random Variables 210

3.1. Continuous Uniform Distribution 210

3.2. The Normal Distribution 214

3.3. Applications of the Normal Distribution 220

3.4. The Lognormal Distribution 222

4. Introduction to Monte Carlo Simulation 228

5. Summary 231

References 233

Practice Problems 234

Chapter 5 Sampling and Estimation 241

Learning Outcomes 241

1. Introduction 242

2. Sampling 242

2.1. Simple Random Sampling 242

2.2. Stratified Random Sampling 244

2.3. Time-Series and Cross-Sectional Data 245

3. Distribution of the Sample Mean 248

3.1. The Central Limit Theorem 248

4. Point and Interval Estimates of the Population Mean 251

4.1. Point Estimators 252

4.2. Confidence Intervals for the Population Mean 253

4.3. Selection of Sample Size 259

5. More on Sampling 261

5.1. Data-Mining Bias 261

5.2. Sample Selection Bias 264

5.3. Look-Ahead Bias 265

5.4. Time-Period Bias 266

6. Summary 267

References 269

Practice Problems 270

Chapter 6 Hypothesis Testing 275

Learning Outcomes 275

1. Introduction 276

2. Hypothesis Testing 277

3. Hypothesis Tests Concerning the Mean 287

3.1. Tests Concerning a Single Mean 287

3.2. Tests Concerning Differences between Means 294

3.3. Tests Concerning Mean Differences 299

4. Hypothesis Tests Concerning Variance and Correlation 303

4.1. Tests Concerning a Single Variance 303

4.2. Tests Concerning the Equality (Inequality) of Two Variances 305

4.3. Tests Concerning Correlation 308

5. Other Issues: Nonparametric Inference 310

5.1. Nonparametric Tests Concerning Correlation: The Spearman Rank Correlation Coefficient 312

5.2. Nonparametric Inference: Summary 313

6. Summary 314

References 317

Practice Problems 317

Chapter 7 Introduction to Linear Regression 327

Learning Outcomes 327

1. Introduction 328

2. Linear Regression 328

2.1. Linear Regression with One Independent Variable 328

3. Assumptions of the Linear Regression Model 332

4. The Standard Error of Estimate 335

5. The Coefficient of Determination 337

6. Hypothesis Testing 339

7. Analysis of Variance in a Regression with One Independent Variable 347

8. Prediction Intervals 350

9. Summary 353

References 354

Practice Problems 354

Chapter 8 Multiple Regression 365

Learning Outcomes 365

1. Introduction 366

2. Multiple Linear Regression 366

2.1. Assumptions of the Multiple Linear Regression Model 372

2.2. Predicting the Dependent Variable in a Multiple Regression Model 376

2.3. Testing Whether All Population Regression Coefficients Equal Zero 378

2.4. Adjusted R2 380

3. Using Dummy Variables in Regressions 381

3.1. Defining a Dummy Variable 381

3.2. Visualizing and Interpreting Dummy Variables 382

3.3. Testing for Statistical Significance 384

4. Violations of Regression Assumptions 387

4.1. Heteroskedasticity 388

4.2. Serial Correlation 394

4.3. Multicollinearity 398

4.4. Heteroskedasticity, Serial Correlation, Multicollinearity: Summarizing the Issues 401

5. Model Specification and Errors in Specification 401

5.1. Principles of Model Specification 402

5.2. Misspecified Functional Form 402

5.3. Time-Series Misspecification (Independent Variables Correlated with Errors) 410

5.4. Other Types of Time-Series Misspecification 414

6. Models with Qualitative Dependent Variables 414

6.1. Models with Qualitative Dependent Variables 414

7. Summary 422

References 425

Practice Problems 426

Chapter 9 Time-Series Analysis 451

Learning Outcomes 451

1. Introduction to Time-Series Analysis 452

2. Challenges of Working with Time Series 454

3. Trend Models 454

3.1. Linear Trend Models 455

3.2. Log-Linear Trend Models 458

3.3. Trend Models and Testing for Correlated Errors 463

4. Autoregressive (AR) Time-Series Models 464

4.1. Covariance-Stationary Series 465

4.2. Detecting Serially Correlated Errors in an Autoregressive Model 466

4.3. Mean Reversion 469

4.4. Multiperiod Forecasts and the Chain Rule of Forecasting 470

4.5. Comparing Forecast Model Performance 473

4.6. Instability of Regression Coefficients 475

5. Random Walks and Unit Roots 478

5.1. Random Walks 478

5.2. The Unit Root Test of Nonstationarity 482

6. Moving-Average Time-Series Models 486

6.1. Smoothing Past Values with an n-Period Moving Average 486

6.2. Moving-Average Time-Series Models for Forecasting 489

7. Seasonality in Time-Series Models 491

8. Autoregressive Moving-Average Models 496

9. Autoregressive Conditional Heteroskedasticity Models 497

10. Regressions with More than One Time Series 500

11. Other Issues in Time Series 504

12. Suggested Steps in Time-Series Forecasting 505

13. Summary 507

References 508

Practice Problems 509

Chapter 10 Machine Learning 527

Learning Outcomes 527

1. Introduction 527

2. Machine Learning and Investment Management 528

3. What is Machine Learning? 529

3.1. Defining Machine Learning 529

3.2. Supervised Learning 529

3.3. Unsupervised Learning 531

3.4. Deep Learning and Reinforcement Learning 531

3.5. Summary of ML Algorithms and How to Choose among Them 532

4. Overview of Evaluating ML Algorithm Performance 533

4.1. Generalization and Overfitting 534

4.2. Errors and Overfitting 534

4.3. Preventing Overfitting in Supervised Machine Learning 537

5. Supervised Machine Learning Algorithms 539

5.1....