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Modern Portfolio Theory. Foundations, Analysis, and New Developments. Edition No. 1. Wiley Finance

  • ID: 2328053
  • Book
  • February 2013
  • 576 Pages
  • John Wiley and Sons Ltd
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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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 Diversification 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 Diversification 38

3.4.1 Diversification 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 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

5.5.1 Solving for One Variable Implicitly 93

5.5.2 Isomean Lines 96

5.5.3 Isovariance Ellipses 97

5.5.4 The Critical Line 99

5.5.5 Inefficient Portfolios 101

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

Appendix: Quadratic Equations 105

A5.1 Quadratic Equations 105

A5.2 Analysis of Quadratics in Two Unknowns 106

A5.3 Analysis of Quadratics in One Unknown 107

A5.4 Solving an Ellipse 108

A5.5 Solving for Lines Tangent to a Set of Ellipses 110

CHAPTER 6 Efficient Portfolios 113

6.1 Risk and Return for Two-Asset Portfolios 113

6.2 The Opportunity Set 114

6.2.1 The Two-Security Case 114

6.2.2 Minimizing Risk in the Two-Security Case 116

6.2.3 The Three-Security Case 117

6.2.4 The n-Security Case 119

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 E(rp) and σp 131

CHAPTER 7 Advanced Mathematical Portfolio Analysis 135

7.1 Efficient Portfolios without a Risk-Free Asset 135

7.1.1 A General Formulation 135

7.1.2 Formulating with Concise Matrix Notation 140

7.1.3 The Two-Fund Separation Theorem 145

7.1.4 Caveat about Negative Weights 146

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

A7.1 No Risk-Free Asset 152

A7.2 With a Risk-Free Asset 156

CHAPTER 8 Index Models and Return-Generating Process 165

8.1 Single-Index Models 165

8.1.1 Return-Generating Functions 165

8.1.2 Estimating the Parameters 168

8.1.3 The Single-Index Model Using Excess Returns 171

8.1.4 The Riskless Rate Can Fluctuate 173

8.1.5 Diversification 176

8.1.6 About the Single-Index Model 177

8.2 Efficient Frontier and the Single-Index Model 178

8.3 Two-Index Models 186

8.3.1 Generating Inputs 187

8.3.2 Diversification 188

8.4 Multi-Index Models 189

8.5 Conclusions 190

Appendix: Index Models 191

A8.1 Solving for Efficient Portfolios with the Single-Index Model 191

A8.2 Variance Decomposition 196

A8.3 Orthogonalizing Multiple Indexes 196

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

9.3.1 Discrete Mixtures of Normal Distributions 204

9.3.2 Sequential Mixtures of Normal Distributions 205

9.4 Poisson Jump-Diffusion Process 206

9.5 Lognormal Distributions 206

9.5.1 Specifications of Lognormal Distributions 207

9.5.2 Portfolio Analysis under Lognormality 208

9.6 Conclusions 213

CHAPTER 10 Non-Mean-Variance Investment Decisions 215

10.1 Geometric Mean Return Criterion 215

10.1.1 Maximizing the Terminal Wealth 216

10.1.2 Log Utility and the GMR Criterion 216

10.1.3 Diversification and the GMR 217

10.2 The Safety-First Criterion 218

10.2.1 Roy’s Safety-First Criterion 218

10.2.2 Kataoka’s Safety-First Criterion 222

10.2.3 Telser’s Safety-First Criterion 225

10.3 Semivariance Analysis 228

10.3.1 Definition of Semivariance 228

10.3.2 Utility Theory 230

10.3.3 Portfolio Analysis with the Semivariance 231

10.3.4 Capital Market Theory with the Semivariance 234

10.3.5 Summary about Semivariance 236

10.4 Stochastic Dominance Criterion 236

10.4.1 First-Order Stochastic Dominance 236

10.4.2 Second-Order Stochastic Dominance 241

10.4.3 Third-Order Stochastic Dominance 244

10.4.4 Summary of Stochastic Dominance Criterion 245

10.5 Mean-Variance-Skewness Analysis 246

