Portfolio Construction and Analytics

Portfolio Construction and Analytics provides an up-to-date understanding of the analytic investment process for students and professionals alike. With complete and detailed coverage of portfolio analytics and modeling methods, this book is unique in its multi-disciplinary approach. Investment analytics involves the input of a variety of areas, and this guide provides the perspective of data management, modeling, software resources, and investment strategy to give you a truly comprehensive understanding of how today's firms approach the process.  Real-world examples provide insight into analytics performed with vendor software, and references to analytics performed with open source software will prove useful to both students and practitioners.

Portfolio analytics refers to all of the methods used to screen, model, track, and evaluate investments. Big data, regulatory change, and increasing risk is forcing a need for a more coherent approach to all aspects of investment analytics, and this book provides the strong foundation and critical skills you need.

• Master the fundamental modeling concepts and widely used analytics
• Learn the latest trends in risk metrics, modeling, and investment strategies
• Get up to speed on the vendor and open-source software most commonly used
• Gain a multi-angle perspective on portfolio analytics at today's firms

Identifying investment opportunities, keeping portfolios aligned with investment objectives, and monitoring risk and performance are all major functions of an investment firm that relies heavily on analytics output. This reliance will only increase in the face of market changes and increased regulatory pressure, and practitioners need a deep understanding of the latest methods and models used to build a robust investment strategy. Portfolio Construction and Analytics is an invaluable resource for portfolio management in any capacity.

DESSISLAVA A. PACHAMANOVA is professor of analytics and computational finance and Zwerling Family Endowed Research Scholar at Babson College.

FRANK J. FABOZZI is professor of finance at EDHEC Business School, a senior scientific adviser at the EDHEC-Risk Institute, and editor of the Journal of Portfolio Management.

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

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