Discover a masterful exploration of the fallacies and challenges of Asset Allocation In Asset Allocation: From Theory to Practice and Beyond--the newly and substantially revised Second Edition of A Practitioner's Guide to Asset Allocation--accomplished finance professionals William Kinlaw, Mark P. Kritzman, and David Turkington deliver a robust and insightful exploration of the core tenets of Asset Allocation. Drawing on their experience working with hundreds of the world's largest and most sophisticated investors, the authors review foundational concepts, debunk fallacies, and address cutting-edge themes like factor investing and scenario analysis. The new edition also includes references to related topics at the end of each chapter and a summary of key takeaways to help readers rapidly locate material of interest. The book also incorporates discussions of: * The characteristics that define an asset class, including stability, investability, and similarity * The fundamentals of Asset Allocation, including definitions of expected return, portfolio risk, and diversification * Advanced topics like factor investing, asymmetric diversification, fat tails, long-term investing, and enhanced scenario analysis as well as tools to address challenges such as liquidity, rebalancing, constraints, and within-horizon risk. Perfect for client-facing practitioners as well as scholars who seek to understand practical techniques, Asset Allocation: From Theory to Practice and Beyond is a must-read resource from an author team of distinguished finance experts and a forward by Nobel prize winner Harry Markowitz.
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Foreword to the First Edition
Chapter 1: What Is an Asset Class?
Chapter 2: Fundamentals of Asset Allocation
Chapter 3: The Importance of Asset Allocation
Chapter 4: Time Diversification
Chapter 5: Divergence
Chapter 6: Correlation Asymmetry
Chapter 7: Error Maximization
Chapter 8: Factors
Chapter 9: 1/N
Chapter 10: Policy Portfolios
Chapter 11: The Private Equity Leverage Myth
Chapter 12: Necessary Conditions for Mean-Variance Analysis
Chapter 13: Forecasting
Chapter 14: The Stock–Bond Correlation
Chapter 15: Constraints
Chapter 16: Asset Allocation Versus Factor Investing
Chapter 17: Illiquidity
Chapter 18: Currency Risk
Chapter 19: Estimation Error
Chapter 20: Leverage Versus Concentration
Chapter 21: Rebalancing
Chapter 22: Regime Shifts
Chapter 23: Scenario Analysis
Chapter 24: Stress Testing
CHAPTER 1: What Is an Asset Class?
POTENTIAL ASSET CLASSES
CHAPTER 2: Fundamentals of Asset Allocation
THE FOUNDATION: PORTFOLIO THEORY
THE SHARPE ALGORITHM
CHAPTER 3: The Importance of Asset Allocation
FALLACY: ASSET ALLOCATION DETERMINES MORE THAN 90% OF PERFORMANCE
THE DETERMINANTS OF PORTFOLIO PERFORMANCE
THE BEHAVIORAL BIAS OF POSITIVE ECONOMICS
THE SAMUELSON DICTUM
THE BOTTOM LINE
CHAPTER 4: Time Diversification
FALLACY: TIME DIVERSIFIES RISK
TIME, VOLATILITY, AND PROBABILITY OF LOSS
TIME AND EXPECTED UTILITY
A PREFERENCE-FREE CONTRADICTION TO TIME DIVERSIFICATION
THE BOTTOM LINE
CHAPTER 5: Divergence
FALLACY: VOLATILITY SCALES WITH THE SQUARE ROOT OF TIME, AND CORRELATION IS CONSTANT ACROSS RETURN INTERVALS
THE BOTTOM LINE
CHAPTER 6: Correlation Asymmetry
FALLACY: DIVERSIFICATION IS SYMMETRIC
CORRELATION ASYMMETRY BETWEEN ASSET CLASSES
IMPLICATIONS FOR PORTFOLIO CONSTRUCTION
THE BOTTOM LINE
CHAPTER 7: Error Maximization
FALLACY: OPTIMIZED PORTFOLIOS ARE HYPERSENSITIVE TO INPUT ERRORS
THE INTUITIVE ARGUMENT
THE EMPIRICAL ARGUMENT
THE ANALYTICAL ARGUMENT
THE BOTTOM LINE
CHAPTER 8: Factors
FALLACY: FACTORS OFFER SUPERIOR DIVERSIFICATION AND NOISE REDUCTION
WHAT IS A FACTOR?
EQUIVALENCE OF ASSET CLASS AND FACTOR DIVERSIFICATION
THE BOTTOM LINE
CHAPTER 9: 1/N
FALLACY: EQUALLY WEIGHTED PORTFOLIOS ARE SUPERIOR TO OPTIMIZED PORTFOLIOS
THE CASE FOR 1/N
SETTING THE RECORD STRAIGHT
EMPIRICAL EVIDENCE IN DEFENSE OF OPTIMIZATION
PRACTICAL PROBLEMS WITH 1/N
THE BOTTOM LINE
CHAPTER 10: Policy Portfolios
FALLACY: POLICY PORTFOLIOS MATTER
WHAT INVESTORS WANT
RESPONDING TO RISK REGIMES
THE BOTTOM LINE
CHAPTER 11: The Private Equity Leverage Myth
FALLACY: PRIVATE EQUITY VOLATILITY SCALES WITH ITS LEVERAGE
THE PRIVATE EQUITY LEVERAGE PUZZLE
LEVERAGE AND VOLATILITY IN THE PUBLIC EQUITY MARKET
THE BOTTOM LINE
CHAPTER 12: Necessary Conditions for Mean-Variance Analysis
DEPARTURES FROM ELLIPTICAL DISTRIBUTIONS
DEPARTURES FROM QUADRATIC UTILITY
THE CURSE OF DIMENSIONALITY
APPLYING FULL-SCALE OPTIMIZATION
THE BOTTOM LINE
CHAPTER 13: Forecasting
CONVENTIONAL LINEAR REGRESSION
PARTIAL SAMPLE REGRESSION
THE BOTTOM LINE
CHAPTER 14: The Stock–Bond Correlation
FUNDAMENTAL PREDICTORS OF THE STOCK–BOND CORRELATION
THE BOTTOM LINE
CHAPTER 15: Constraints
WRONG AND ALONE
MEAN-VARIANCE-TRACKING ERROR OPTIMIZATION
THE BOTTOM LINE
CHAPTER 16: Asset Allocation Versus Factor Investing
THE BOTTOM LINE
CHAPTER 17: Illiquidity
SHADOW ASSETS AND LIABILITIES
EXPECTED RETURN AND RISK OF SHADOW ALLOCATIONS
THE BOTTOM LINE
CHAPTER 18: Currency Risk
WHY NOT HEDGE EVERYTHING?
