© CFA Institute. For candidate use only. Not for distribution.
QUANTITATIVE
METHODS
CFA® Program Curriculum
2024 • LEVEL PREREQUISITE READING • VOLUME 1
,© CFA Institute. For candidate use only. Not for distribution.
©2023 by CFA Institute. All rights reserved. This copyright covers material written
expressly for this volume by the editor/s as well as the compilation itself. It does
not cover the individual selections herein that first appeared elsewhere. Permission
to reprint these has been obtained by CFA Institute for this edition only. Further
reproductions by any means, electronic or mechanical, including photocopying and
recording, or by any information storage or retrieval systems, must be arranged with
the individual copyright holders noted.
CFA®, Chartered Financial Analyst®, AIMR-PPS®, and GIPS® are just a few of the
trademarks owned by CFA Institute. To view a list of CFA Institute trademarks and the
Guide for Use of CFA Institute Marks, please visit our website at www.cfainstitute.org.
This publication is designed to provide accurate and authoritative information
in regard to the subject matter covered. It is sold with the understanding that the
publisher is not engaged in rendering legal, accounting, or other professional service.
If legal advice or other expert assistance is required, the services of a competent pro-
fessional should be sought.
All trademarks, service marks, registered trademarks, and registered service marks
are the property of their respective owners and are used herein for identification
purposes only.
, © CFA Institute. For candidate use only. Not for distribution.
CONTENTS
How to Use the CFA Program Curriculum vii
Errata vii
Quantitative Methods
Learning Module 1 Interest Rates, Present Value, and Future Value 3
Introduction 3
Interest Rates 4
Future Value of a Single Cash Flow 6
Non-Annual Compounding (Future Value) 10
Continuous Compounding 12
Stated and Effective Rates 14
Future Value of a Series of Cash Flows 15
Equal Cash Flows—Ordinary Annuity 15
Unequal Cash Flows 17
Present Value of a Single Cash Flow 18
Non-Annual Compounding (Present Value) 20
Present Value of a Series of Equal and Unequal Cash Flows 21
The Present Value of a Series of Equal Cash Flows 21
The Present Value of a Series of Unequal Cash Flows 25
Present Value of a Perpetuity 26
Present Values Indexed at Times Other than t = 0 27
Solving for Interest Rates, Growth Rates, and Number of Periods 29
Solving for Interest Rates and Growth Rates 29
Solving for the Number of Periods 32
Solving for Size of Annuity Payments 32
Present and Future Value Equivalence and the Additivity Principle 36
The Cash Flow Additivity Principle 38
Summary 39
Practice Problems 40
Solutions 45
Learning Module 2 Organizing, Visualizing, and Describing Data 59
Introduction 59
Data Types 60
Numerical versus Categorical Data 60
Cross-Sectional versus Time-Series versus Panel Data 63
Structured versus Unstructured Data 64
Data Summarization 68
Organizing Data for Quantitative Analysis 68
Summarizing Data Using Frequency Distributions 71
Summarizing Data Using a Contingency Table 77
Data Visualization 80
Histogram and Frequency Polygon 80
Bar Chart 82
indicates an optional segment
, © CFA Institute. For candidate use only. Not for distribution.
iv Contents
Tree-Map 85
Word Cloud 86
Line Chart 88
Scatter Plot 90
Heat Map 94
Guide to Selecting among Visualization Types 96
Measures of Central Tendency 98
The Arithmetic Mean 99
The Median 103
The Mode 105
Other Concepts of Mean 106
Quantiles 115
Quartiles, Quintiles, Deciles, and Percentiles 115
Quantiles in Investment Practice 121
Measures of Dispersion 122
The Range 122
The Mean Absolute Deviation 122
Sample Variance and Sample Standard Deviation 124
Downside Deviation and Coefficient of Variation 127
Coefficient of Variation 130
Summary 132
Practice Problems 136
Solutions 147
Learning Module 3 Probability Concepts 155
Probability Concepts and Odds Ratios 156
Probability and Odds 156
Conditional and Joint Probability 161
Principles of Counting 173
Summary 179
References 182
Practice Problems 183
Solutions 186
Learning Module 4 Common Probability Distributions 189
Discrete Random Variables 190
Discrete Random Variables 191
Discrete and Continuous Uniform Distribution 195
Continuous Uniform Distribution 197
Binomial Distribution 200
Normal Distribution 208
The Normal Distribution 208
Probabilities Using the Normal Distribution 212
Standardizing a Random Variable 214
Probabilities Using the Standard Normal Distribution 214
Student’s t-, Chi-Square, and F-Distributions 216
Student’s t-Distribution 216
Chi-Square and F-Distribution 218
Summary 223
indicates an optional segment
QUANTITATIVE
METHODS
CFA® Program Curriculum
2024 • LEVEL PREREQUISITE READING • VOLUME 1
,© CFA Institute. For candidate use only. Not for distribution.