10.5.1 Only Two Moments Can Be Inadequate 246

10.5.2 Portfolio Analysis in Three Moments 247

10.5.3 Efficient Frontier in Three-Dimensional Space 249

10.5.4 Undiversifiable Risk and Undiversifiable Skewness 252

10.6 Summary and Conclusions 254

Appendix A: Stochastic Dominance 254

A10.1 Proof for First-Order Stochastic Dominance 254

A10.2 Proof That FA(r) ≤ FB(r) Is Equivalent to EA(r) ≥ EB(r) for Positive r 255

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

11.3.1 Marginal VaR 265

11.3.2 Incremental VaR 266

11.3.3 Component VaR 267

11.4 Other VaRs 269

11.4.1 Modified VaR (MVaR) 269

11.4.2 Conditional VaR (CVaR) 270

11.5 Methods of Measuring VaR 270

11.5.1 Variance-Covariance (Delta-Normal) Method 270

11.5.2 Historical Simulation Method 274

11.5.3 Monte Carlo Simulation Method 276

11.6 Estimation of Volatilities 277

11.6.1 Unconditional Variance 277

11.6.2 Simple Moving Average 277

11.6.3 Exponentially Weighted Moving Average 278

11.6.4 GARCH-Based Volatility 278

11.6.5 Volatility Measures Using Price Range 279

11.6.6 Implied Volatility 281

11.7 The Accuracy of VaR Models 282

11.7.1 Back-Testing 283

11.7.2 Stress Testing 284

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

12.2.1 The Market Portfolio 292

12.2.2 The Separation Theorem 293

12.2.3 Efficient Frontier Equation 294

12.2.4 Portfolio Selection 294

12.3 The Capital Asset Pricing Model 295

12.3.1 Background 295

12.3.2 Derivation of the CAPM 296

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

A12.1 Other Approaches 301

A12.2 Tangency Portfolio Research 305

CHAPTER 13 Extensions of the Standard CAPM 311

13.1 Risk-Free Borrowing or Lending 311

13.1.1 The Zero-Beta Portfolio 311

13.1.2 No Risk-Free Borrowing 314

13.1.3 Lending and Borrowing Rates Can Differ 314

13.2 Homogeneous Expectations 316

13.2.1 Investment Horizons 316

13.2.2 Multivariate Distribution of Returns 317

13.3 Perfect Markets 318

13.3.1 Taxes 318

13.3.2 Transaction Costs 320

13.3.3 Indivisibilities 321

13.3.4 Price Competition 321

13.4 Unmarketable Assets 322

13.5 Summary and Conclusions 323

Appendix: Derivations of a Non-Standard CAPM 324

A13.1 The Characteristics of the Zero-Beta Portfolio 324

A13.2 Derivation of Brennan’s After-Tax CAPM 325

A13.3 Derivation of Mayers’s CAPM for Nonmarketable Assets 328

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

14.2.1 Black, Jensen, and Scholes’s (1972) Tests 336

14.2.2 Fama and MacBeth’s (1973) Tests 340

14.2.3 Fama and French’s (1992) Tests 344

14.3 Empirical Misspecifications in Cross-Sectional Regression Tests 345

14.3.1 The Errors-in-Variables Problem 346

14.3.2 Sensitivity of Beta to the Return Measurement Intervals 351

14.4 Multivariate Tests 353

14.4.1 Gibbons’s (1982) Test 353

14.4.2 Stambaugh’s (1982) Test 355

14.4.3 Jobson and Korkie’s (1982) Test 355

14.4.4 Shanken’s (1985) Test 356

14.4.5 Generalized Method of Moment (GMM) Tests 356

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

15.2.1 Derivation 363

15.2.2 The Consumption-Based CAPM with a Power Utility Function 365

15.3 Conclusions 366

Appendix: Lognormality and the Consumption-Based CAPM 367

A15.1 Lognormality 367

A15.2 The Consumption-Based CAPM with Lognormality 367

CHAPTER 16 Arbitrage Pricing Theory 371

16.1 Arbitrage Concepts 371

16.2 Index Arbitrage 375

16.2.1 Basic Ideas of Index Arbitrage 376

16.2.2 Index Arbitrage and Program Trading 377

16.2.3 Use of ETFs for Index Arbitrage 377

16.3 The Asset Pricing Equation 378

16.3.1 One Single Factor with No Residual Risk 379

16.3.2 Two Factors with No Residual Risk 380

16.3.3 K Factors with No Residual Risk 381

16.3.4 K Factors with Residual Risk 382

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

17.1.1 Fama’s Classifications 395

