Summary In Active Portfolio Management, we have attempted to provide a comprehensive treatment of the process of active management, covering both basic principles and many practical details. In summary, we will review what we have covered, the major themes of the book, and what is now left for the active manager to do. What We Have Covered The book began by covering the foundations: the appropriate framework for active management, and the basic portfolio theory required to navigate in that framework. The active management framework begins with a benchmark portfolio and defines exceptional returns relative to that benchmark. Active managers seek exceptional returns, at the cost of assuming risk. Active managers trade off their forecasts of exceptional return against this additional risk. We measure value added as the risk-adjusted exceptional return. The key characteristic measuring a manager's ability to add value is the information ratio, the amount of additional exceptional return he or she can generate for each additional unit of risk. The information ratio is both a figure of merit and a budget constraint. A manager's ability to add value is constrained by her or his information ratio. Given this framework, portfolio theory connects exceptional return forecasts—return forecasts which differ from consensus ex-
Page 578 pected returns—with portfolios that differ from the benchmark. If a manager's forecasts agree with the consensus, that manager will hold the benchmark. To the extent that a manager's forecasts differ from the consensus, and to the extent that his or her information ratio is positive, that manager will hold a portfolio that differs from the consensus. The information ratio arises repeatedly as the variable governing active management, and the fundamental law of active management provides insight into its components. High information ratios require both skill and breadth. Skill is captured by information coefficients—correlations between a manager's forecasts of exceptional return and their subsequent realization. Breadth measures the manager's available number of independent forecasts per year. Breadth allows the manager to diversify his or her imperfect forecasts of the future. High information ratios may combine low skill with large breadth, high skill with small breadth, or something in between. With the framework, basic theory, and insights in place, the book went on to cover the process of active management. Day-to-day active management begins with the processing of raw signals into exceptional return forecasts and moves on to implementation: portfolio construction, trading, and subsequent performance analysis. The forecasting process may depend on a factor model (like APT) or on individual stock valuation models. Forecasting includes the processing of raw information into refined alpha forecasts. Active management also requires research in order to find valuable information. Once again, a process exists for analyzing the information content of potential signals and refining them for use in active management. Themes We hope that several themes have strongly emerged from the text and the equations. First, active management is a process. Active management begins with raw information, refines it into forecasts, and then optimally and efficiently constructs portfolios balancing those forecasts of return against risk. Active management should consist of more than merely buying a few stocks you think will go up. The raw information may be the list of stocks you think will
Page 579 go up, and it certainly need not be derived from a quantitative model. But starting with this information, active management is a disciplined approach to acting on that information, based on a rigorous analysis of its content. A second theme of the book is that active management is forecasting, and a key to active manager performance is superior information. In fact, most of this book describes the machinery for processing this superior information into portfolios. If your forecasts match the consensus, or if your forecasts differ from the consensus but contain no information, this machinery will lead you back to the benchmark. Only as you develop superior information will your portfolio deviate from the benchmark. The third strong theme of the book is that active managers should forecast as often as possible. The fundamental law shows that the information ratio depends on both skill and breadth, the number of independent forecasts or bets per year. Given the realities (and difficulties) of active management, the best hope for a large information ratio is to develop a small edge and bet very often—e.g., forecast returns to 500 stocks every quarter. In this search for breadth, we also advocate using multiple sources of information—the more the better. In line with this theme of breadth, the reader should also notice that we are not strong proponents of benchmark timing. The fundamental law shows that benchmark timing is seldom fruitful. A fourth, and to some readers surprising, theme that we hope has emerged is that mathematics cannot overcome ignorance. If your raw information is valueless, no mathematical transformation will help. In this book, we have presented the mathematics for investing efficiently based on superior information from any source. We have tried to avoid wherever possible the use of mathematics to obscure lack of information. What's Left? We have described the process and machinery of active management, starting from superior information. Much of this machinery is available from vendors, or available to implement on your own, if you wish. But clearly, the focus of the active manager, and what
Page 580 this book ultimately can't help with, is the search for superior information. Seeking superior information in this zero-sum game is lonely. Jack Treynor once described the process this way: If he identifies a stock he thinks will go up, he talks to his wife about it. If she is enthusiastic, he asks his barber. From there, he discusses the idea with his accountant and his lawyer. If they all agree it's a great idea—he doesn't buy the stock. If everyone agrees with him, the price must already reflect his insight. We have covered where to look for superior information, we have discussed forecasting factor returns and forecasting asset specific returns, and we have described particular information sources that have proven valuable in the past. These may still be valuable now, but over time they must begin to inform the consensus expected returns. New, clever ideas will always help the active manager. Once you have found superior information, this book provides the best path to success with active management.