©2023 by CFA Institute. All rights reserved. This copyright covers material written
expressly for this volume by the editor/s as well as the compilation itself. It does
not cover the individual selections herein that first appeared elsewhere. Permission
to reprint these has been obtained by CFA Institute for this edition only. Further
reproductions by any means, electronic or mechanical, including photocopying and
recording, or by any information storage or retrieval systems, must be arranged with
the individual copyright holders noted.
CFA®, Chartered Financial Analyst®, AIMR-PPS®, and GIPS® are just a few of the
trademarks owned by CFA Institute. To view a list of CFA Institute trademarks and the
Guide for Use of CFA Institute Marks, please visit our website at www.cfainstitute.org.
This publication is designed to provide accurate and authoritative information
in regard to the subject matter covered. It is sold with the understanding that the
publisher is not engaged in rendering legal, accounting, or other professional service.
If legal advice or other expert assistance is required, the services of a competent pro-
fessional should be sought.
All trademarks, service marks, registered trademarks, and registered service marks
are the property of their respective owners and are used herein for identification
purposes only.
, © CFA Institute. For candidate use only. Not for distribution.
CONTENTS
How to Use the CFA Program Curriculum vii
Errata vii
Quantitative Methods
Learning Module 1 Interest Rates, Present Value, and Future Value 3
Introduction 3
Interest Rates 4
Future Value of a Single Cash Flow 6
Non-Annual Compounding (Future Value) 10
Continuous Compounding 12
Stated and Effective Rates 14
Future Value of a Series of Cash Flows 15
Equal Cash Flows—Ordinary Annuity 15
Unequal Cash Flows 17
Present Value of a Single Cash Flow 18
Non-Annual Compounding (Present Value) 20
Present Value of a Series of Equal and Unequal Cash Flows 21
The Present Value of a Series of Equal Cash Flows 21
The Present Value of a Series of Unequal Cash Flows 25
Present Value of a Perpetuity 26
Present Values Indexed at Times Other than t = 0 27
Solving for Interest Rates, Growth Rates, and Number of Periods 29
Solving for Interest Rates and Growth Rates 29
Solving for the Number of Periods 32
Solving for Size of Annuity Payments 32
Present and Future Value Equivalence and the Additivity Principle 36
The Cash Flow Additivity Principle 38
Summary 39
Practice Problems 40
Solutions 45
Learning Module 2 Organizing, Visualizing, and Describing Data 59
Introduction 59
Data Types 60
Numerical versus Categorical Data 60
Cross-Sectional versus Time-Series versus Panel Data 63
Structured versus Unstructured Data 64
Data Summarization 68
Organizing Data for Quantitative Analysis 68
Summarizing Data Using Frequency Distributions 71
Summarizing Data Using a Contingency Table 77
Data Visualization 80
Histogram and Frequency Polygon 80
Bar Chart 82
indicates an optional segment
, © CFA Institute. For candidate use only. Not for distribution.
iv Contents
Tree-Map 85
Word Cloud 86
Line Chart 88
Scatter Plot 90
Heat Map 94
Guide to Selecting among Visualization Types 96
Measures of Central Tendency 98
The Arithmetic Mean 99
The Median 103
The Mode 105
Other Concepts of Mean 106
Quantiles 115
Quartiles, Quintiles, Deciles, and Percentiles 115
Quantiles in Investment Practice 121
Measures of Dispersion 122
The Range 122
The Mean Absolute Deviation 122
Sample Variance and Sample Standard Deviation 124
Downside Deviation and Coefficient of Variation 127
Coefficient of Variation 130
Summary 132
Practice Problems 136
Solutions 147
Learning Module 3 Probability Concepts 155
Probability Concepts and Odds Ratios 156
Probability and Odds 156
Conditional and Joint Probability 161
Principles of Counting 173
Summary 179
References 182
Practice Problems 183
Solutions 186
Learning Module 4 Common Probability Distributions 189
Discrete Random Variables 190
Discrete Random Variables 191
Discrete and Continuous Uniform Distribution 195
Continuous Uniform Distribution 197
Binomial Distribution 200
Normal Distribution 208
The Normal Distribution 208
Probabilities Using the Normal Distribution 212
Standardizing a Random Variable 214
Probabilities Using the Standard Normal Distribution 214
Student’s t-, Chi-Square, and F-Distributions 216
Student’s t-Distribution 216
Chi-Square and F-Distribution 218
Summary 223
indicates an optional segment
