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Page iii Active Portfolio Management A Quantitative Approach for Providing Superior Returns and Controlling Risk Richard C Grinold Ronald N Kahn SECOND EDITION Page vii CONTENTS Preface xi Acknowledgments xv Chapter Introduction Part One Foundations Chapter Consensus Expected Returns: The Capital Asset Pricing Model 11 Chapter Risk 41 Chapter Exceptional Return, Benchmarks, and Value Added 87 Chapter Residual Risk and Return: The Information Ratio 109 Chapter The Fundamental Law of Active Management 147 Part Two Expected Returns and Valuation Chapter Expected Returns and the Arbitrage Pricing Theory 173 Page viii Chapter Valuation in Theory 199 Chapter Valuation in Practice 225 Part Three Information Processing Chapter 10 Forecasting Basics 261 Chapter 11 Advanced Forecasting 295 Chapter 12 Information Analysis 315 Chapter 13 The Information Horizon 347 Part Four Implementation Chapter 14 Portfolio Construction 377 Chapter 15 Long/Short Investing 419 Chapter 16 Transactions Costs, Turnover, and Trading 445 Chapter 17 Performance Analysis 477 Page ix Chapter 18 Asset Allocation 517 Chapter 19 Benchmark Timing 541 Chapter 20 The Historical Record for Active Management 559 Chapter 21 Open Questions 573 Chapter 22 Summary 577 Appendix A Standard Notation 581 Appendix B Glossary 583 Appendix C Return and Statistics Basics 587 Index 591 Page xi PREFACE Why a second edition? Why take time from busy lives? Why devote the energy to improving an existing text rather than writing an entirely new one? Why toy with success? The short answer is: our readers We have been extremely gratified by Active Portfolio Management's reception in the investment community The book seems to be on the shelf of every practicing or aspiring quantitatively oriented investment manager, and the shelves of many fundamental portfolio managers as well But while our readers have clearly valued the book, they have also challenged us to improve it Cover more topics of relevance to today Add empirical evidence where appropriate Clarify some discussions The long answer is that we have tried to improve Active Portfolio Management along exactly these dimensions First, we have added significant amounts of new material in the second edition New chapters cover Advanced Forecasting (Chap 11), The Information Horizon (Chap 13), Long/Short Investing (Chap 15), Asset Allocation (Chap 18), The Historical Record for Active Management (Chap 20), and Open Questions (Chap 21) Some previously existing chapters also cover new material This includes a more detailed discussion of risk (Chap 3), dispersion (Chap 14), market impact (Chap 16), and academic proposals for performance analysis (Chap 17) Second, we receive exhortations to add more empirical evidence, where appropriate At the most general level: how we know this entire methodology works? Chapter 20, on The Historical Record for Active Management, provides some answers We have also added empirical evidence about the accuracy of risk models, in Chap At the more detailed level, readers have wanted more information on typical numbers for information ratios and active risk Chapter now includes empirical distributions of these statistics Chapter 15 provides similar empirical results for long/short portfolios Chapter includes empirical distributions of asset level risk statistics Page xii Third, we have tried to clarify certain discussions We received feedback on how clearly we had conveyed certain ideas through at least two channels First, we presented a talk summarizing the book at several investment management conferences.1 "Seven Quantitative Insights into Active Management" presented the key ideas as: Active Management is Forecasting: consensus views lead to the benchmark The Information Ratio (IR) is the Key to Value-Added The Fundamental Law of Active Management: Alphas must control for volatility, skill, and expectations: Alpha = Volatility · IC · Score Why Datamining is Easy, and guidelines to avoid it Implementation should subtract as little value as possible Distinguishing skill from luck is difficult This talk provided many opportunities to gauge understanding and confusion over these basic ideas We also presented a training course version of the book, called "How to Research Active Strategies." Over 500 investment professionals from New York to London to Hong Kong and Tokyo have participated This course, which involved not only lectures, but problem sets and extensive discussions, helped to identify some remaining confusions with the material For example, how does the forecasting methodology in the book, which involves information about returns over time, apply to the standard case of information about many assets at one time? We have devoted Chap 11, Advanced Forecasting, to that important discussion Finally, we have fixed some typographical errors, and added more problems and exercises to each chapter We even added a new type