Preface xix
About the Authors xxv
Acknowledgments xxvii
CHAPTER 1 Introduction to Portfolio Management and Analytics 1
1.1 Asset Classes and the Asset Allocation Decision 1
1.2 The Portfolio Management Process 4
1.2.1 Setting the Investment Objectives 4
1.2.2 Developing and Implementing a Portfolio Strategy 6
1.2.3 Monitoring the Portfolio 8
1.2.4 Adjusting the Portfolio 9
1.3 Traditional versus Quantitative Asset Management 9
1.4 Overview of Portfolio Analytics 10
1.4.1 Market Analytics 12
1.4.2 Financial Screening 15
1.4.3 Asset Allocation Models 16
1.4.4 Strategy Testing and Evaluating Portfolio Performance 17
1.4.5 Systems for Portfolio Analytics 20
1.5 Outline of Topics Covered in the Book 22
PART ONE Statistical Models of Risk and Uncertainty
CHAPTER 2 Random Variables, Probability Distributions, and Important Statistical Concepts 31
2.1 What Is a Probability Distribution? 31
2.2 The Bernoulli Probability Distribution and Probability Mass Functions 32
2.3 The Binomial Probability Distribution and Discrete Distributions 34
2.4 The Normal Distribution and Probability Density Functions 38
2.5 The Concept of Cumulative Probability 41
2.6 Describing Distributions 44
2.6.1 Measures of Central Tendency 44
2.6.2 Measures of Risk 47
2.6.3 Skew 54
2.6.4 Kurtosis 55
2.7 Dependence between Two Random Variables: Covariance and Correlation 55
2.8 Sums of Random Variables 57
2.9 Joint Probability Distributions and Conditional Probability 61
2.10 Copulas 64
2.11 From Probability Theory to Statistical Measurement: Probability Distributions and Sampling 66
2.11.1 Central Limit Theorem 70
2.11.2 Confidence Intervals 71
2.11.3 Bootstrapping 72
2.11.4 Hypothesis Testing 73
CHAPTER 3 Important Probability Distributions 77
3.1 Examples of Probability Distributions 79
3.1.1 Notation Used in Describing Continuous Probability Distributions 79
3.1.2 Discrete and Continuous Uniform Distributions 80
3.1.3 Student's t Distribution 82
3.1.4 Lognormal Distribution 83
3.1.5 Poisson Distribution 85
3.1.6 Exponential Distribution 87
3.1.7 Chi-Square Distribution 88
3.1.8 Gamma Distribution 90
3.1.9 Beta Distribution 90
3.2 Modeling Financial Return Distributions 91
3.2.1 Elliptical Distributions 92
3.2.2 Stable Paretian Distributions 94
3.2.3 Generalized Lambda Distribution 96
3.3 Modeling Tails of Financial Return Distributions 98
3.3.1 Generalized Extreme Value Distribution 98
3.3.2 Generalized Pareto Distribution 99
3.3.3 Extreme Value Models 101
CHAPTER 4 Statistical Estimation Models 106
4.1 Commonly Used Return Estimation Models 106
4.2 Regression Analysis 108
4.2.1 A Simple Regression Example 109
4.2.2 Regression Applications in the Investment Management Process 114
4.3 Factor Analysis 116
4.4 Principal Components Analysis 118
4.5 Autoregressive Conditional Heteroscedastic Models 125
PART TWO Simulation and Optimization Modeling
CHAPTER 5 Simulation Modeling 133
5.1 Monte Carlo Simulation: A Simple Example 133
5.1.1 Selecting Probability Distributions for the Inputs 135
5.1.2 Interpreting Monte Carlo Simulation Output 137
5.2 Why Use Simulation? 140
5.2.1 Multiple Input Variables and Compounding Distributions 141
5.2.2 Incorporating Correlations 142
5.2.3 Evaluating Decisions 144
5.3 How Many Scenarios? 147
5.4 Random Number Generation 149
CHAPTER 6 Optimization Modeling 151
6.1 Optimization Formulations 152
6.1.1 Minimization versus Maximization 154
6.1.2 Local versus Global Optima 155
6.1.3 Multiple Objectives 156
6.2 Important Types of Optimization Problems 157
6.2.1 Convex Programming 157
6.2.2 Linear Programming 158
6.2.3 Quadratic Programming 159
6.2.4 Second-Order Cone Programming 160
6.2.5 Integer and Mixed Integer Programming 161
6.3 A Simple Optimization Problem Formulation Example: Portfolio Allocation 161
6.4 Optimization Algorithms 166
6.5 Optimization Software 168
6.6 A Software Implementation Example 170
6.6.1 Optimization with Excel Solver 171
6.6.2 Solution to the Portfolio Allocation Example 175
CHAPTER 7 Optimization under Uncertainty 180
7.1 Dynamic Programming 181
7.2 Stochastic Programming 183
7.2.1 Multistage Models 184
