A through guide covering Modern Portfolio Theory as well as the
recent developments surrounding it

Modern portfolio theory (MPT), which originated with Harry
Markowitz's seminal paper "Portfolio Selection" in 1952, has stood
the test of time and continues to be the intellectual foundation
for real-world portfolio management. This book presents a
comprehensive picture of MPT in a manner that can be effectively
used by financial practitioners and understood by students.

Modern Portfolio Theory provides a summary of the
important findings from all of the financial research done since
MPT was created and presents all the MPT formulas and models using
one consistent set of mathematical symbols. Opening with an
informative introduction to the concepts of probability and utility
theory, it quickly moves on to discuss Markowitz's seminal work on
the topic with a thorough explanation of the underlying
mathematics.

* Analyzes portfolios of all sizes and types, shows how the
advanced findings and formulas are derived, and offers a concise
and comprehensive review of MPT literature

* Addresses logical extensions to Markowitz's work, including the
Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio
ranking models, and performance attribution

* Considers stock market developments like decimalization, high
frequency trading, and algorithmic trading, and reveals how they
align with MPT

* Companion Website contains Excel spreadsheets that allow you to
compute and graph Markowitz efficient frontiers with riskless and
risky assets

If you want to gain a complete understanding of modern portfolio
theory this is the book you need to read.

JACK CLARK FRANCIS is Professor of Economics and Finance at Bernard M. Baruch College in New York City. His research focuses on investments, banking, and monetary economics, and he has had dozens of articles published in many refereed academic, business, and government journals. Dr. Francis was an assistant professor of finance at the University of Pennsylvania's Wharton School of Finance for five years and was a Federal Reserve economist for two years. He received his bachelor's and MBA from Indiana University and earned his PhD in finance from the University of Washington in Seattle.

DONGCHEOL KIM is a Professor of Finance at Korea University in Seoul. He served as president of the Korea Securities Association and editor-in-chief of the Asia-Pacific Journal of Financial Studies. Previously, he was a finance professor at Rutgers University. Kim has published articles in Financial Management, the Accounting Review, Journal of Financial and Quantitative Analysis, Journal of Economic Research, Journal of Finance, and Journal of the Futures Market.

Zusammenfassung
A through guide covering Modern Portfolio Theory as well as the recent developments surrounding it

Modern portfolio theory (MPT), which originated with Harry Markowitz's seminal paper "Portfolio Selection" in 1952, has stood the test of time and continues to be the intellectual foundation for real-world portfolio management. This book presents a comprehensive picture of MPT in a manner that can be effectively used by financial practitioners and understood by students.

Modern Portfolio Theory provides a summary of the important findings from all of the financial research done since MPT was created and presents all the MPT formulas and models using one consistent set of mathematical symbols. Opening with an informative introduction to the concepts of probability and utility theory, it quickly moves on to discuss Markowitz's seminal work on the topic with a thorough explanation of the underlying mathematics.

• Analyzes portfolios of all sizes and types, shows how the advanced findings and formulas are derived, and offers a concise and comprehensive review of MPT literature
• Addresses logical extensions to Markowitz's work, including the Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio ranking models, and performance attribution
• Considers stock market developments like decimalization, high frequency trading, and algorithmic trading, and reveals how they align with MPT
• Companion Website contains Excel spreadsheets that allow you to compute and graph Markowitz efficient frontiers with riskless and risky assets

If you want to gain a complete understanding of modern portfolio theory this is the book you need to read.

Preface xvii

CHAPTER 1 Introduction 1

1.1 The Portfolio Management Process 1

1.2 The Security Analyst's Job 1

1.3 Portfolio Analysis 2

1.3.1 Basic Assumptions 3

1.3.2 Reconsidering the Assumptions 3

1.4 Portfolio Selection 5

1.5 The Mathematics is Segregated 6

1.6 Topics to be Discussed 6

Appendix: Various Rates of Return 7

A1.1 Calculating the Holding Period Return 7

A1.2 After-Tax Returns 8

A1.3 Discrete and Continuously Compounded Returns 8

PART ONE Probability Foundations

CHAPTER 2 Assessing Risk 13

2.1 Mathematical Expectation 13

2.2 What Is Risk? 15

2.3 Expected Return 16

2.4 Risk of a Security 17

2.5 Covariance of Returns 18

2.6 Correlation of Returns 19

2.7 Using Historical Returns 20

2.8 Data Input Requirements 22

2.9 Portfolio Weights 22

2.10 A Portfolio's Expected Return 23

2.11 Portfolio Risk 23

2.12 Summary of Notations and Formulas 27

CHAPTER 3 Risk and Diversication 29

3.1 Reconsidering Risk 29

3.1.1 Symmetric Probability Distributions 31

3.1.2 Fundamental Security Analysis 32

3.2 Utility Theory 32

3.2.1 Numerical Example 33

3.2.2 Indifference Curves 35

3.3 Risk-Return Space 36

3.4 Diversication 38

3.4.1 Diversication Illustrated 38

3.4.2 Risky A + Risky B = Riskless Portfolio 39

3.4.3 Graphical Analysis 40

3.5 Conclusions 41

PART TWO Utility Foundations

CHAPTER 4 Single-Period Utility Analysis 45

4.1 Basic Utility Axioms 46

4.2 The Utility of Wealth Function 47

4.3 Utility of Wealth and Returns 47

4.4 Expected Utility of Returns 48

4.5 Risk Attitudes 52

4.5.1 Risk Aversion 52

4.5.2 Risk-Loving Behavior 56

4.5.3 Risk-Neutral Behavior 57

4.6 Absolute Risk Aversion 59

4.7 Relative Risk Aversion 60

4.8 Measuring Risk Aversion 62

4.8.1 Assumptions 62

4.8.2 Power, Logarithmic, and Quadratic Utility 62

4.8.3 Isoelastic Utility Functions 64

4.8.4 Myopic, but Optimal 65

4.9 Portfolio Analysis 66

4.9.1 Quadratic Utility Functions 67

4.9.2 Using Quadratic Approximations to Delineate Max[E(Utility)] Portfolios 68

4.9.3 Normally Distributed Returns 69

4.10 Indifference Curves 69

4.10.1 Selecting Investments 71

4.10.2 Risk-Aversion Measures 73

4.11 Summary and Conclusions 74

Appendix: Risk Aversion and Indifference Curves 75

A4.1 Absolute Risk Aversion (ARA) 75

A4.2 Relative Risk Aversion (RRA) 76

A4.3 Expected Utility of Wealth 77

A4.4 Slopes of Indifference Curves 77

A4.5 Indifference Curves for Quadratic Utility 79

PART THREE Mean-Variance Portfolio Analysis

CHAPTER 5 Graphical Portfolio Analysis 85

5.1 Delineating Efcient Portfolios 85

5.2 Portfolio Analysis Inputs 86

5.3 Two-Asset Isomean Lines 87

5.4 Two-Asset Isovariance Ellipses 90

5.5 Three-Asset Portfolio Analysis 92

5.5.1 Solving for One Variable Implicitly 93…