2022 CFA Program Curriculum Level I Box Set (CFA Institute)

How to Use the CFA Program Curriculum vii
Background on the CBOK vii
Organization of the Curriculum viii
Features of the Curriculum viii
Designing Your Personal Study Program ix
CFA Institute Learning Ecosystem (LES) x
Prep Providers xi
Feedback xii
Quantitative Methods
Study Session 1 Quantitative Methods (1) 3
Reading 1 The Time Value of Money 5
Introduction 5
Interest Rates 6
Future Value of a Single Cash Flow (Lump Sum) 8
Non-Annual
Compounding (Future Value) 13
Continuous Compounding, Stated and Effective Rates 15
Stated and Effective Rates 16
Future Value of a Series of Cash Flows, Future Value Annuities 17
Equal Cash Flows—Ordinary Annuity 17
Unequal Cash Flows 19
Present Value of a Single Cash Flow (Lump Sum) 20
Non-Annual
Compounding (Present Value) 22
Present Value of a Series of Equal Cash Flows (Annuities) and Unequal
Cash Flows 23
The Present Value of a Series of Equal Cash Flows 24
The Present Value of a Series of Unequal Cash Flows 28
Present Value of a Perpetuity and Present Values Indexed at Times other
than t=0 29
Present Values Indexed at Times Other than t = 0 30
Solving for Interest Rates, Growth Rates, and Number of Periods 32
Solving for Interest Rates and Growth Rates 32
Solving for the Number of Periods 35
Solving for Size of Annuity Payments (Combining Future Value and
Present Value Annuities) 36
Present Value and Future Value Equivalence, Additivity Principle 39
The Cash Flow Additivity Principle 41
Summary 42
Practice Problems 44
Solutions 49
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ii Contents
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Reading 2 Organizing, Visualizing, and Describing Data 63
Introduction 64
Data Types 64
Numerical versus Categorical Data 65
Cross-Sectional
versus Time-Series
versus Panel Data 67
Structured versus Unstructured Data 68
Data Summarization 72
Organizing Data for Quantitative Analysis 72
Summarizing Data Using Frequency Distributions 75
Summarizing Data Using a Contingency Table 81
Data Visualization 86
Histogram and Frequency Polygon 86
Bar Chart 88
Tree-Map
91
Word Cloud 92
Line Chart 93
Scatter Plot 95
Heat Map 99
Guide to Selecting among Visualization Types 100
Measures of Central Tendency 103
The Arithmetic Mean 103
The Median 107
The Mode 109
Other Concepts of Mean 110
Quantiles 120
Quartiles, Quintiles, Deciles, and Percentiles 120
Quantiles in Investment Practice 126
Measures of Dispersion 126
The Range 126
The Mean Absolute Deviation 127
Sample Variance and Sample Standard Deviation 128
Downside Deviation and Coefficient of Variation 131
Coefficient of Variation 135
The Shape of the Distributions 136
The Shape of the Distributions: Kurtosis 139
Correlation between Two Variables 142
Properties of Correlation 143
Limitations of Correlation Analysis 146
Summary 149
Practice Problems 154
Solutions 166
Reading 3 Probability Concepts 175
Introduction, Probability Concepts, and Odds Ratios 176
Probability, Expected Value, and Variance 176
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Contents iii
Conditional and Joint Probability 181
Expected Value (Mean), Variance, and Conditional Measures of Expected
Value and Variance 192
Expected Value, Variance, Standard Deviation, Covariances, and
Correlations of Portfolio Returns 199
Covariance Given a Joint Probability Function 205
Bayes' Formula 208
Bayes’ Formula 208
Principles of Counting 214
Summary 220
Practice Problems 224
Solutions 230
Study Session 2 Quantitative Methods (2) 237
Reading 4 Common Probability Distributions 239
Introduction and Discrete Random Variables 240
Discrete Random Variables 241
Discrete and Continuous Uniform Distribution 244
Continuous Uniform Distribution 246
Binomial Distribution 250
Normal Distribution 257
The Normal Distribution 257
Probabilities Using the Normal Distribution 261
Standardizing a Random Variable 263
Probabilities Using the Standard Normal Distribution 263