Page 581 APPENDIX A— STANDARD NOTATION This appendix covers standard notation used repeatedly throughout the book. It does not cover notation introduced and used only in one particular section. In general, we represent vectors in lowercase bold letters and matrices in uppercase bold letters. To refer to an element of a vector or matrix, we use subscripts and do not use bold, e.g., rn, the excess return to asset n, is the nth element of r, the vector of asset excess returns. Realized Returns R total returns [(Pnew + dividend) / Pold) iF risk-free rate of return RF risk-free total return r excess returns θ residual returns b factor returns u specific returns Expected Returns f expected excess returns µ long-term expected excess returns α expected residual returns φ expected exceptional returns m expected factor returns Risk σ total risk ω residual risk ψ active risk β asset betas βP portfolio beta (exposure to benchmark risk)
βPA active portfolio beta
Page 582 V asset-by-asset covariance matrix F factor covariance matrix Δ specific variance matrix Portfolios and Assets hP portfolio holdings hPR residual portfolio holdings hPA active portfolio holdings X matrix of all assets' exposures to factors xP vector of portfolio P's exposure to factors Performance and Value Added λT total risk aversion λBT benchmark timing risk aversion λR residual risk aversion λA active risk aversion λS short-term risk aversion SR Sharpe ratio IR information ratio IC information coefficient BR breadth Portfolio Names B benchmark portfolio M market portfolio Q fully invested portfolio with maximum Sharpe ratio C fully invested portfolio with minimum risk q minimum-risk portfolio with expected return = 1 A minimum-risk portfolio with α = 1
S portfolio with minimum expected Other e vector of 1s
Page 583 APPENDIX B— GLOSSARY This glossary defines some of the most commonly used terms in the book. A Active management—The pursuit of investment returns in excess of a specified benchmark. Active return—Return relative to a benchmark. If a portfolio's return is 5 percent, and the benchmark's return is 3 percent, then the portfolio's active return is 2 percent. Active risk—The risk (annualized standard deviation) of the active return. This is also called the tracking error. Alpha—The expected residual return. Outside the pages of this book, alpha is sometimes defined as the expected exceptional return and sometimes as the realized residual or exceptional return. Arbitrage—To profit because a set of cash flows has different prices in different markets. B Benchmark—A reference portfolio for active management. The goal of the active manager is to exceed the benchmark return. Beta—The sensitivity of a portfolio (or asset) to a benchmark. For every 1 percent return to the benchmark, we expect a β percent return to the portfolio. Breadth—The number of independent forecasts available per year. A stock picker forecasting returns to 100 stocks every quarter exhibits a breadth of 400 if each forecast is independent (based on separate information). C Certainty equivalent return—The certain (zero-risk) return an investor would trade for a given (larger) return with an associated risk. For example, a particular investor might trade an expected 3 percent active return with 4 percent risk for a certain active return of 1.4 percent. Characteristic portfolio—A portfolio which efficiently represents a particular asset characteristic. For a given characteristic, it is the minimum-risk portfolio with the portfolio characteristic equal to 1. For example, the characteristic portfolio of asset betas is the benchmark. It is the minimum-risk β = 1 portfolio. Common factor—An element of return that influences many assets. According to multiple-factor risk models, the common factors determine correlations between asset returns. Common factors include industries and risk indices.