LINEAR HEDGING STRATEGIES
NONLINEAR HEDGING STRATEGIES
THE BOTTOM LINE
CHAPTER 19: Estimation Error
TRADITIONAL APPROACHES TO ESTIMATION ERROR
BUILDING A STABILITY-ADJUSTED RETURN DISTRIBUTION
DETERMINING THE OPTIMAL ALLOCATION
THE BOTTOM LINE
CHAPTER 20: Leverage Versus Concentration
LEVERAGE IN THEORY
LEVERAGE IN PRACTICE
THE BOTTOM LINE
CHAPTER 21: Rebalancing
THE DYNAMIC PROGRAMMING SOLUTION
THE MVD HEURISTIC
THE BOTTOM LINE
CHAPTER 22: Regime Shifts
PREDICTABILITY OF RETURN AND RISK
TACTICAL ASSET ALLOCATION
THE BOTTOM LINE
APPENDIX: BAUM–WELCH ALGORITHM
CHAPTER 23: Scenario Analysis
COMPARISON TO MEAN-VARIANCE ANALYSIS
THE MAHALANOBIS DISTANCE APPLIED TO SCENARIO ANALYSIS
THE MAHALANOBIS DISTANCE AND PROBABILITY
MAPPING ECONOMIC VARIABLES ONTO ASSET CLASS RETURNS
THE BOTTOM LINE
CHAPTER 24: Stress Testing
END-OF-HORIZON EXPOSURE TO LOSS
WITHIN-HORIZON EXPOSURE TO LOSS
THE BOTTOM LINE
CHAPTER 25: Statistical and Theoretical Concepts
DISCRETE AND CONTINUOUS RETURNS
ARITHMETIC AND GEOMETRIC AVERAGE RETURNS
MAXIMUM LIKELIHOOD ESTIMATION
MAPPING HIGH-FREQUENCY STATISTICS ONTO LOW-FREQUENCY STATISTICS
THE CENTRAL LIMIT THEOREM
THE NORMAL DISTRIBUTION
THE LOGNORMAL DISTRIBUTION
THE MAHALANOBIS DISTANCE
PROBABILITY OF LOSS
VALUE AT RISK
SAMPLE UTILITY FUNCTIONS
ALTERNATIVE UTILITY FUNCTIONS
MEAN-VARIANCE ANALYSIS FOR MORE THAN TWO ASSETS
EQUIVALENCE OF MEAN-VARIANCE ANALYSIS AND EXPECTED UTILITY MAXIMIZATION
MONTE CARLO SIMULATION
Glossary of Terms
End User License Agreement
TABLE 2.1 Expected Returns
TABLE 2.2 Standard Deviations and Correlations
TABLE 2.3 Optimal Allocation to Stocks and Bonds
TABLE 2.4 Conservative, Moderate, and Aggressive Efficient Portfolios
TABLE 2.5 Exposure to Loss
TABLE 2.6 Distribution of Wealth 15 Years Forward (as a Multiple of Initial I...
TABLE 3.1 Standard Deviation, Correlation, and Relative Volatility
TABLE 4.1 Time, Volatility, and Probability of Loss
TABLE 4.2 Expected Wealth and Expected Utility
TABLE 4.3 Probability of a Within-Horizon 10% Loss
TABLE 5.1 Attribution of Excess Dispersion of Triennial Relative Returns
TABLE 5.2 Monthly and Triennial Standard Deviations and Correlations
TABLE 6.1 Correlation Asymmetry of Mean-Variance and Full-Scale Optimal Portf...
TABLE 7.1 Country Expected Returns, Standard Deviations, and Correlations
TABLE 7.2 Misestimated Country Expected Returns
TABLE 7.3 Distortion in Optimal Country Weights
TABLE 7.4 Exposure to Loss for Correct and Incorrect Country Weights
TABLE 7.5 Asset Class Expected Returns, Standard Deviations, and Correlations
TABLE 7.6 Misestimated Asset Class Expected Returns
TABLE 7.7 Distortion in Optimal Asset Class Weights
TABLE 7.8 Exposure to Loss for Correct and Incorrect Asset Class Weights
TABLE 7.9 Sensitivity of Weights to Changes in Expected Return
TABLE 7.10 Sensitivity of Portfolio Standard Deviation to Changes in Expected...
TABLE 8.1 Principal Components
TABLE 8.2 Instability of Industry, Size, Value, and Momentum Portfolios
TABLE 10.1 Characteristics of realized three-year volatilities
TABLE 11.1 Expected and Actual Volatility of Private Equity (December 1996–Se...
TABLE 12.1 Skewness over Increasing Return Intervals
TABLE 12.2 Excess Kurtosis over Increasing Return Intervals
TABLE 12.3 Expected Utility for 75/25 Percent Stock/Bond Portfolio
TABLE 12.4 Expected Utility for 45/55 Percent Stock/Bond Portfolio
TABLE 12.5 The Curse of Dimensionality
TABLE 12.6 Full-Scale and Mean-Variance Allocations and Characteristics
TABLE 13.1 Equivalence of Prediction from Linear Regression and Relevance-Wei...
TABLE 14.1 Henriksson–Merton Scores: Positive Versus Negative
TABLE 15.1 Potential Absolute and Relative Performance Outcomes
TABLE 16.1 Return and Risk Assumptions for Asset Classes and Factors
TABLE 16.2 Factor-Sensitive Optimal Portfolios
TABLE 16.3 Conditional Average Annual Returns of Factor-Sensitive Optimal Por...
TABLE 17.1 Expected Returns, Standard Deviations, and Correlations (Unadjuste...
