© CFA Institute. For candidate use only. Not for distribution.
QUANTITATIVE
METHODS,
ECONOMICS
CFA® Program Curriculum
2024 • LEVEL 1 • 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.
ISBN 978-1-953337-49-8 (paper)
ISBN 978-1-953337-23-8 (ebook)
May 2023
, © CFA Institute. For candidate use only. Not for distribution.
CONTENTS
How to Use the CFA Program Curriculum xi
Errata xi
Designing Your Personal Study Program xi
CFA Institute Learning Ecosystem (LES) xii
Feedback xii
Quantitative Methods
Learning Module 1 Rates and Returns 3
Introduction 3
Interest Rates and Time Value of Money 5
Determinants of Interest Rates 6
Rates of Return 8
Holding Period Return 8
Arithmetic or Mean Return 9
Geometric Mean Return 10
The Harmonic Mean 14
Money-Weighted and Time-Weighted Return 19
Calculating the Money Weighted Return 19
Annualized Return 28
Non-annual Compounding 29
Annualizing Returns 30
Continuously Compounded Returns 32
Other Major Return Measures and Their Applications 33
Gross and Net Return 33
Pre-Tax and After-Tax Nominal Return 34
Real Returns 34
Leveraged Return 36
Practice Problems 38
Solutions 42
Learning Module 2 The Time Value of Money in Finance 45
Introduction 45
Time Value of Money in Fixed Income and Equity 46
Fixed-Income Instruments and the Time Value of Money 47
Equity Instruments and the Time Value of Money 55
Implied Return and Growth 60
Implied Return for Fixed-Income Instruments 60
Equity Instruments, Implied Return, and Implied Growth 65
Cash Flow Additivity 69
Implied Forward Rates Using Cash Flow Additivity 71
Forward Exchange Rates Using No Arbitrage 74
Option Pricing Using Cash Flow Additivity 76
Practice Problems 81
, © CFA Institute. For candidate use only. Not for distribution.
iv Contents
Solutions 84
Learning Module 3 Statistical Measures of Asset Returns 87
Introduction 87
Measures of Central Tendency and Location 89
Measures of Central Tendency 90
Dealing with Outliers 92
Measures of Location 93
Measures of Dispersion 100
The Range 101
Mean Absolute Deviations 101
Sample Variance and Sample Standard Deviation 101
Downside Deviation and Coefficient of Variation 102
Measures of Shape of a Distribution 110
Correlation between Two Variables 117
Scatter Plot 117
Covariance and Correlation 118
Properties of Correlation 119
Limitations of Correlation Analysis 120
Practice Problems 126
Solutions 129
Learning Module 4 Probability Trees and Conditional Expectations 131
Introduction 131
Expected Value and Variance 132
Probability Trees and Conditional Expectations 134
Total Probability Rule for Expected Value 135
Bayes' Formula and Updating Probability Estimates 139
Bayes’ Formula 140
Practice Problems 149
Solutions 150
Learning Module 5 Portfolio Mathematics 151
Introduction 151
Portfolio Expected Return and Variance of Return 153
Covariance 153
Correlation 156
Forecasting Correlation of Returns: Covariance Given a Joint Probability
Function 161
Portfolio Risk Measures: Applications of the Normal Distribution 164
Practice Problems 171
Solutions 172
Learning Module 6 Simulation Methods 173
Introduction 173
Lognormal Distribution and Continuous Compounding 174
The Lognormal Distribution 174
Continuously Compounded Rates of Return 177
QUANTITATIVE
METHODS,
ECONOMICS
CFA® Program Curriculum
2024 • LEVEL 1 • 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.
ISBN 978-1-953337-49-8 (paper)
ISBN 978-1-953337-23-8 (ebook)
May 2023
, © CFA Institute. For candidate use only. Not for distribution.
CONTENTS
How to Use the CFA Program Curriculum xi
Errata xi
Designing Your Personal Study Program xi
CFA Institute Learning Ecosystem (LES) xii
Feedback xii
Quantitative Methods
Learning Module 1 Rates and Returns 3
Introduction 3
Interest Rates and Time Value of Money 5
Determinants of Interest Rates 6
Rates of Return 8
Holding Period Return 8
Arithmetic or Mean Return 9
Geometric Mean Return 10
The Harmonic Mean 14
Money-Weighted and Time-Weighted Return 19
Calculating the Money Weighted Return 19
Annualized Return 28
Non-annual Compounding 29
Annualizing Returns 30
Continuously Compounded Returns 32
Other Major Return Measures and Their Applications 33
Gross and Net Return 33
Pre-Tax and After-Tax Nominal Return 34
Real Returns 34
Leveraged Return 36
Practice Problems 38
Solutions 42
Learning Module 2 The Time Value of Money in Finance 45
Introduction 45
Time Value of Money in Fixed Income and Equity 46
Fixed-Income Instruments and the Time Value of Money 47
Equity Instruments and the Time Value of Money 55
Implied Return and Growth 60
Implied Return for Fixed-Income Instruments 60
Equity Instruments, Implied Return, and Implied Growth 65
Cash Flow Additivity 69
Implied Forward Rates Using Cash Flow Additivity 71
Forward Exchange Rates Using No Arbitrage 74
Option Pricing Using Cash Flow Additivity 76
Practice Problems 81
, © CFA Institute. For candidate use only. Not for distribution.
iv Contents
Solutions 84
Learning Module 3 Statistical Measures of Asset Returns 87
Introduction 87
Measures of Central Tendency and Location 89
Measures of Central Tendency 90
Dealing with Outliers 92
Measures of Location 93
Measures of Dispersion 100
The Range 101
Mean Absolute Deviations 101
Sample Variance and Sample Standard Deviation 101
Downside Deviation and Coefficient of Variation 102
Measures of Shape of a Distribution 110
Correlation between Two Variables 117
Scatter Plot 117
Covariance and Correlation 118
Properties of Correlation 119
Limitations of Correlation Analysis 120
Practice Problems 126
Solutions 129
Learning Module 4 Probability Trees and Conditional Expectations 131
Introduction 131
Expected Value and Variance 132
Probability Trees and Conditional Expectations 134
Total Probability Rule for Expected Value 135
Bayes' Formula and Updating Probability Estimates 139
Bayes’ Formula 140
Practice Problems 149
Solutions 150
Learning Module 5 Portfolio Mathematics 151
Introduction 151
Portfolio Expected Return and Variance of Return 153
Covariance 153
Correlation 156
Forecasting Correlation of Returns: Covariance Given a Joint Probability
Function 161
Portfolio Risk Measures: Applications of the Normal Distribution 164
Practice Problems 171
Solutions 172
Learning Module 6 Simulation Methods 173
Introduction 173
Lognormal Distribution and Continuous Compounding 174
The Lognormal Distribution 174
Continuously Compounded Rates of Return 177