7.2.2 Mean-Risk Stochastic Models 189
7.2.3 Chance-Constrained Models 191
7.3 Robust Optimization 194
PART THREE Portfolio Theory
CHAPTER 8 Asset Diversification 203
8.1 The Case for Diversification 204
8.2 The Classical Mean-Variance Optimization Framework 208
8.3 Efficient Frontiers 212
8.4 Alternative Formulations of the Classical Mean-Variance Optimization Problem 215
8.4.1 Expected Return Formulation 215
8.4.2 Risk Aversion Formulation 215
8.5 The Capital Market Line 216
8.6 Expected Utility Theory 220
8.6.1 Quadratic Utility Function 221
8.6.2 Linear Utility Function 223
8.6.3 Exponential Utility Function 224
8.6.4 Power Utility Function 224
8.6.5 Logarithmic Utility Function 224
8.7 Diversification Redefined 226
CHAPTER 9 Factor Models 232
9.1 Factor Models in the Financial Economics Literature 233
9.2 Mean-Variance Optimization with Factor Models 236
9.3 Factor Selection in Practice 239
9.4 Factor Models for Alpha Construction 243
9.5 Factor Models for Risk Estimation 245
9.5.1 Macroeconomic Factor Models 245
9.5.2 Fundamental Factor Models 246
9.5.3 Statistical Factor Models 248
9.5.4 Hybrid Factor Models 250
9.5.5 Selecting the Right Factor Model 250
9.6 Data Management and Quality Issues 251
9.6.1 Data Alignment 252
9.6.2 Survival Bias 253
9.6.3 Look-Ahead Bias 253
9.6.4 Data Snooping 254
9.7 Risk Decomposition, Risk Attribution, and Performance Attribution 254
9.8 Factor Investing 256
CHAPTER 10 Benchmarks and the Use of Tracking Error in Portfolio Construction 260
10.1 Tracking Error versus Alpha: Calculation and Interpretation 261
10.2 Forward-Looking versus Backward-Looking Tracking Error 264
10.3 Tracking Error and Information Ratio 265
10.4 Predicted Tracking Error Calculation 265
10.4.1 Variance-Covariance Method for Tracking Error Calculation 266
10.4.2 Tracking Error Calculation Based on a Multifactor Model 266
10.5 Benchmarks and Indexes 268
10.5.1 Market Indexes 268
10.5.2 Noncapitalization Weighted Indexes 270
10.6 Smart Beta Investing 272
PART FOUR Equity Portfolio Management
CHAPTER 11 Advances in Quantitative Equity Portfolio Management 281
11.1 Portfolio Constraints Commonly Used in Practice 282
11.1.1 Long-Only (No-Short-Selling) Constraints 283
11.1.2 Holding Constraints 283
11.1.3 Turnover Constraints 284
11.1.4 Factor Constraints 284
11.1.5 Cardinality Constraints 286
11.1.6 Minimum Holding and Transaction Size Constraints 287
11.1.7 Round Lot Constraints 288
11.1.8 Tracking Error Constraints 290
11.1.9 Soft Constraints 291
11.1.10 Misalignment Caused by Constraints 291
11.2 Portfolio Optimization with Tail Risk Measures 291
11.2.1 Portfolio Value-at-Risk Optimization 292
11.2.2 Portfolio Conditional Value-at-Risk Optimization 294
11.3 Incorporating Transaction Costs 297
11.3.1 Linear Transaction Costs 299
11.3.2 Piecewise-Linear Transaction Costs 300
11.3.3 Quadratic Transaction Costs 302
11.3.4 Fixed Transaction Costs 302
11.3.5 Market Impact Costs 303
11.4 Multiaccount Optimization 304
11.5 Incorporating Taxes 308
11.6 Robust Parameter Estimation 312
11.7 Portfolio Resampling 314
11.8 Robust Portfolio Optimization 317
CHAPTER 12 Factor-Based Equity Portfolio Construction and Performance Evaluation 325
12.1 Equity Factors Used in Practice 325
12.1.1 Fundamental Factors 326
12.1.2 Macroeconomic Factors 327
12.1.3 Technical Factors 327
12.1.4 Additional Factors 327
12.2 Stock Screens 328
12.3 Portfolio Selection 331
12.3.1 Ad-Hoc Portfolio Selection 331
12.3.2 Stratification 332
12.3.3 Factor Exposure Targeting 333
12.4 Risk Decomposition 334
12.5 Stress Testing 343
12.6 Portfolio Performance Evaluation 346
12.7 Risk Forecasts and Simulation 350
PART FIVE Fixed Income Portfolio Management
CHAPTER 13 Fundamentals of Fixed Income Portfolio Management 361
13.1 Fixed Income Instruments and Major Sectors of the Bond Market 361
13.1.1 Treasury Securities 362
13.1.2 Federal Agency Securities 363
13.1.3 Corporate Bonds 363
13.1.4 Municipal Bonds 364
13.1.5 Structured Products 364
13.2 Features of Fixed Income Securities 365
13.2.1 Term to Maturity and Maturity 365
13.2.2 Par Value 366
13.2.3 Coupon Rate 366