TABLE 17.2 Optimal Allocations Including and Excluding Real Estate (Unadjuste...
TABLE 17.3 Expected Returns, Standard Deviations, and Correlations (Adjusted ...
TABLE 17.4 Expected Return and Standard Deviation of Shadow Asset and Liabili...
TABLE 17.5 Expected Returns, Standard Deviations, and Correlations (Adjusted ...
TABLE 17.6 Optimal Allocations Accounting for Performance Fees, Valuation Smo...
TABLE 18.1 Linear Hedging Strategies and Their Constraints
TABLE 18.2 Expected Returns, Standard Deviations, and Correlations for Assets...
TABLE 18.3 Risk-Minimizing Hedge Ratios (%)
TABLE 18.4 Hedging Performance with Individual Quarterly Put Options (%)
TABLE 18.5 Full-Scale Optimal Hedging Results with Forwards and Options (%)
TABLE 19.1 Risk Instability Across Asset Classes (in Standardized Units)
TABLE 19.2 Full-Scale Optimization
TABLE 19.3 Mean-Variance Approach to Stability Optimization
TABLE 20.1 Leverage Versus Concentration in Theory
TABLE 20.2 Leverage Versus Concentration with Nonelliptical Returns and Kinke...
TABLE 20.3 Asset Class Semi-Standard Deviations
TABLE 20.4 Leverage Versus Concentration with Estimation Error
TABLE 20.5 Leverage Versus Concentration with Borrowing Costs
TABLE 20.6 Leverage Versus Concentration with Kinked Utility, Nonellipticalit...
TABLE 21.1 Return Distribution and Expected Log-Wealth Utility for a 60/40 Po...
TABLE 21.2 Asset Class Transaction Costs
TABLE 21.3 Performance of Rebalancing Strategies
TABLE 22.1 Risk Characteristics in Turbulent and Nonturbulent Regimes
TABLE 22.2 Full-Sample and Regime-Conditioned Optimal Portfolios
TABLE 22.3 Hidden Markov Model Fit and Conditional Asset Class Performance
TABLE 22.4 Backtest Performance
TABLE 23.1 Current Path and Prospective Scenarios
TABLE 23.2 Initial Revisions
TABLE 23.3 Revised Scenario Probabilities
TABLE 23.4 Asset Class Returns
TABLE 23.5 Portfolio Returns
TABLE 24.1 Conditional Annualized Returns to Risky Assets January 1976–Decemb...
TABLE 24.2 Value at Risk (1%)
TABLE 24.3 Probability of 35.9% or Greater Loss
FIGURE 2.1 Efficient frontier.
FIGURE 3.1 Fractional contribution to total variance.
FIGURE 4.1 Log-wealth utility function.
FIGURE 5.1 Excess dispersion of US and emerging markets relative returns
FIGURE 5.2 Median R-squared from cross-sectional regression of sector return...
FIGURE 5.3 Stylized iso-expected return curve balancing short- and long-hori...
FIGURE 6.1 Return observations for two assets.
FIGURE 6.2 Subsamples of returns for assets X and Y where one or both assets...
FIGURE 6.3 Expected upside and downside correlations for US and foreign deve...
FIGURE 6.4 Expected and empirical upside and downside correlations for US an...
FIGURE 6.5 Expected and empirical upside and downside correlations for US eq...
FIGURE 6.6 Asset class pairs with most desirable and undesirable correlation...
FIGURE 8.1 Asset class and principal component efficient frontiers.
FIGURE 10.1 The instability of risk.
FIGURE 10.2 Risk variation over time.
FIGURE 11.1 High leverage portfolios versus low leverage portfolios (control...
FIGURE 11.2 Leverage and volatility: Motorola and Clorox.
FIGURE 12.1 Annual skewness, excess kurtosis, and statistical significance b...
FIGURE 12.2 US and foreign equity returns (12-month horizon).
FIGURE 12.3 Kinked utility function.
FIGURE 12.4 S-shaped utility function.
FIGURE 12.5 Expected utility for different allocations to stocks (5% increme...
FIGURE 13.1 Relevance and dependent variable values for a sample input.
FIGURE 13.2 The most relevant observations.
FIGURE 13.3 Prediction efficacy for partial sample regression versus traditi...
FIGURE 14.1 Illustration of single-period correlation.
FIGURE 14.2 Correlation of model predictions and actual correlations.
FIGURE 15.1 Efficient surface.
FIGURE 15.2 Iso-expected return curve.
FIGURE 17.1 Optimal allocation to real estate with and without adjustments....
FIGURE 18.1 Minimum-variance hedge ratio.
FIGURE 18.2 Currency exposure as a percentage of portfolio value.
FIGURE 18.3 Impact of hedging strategies on distribution of portfolio curren...
FIGURE 19.1 Components of estimation error.
FIGURE 19.2 Monthly returns of US and emerging market equities.
FIGURE 19.3 Five-year returns of US and emerging market equities.
FIGURE 19.4 Constructing the stability-adjusted return distribution.
FIGURE 19.5 Mixture of two normal distributions.
FIGURE 19.6 Multivariate mixture of asset classes with unstable correlation....
FIGURE 19.7 Stability adjustment improvement to optimization that ignores er...
FIGURE 20.1 Efficient frontier with borrowing and lending.
FIGURE 20.2 Outperformance of leverage versus concentration.
FIGURE 21.1 Trading and suboptimality costs over two periods (basis points)....
FIGURE 21.2 Rebalancing strategies: trade-off between transaction and subopt...
FIGURE 21.3 Rebalancing strategies: performance.
FIGURE 22.1 Monthly correlation of US equities and Treasury bonds (five-year...
FIGURE 22.2 Financial turbulence.
FIGURE 22.3 Hidden Markov model regime probabilities.
FIGURE 22.4 Hidden Markov model regime probability forecasts (out-of-sample)...
FIGURE 22.5 Cumulative returns.
FIGURE 24.1 Scatter plot of US and foreign equities.
FIGURE 25.1 Kinked utility function.
FIGURE 25.2 S-shaped utility function.
Table of Contents
“Asset allocation is the most important yet challenging decision faced by every investor. By masterfully bridging theory and practice, Kinlaw, Kritzman, and Turkington have produced a modern guide to the topic that will be useful to practitioners and scholars alike.”
