# Modern Portfolio Theory: Foundations, Analysis, and New Developments, + Website

ISBN: 978-1-118-41720-1

Jan 2013

576 pages

Select type: E-Book

\$61.99

## Description

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.

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Contents

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

1.4 Portfolio Selection 5

1.5 The Mathematics is Segregated 6

1.6 Topics to be Discussed 6

Appendix: Various Rates of Return 7

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 Diversification 29

3.1 Reconsidering Risk 29

3.2 Utility Theory 32

3.3 Risk-Return Space 36

3.4 Diversification 38

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

4.6 Absolute Risk Aversion 59

4.7 Relative Risk Aversion 60

4.8 Measuring Risk Aversion 62

4.9 Portfolio Analysis 66

4.10 Indifference Curves 69

4.11 Summary and Conclusions 74

Appendix: Risk Aversion and Indifference Curves 75

PART THREE Mean-Variance Portfolio Analysis

CHAPTER 5 Graphical Portfolio Analysis 85

5.1 Delineating Efficient 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

5.6 Legitimate Portfolios 102

5.7 ‘‘Unusual’’ Graphical Solutions Don’t Exist 103

5.8 Representing Constraints Graphically 103

5.9 The Interior Decorator Fallacy 103

5.10 Summary 104

CHAPTER 6 Efficient Portfolios 113

6.1 Risk and Return for Two-Asset Portfolios 113

6.2 The Opportunity Set 114

6.3 Markowitz Diversification 120

6.4 Efficient Frontier without the Risk-Free Asset 123

6.5 Introducing a Risk-Free Asset 126

6.6 Summary and Conclusions 131

Appendix: Equations for a Relationship between Erp) and σp

CHAPTER 7 Advanced Mathematical Portfolio Analysis 135

7.1 Efficient Portfolios without a Risk-Free Asset 135

7.2 Efficient Portfolios with a Risk-Free Asset 146

7.3 Identifying the Tangency Portfolio 150

7.4 Summary and Conclusions 152

Appendix: Mathematical Derivation of the Efficient Frontier 152

CHAPTER 8 Index Models and Return-Generating Process 165

8.1 Single-Index Models 165

8.2 Efficient Frontier and the Single-Index Model 178

8.3 Two-Index Models 186

8.4 Multi-Index Models 189

8.5 Conclusions 190

Appendix: Index Models 191

PART FOUR Non-Mean-Variance Portfolios

CHAPTER 9 Non-Normal Distributions of Returns 201

9.1 Stable Paretian Distributions 201

9.2 The Student’s t -Distribution 204

9.3 Mixtures of Normal Distributions 204

9.4 Poisson Jump-Diffusion Process 206

9.5 Lognormal Distributions 206

9.6 Conclusions 213

CHAPTER 10 Non-Mean-Variance Investment Decisions 215

10.1 Geometric Mean Return Criterion 215

10.2 The Safety-First Criterion 218

10.3 Semivariance Analysis 228

10.4 Stochastic Dominance Criterion 236

10.5 Mean-Variance-Skewness Analysis 246

10.6 Summary and Conclusions 254

Appendix A: Stochastic Dominance 254

Appendix B: Expected Utility as a Function of Three Moments 257

CHAPTER 11 Risk Management: Value at Risk 261

11.1 VaR of a Single Asset 261

11.2 Portfolio VaR 263

11.3 Decomposition of a Portfolio’s VaR 265

11.4 Other VaRs 269

11.5 Methods of Measuring VaR 270

11.6 Estimation of Volatilities 277

11.7 The Accuracy of VaR Models 282

11.8 Summary and Conclusions 285

Appendix: The Delta-Gamma Method 285

PART FIVE Asset Pricing Models

CHAPTER 12 The Capital Asset Pricing Model 291

12.1 Underlying Assumptions 291

12.2 The Capital Market Line 292

12.3 The Capital Asset Pricing Model 295

12.4 Over- and Under-priced Securities 299

12.5 The Market Model and the CAPM 300

12.6 Summary and Conclusions 301

Appendix: Derivations of the CAPM 301

CHAPTER 13 Extensions of the Standard CAPM 311

13.1 Risk-Free Borrowing or Lending 311

13.2 Homogeneous Expectations 316

13.3 Perfect Markets 318

13.4 Unmarketable Assets 322

13.5 Summary and Conclusions 323

Appendix: Derivations of a Non-Standard CAPM 324

CHAPTER 14 Empirical Tests of the CAPM 333

14.1 Time-Series Tests of the CAPM 333

14.2 Cross-Sectional Tests of the CAPM 335

14.3 Empirical Misspecifications in Cross-Sectional Regression Tests 345

14.4 Multivariate Tests 353

14.5 Is the CAPM Testable? 356

14.6 Summary and Conclusions 357

CHAPTER 15 Continuous-Time Asset Pricing Models 361

15.1 Intertemporal CAPM (ICAPM) 361

15.2 The Consumption-Based CAPM (CCAPM) 363

15.3 Conclusions 366

Appendix: Lognormality and the Consumption-Based CAPM 367

CHAPTER 16 Arbitrage Pricing Theory 371

16.1 Arbitrage Concepts 371

16.2 Index Arbitrage 375

16.4 Asset Pricing on a Security Market Plane 383

16.5 Contrasting APT with CAPM 385

16.6 Empirical Evidence 386

16.7 Comparing the APT and CAPM Empirically 388

16.8 Conclusions 389

PART SIX Implementing the Theory

CHAPTER 17 Portfolio Construction and Selection 395

17.1 Efficient Markets 395

17.2 Using Portfolio Theories to Construct and Select Portfolios 398

17.3 Security Analysis 400

17.4 Market Timing 401

17.5 Diversification 407

17.6 Constructing an Active Portfolio 415

17.7 Portfolio Revision 424

17.8 Summary and Conclusions 430

Appendix: Proofs for Some Ratios from Active Portfolios 431

CHAPTER 18 Portfolio Performance Evaluation 435

18.1 Mutual Fund Returns 435

18.2 Portfolio Performance Analysis in the Good Old Days 436

18.3 Capital Market Theory Assumptions 438

18.4 Single-Parameter Portfolio Performance Measures 438

18.5 Market Timing 449

18.6 Comparing Single-Parameter Portfolio Performance Measures 452

18.7 The Index of Total Portfolio Risk (ITPR) and the Portfolio Beta 454

18.8 Measurement Problems 457

18.9 Do Winners or Losers Repeat? 461

18.10 Summary about Investment Performance Evaluation 465

Appendix: Sharpe Ratio of an Active Portfolio 467

19.1 Factor Model Analysis 474

19.2 Return-Based Style Analysis 475

19.3 Return Decomposition-Based Analysis 479

19.4 Conclusions 485

Appendix: Regression Coefficients Estimation with Constraints 486

CHAPTER 20 Stock Market Developments 489

20.1 Recent NYSE Consolidations 489

20.2 International Securities Exchange (ISE) 492

20.3 Nasdaq 492

20.4 Downward Pressures on Transactions Costs 494

20.5 The Venerable Limit Order 497

20.6 Market Microstructure 498

20.8 Alternative Trading Systems (ATSs) 500

20.10 Symbiotic Stock Market Developments 505

20.11 Detrimental Stock Market Developments 505

20.12 Summary and Conclusions 506

Mathematical Appendixes 509

Bibliography 519