Portfolio Construction and Analytics

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