—Robin Greenwood, George Gund Professor of Finance and Banking, Harvard Business School
“A Practitioner’s Guide to Asset Allocation is an exceptionally comprehensive treatise on the subject, as can be seen from just a sampling of the chapter headings—Fallacies (of which there are many), Time Diversification (not as easy as it may seem), Factors (points out some issues with this current hot trend), Illiquidity (what does it really cost), Risks (not just at-horizon, but also within- and beyond-horizon), and perhaps most important of all, Regime Shifts. This book has a lot to say, and a page-by-page read may be a bit much for the typical ‘Practitioner,’ but the authors provide a very readable chapter of Takeaways that should perhaps be the first point of entry. But even these more compact Takeaways are full of fresh insights into this truly important topic that is all too often given too short a shrift.”
—Martin L. Leibowitz, PhD, Vice Chairman – Research, Morgan Stanley
“Kinlaw, Kritzman, and Turkington have a long history of discovering and very clearly describing surprising and useful investment results. This book continues that tradition by correcting several common myths about asset allocation and presenting the latest thinking about this fundamental issue. All investors who practice asset allocation for a living will benefit from reading this.”
—Ronald N. Kahn, Global Head of Scientific Equity Research, BlackRock
“One of the best books ever written on applied research for asset allocation. This outstanding effort provides the missing link between academic research and practice. With remarkable clarity, the authors explain how to put risk at the center of portfolio construction. Speaking from experience advising some of the largest pools of assets in the world, they bring the practice and science of risk-based investing to a whole new level, and challenge conventional wisdom along the way. Everyone involved in asset allocation should read this book, including CIOs, quants, non-quants, academics, consultants, portfolio managers, advisors, individual investors, and plan sponsors. It will become a reference for the next wave of innovation in our industry. Bravo!”
—Sébastien Page, CFA, Head of Asset Allocation, T. Rowe Price; author, Beyond Diversification: What Every Investor Needs to Know About Asset Allocation
“Everything you ever wanted and need to know about asset allocation but were afraid to ask, written by three accomplished practitioners who put their money where their mouths are.”
—Andrew W. Lo, Charles E. and Susan T. Harris Professor, MIT Sloan School of Management
WILLIAM KINLAWMARK KRITZMANDAVID TURKINGTON
Copyright © 2021 by William Kinlaw, Mark Kritzman, and David Turkington. All rights reserved.
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A Practitioner’s Guide to Asset Allocation by William Kinlaw, Mark Kritzman, and David Turkington speaks to the “forgotten man” of our field: he or she who interacts with the client and delivers professional investment advice. They are the foot soldiers of our field. Our field has an abundance of articles by academics trying to persuade other academics as to how practitioners should advise clients; articles written by academics for “quantitative” practitioners, who are actually academics, usually employed by large institutional investors, either as window dressing, or to build systems to replace “nonquantitative” academics; textbooks trying to educate students as to how they too can write academic articles – enough of them to achieve tenure – on how practitioners should practice; and, now and then, books written by academics for practitioners on “what every academic knows and I'll try to explain to you.” But there are remarkably few well-written books or articles, by learned scholars, for practitioners, without calculus, on controversial topics of practical importance, on which the scholar has published strong views.
The Kinlaw, Kritzman, and Turkington “Guide” fills this void. Specifically, among its 16 chapters for practitioners (plus an “Addendum” with chapters on statistical concepts and a glossary of terms) is a discussion of why it is not true that the Markowitz optimization procedure maximizes rather than minimizes risk for given return, and why the investment practitioner's clients would not be better served by the practitioner recommending an equal weighted portfolio rather than going through the demanding modern portfolio theory (MPT) process.
This guide should be of interest to practitioners; scholars who seek to develop or evaluate techniques that can be of practical value in practitioners' hands; academics who would like to create, explore, or evaluate, empirically or theoretically, relationships that can guide the development of such techniques; investors (especially institutional investors) who must evaluate alternative current or potential advisors; and broadly read non-finance readers who enjoy a good intellectual fight.
Harry Markowitz, Nobel Prize Recipient, 1990, Economic Sciences; President, Harry Markowitz Company
Harry Markowitz published his landmark article on portfolio selection more than 60 years ago. This groundbreaking theory empowered generations of academics and practitioners to pursue asset allocation with rigor. Many have made great strides to extend and enhance the application of portfolio theory. And yet, despite all this progress, few would argue that allocating assets effectively is an easy task today. As in many areas of scientific development, progress has been uneven. It has been punctuated with instances of misleading research, which has contributed to the stubborn persistence of certain fallacies about asset allocation. In addition, new markets, technologies, and economic realities continue to present opportunities as well as challenges. Our goal in writing this book is twofold: to describe several important innovations that address key challenges to asset allocation and to dispel certain fallacies about asset allocation.
This book contains the 16 chapters from our 2017 book A Practitioner's Guide to Asset Allocation, plus 8 additional chapters on topics that have come into sharp focus in recent years. The core tenets of asset allocation do not change over time, but new themes emerge. Designing portfolios and strategies to hedge against downside loss is an important theme today. We include new chapters on the divergence of long-run risk from short-term risk (Chapter 5), the asymmetry of correlations during market gains and losses (Chapter 6), the need for more dynamic asset allocation (Chapter 10), and how to forecast the correlation between stocks and bonds (Chapter 14). Another hot topic is factor investing. We add a new chapter on asset allocation and factor investing, including a way to get the best of both worlds (Chapter 16). As a third theme, we have noticed that many investors benefit from qualitative judgment and debate but struggle to marry these techniques with quantitative analysis. We include new models for forecasting (Chapter 13) and scenario analysis (Chapter 23) that can improve the rigor and effectiveness of traditional quantitative techniques while offering easy interpretation to complement judgment and debate. We also expand our discussion of illiquid alternative assets to address specific challenges associated with measuring the true risk exposure of private equity (Chapter 11). The topics and methodologies introduced in other chapters remain as relevant today as they were in 2017.