of problem—applications exercises These use commercially available analytics to demonstrate many of the ideas in the 1The BARRA Newsletter presented a serialized version of this talk during 1997 and 1998 Page xiii book These should help make some of the more technical results accessible to less mathematical readers Beyond these many reader-inspired improvements, we may also bring a different perspective to the second edition of Active Portfolio Management Both authors now earn their livelihoods as active managers To readers of the first edition of Active Portfolio Management, we hope this second edition answers your challenges To new readers, we hope you continue to find the book important, useful, challenging, and comprehensive RICHARD C GRINOLD RONALD N KAHN Page xv ACKNOWLEDGMENTS Many thanks to Andrew Rudd for his encouragement of this project while the authors were employed at BARRA, and to Blake Grossman for his continued enthusiasm and support of this effort at Barclays Global Investors Any close reader will realize that we have relied heavily on the path breaking work of Barr Rosenberg Barr was the pioneer in applying economics, econometrics and operations research to solve practical investment problems To a lesser, but not less crucial extent, we are indebted to the original and practical work of Bill Sharpe and Fischer Black Their ideas are the foundation of much of our analysis Many people helped shape the final form of this book Internally at BARRA and Barclays Global Investors, we benefited from conversations with and feedback from Andrew Rudd, Blake Grossman, Peter Algert, Stan Beckers, Oliver Buckley, Vinod Chandrashekaran, Naozer Dadachanji, Arjun DiVecha, Mark Engerman, Mark Ferrari, John Freeman, Ken Hui, Ken Kroner, Uzi Levin, Richard Meese, Peter Muller, George Patterson, Scott Scheffler, Dan Stefek, Nicolo Torre, Marco Vangelisti, Barton Waring, and Chris Woods Some chapters appeared in preliminary form at BARRA seminars and as journal articles, and we benefited from broader feedback from the quantitative investment community At the more detailed level, several members of the research groups at BARRA and Barclays Global Investors helped generate the examples in the book, especially Chip Castille, Mikhail Dvorkin, Cliff Gong, Josh Rosenberg, Mike Shing, Jennifer Soller, and Ko Ushigusa BARRA and Barclays Global Investors have also been supportive throughout Finally, we must thank Leslie Henrichsen, Amber Mayes, Carolyn Norton, and Mary Wang for their administrative help over many years Page Chapter 1— Introduction The art of investing is evolving into the science of investing This evolution has been happening slowly and will continue for some time The direction is clear; the pace varies As new generations of increasingly scientific investment managers come to the task, they will rely more on analysis, process, and structure than on intuition, advice, and whim This does not mean that heroic personal investment insights are a thing of the past It means that managers will increasingly capture and apply those insights in a systematic fashion We hope this book will go part of the way toward providing the analytical underpinnings for the new class of active investment managers We are addressing a fresh topic Quantitative active management—applying rigorous analysis and a rigorous process to try to beat the market—is a cousin of the modern study of financial economics Financial economics is conducted with much vigor at leading universities, safe from any need to deliver investment returns Indeed, from the perspective of the financial economist, active portfolio management appears to be a mundane consideration, if not an entirely dubious proposition Modern financial economics, with its theories of market efficiency, inspired the move over the past decade away from active management (trying to beat the market) to passive management (trying to match the market) This academic view of active management is not monolithic, since the academic cult of market efficiency has split One group now enthusiastically investigates possible market inefficiencies Page 593 (Cont.) Forecasts/forecasting two forecasts for each of n assets, 310–311 and uncertain information coefficients, 305–308, 312–313 Fractiles, 273–274 Fundamental law of active management, 147–168, 225, 550 additivity of, 154–157 assumptions of, 157–160 attributes of, 148 derivation of, 163–168 examples using, 150–154 and investment style, 161 statement of, 148 and statistical law of large numbers, 160 tests of, 160–161 usefulness of, 149–150 Futures, 543–544 G GARCH, 279–280 General Electric, 47–50, 60, 63 Generalized least squares (GLS) regressions, 73, 246, 249 Genetic algorithms, 284–285 Gini coefficient, 428 GLS regressions (see Generalized least squares regressions) Golden Rule of the Dividend Discount Model, 235, 236 Growth, 231–239 and constant-growth dividend discount model, 231–232 implied rates of, 235–236 with multiple