13.2.4 Bond Valuation and Yield 367
13.2.5 Provisions for Paying Off Bonds 368
13.2.6 Bondholder Option Provisions 370
13.3 Major Risks Associated with Investing in Bonds 371
13.3.1 Interest Rate Risk 371
13.3.2 Call and Prepayment Risk 372
13.3.3 Credit Risk 373
13.3.4 Liquidity Risk 374
13.4 Fixed Income Analytics 375
13.4.1 Measuring Interest Rate Risk 375
13.4.2 Measuring Spread Risk 383
13.4.3 Measuring Credit Risk 384
13.4.4 Estimating Fixed Income Portfolio Risk Using Simulation 384
13.5 The Spectrum of Fixed Income Portfolio Strategies 386
13.5.1 Pure Bond Indexing Strategy 387
13.5.2 Enhanced Indexing/Primary Factor Matching 388
13.5.3 Enhanced Indexing/Minor Factor Mismatches 389
13.5.4 Active Management/Larger Factor Mismatches 389
13.5.5 Active Management/Full-Blown Active 390
13.5.6 Smart Beta Strategies for Fixed Income Portfolios 390
13.6 Value-Added Fixed Income Strategies 391
13.6.1 Interest Rate Expectations Strategies 391
13.6.2 Yield Curve Strategies 392
13.6.3 Inter- and Intra-sector Allocation Strategies 393
13.6.4 Individual Security Selection Strategies 394
CHAPTER 14 Factor-Based Fixed Income Portfolio Construction and Evaluation 398
14.1 Fixed Income Factors Used in Practice 398
14.1.1 Term Structure Factors 399
14.1.2 Credit Spread Factors 400
14.1.3 Currency Factors 401
14.1.4 Emerging Market Factors 401
14.1.5 Volatility Factors 402
14.1.6 Prepayment Factors 402
14.2 Portfolio Selection 402
14.2.1 Stratification Approach 403
14.2.2 Optimization Approach 405
14.2.3 Portfolio Rebalancing 408
14.3 Risk Decomposition 410
CHAPTER 15 Constructing Liability-Driven Portfolios 420
15.1 Risks Associated with Liabilities 421
15.1.1 Interest Rate Risk 421
15.1.2 Inflation Risk 422
15.1.3 Longevity Risk 423
15.2 Liability-Driven Strategies of Life Insurance Companies 423
15.2.1 Immunization 424
15.2.2 Advanced Optimization Approaches 435
15.2.3 Constructing Replicating Portfolios 437
15.3 Liability-Driven Strategies of Defined Benefit Pension Funds 438
15.3.1 High-Grade Bond Portfolio Solution 439
15.3.2 Including Other Assets 442
15.3.3 Advanced Modeling Strategies 443
PART SIX Derivatives and Their Application to Portfolio Management
CHAPTER 16 Basics of Financial Derivatives 449
16.1 Overview of the Use of Derivatives in Portfolio Management 449
16.2 Forward and Futures Contracts 451
16.2.1 Risk and Return of Forward/Futures Position 453
16.2.2 Leveraging Aspect of Futures 453
16.2.3 Pricing of Futures and Forward Contracts 454
16.3 Options 459
16.3.1 Risk and Return Characteristics of Options 460
16.3.2 Option Pricing Models 470
16.4 Swaps 485
16.4.1 Interest Rate Swaps 485
16.4.2 Equity Swaps 486
16.4.3 Credit Default Swaps 487
CHAPTER 17 Using Derivatives in Equity Portfolio Management 490
17.1 Stock Index Futures and Portfolio Management Applications 490
17.1.1 Basic Features of Stock Index Futures 490
17.1.2 Theoretical Price of a Stock Index Futures Contract 491
17.1.3 Portfolio Management Strategies with Stock Index Futures 494
17.2 Equity Options and Portfolio Management Applications 504
17.2.1 Types of Equity Options 504
17.2.2 Equity Portfolio Management Strategies with Options 506
17.3 Equity Swaps 511
CHAPTER 18 Using Derivatives in Fixed Income Portfolio Management 515
18.1 Controlling Interest Rate Risk Using Treasury Futures 515
18.1.1 Strategies for Controlling Interest Rate Risk with Treasury Futures 518
18.1.2 Pricing of Treasury Futures 520
18.2 Controlling Interest Rate Risk Using Treasury Futures Options 521
18.2.1 Strategies for Controlling Interest Rate Risk Using Treasury Futures Options 524
18.2.2 Pricing Models for Treasury Futures Options 526
18.3 Controlling Interest Rate Risk Using Interest Rate Swaps 527
18.3.1 Strategies for Controlling Interest Rate Risk Using Interest Rate Swaps 528
18.3.2 Pricing of Interest Rate Swaps 530
18.4 Controlling Credit Risk with Credit Default Swaps 532
18.4.1 Strategies for Controlling Credit Risk with Credit Default Swaps 534
18.4.2 General Principles for Valuing a Single-Name Credit Default Swap 535
Appendix: Basic Linear Algebra Concepts 541
References 549
Index 563