We have made two enhancements to this edition to help readers navigate the content more efficiently. First, there are a number of common threads in this book that link the chapters, both new and old, together. To highlight these linkages, we now include references to related topics at the end of each chapter so that readers can explore their particular interests efficiently. Second, we now begin the book with a summary of key takeaways from each of the chapters. Readers can peruse these takeaways and then decide which chapters are of particular interest. Of course, we hope that readers will find all the chapters interesting.
We divide the rest of the book into four sections. Section I covers the fundamentals of asset allocation, including a discussion of the attributes that qualify a group of securities as an asset class, as well as a detailed description of the conventional application of mean-variance analysis to asset allocation. In describing the conventional approach to asset allocation, we include an illustrative example that serves as a base case, which we use to demonstrate the impact of the innovations we describe in subsequent chapters.
Section II presents certain fallacies about asset allocation, which we attempt to dispel either by logic or with evidence. These fallacies include the notion that asset allocation determines more than 90% of investment performance, that time diversifies risk, that risk parameters are stable across return intervals, that correlations are symmetric, that optimization is hypersensitive to estimation error, that factors provide greater diversification than assets and are more effective at reducing noise, that equally weighted portfolios perform more reliably out-of-sample than optimized portfolios, that policy portfolios matter, and that the volatility of private equity is greater than that of public equity due to private equity's higher leverage.
Section III describes several innovations that address key challenges to asset allocation. We present an alternative optimization procedure to address the challenge that some investors have complex preferences and returns may not be elliptically distributed. We introduce a new forecasting technique that exploits information about the relevance of historical observations. We apply advances in quantitative methods to forecast the stock–bond correlation. We show how to overcome inefficiencies that result from constraints by augmenting the optimization objective function to incorporate absolute and relative goals simultaneously. We describe how to integrate asset allocation with factor investing. We demonstrate how to use shadow assets and liabilities to unify liquidity with expected return and risk. And we address the challenge of currency risk by presenting a cost/benefit analysis of several linear and nonlinear currency-hedging strategies.
We show how to reduce estimation error in covariances by introducing a nonparametric procedure for incorporating the relative stability of covariances directly into the asset allocation process. We address the challenge of choosing between leverage and concentration to raise expected return by relaxing the simplifying assumptions that support the theoretical arguments. We describe a dynamic programming algorithm as well as a quadratic heuristic to determine a portfolio's optimal rebalancing schedule. We address the challenge of regime shifts with several innovations, including stability-adjusted optimization, blended covariances, and regime indicators. We introduce a mathematically rigorous and empirically driven approach for carrying out scenario analysis. Finally, we show how to evaluate alternative asset mixes by assessing exposure to loss throughout the investment horizon based on regime-dependent risk.
Section IV provides supplementary material, including an expanded chapter on relevant statistical and theoretical concepts as well as a comprehensive glossary of terms.
This book is not an all-inclusive treatment of asset allocation. There are certainly some innovations that are not known to us, and there are other topics that we do not cover because they are well described elsewhere. The topics that we choose to write about are ones that we believe to be especially important, yet not well known nor understood. We hope that readers will benefit from our efforts to convey this material, and we sincerely welcome feedback, be it favorable or not.
Some of the ideas in this book originally appeared in journal articles that we coauthored with past and current colleagues. We would like to acknowledge the contributions of Nelson Aruda, Alain Bergeron, Wei Chen, George Chow, David Chua, Paula Cocoma, Eric Jacquier, Ding Li, Kenneth Lowry, Simon Myrgren, Sébastien Page, Baykan Pamir, Grace (Tiantian) Qiu, Don Rich, and Gleb Sivitsky. And we would like to express special gratitude to Megan Czasonis, who coauthored many of the articles that underpin much of this book's content and who has contributed importantly to shaping our views and understanding of asset allocation.
In addition, we have benefited enormously from the wisdom and valuable guidance, both directly and indirectly, from a host of friends and scholars, including Peter Bernstein, Stephen Brown, John Campbell, Edwin Elton, Frank Fabozzi, Gifford Fong, Martin Gruber, Martin Leibowitz, Andrew Lo, Harry Markowitz, Robert C. Merton, Krishna Ramaswamy, Stephen Ross, Paul A. Samuelson, William Sharpe, and Jack Treynor. Obviously, we accept sole responsibility for any errors.
Finally, we would like to thank our wives, Michelle Kinlaw, Abigail Turkington, and Elizabeth Gorman, for their support of this project as well as their support in more important ways.
William KinlawMark KritzmanDavid Turkington
The composition of an asset class should be stable.
The components of an asset class should be directly investable.
The components of an asset class should be similar to each other.
An asset class should be dissimilar from other asset classes in the port- folio as well as combinations of other asset classes.
The addition of an asset class to a portfolio should raise its expected utility.
An asset class should not require selection skill to identify managers within the asset class.
An asset class should have the capacity to absorb a meaningful fraction of a portfolio cost-effectively.
A portfolio's expected return is the weighted average of the expected returns of the asset classes within it.
Expected return is measured as the arithmetic average, not the geometric average.
A portfolio's risk is measured as the variance of returns or its square root, the standard deviation.
Portfolio risk must account for how asset classes co-vary with one another.
Portfolio risk is less than the weighted average of the variances or stan- dard deviations of the asset classes within it.
Diversification cannot eliminate portfolio variance entirely. It can only reduce it to the average covariance of the asset classes within it.
The efficient frontier comprises portfolios that offer the highest expected return for a given level of risk.
The optimal portfolio balances an investor's goal to increase wealth with the investor's aversion to risk.
Mean-variance analysis is an optimization process that identifies effi- cient portfolios. It is remarkably robust. For a given time horizon or assuming returns are expressed in continuous units, it delivers the correct result if returns are approximately elliptically distributed, which holds for return distributions that are not skewed, have stable correlations, and comprise asset classes with relatively uniform kurtosis, or if investor preferences are well described by mean and variance.
It is commonly assumed that asset allocation explains more than 90% of investment performance.
This belief is based on flawed analysis by Brinson, Hood, and Beebower.
The analysis is flawed because it implicitly assumes that the default portfolio is not invested; it thereby fails to distinguish between the risk driven by asset allocation decisions and the risk driven by the fundamental decision to invest in the first place.