Page 584 D Descriptor—A variable describing assets, used as an element of a risk index. For example, a volatility risk index, distinguishing high-volatility assets from low-volatility assets, could consist of several descriptors based on short-term volatility, long-term volatility, systematic and residual volatility, etc. Dividend discount model—A model of asset pricing, based on discounting the future expected dividends. Dividend yield—The dividend per share divided by the price per share. Also known as the yield. E Earnings yield—The earnings per share divided by the price per share. Efficient frontier—A set of portfolios, one for each level of expected return, with minimum risk. We sometimes distinguish different efficient frontiers based on additional constraints, e.g., the fully invested efficient frontier. Exceptional return—Residual return plus benchmark timing return. For a given asset with β = 1, if the residual return is 2 percent and the benchmark portfolio exceeds its consensus expected returns by 1 percent, then the asset's exceptional return is 3 percent. Excess return—Return relative to the risk-free return. If an asset's return is 3 percent and the riskfree return is 0.5 percent, then the asset's excess return is 2.5 percent. F Factor portfolio—The minimum-risk portfolio with unit exposure to the factor and zero exposure to all other factors. The excess return to the factor portfolio is the factor return. Factor return—The return attributable to a particular common factor. We decompose asset returns into a common factor component, based on the asset's exposures to common factors times the factor returns, and a specific return. I Information coefficient—The correlation of forecast returns with their subsequent realizations. A measure of skill. Information ratio—The ratio of annualized expected residual return to residual risk, a central measurement for active management. Value added is proportional to the square of the information ratio. M Market—The portfolio of all assets. We typically replace this abstract construct with a more concrete benchmark portfolio. N Normal—A benchmark portfolio.
Page 585 P Passive management—Managing a portfolio to match (not exceed) the return of a benchmark. Payout ratio—The ratio of dividends to earnings. The fraction of earnings paid out as dividends. R Regression—A data analysis technique which optimally fits a model based on the squared differences between data points and model fitted points. Typically, regression chooses model coefficients to minimize the (possibly weighted) sum of these squared differences. Residual return—Return independent of the benchmark. The residual return is the return relative to beta times the benchmark return. To be exact, an asset's residual return equals its excess return minus beta times the benchmark excess return. Residual risk—The risk (annualized standard deviation) of the residual return. Risk-free return—The return achievable with absolute certainty. In the U.S. market, short-maturity Treasury bills exhibit effectively risk-free returns. The risk-free return is sometimes called the time premium, as distinct from the risk premium. Risk index—A common factor typically defined by some continuous measure, as opposed to a common industry membership factor defined as 0 or 1. Risk index factors include size, volatility, value, and momentum. Risk premium—The expected excess return to the benchmark. R squared—A statistic usually associated with regression analysis, where it describes the fraction of observed variation in data captured by the model. It varies between 0 and 1. S Score—A normalized asset return forecast. An average score is 0, with roughly two-thirds of the scores between –1 and 1. Only one-sixth of the scores lie above 1. Security market line—The linear relationship between asset returns and betas posited by the capital asset pricing model. Sharpe ratio—The ratio of annualized excess returns to total risk. Skill—The ability to accurately forecast returns. We measure skill using the information coefficient. Specific Return—The part of the excess return not explained by common factors. The specific return is independent of (uncorrelated with) the common factors and the specific returns to other assets. It is also called the idiosyncratic return. Specific risk—The risk (annualized standard deviation) of the specific return. Standard error—The standard deviation of the error in an estimate; a measure of the statistical confidence in the estimate. Systematic return—The part of the return dependent on the benchmark return. We can break excess returns into two components: systematic and residual. The systematic return is the beta times the benchmark excess return.
Page 586 Systematic risk—The risk (annualized standard deviation) of the systematic return. T t statistic—The ratio of an estimate to its standard error. The t statistic can help test the hypothesis that the estimate differs from zero. With some standard statistical assumptions, the probability that a variable with a true value of zero would exhibit a t statistic greater than 2 in magnitude is less than 5 percent. Tracking error—See active risk. V Value added—In the context of this book, the utility, or risk-adjusted return, generated by an investment strategy: the return minus a risk aversion constant times the variance. The value added depends on the performance of the manager and the preferences of the owner of the funds. Volatility—A loosely defined term for risk. In this book, we define volatility as the annualized standard deviation of return. Y Yield—See dividend yield.
Page 587 APPENDIX C— RETURN AND STATISTICS BASICS This appendix will very briefly cover the basics of returns, statistics, and simple linear regression. We provide a list of basic references at the end. Returns We define returns over a period t, of length Δt, which runs fromt to t + Δt. If the asset's price at t is P (t) and at t + Δt is P(t + Δt), and the distributions1 over the period total d(t), then the asset's total return is The asset's total rate of return is We can also calculate a total return RF and total rate of return iF for the risk-free asset (e.g., a Treasury bill of maturity Δt). Then we define the asset's excess return as Throughout this book, we focus mainly on excess returns and decompositions of excess returns. We occasionally use total returns, and never explicitly use total rates of return. Return calculations become more difficult where they involve stock splits, stock dividends, and other corporate actions. We will not explicitly treat those critical details here. 1We label the distributions over the period d(t). If the period Δt is relatively long and a cash distribution occurs in midperiod, we could assume reinvestment of the distribution over the rest of the period at either the risk-free rate of return or the asset rate of return.