stocks, 233–235 unrealistic rates of, 236–239 H Heterokedasticity, 491 Historical alpha, 111 Historical beta, 111 Humility principle, 225 I IBM, 47–50, 67 ICs (see Information coefficients) Implementation (see Portfolio construction) Implied growth rates, 235–236 Implied transactions costs, 459–460 Industry factors, 60–62 Information analysis, 7, 315–338 and active management, 316–318 and event studies, 329–333, 343–345 flexibility of, 318 pitfalls of, 333–338 and portfolio creation, 319–321 and portfolio evaluation, 321–329 technical aspects of, 341–345 as two-step process, 318 Information coefficients (ICs), 148 and information horizon, 354–362 uncertain, 305–308, 312–313 Information horizon, 347–363 and gradual decline in value of information, 359–363 macroanalysis of, 348–353 microanalysis of, 353–357 and realization of alpha, 357–359 return/signal correlations as function of, 371–372 technical aspects of, 364–373 Information ratio (IR), 5–6, 109, 132, 135–139 and alpha, 111–112, 127–129 and beta, 125–127, 140 calculation/approximation of, 166–168 empirical results, 129–132 as key to active management, 125 and level of risk, 116 as measure of achievement, 112 as measure of opportunity, 113–117 negative, 112 and objective of active management, 119–121 and preferences vs opportunities, 121–122 and residual frontier, 117–119 and residual risk aversion, 122–124 and time horizon, 116–117 and value-added, 124–125 See also Fundamental law of active management Information-efficient portfolios, 341–342 Inherent risk, 107 Intuition, 267–268 Inventory risk model, 450–451 Investment research, 336–338 Investment style, 161 IR (see Information ratio) K Kalman filters, 280 L Liabilities, 575 Page 594 Linear programming (LP), 395–396 Linear regression, 589–590 Long/short investing, 419–441 appeal of, 438–439 and benchmark distribution, 426–428 benefits of, 431–438 capitalization model for, 427–431 controversy surrounding, 421 empirical results, 439–440 long-only constraint, impact of, 421–426 LP (see Linear programming) Luck, skill vs., 479–483 M Magellan Fund, 43–44, 46 Major Market Index (MMI), 65–67, 235–236, 268, 488 Managers, 564–567 Marginal contribution for total risk, 78–81 factor marginal contributions, 79–80 sector marginal contributions, 80–81 Market microstructure studies, 447–448 Market volatility, 83–84 Market-dependent valuation, 207 Markowitz, Harry, 44 MIDCAP, 275–277 Mixture strategies, 365–369 MMI (see Major Market Index) Modern portfolio theory, 3–4, 93 Modern theory of corporate finance, 226–228 Mosteller, Frederick, 335 Multiple-factor risk models, 57–60 cross-sectional comparisons in, 58 and current portfolio risk analysis, 64–67 external influences, responses to, 57–58 statistical factors in, 58–60 N Naïve forecasts, 262 Neural nets, 281–283 Neutralization, 383 Nixon, Richard, 357 Nonlinearities, 575 O OLS (ordinary least squares) regressions, 246 Operational value, 227 Opportunity(-ies): arbitrage, 214 information ratio as measure of, 113–117 preferences vs., 121–122 Options pricing, 217–218 Ordinary least squares (OLS) regressions, 246 Out-of-sample portfolio performance, 532–533 P Performance, 559–569 and manager population, 564–567 persistence of, 562–564 predictors of, 567–568 studies of, 560–562 Performance analysis, 477–507 and benchmark timing, 552–554 with cross-sectional comparisons, 484–487 and cumulation of attributed returns, 510–512 and definition of returns, 483–484 goal of, 477 portfolio-based, 497–506 returns-based, 487–497 risk estimates for, 512–513 and skill vs luck, 479–483 usefulness of, 478 valuation-based approach to, 513–515 Persistence, performance, 562–564 Plan Sponsor Network (PSN), 484 Portfolio construction, 377–409 and alphas, 379–385, 411–413 and alternative risk measures, 400–402 and dispersion, 402–408, 414–416 inputs required for, 377–378 with linear programming, 395–396 practical details of, 387–389 with quadratic programming, 396–398 revisions, portfolio, 389–392 with screens, 393–394 with stratification, 394–395 technical aspects of, 410–418 techniques for, 392–398 testing methods of, 398–400 and transaction costs, 385–387 Portfolio-based performance analysis, 497–506 Predictors, 317 Preferences, 5–6, 121–122 Proust, Marcel, 336 PSN (Plan Sponsor Network), 484 Q Quadratic programming (QP), 396–398 Quantitative active management, 1, 3–4 Page 595 R Rankings, 274 Raw forecasts, 262 Realized alpha, 111 Realized beta, 111 Refining forecasts, 262–265 and intuition, 267–268 with multiple assets/multiple forecasts, 271–275 with one asset/one forecast, 264–268 with one asset/two forecasts, 268–271 Regression analysis, 589–590 Residual frontier, 117–119 Residual returns, active vs., 102–103 Residual risk, 16–17, 50, 100–101, 122–124 Return forecasting, Returns, 483–484, 587 Returns regression, 487–491 Returns-based analysis, 248–252 Returns-based performance analysis, 487–497 Revisions, portfolio, 389–392 Risk, 41–84 active, 50 and active vs