Also, this study, as well as many others, analyzes actual investment choices rather than investment opportunity. By analyzing actual investment choices, these analyses confound the natural importance of an investment activity with an investor's choice to emphasize that activity.
Bootstrap simulation of the potential range of outcomes associated with asset allocation and security selection reveals that security selection has as much or more potential to affect investment performance as asset allocation does.
It does not necessarily follow, though, that investors should devote more resources to security selection than asset allocation, because, as argued by Paul Samuelson, it is easier to be successful at asset allocation than security selection.
Asset allocation is very important, but not for the reasons put forth by Brinson, Hood, and Beebower.
It is widely assumed that investing over long horizons is less risky than investing over short horizons, because the likelihood of loss is lower over long horizons.
Paul A. Samuelson showed that time does not diversify risk because, though the probability of loss decreases with time, the magnitude of potential losses increases with time.
It is also true that the probability of loss
an investment horizon never decreases with time.
Finally, the cost of a protective put option increases with time to expira-tion. Therefore, because it costs more to insure against losses over longer periods than shorter periods, it follows that risk does not diminish with time.
Investors commonly assume that standard deviations of asset returns scale with the square root of time and that correlations of returns between assets are invariant to the return interval from which they are estimated.
Both beliefs rest on the same underlying assumption that returns are serially independent from one period to the next.
However, this assumption is empirically false; standard deviations and correlations of longer-interval returns diverge substantially from the standard deviations and correlations estimated from shorter-interval returns.
Investors usually attribute this divergence to non-normality of the returns, but instead it is usually driven by nonzero lagged autocorrelations and cross-correlations.
The divergence of high- and low-frequency estimates of standard deviations and correlations has important implications for portfolio construction, performance measurement, and risk management.
Investors mistakenly believe that diversification is unconditionally beneficial because they implicitly assume that correlations are symmetric.
The evidence shows, however, that correlations differ significantly depending on the size and direction of returns.
Investors should seek diversification when their portfolios' main growth component is performing poorly and unification when their portfolios' main growth component is performing well.
Unfortunately, most asset class pairs exhibit unfavorable correlation profiles characterized by unification on the downside, when it is not wanted, and diversification on the upside, when it is not needed.
Investors can employ full-scale optimization, which is introduced in Chapter 12, to construct portfolios that account implicitly for asymmetric correlations.
Some investors believe that optimization is hypersensitive to estimation error because, by construction, optimization overweights asset classes for which expected return is overestimated and risk is underestimated, and it underweights asset classes for which the opposite is true.
We argue that optimization is not hypersensitive to estimation error for reasonably constrained portfolios.
If asset classes are close substitutes for each other, it is true that their weights are likely to change substantially given small input errors, but because they are close substitutes, the correct and incorrect portfolios will have similar expected returns and risk.
If asset classes are dissimilar from each other, small input errors will not cause significant changes to the correct allocations; thus, again the correct and incorrect portfolios will have similar expected returns and risk.
Nevertheless, estimation error is an important challenge to optimization, and investors would be well served to explore ameliorative measures such as Bayesian shrinkage, resampling, and the use of stability-adjusted return distributions.
Some investors believe that factors offer greater potential for diversification than asset classes because they appear less correlated than asset classes.
Factors appear less correlated only because the portfolio of assets designed to mimic them includes short positions.
Given the same constraints and the same investable universe, it is mathematically impossible to regroup assets into factors and produce a better efficient frontier.
Some investors also believe that consolidating a large group of securities into a few factors reduces noise more effectively than consolidating them into a few asset classes.
Consolidation reduces noise around means, but no more so by using factors than by using asset classes.
Consolidation does not reduce noise around covariances.
Our results challenge the notion that investors should use factors as portfolio building blocks.
Nevertheless, factors can be useful for other reasons. Factor analysis can help investors understand and manage risk, harvest risk premiums, and enhance returns for investors who are skilled at predicting factor behavior. But we should weigh these potential benefits of factor investing against the incremental noise and trading costs associated with factor replication.
It has been argued that equally weighted portfolios perform better out of sample than optimized portfolios.
The evidence for this result is misleading because it relies on extrapolation of historical means from short samples to estimate expected return. In some samples, the historical means for riskier assets are lower than the historical means for less risky assets, implying, contrary to reason, that investors are occasionally risk seeking.
Optimization with plausible estimates of expected return reliably per- forms better than equal weighting.
Also, equal weighting limits the investor to a single portfolio, regardless of the investor's risk tolerance, whereas optimization offers a wide array of investment choices.
Investors seek to grow wealth and avoid large drawdowns along the way, but these goals conflict with each other.
A policy portfolio, which prescribes a fixed allocation to a set of asset classes, is intended to balance these conflicting goals.
However, a policy portfolio is just a means to an end.
Investors do not care about a specific asset mix, but rather the return distribution they expect it to generate.
Unfortunately, a fixed-weight portfolio delivers a highly unstable return distribution that often conflicts with an investor's risk preference.
It is preferable to implement a flexible investment policy that delivers a relatively stable return distribution than a rigid policy portfolio that delivers an unstable return distribution.
The standard deviation of observed private equity returns is unrealistically low compared to the standard deviation of public equity returns.
This apparent low volatility is caused by valuing private equity based on appraisals that are anchored to prior period valuations, which has the effect of smoothing returns.
When private equity volatility is estimated from longer-interval returns, which offsets the smoothing effect, private equity volatility is about the same as public equity volatility.
Many investors believe that private equity volatility should be much higher than public equity volatility because private equity is more highly levered than public equity.
However, not only is there no discernible relationship between leverage and private equity volatility, it does not exist in the public market either.
Leverage does not appear to affect private equity volatility because private equity managers tend to invest in companies whose underlying business activities are inherently less risky, which cancels out the leverage effect.
The volatility estimated from longer-interval private equity returns is the correct approximation of volatility because it approximates the actual distribution of outcomes realized by private equity investors over longer horizons.
It is a widely held view that the validity of mean-variance analysis requires that investors have quadratic utility and that returns are normally distributed. This view is incorrect.
