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 Diversi¿cation 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 Diversi¿cation 38
3.4.1 Diversi¿cation 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 Ef¿cient 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 Inef¿cient 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 Ef¿cient 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 Diversi¿cation 120
6.4 Ef¿cient 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 ¿p 131
CHAPTER 7 Advanced Mathematical Portfolio Analysis 135
7.1 Ef¿cient 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 Ef¿cient 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 Ef¿cient 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 Diversi¿cation 176
8.1.6 About the Single-Index Model 177
8.2 Ef¿cient Frontier and the Single-Index Model 178
8.3 Two-Index Models 186
8.3.1 Generating Inputs 187
8.3.2 Diversi¿cation 188
8.4 Multi-Index Models 189
8.5 Conclusions 190
Appendix: Index Models 191
A8.1 Solving for Ef¿cient 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 Speci¿cations 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 Diversi¿cation 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 De¿nition 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 Ef¿cient Frontier in Three-Dimensional Space 249
10.5.4 Undiversi¿able Risk and Undiversi¿able 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 Modi¿ed 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 Ef¿cient 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 Misspeci¿cations 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 Ef¿cient Markets 395
17.1.1 Fama's Classi¿cations 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 Diversi¿cation 407
17.5.1 Simple Diversi¿cation 408
17.5.2 Timing and Diversi¿cation 409
17.5.3 International Diversi¿cation 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 Ef¿cient 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 ¿A/¿2 ¿A= ¿Ki=1(¿i/¿2 ¿i) 431
A17.2 Proof for (¿AßA/ ¿2 ¿A) = ¿Ki=1 (¿ißi/¿2 ¿i) 431
A17.3 Proof for (¿2A/ ¿2 ¿A) = ¿Ki=1 (¿2 i/¿2 ¿i) 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 Undiversi¿ed 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+ [¿A/¿ (¿A)]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 Coef¿cients Estimation with Constraints 486
A19.1 With No Constraints 487
A19.2 With the Constraint of ¿Kk=1 ßik 475
CHAPTER 20 Stock Market Developments 489
20.1 Recent NYSE Consolidations 489
20.1.1 Archipelago 490
20.1.2 Paci¿c 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 Diversi¿es 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