residual returns, 102–103 annualizing of, 49 attribution of, 78, 81–83 aversion to residual, 122–124 aversion to total, 96 benchmark, 100–101 definitions of, 41–46 downside, 44–45 elementary models of, 52–54 and forecasting, 275–277 indices of, 60, 62–63 and industry factors, 60–62 information ratio and level of, 116 inherent, 107 marginal impact on, 78–81 and market volatility, 83–84 and model estimation, 72–73 multiple-factor models of, 57–60, 73–75 over time, 575 residual, 16–17, 50, 100–101, 122–124 and semivariance, 44–45 as shortfall probability, 45–46 specific, 75–76 and standard deviation of return, 43–44, 47–52 structural models of, 55–56 total, 51 total risk and return, 93–99 and usefulness of risk models, 64–70 value at, 46 Risk analysis, 76–78 Risk estimates (for performance analysis), 512–513 Risk indices, 60, 62–63 Risk premium, 91 Risk-adjusted expectations, 203–206 S Scheduling trades, 457–458 Science of investing, Screens, 393–394 Security market line (in CAPM), 19–20 Semivariance, 44–45 Sharpe ratio (SR), 27, 32–33, 135–137, 487, 489–490 Shelf life (see Information horizon) Shortfall probability, 45–46 Shrinkage factor, 433 Skill, luck vs., 479–483 S&P 500, 100, 275–277, 439, 445, 488, 505 Specific asset selection, 499 Specific risk, 75–76 Standard deviation, 43–44, 47–52 Standard errors, 589 Statistical law of large numbers, 160 Statistical risk factors, 58–60 Statistics, 588–589 Strategic asset allocation, 517 Strategy mixtures, 365–369 Stratification, 394–395 Structural risk models, 55–56 Style, investment, 161 T t statistics, 325–327, 336–337 Tactical asset allocation, 517 Target portfolio, 464 Target semivariance, 45 Theory of Investment Value (John Burr Williams), 229 Tick-by-tick data, 450 Time premium, 91 Time series analysis, 278–279 Timing, benchmark (see Benchmark timing) Total risk, 51, 96 Tracking error, 49 Trading, 447 implementation, strategy, 467–468 Page 596 (Cont.) Trading optimization of, 473–475 as portfolio optimization problem, 463–467 Transactions costs, 385–387, 445–454, 458–459, 462–463, 574–575 analyzing/estimating, 448–454 implied, 459–460 and market microstructure, 447–448 See also Turnover Treynor, Jack, 445, 580 Turnover, 446–447, 454–463 definition of, 456 and implied transactions costs, 459–460 and scheduling of trades, 457–458 and value added, 455–457, 471–472 U Unrealistic growth rates, 236–239 V Valuation, 109, 199–210, 225–257 and CAPM/APT, 218–220 comparative, 244–248 and dividend discount model, 229–233, 242–244 and expected return, 207–210 formula for, 202–203 market-dependent, 207 and modeling of growth, 232–239 modern theory of, 199–201, 212–217 and modern theory of corporate finance, 226–228 with nonlinear models/fractiles, 255–257 and options pricing, 217–218 of Portfolio S, 220–223 and returns-based analysis, 248–252 and risk-adjusted expectations, 203–206 and three-stage dividend discount model, 239–242 Value added, 5–6, 99–101 and benchmark timing, 544–549 and information ratio, 124–125 objective for management of, 106–108 optimal, 139–140 and performance analysis, 493, 513–515 and turnover, 455–457 Value at risk, 46 Volatility: cross-sectional, 302 market, 83–84 See also Risk Volume-weighted average price (VWAP), 450 W Wall Street Journal, 245 Williams, John Burr, 229 Page 597 ABOUT THE AUTHORS Richard C Grinold, Ph.D., is Managing Director, Advanced Strategies and Research at Barclays Global Investors Dr Grinold spent 14 years at BARRA, where he served as Director of Research, Executive Vice President, and President; and 20 years on the faculty at the School of Business Administration at the University of California, Berkeley, where he served as the chairman of the finance faculty, chairman of the management science faculty, and director of the Berkeley Program in Finance Ronald N Kahn, Ph.D., is Managing Director in the Advanced Active Strategies Group at Barclays Global Investors Dr Kahn spent 11 years at BARRA, including over seven years as Director of Research He is on the editorial advisory board of the Journal of Portfolio Management and the Journal of Investment Consulting Both authors have published extensively, and are widely known in the industry for their pioneering work on risk models, portfolio optimization, and trading analysis, equity, fixed income, and international investing; and quantitative approaches to active management ... perspective to the second edition of Active Portfolio Management Both authors now earn their livelihoods as active managers To readers of the first edition of Active Portfolio Management, we hope this second...Page iii Active Portfolio Management A Quantitative Approach for Providing Superior Returns and Controlling Risk Richard C Grinold Ronald N Kahn SECOND EDITION Page vii CONTENTS... Overview Quantitative active management is the poor relation of modern portfolio theory It has the power and structure of modern portfolio theory without the legitimacy Modern portfolio theory brought