For a given time horizon or assuming returns are expressed in continuous units, mean-variance analysis is precisely equivalent to expected utility maximization if returns are elliptically distributed, of which the normal distribution is a more restrictive special case, or (not “and”) if investors have quadratic utility.
For practical purposes, mean-variance analysis is an excellent approx- imation to expected utility maximization if returns are approximately elliptically distributed or investor preferences can be well described by mean and variance.
For intuitive insight into an elliptical distribution, consider a scatter plot of the returns of two asset classes. If the returns are evenly distributed along the boundaries of concentric ellipses that are centered on the average of the return pairs, the distribution is elliptical. This is usually true if the distribution is symmetric, kurtosis is relatively uniform across asset classes, and the correlation of returns is reasonably stable across subsamples.
For a given elliptical distribution, the relative likelihood of any multivariate return can be determined using only mean and variance.
Levy and Markowitz have shown using Taylor series approximations that power utility functions, which are always upward sloping, can be well approximated across a wide range of returns using just mean and variance.
In rare circumstances, in which returns are not elliptical and investors have preferences that cannot be approximated by mean and variance, it may be preferable to employ full-scale optimization to identify the optimal portfolio.
Full-scale optimization is a numerical process that evaluates a large number of portfolios to identify the optimal portfolio, given a utility function and return sample. For example, full-scale optimization can accommodate a kinked utility function to reflect an investor's strong aversion to losses that exceed a chosen threshold.
Asset allocation requires investors to forecast expected returns, standard deviations, and correlations whose values vary over time.
Long-run averages are poor forecasts because they fail to capture this time variation.
But extrapolating from a short sample of recent history is ineffective because it introduces noise and assumes a level of persistence that does not reliably occur.
As an alternative, investors often regress these asset class variables on economic variables to derive forecasts, but this approach may not help because additional variables contribute noise along with information.
The investor's challenge is to maximize the information content and minimize the noise, thereby generating the most reliable predictions.
The prediction from a linear regression equation can be equivalently expressed as a weighted average of the past values of the dependent variable in which the weights are the relevance of the past observations of the independent variables.
Within this context, relevance has a precise mathematical meaning. It is the sum of statistical similarity and informativeness.
Statistical similarity equals the negative of the Mahalanobis distance of the past values for the independent variables from their current values, and informativeness equals the Mahalanobis distance of the past values of the independent variables from their average values. In other words, prior periods that are more like the current period but different from the historical average are more relevant than those that are not.
Investors may be able to improve the reliability of their forecasts by filtering historical observations for their relevance and using this mathematical equivalence to produce new forecasts.
Investors rely on the stock–bond correlation to construct optimal portfolios and to assess risk.
Investors should care less about how stocks and bonds co-move from month to month as they do about their co-movement over the duration of their investment horizon.
The most common approach to estimating the longer-term correlation of stocks and bonds is to extrapolate the correlation of monthly returns over a prior period. This approach is decidedly unreliable, because the autocorrelations and lagged cross-correlations of stock and bond returns are nonzero.
As an alternative, investors may consider estimating the stock–bond correlation from longer-horizon returns, but this approach is unreliable because the stock–bond correlation varies over time.
To address these problems, this chapter introduces the notion of a single-period correlation that measures the extent to which stock and bond returns move synchronously or drift apart over the course of the investment horizon.
In addition, this chapter introduces several fundamental variables to predict the longer-horizon stock–bond correlation, some of which are expressed as paths rather than as single-period average values.
This chapter also describes how to filter historical observations for their historical relevance, as discussed more fully in Chapter 13.
Together, these innovations significantly improve the reliability of the forecast of the stock–bond correlation.
Investors constrain their allocation to certain asset classes because they do not want to perform poorly when other investors perform well.
Constraints are inefficient because, of necessity, they are arbitrary.
Investors can derive more efficient portfolios by expanding the optimization objective function to include aversion to tracking error as well as aversion to absolute risk.
Mean-variance-tracking error optimization produces an efficient surface in the dimensions of expected return, standard deviation, and tracking error.
This approach usually delivers a portfolio that is more efficient in three dimensions than the portfolio that is produced by constrained mean-variance analysis.
Some investors prefer to construct portfolios from asset classes because asset classes are readily observable and directly investable.
Other investors prefer to allocate to factors because they believe asset classes are defined arbitrarily and do not capture the fundamental determinants of performance as directly as factors do. Also, some factors carry risk premiums that are not directly available from asset classes.
Investors can have it both ways by continuing to invest in asset classes but augmenting the Markowitz objective function to include a term that penalizes deviation from a desired factor profile.
Investors rely on liquidity to implement tactical asset allocation decisions, to rebalance a portfolio, and to meet demands for cash, among other uses.
To account for the impact of liquidity, investors should attach a shadow asset to the liquid asset classes in a portfolio that enable them to use liquidity to increase a portfolio's expected utility, and they should attach a shadow liability to illiquid asset classes in a portfolio that prevent them from preserving a portfolio's expected utility.
These shadow allocations allow investors to address illiquidity within a single unified framework of expected return and risk.
Investors may improve portfolio efficiency by optimally hedging a portfolio's currency exposure.
Linear hedging strategies use forward or futures contracts to offset cur- rency exposure. They hedge both upside returns and downside returns. They are called linear hedging strategies because the portfolio's returns are a linear function of the hedged currencies' returns.
Investors can reduce risk more effectively by allowing currency-specific hedging, cross-hedging, and overhedging. These strategies retain exposure to currencies that diversify the portfolio and reduce exposure to currencies that do not.
Nonlinear hedging strategies use put options to protect a portfolio from downside returns arising from currency exposure while allowing it to benefit from upside currency returns. They are called nonlinear hedging strategies because the portfolio's returns are a nonlinear function of the hedged currencies' returns.
Nonlinear hedging strategies are more expensive than linear hedging strategies because they preserve the upside potential of currencies.
A basket option is an option on a portfolio of currencies and therefore provides protection against a collective decline in currencies.
A portfolio of options offers protection against a decline in any of a portfolio's currencies.
A basket option is less expensive than a portfolio of options because it offers less protection.