Applications of the Normal Distribution 265
Lognormal Distribution and Continuous Compounding 269
The Lognormal Distribution 269
Continuously Compounded Rates of Return 272
Student’s t-, Chi-Square,
and F-Distributions 275
Student’s t-Distribution 275
Chi-Square
and F-Distribution 277
Monte Carlo Simulation 282
Summary 288
Practice Problems 292
Solutions 299
Reading 5 Sampling and Estimation 305
Introduction 306
Sampling Methods 306
Simple Random Sampling 307
Stratified Random Sampling 308
Cluster Sampling 309
Non-Probability
Sampling 310
Sampling from Different Distributions 315
Distribution of the Sample Mean and the Central Limit Theorem 316
The Central Limit Theorem 317
Standard Error of the Sample Mean 319
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Point Estimates of the Population Mean 322
Point Estimators 322
Confidence Intervals for the Population Mean and Selection of Sample Size 326
Selection of Sample Size 332
Resampling 334
Data Snooping Bias, Sample Selection Bias, Look-Ahead
Bias, and Time-Period
Bias 338
Data Snooping Bias 338
Sample Selection Bias 340
Look-Ahead
Bias 342
Time-Period
Bias 342
Summary 344
Practice Problems 347
Solutions 351
Reading 6 Hypothesis Testing 357
Introduction 358
Why Hypothesis Testing? 358
Implications from a Sampling Distribution 359
The Process of Hypothesis Testing 360
Stating the Hypotheses 361
Two-Sided
vs. One-Sided
Hypotheses 361
Selecting the Appropriate Hypotheses 362
Identify the Appropriate Test Statistic 363
Test Statistics 363
Identifying the Distribution of the Test Statistic 364
Specify the Level of Significance 364
State the Decision Rule 366
Determining Critical Values 367
Decision Rules and Confidence Intervals 368
Collect the Data and Calculate the Test Statistic 369
Make a Decision 370
Make a Statistical Decision 370
Make an Economic Decision 370
Statistically Significant but Not Economically Significant? 370
The Role of p-Values 371
Multiple Tests and Interpreting Significance 374
Tests Concerning a Single Mean 377
Test Concerning Differences between Means with Independent Samples 381
Test Concerning Differences between Means with Dependent Samples 384
Testing Concerning Tests of Variances (Chi-Square
Test) 388
Tests of a Single Variance 388
Test Concerning the Equality of Two Variances (F-Test) 391
Parametric vs. Nonparametric Tests 396
Uses of Nonparametric Tests 397
Nonparametric Inference: Summary 397
Tests Concerning Correlation 398
Parametric Test of a Correlation 399
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Contents v
Tests Concerning Correlation: The Spearman Rank Correlation
Coefficient 401
Test of Independence Using Contingency Table Data 404
Summary 409
Practice Problems 412
Solutions 422
Reading 7 Introduction to Linear Regression 431
Simple Linear Regression 431
Estimating the Parameters of a Simple Linear Regression 434
The Basics of Simple Linear Regression 434
Estimating the Regression Line 435
Interpreting the Regression Coefficients 438
Cross-Sectional
vs. Time-Series
Regressions 440
Assumptions of the Simple Linear Regression Model 443
Assumption 1: Linearity 443
Assumption 2: Homoskedasticity 445
Assumption 3: Independence 447
Assumption 4: Normality 448
Analysis of Variance 450
Breaking down the Sum of Squares Total into Its Components 450
Measures of Goodness of Fit 451
ANOVA and Standard Error of Estimate in Simple Linear Regression 453
Hypothesis Testing of Linear Regression Coefficients 455
Hypothesis Tests of the Slope Coefficient 455
Hypothesis Tests of the Intercept 459
Hypothesis Tests of Slope When Independent Variable Is an
Indicator Variable 459
Test of Hypotheses: Level of Significance and p-Values 461
Prediction Using Simple Linear Regression and Prediction Intervals 463
Functional Forms for Simple Linear Regression 467
The Log-Lin
Model 468
The Lin-Log
Model 469
The Log-Log
Model 470
Selecting the Correct Functional Form 472
Summary 474
Practice Problems 477
Solutions 490
Appendices 495
Glossary