QUANTITATIVE INVESTMENT
ANALYSIS
Second Edition
Richard A. DeFusco, CFA
Dennis W. McLeavey, CFA
Jerald E. Pinto, CFA
David E. Runkle, CFA
John Wiley & Sons, Inc.
QUANTITATIVE INVESTMENT
ANALYSIS
Second Edition
Richard A. DeFusco, CFA
Dennis W. McLeavey, CFA
Jerald E. Pinto, CFA
David E. Runkle, CFA
John Wiley & Sons, Inc.
Copyright c⃝ 2004, 2007 by CFA Institute. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Quantitative investment analysis / Richard A. DeFusco . . . [et al.].— 2nd ed.
p. cm.—(The CFA Institute investment series) Includes bibliographical references. ISBN-13 978-0-470-05220-4 (cloth) ISBN-10 0-470-05220-1 (cloth)
1. Investment analysis—Mathematical models. I. DeFusco, Richard Armand.
HG4529.Q35 2006 332.601’5195—dc22
2006052578 Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
To Margo, Rachel, and Rebekah R.A.D.
To Jan, Christine, and Andy D.W.M.
In memory of Irwin T. Vanderhoof, CFA J.E.P.
To Patricia, Anne, and Sarah D.E.R.
CONTENTS
Foreword xiii
Acknowledgments xvii
Introduction xix
CHAPTER 1 The Time Value of Money 1
1 Introduction 1 2 Interest Rates: Interpretation 1 3 The Future Value of a Single Cash Flow 3
3.1 The Frequency of Compounding 8 3.2 Continuous Compounding 10 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 13 4.2 Unequal Cash Flows 15
5 The Present Value of a Single Cash Flow 15 5.1 Finding the Present Value of a Single Cash Flow 15 5.2 The Frequency of Compounding 17
6 The Present Value of a Series of Cash Flows 19 6.1 The Present Value of a Series of Equal Cash Flows 19 6.2 The Present Value of an Infinite Series of Equal Cash Flows—Perpetuity 23 6.3 Present Values Indexed at Times Other Than t = 0 24 6.4 The Present Value of a Series of Unequal Cash Flows 26
7 Solving for Rates, Number of Periods, or Size of Annuity Payments 27 7.1 Solving for Interest Rates and Growth Rates 27 7.2 Solving for the Number of Periods 30 7.3 Solving for the Size of Annuity Payments 30 7.4 Review of Present and Future Value Equivalence 35 7.5 The Cash Flow Additivity Principle 36
vii
viii Contents
CHAPTER 2 Discounted Cash Flow Applications 39
1 Introduction 39 2 Net Present Value and Internal Rate of Return 39
2.1 Net Present Value and the Net Present Value Rule 40 2.2 The Internal Rate of Return and the Internal Rate of
Return Rule 42 2.3 Problems with the IRR Rule 45
3 Portfolio Return Measurement 47 3.1 Money-Weighted Rate of Return 47 3.2 Time-Weighted Rate of Return 49
4 Money Market Yields 54
CHAPTER 3 Statistical Concepts and Market Returns 61
1 Introduction 61 2 Some Fundamental Concepts 61
2.1 The Nature of Statistics 62 2.2 Populations and Samples 62 2.3 Measurement Scales 63
3 Summarizing Data Using Frequency Distributions 65 4 The Graphic Presentation of Data 72
4.1 The Histogram 73 4.2 The Frequency Polygon and the Cumulative Frequency
Distribution 74 5 Measures of Central Tendency 76
5.1 The Arithmetic Mean 77 5.2 The Median 81 5.3 The Mode 84 5.4 Other Concepts of Mean 85
6 Other Measures of Location: Quantiles 94 6.1 Quartiles, Quintiles, Deciles, and Percentiles 94 6.2 Quantiles in Investment Practice 98
7 Measures of Dispersion 100 7.1 The Range 100 7.2 The Mean Absolute Deviation 101 7.3 Population Variance and Population Standard
Deviation 103 7.4 Sample Variance and Sample Standard Deviation 106 7.5 Semivariance, Semideviation, and Related Concepts 110 7.6 Chebyshev’s Inequality 111 7.7 Coefficient of Variation 113 7.8 The Sharpe Ratio 115
8 Symmetry and Skewness in Return Distributions 118 9 Kurtosis in Return Distributions 123 10 Using Geometric and Arithmetic Means 127
Contents ix
CHAPTER 4 Probability Concepts 129
1 Introduction 129 2 Probability, Expected Value, and Variance 129 3 Portfolio Expected Return and Variance of Return 152 4 Topics in Probability 161
4.1 Bayes’ Formula 161 4.2 Principles of Counting 166
CHAPTER 5 Common Probability Distributions 171
1 Introduction 171 2 Discrete Random Variables 171
2.1 The Discrete Uniform Distribution 173 2.2 The Binomial Distribution 175
3 Continuous Random Variables 185 3.1 Continuous Uniform Distribution 186 3.2 The Normal Distribution 189 3.3 Applications of the Normal Distribution 197 3.4 The Lognormal Distribution 200
4 Monte Carlo Simulation 206