17.1.2 Formal Models 396

17.2 Using Portfolio Theories to Construct and Select Portfolios 398

17.3 Security Analysis 400

17.4 Market Timing 401

17.4.1 Forecasting Beta 401

17.4.2 Nonstationarity of Beta 404

17.4.3 Determinants of Beta 406

17.5 Diversification 407

17.5.1 Simple Diversification 408

17.5.2 Timing and Diversification 409

17.5.3 International Diversification 411

17.6 Constructing an Active Portfolio 415

17.7 Portfolio Revision 424

17.7.1 Portfolio Revision Costs 424

17.7.2 Controlled Transition 426

17.7.3 The Attainable Efficient Frontier 428

17.7.4 A Turnover-Constrained Approach 428

17.8 Summary and Conclusions 430

Appendix: Proofs for Some Ratios from Active Portfolios 431

A17.1 Proof for αA2 εA= ∑Ki=1(αi2 εi) 431

A17.2 Proof for (αAβA/ σ2 εA) = ∑Ki=1 (αiβi2 εi) 431

A17.3 Proof for (α2A/ σ2 εA) = ∑Ki=1 (σ2 i2 εi) 432

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

18.4.1 Sharpe’s Reward-to-Variability Ratio 439

18.4.2 Treynor’s Reward-to-Risk Ratio 441

18.4.3 Jensen’s Measure 444

18.4.4 Information Ratio (or Appraisal Ratio) 447

18.4.5 M2 Measure 448

18.5 Market Timing 449

18.5.1 Interpreting the Market Timing Coefficient 450

18.5.2 Henriksson and Merton’s Model 451

18.5.3 Descriptive Comments 452

18.6 Comparing Single-Parameter Portfolio Performance Measures 452

18.6.1 Ranking Undiversified Investments 452

18.6.2 Contrasting the Three Models 453

18.6.3 Survivorship Bias 454

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

18.8 Measurement Problems 457

18.8.1 Measurement of the Market Portfolio’s Returns 458

18.8.2 Nonstationarity of Portfolio Return Distributions 460

18.9 Do Winners or Losers Repeat? 461

18.10 Summary about Investment Performance Evaluation 465

Appendix: Sharpe Ratio of an Active Portfolio 467

A18.1 Proof that S2q= S2m+ [αA/σ (εA)]2 467

CHAPTER 19 Performance Attribution 473

19.1 Factor Model Analysis 474

19.2 Return-Based Style Analysis 475

19.3 Return Decomposition-Based Analysis 479

19.4 Conclusions 485

19.4.1 Detrimental Uses of Portfolio Performance Attribution 486

19.4.2 Symbiotic Possibilities 486

Appendix: Regression Coefficients Estimation with Constraints 486

A19.1 With No Constraints 487

A19.2 With the Constraint of ∑Kk=1 βik 475

CHAPTER 20 Stock Market Developments 489

20.1 Recent NYSE Consolidations 489

20.1.1 Archipelago 490

20.1.2 Pacific Stock Exchange (PSE) 490

20.1.3 ArcaEx 490

20.1.4 New York Stock Exchange (NYSE) 490

20.1.5 NYSE Group 491

20.1.6 NYSE Diversifies Internationally 491

20.1.7 NYSE Alliances 491

20.2 International Securities Exchange (ISE) 492

20.3 Nasdaq 492

20.3.1 London Stock Exchange (LSE) 493

20.3.2 OMX Group 493

20.3.3 Bourse Dubai 493

20.3.4 Boston Stock Exchange (BSE) 494

20.3.5 Philadelphia Stock Exchange (PHLX) 494

20.4 Downward Pressures on Transactions Costs 494

20.4.1 A National Market System (NMS) 495

20.4.2 The SEC’s Reg ATS 496

20.4.3 Reg FD 496

20.4.4 Decimalization of Stock Prices 496

20.4.5 Technological Advances 496

20.5 The Venerable Limit Order 497

20.5.1 What Are Limit Orders? 497

20.5.2 Creating Market Liquidity 498

20.6 Market Microstructure 498

20.6.1 Inventory Management 498

20.6.2 Brokers 499

20.7 High-Frequency Trading 499

20.8 Alternative Trading Systems (ATSs) 500

20.8.1 Crossing Networks 500

20.8.2 Dark Pools 500

20.9 Algorithmic Trading 501

20.9.1 Some Algorithmic Trading Applications 501

20.9.2 Trading Curbs 503

20.9.3 Conclusions about Algorithmic Trading 504

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

About the Authors 539

Author Index 541

Subject Index 547

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Dongcheol Kim
Jack Clark Francis
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