Quantitative investment analysis

QUANTITATIVE

INVESTMENT

AN ALYSIS

c h a r d A. D e F u s c o . C F A / D e n n i s W. M c L e a v e y , CFA / J e r a l d E. P i n t o , C F A / D a v i d E. R u n k l e , CFA

F o r e w o r d by MARK J . P. A N S O N , P H D . C F A

QUANTITATIVE

INVESTMENT

ANALYSIS

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CFA Institute is the premier association for investment professionals around the world,

with over 85,000 members in 129 countries. Since 1963 the organization has developed

and administered the renowned Chartered Financial Analyst® Program. With a rich history

of leading the investment profession, CFA Institute has set the highest standards in ethics,

education, and professional excellence within the global investment community, and is the

foremost authority on investment profession conduct and practice.

Each book in the CFA Institute Investment Series is geared toward industry practitioners

along with graduate-level finance students and covers the most important topics in the

industry. The authors of these cutting-edge books are themselves industry professionals and

academics and bring their wealth of knowledge and expertise to this series.

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QUANTITATIVE

INVESTMENT

ANALYSIS

Second Edition

Richard A. DeFusco, CFA

Dennis W . McLeavey, CFA

Jerald E. Pinto, CFA

David E. Runkle, CFA

\ 1 8 0 7 j

| ®WILEY \

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John Wiley & Sons, Inc.

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Library o f 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.

IS B N -13 978-0-470-05220-4 (cloth)

IS B N -10 0-470-05220-1 (cloth)

1. Investment analysis— Mathematical models. I. DeFusco, Richard

Armand.

H G 4529.Q 35 2006

3 3 2 .6 0 1’5 195— dc22

2006052578

Printed in the United States o f America.

10 9 8 7 6 5 4

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To Margo, Rachel, and Rebekah

R. A.D.

To Jan, Christine, and Andy

D.W.M.

In memory o f Irwin T. Vanderhoof, CFA

J.E.P.

To Patricia, Anne, and Sarah

D. E. R.

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CONTENTS

Forew ord xiii

Acknow ledgm ents 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 o f 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 o f 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 o f 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 o f Annuity Payments 30

7.4 Review o f Present and Future Value Equivalence 35

7.5 The Cash Flow Additivity Principle 36

vii

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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

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 12“

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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

CHAPTER 6

Sampling and Estimation 215

1 Introduction 215

2 Sampling 215

2.1 Simple Random Sampling 216

2.2 Stratified Random Sampling 217

2.3 Time-Series and Cross-Sectional Data 219

3 Distribution o f the Sample Mean 221

3.1 The Central Limit Theorem 222

4 Point and Interval Estimates of the Population Mean 225

4.1 Point Estimators 225

4.2 Confidence Intervals for the Population Mean 227

4.3 Selection of Sample Size 233

5 More on Sampling 235

5.1 Data-Mining Bias 236

5.2 Sample Selection Bias 238

5.3 Look-Ahead Bias 240

5.4 Time-Period Bias 240

CHAPTER 7

Hypothesis Testing 243

1 Introduction 243

2 Hypothesis Testing 244

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