Page 588 Statistics Here we will briefly define how to calculate means, standard deviations, variances, covariances, and correlations, and briefly discuss their standard errors. Let's start with a set (a sample) of observed excess returns to stock n, rn(t), where t = 1, . . . , T. So we have observed stock n for T months. The mean return over the period (the sample mean) is The sample variance is and the sample standard deviation is Note the use of T – 1 in the denominator of Eq. (C.6). We use T – 1 instead of T to calculate an unbiased estimate of the variance, on the assumption that we are estimating both the sample mean and the sample variance. If we knew the mean with certainty, independent of the sample mean, we would use T in the denominator of Eq. (C.6). We recommend limited use of statistics in very-smallsample situations, where using T versus T – 1 can lead to very different results. To complete our discussion of basic statistical calculations, consider the excess returns to another asset m, rm(t), t = 1, . . . , T. The covariance of returns to assets n and m is
Page 589 Finally, the correlation of returns to assets n and m is Standard Errors The standard error of an estimate is the standard deviation of the errors in its estimation, a basic measure of its accuracy. Assuming that the errors in the estimate are normally distributed, the standard error for the estimated mean is The standard error of the estimated standard deviation is approximately and the standard error of the estimated variance is approximately These approximations become more exact in the limit of large sample size, i.e., very large T. Simple Linear Regression Throughout the book, we make extensive use of regression analysis. The simplest type of regression in the book estimates betas by regressing excess returns against market returns: Simple linear regression (OLS, or ordinarily least squares) estimates αn and βn by minimizing the sum of squared errors (ESS):
Page 590 The estimate of βn is These results use sample estimates of means, variances, and covariances. In the book, we generally define betas using Eq. (C.17), but with variances and covariances forecast using a covariance matrix. The R2 of the regression is defined as Another useful result of basic regression is that the errors ∈n(t) are uncorrelated with the excess returns rn(t): More general regression analysis can involve more independent variables and use weighted sums of squares, but the basic idea is the same. The procedure estimates model parameters by minimizing the (possibly weighted) sum of squared errors. The resulting errors are uncorrelated with the returns. The definition of R2 remains the same. For a thorough introduction to regression analysis, see the texts of Hoel, Port, and Stone; Hogg and Craig; and Neter and Wasserman. References Hoel, Paul G., Sidney C. Port, and Charles J. Stone. Introduction to Probability Theory (Boston: Houghton Mifflin, 1971). ———. Introduction to Statistical Theory (Boston: Houghton Mifflin, 1971). Hogg, Robert V., and Allen T Craig. Introduction to Mathematical Statistics (New York: Macmillan, 1970). Neter, John, and William Wasserman. Applied Linear Statistical Models (Homewood Ill.: Richard D. Irwin, 1974). Pindyck, Robert S., and Daniel L. Rubinfeld. Econometric Models & Economic Forecasts, 3d ed. (New York: McGraw-Hill, 1991).