When investors estimate asset class covariances from historical returns, they face three types of estimation error: small-sample error, independent-sample error, and interval error.
Small-sample error arises because the investor's investment horizon is typically shorter than the historical sample from which covariances are estimated.
Independent-sample error arises because the investor's investment horizon is independent of history.
Interval error arises because investors estimate covariances from higher-frequency returns than the return frequency they care about. If returns have nonzero autocorrelations, the standard deviation does not scale with the square root of time. If returns have nonzero autocorrelations or nonzero lagged cross-correlations, correlation is not invariant to the return interval used to measure it.
Common approaches to controlling estimation error, such as Bayesian shrinkage and resampling, make portfolios less sensitive to estimation error.
A new approach, called stability-adjusted optimization, assumes that some covariances are reliably more stable than other covariances. It delivers portfolios that rely more on relatively stable covariances and less on relatively unstable covariances.
Theory shows that it is more efficient to raise a portfolio's expected return by employing leverage rather than concentrating the portfolio in higher-expected-return asset classes.
The assumptions that support this theoretical result do not always hold in practice.
If we collectively allow for asymmetric preferences, nonelliptical returns, and realistic borrowing costs, it may be more efficient to raise expected return by concentrating a portfolio in higher-expected-return asset classes than by using leverage.
However, if we also assume that an investor has even a modest amount of skill in predicting asset class returns, then leverage is better than con- centration even in the presence of asymmetric preferences, nonelliptical distributions, and realistic borrowing costs.
Investors typically rebalance a portfolio whose weights have drifted away from its optimal targets based on the passage of time or distance from the optimal targets.
Investors should approach rebalancing more rigorously by recognizing that the decision to rebalance or not affects the choices the investor will face in the future.
Dynamic programming can be used to determine an optimal rebalancing schedule that explicitly balances the cost of transacting with the cost of holding a suboptimal portfolio.
Unfortunately, dynamic programming can only be applied to portfolios with a few asset classes because it suffers from the curse of dimensionality.
For portfolios with more than just a few asset classes, investors should use a quadratic heuristic developed by Harry Markowitz and Erik van Dijk, which easily accommodates several hundred assets.
Rather than characterizing returns as coming from a single, stable regime, it might be more realistic to assume they are generated by disparate regimes such as a calm regime and a turbulent regime.
Investors may wish to build portfolios that are more resilient to turbulent regimes by employing stability-adjusted optimization, which relies more on relatively stable covariances than on unstable covariances, or by blending the covariances from calm and turbulent subsamples in a way that places greater emphasis on covariances that prevailed during turbulent regimes.
These approaches produce static portfolios, which still display unstable risk profiles.
Investors may instead prefer to manage a portfolio's asset mix dynam- ically, by switching to defensive asset classes during turbulent periods and to aggressive asset classes during calm periods.
It has been shown that hidden Markov models are effective at distin-guishing between calm and turbulent regimes by accounting for the level, volatility, and persistence of the regime characteristics.
Scenario analysis requires investors to define prospective economic scenarios, assign probabilities to them, translate the scenarios into expected asset class returns, and identify the most suitable portfolio given all these inputs.
The greatest challenge to scenario analysis is determining each scenario's probability.
We can estimate a scenario's probability by measuring its statistical similarity to current economic conditions or normal economic conditions using a statistic called the Mahalanobis distance.
This framework also allows us to identify the smallest changes in the scenario descriptions that would be required to equate the empirical probabilities with our subjective views.
We can further enhance scenario analysis by describing scenarios as paths rather than as single-period average outcomes.
Investors typically evaluate exposure to loss based on a portfolio's full- sample distribution of returns at the end of their investment horizon.
However, investors care about what happens throughout their investment horizon and not just at its conclusion.
They also recognize that losses are more common when markets are turbulent than when they are calm.
First passage time probabilities enable investors to estimate probability of loss and value at risk throughout their investment horizon.
The Mahalanobis distance allows investors to distinguish between calm and turbulent markets.
Investors can assess risk more realistically by applying first passage time probabilities to the returns that prevailed during turbulent subsamples.
Investors have access to a vast array of assets with which to form portfolios, ranging from individual securities to broadly diversified funds. The first order of business is to organize this massive opportunity set into a manageable set of choices. If investors stratify their opportunity set at too granular a level, they will struggle to process the mass of information required to make informed decisions. If, instead, they stratify their opportunity set at a level that is too coarse, they will be unable to diversify risk efficiently. Asset classes serve to balance this trade-off between unwieldy granularity and inefficient aggregation.
In light of this trade-off and other considerations, we propose the following definition of an asset class.
An asset class is a stable aggregation of investable units that is internally homogeneous and externally heterogeneous, that when added to a portfolio raises its expected utility without requiring selection skill, and which can be accessed cost-effectively in size.
This definition captures seven essential characteristics of an asset class. Let us consider each one in detail.
The composition of an asset class should be relatively stable. Otherwise, ascertaining its appropriate composition would require continual monitoring and analysis, and maintaining the appropriate composition would necessitate frequent rebalancing. Both efforts could be prohibitively expensive.
Asset classes whose constituents are weighted according to their relative capitalizations are stable, because when their prices change, their relative capitalizations change proportionately. By contrast, a proposed asset class whose constituents are weighted according to attributes that shift through time, such as momentum, value, or size, may not have a sufficiently stable composition to qualify as an asset class. Sufficiency, of course, is an empirical issue. Momentum is less stable than value, which is less stable than size. Therefore, a group of momentum stocks would likely fail to qualify as an asset class, while stocks within a certain capitalization range might warrant status as an asset class. Value stocks reside somewhere near the center of the stability spectrum and may or may not qualify as an asset class.
The underlying components of an asset class should be directly investable. If they are not directly investable, such as economic variables, then the investor would need to identify a set of replicating securities that tracks the economic variable. Replication poses two challenges. First, in addition to the uncertainty surrounding the out-of-sample behavior of the economic variable itself, the investor is exposed to the uncertainty of the mapping coefficients that define the association between the economic variable and the replicating securities. Second, because the optimal composition of the replicating securities changes through time, the investor is exposed to additional rebalancing costs.
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