Page 591 INDEX A Achievement, information ratio as measure of, 112 Active management, 1–2 as dynamic problem, 574 as forecasting, 261 and information, 316–318 information ratio as key to, 125 objective of, 119–121 as process, 578–579 Active returns, 89, 102–103 Active risk, 50 After-tax investing, 575–576 Allocation (see Asset allocation) Alpha(s), 91–92 benchmark-neutral, 384–385 characteristic portfolio of, 134 definition of, 111–112 and event studies, 331–332 extreme values, trimming, 382–383 and information horizon, 357–359 and information ratio, 127–129 and portfolio construction, 379–385, 411–413 risk-factor-neutral, 385 scaling, 311–312, 382 American Express, 20–21, 67 Arbitrage pricing theory (APT), 13, 26, 173–192
applications of, 187–190 assumptions of, 177–178 examples using, 178–181 and factor forecasting, 185–190, 194–197, 304 and Portfolio Q, 182–185 rationale of, 181–182 and returns-based analysis, 249 and valuation, 203–205, 207, 208, 218–220 and weaknesses of CAPM, 174–177 ARCH, 279–280 Asset allocation, 517–532 asset selection vs., 518 and construction of optimal portfolios, 525–532 and forecasting of returns, 520–525 and international consensus expected returns, 526–532 and liability, 575 out-of-sample portfolio performance, 532–533 technical aspects of, 536–539 as three-step process, 519–520 types of, 517 Asset valuation, 6–7 AT&T, 67 Attributed returns, cumulation of, 510–512 Attribution, performance, 498–503 Attribution of risk, 78, 81–83 Autocorrelation, 491 Aversion to total risk, 96 B BARRA, 4, 51, 60, 63, 73, 184–186, 188, 252, 284, 435, 438, 449, 454, 500 Behavioral finance, 576
Benchmark risk, 100–101 Benchmark timing, 101–102, 491–493, 541–554 defining, 541–542 and forecasting frequency, 549–552 with futures, 543–544 and performance analysis, 552–554 technical aspects of, 555–558 and value added, 544–549 Benchmarks, 5, 88–90, 426–428 Beta, 13–16 forecasts of, 24 and information ratio, 125–127, 140 a priori estimates of, 493 Biased data, 450 Book-to-price ratios, 322, 323 Breadth, 6, 148 C Capital asset pricing model (CAPM), 11–40, 487–489, 494, 496, 503, 560 assumptions of, 13–16, 27–28 characteristic portfolios in, 28–35 and efficient frontier, 35–37 and efficient markets theory, 17–18 example of analysis using, 20–21 and expected returns, 11, 18–19
Page 592 (Cont.) Capital asset pricing model (CAPM) and forecasting, 24 logic of, 16–17 mathematical notation in, 27 security market line in, 19–20 statement of, 16 as tool for active managers, 22–23 usefulness of, 22 and valuation, 203–205, 207, 208, 218–220 weaknesses of, 174–177 Cash flows: certain, 200 uncertain, 200–201 Casinos, 150–151 Censored data, 450 Chaos theory, 280–281 Characteristic portfolios, 28–35 Commissions (see Transactions costs) Comparative valuation, 244–248 Consensus expected returns, 11, 526–532 Constant-growth dividend discount model, 231–232 Corporate finance, 226–228 Covariance, 206–207 Covariance matrices, 52, 64 Cross-sectional comparisons, 58, 296–302, 332–333, 484–487 Currency, 527–532 D Data mining, 335–336
Descriptors, 63 Diaconis, Percy, 335 Dispersion, 402–408, 414–416 characterizing, 404 definition of, 402 example of, 403–404 managing, 404–408 Diversification, 184, 196–197 Dividend discount model(s), 7, 229–233, 242–244 beneficial side effects of, 244 certainty in, 229–230 constant-growth, 231–232 Golden Rule of, 235, 236 and returns, 242–244 three-stage, 239–242 uncertainty in, 230 Downside risk, 44–45 Duality theory of linear programming, 215 E Efficient frontier, 35–37 Efficient markets theory, 17–18 Elementary risk models, 52–54 Event studies, 329–333, 343–345 Exceptional benchmark return, 91 Expectations, risk-adjusted, 203–206 Expected cash flows, 201 Expected return: and CAPM, 11, 18–19 components of, 90–93
and value, 207–210 Expected utility, 96 F Factor forecasts, 303–305 Factor models, 194–197 Factor portfolios, 74 Factor-mimicking portfolios, 74 Fama-MacBeth procedure, 72–73 Financial economics, 1 Financial value, 227 Forecast horizon, 274–275 Forecasts/forecasting, 7, 261–285, 295–313 active management as, 261, 579 advanced techniques for, 278–285 alpha scaling, testing, 311–312 with ARCH/GARCH, 279–280 and asset allocation, 520–525 basic formula for, 287–290 and chaos theory, 280–281 and cross-sectional scores, 296–302 examples of, 290–292 factor forecasts, 303–305 frequency of, 549–552, 579 with genetic algorithms, 284–285 and intuition, 267–268 with Kalman filters, 280 with multiple assets/multiple forecasts, 271–275, 296 multiple forecasts for each of n assets, 302–303, 311 naïve, 262
with neural nets, 281–283 with one asset/one forecast, 264–268 with one asset/two forecasts, 268–271 one forecast for each of n assets, 309–310 raw, 262 refined, 262–265, 268–275 and risk, 275–277 rule of thumb for, 265–268 with time series analysis, 278–279
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, 7 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, 1 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.