Modern Asset Allocation for Wealth Management E-Book

David M. Berns

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 242

Veröffentlichungsjahr: 2020

Beschreibung

An authoritative resource for the wealth management industry that bridges the gap between modern perspectives on asset allocation and practical implementation An advanced yet practical dive into the world of asset allocation, Modern Asset Allocation for Wealth Management provides the knowledge financial advisors and their robo-advisor counterparts need to reclaim ownership of the asset allocation component of their fiduciary responsibility. Wealth management practitioners are commonly taught the traditional mean-variance approach in CFA and similar curricula, a method with increasingly limited applicability given the evolution of investment products and our understanding of real-world client preferences. Additionally, financial advisors and researchers typically receive little to no training on how to implement a robust asset allocation framework, a conceptually simple yet practically very challenging task. This timely book offers professional wealth managers and researchers an up-to-date and implementable toolset for managing client portfolios. The information presented in this book far exceeds the basic models and heuristics most commonly used today, presenting advances in asset allocation that have been isolated to academic and institutional portfolio management settings until now, while simultaneously providing a clear framework that advisors can immediately deploy. This rigorous manuscript covers all aspects of creating client portfolios: setting client risk preferences, deciding which assets to include in the portfolio mix, forecasting future asset performance, and running an optimization to set a final allocation. An important resource for all wealth management fiduciaries, this book enables readers to: * Implement a rigorous yet streamlined asset allocation framework that they can stand behind with conviction * Deploy both neo-classical and behavioral elements of client preferences to more accurately establish a client risk profile * Incorporate client financial goals into the asset allocation process systematically and precisely with a simple balance sheet model * Create a systematic framework for justifying which assets should be included in client portfolios * Build capital market assumptions from historical data via a statistically sound and intuitive process * Run optimization methods that respect complex client preferences and real-world asset characteristics Modern Asset Allocation for Wealth Management is ideal for practicing financial advisors and researchers in both traditional and robo-advisor settings, as well as advanced undergraduate and graduate courses on asset allocation.

Leseprobe

Table of Contents

Cover

Preface

Acknowledgments

CHAPTER 1: Preliminaries

EXPECTED UTILITY

ESTIMATION ERROR

A MODERN DEFINITION OF ASSET ALLOCATION

NOTES

CHAPTER 2: The Client Risk Profile

INTRODUCTION

MEASURING PREFERENCES

INCORPORATING GOALS

NOTES

CHAPTER 3: Asset Selection

INTRODUCTION

MOMENT CONTRIBUTIONS

MIMICKING PORTFOLIOS

A NEW ASSET CLASS PARADIGM

NOTES

CHAPTER 4: Capital Market Assumptions

INTRODUCTION

USING HISTORY AS OUR FORECAST

ADJUSTING FORECASTS

NOTES

CHAPTER 5: Portfolio Optimization

INTRODUCTION

OPTIMIZATION RESULTS

TO MPT OR NOT TO MPT?

ASSET ALLOCATION SENSITIVITY

FINAL REMARKS

NOTES

Bibliography

Index

End User License Agreement

List of Illustrations

Chapter 1

FIGURE 1.1 Choice Under Uncertainty: Expected Return vs. Expected Utility

FIGURE 1.2 Skew and Kurtosis Effects on a Normal Distribution

FIGURE 1.3 Skew and Kurtosis of Common Modern Assets (Historical Data from 1...

FIGURE 1.4 Graphical Representation of Utility Functions (

,

)

FIGURE 1.5 Allocation Sensitivity to Forecasts

FIGURE 1.6 Estimation Error vs. Sample Size T (Reprinted with Permission fro...

Chapter 2

FIGURE 2.1 Risk Aversion Questionnaire

FIGURE 2.2 Risk Aversion Mapping

FIGURE 2.3 Loss Aversion Questionnaire

FIGURE 2.4 Loss Aversion Mapping

FIGURE 2.5 Reflection Questionnaire

FIGURE 2.6 Moderation vs. Accommodation of Behavioral Biases

FIGURE 2.7 Balance Sheet Model

FIGURE 2.8 Preference Moderation via SLR

Chapter 3

FIGURE 3.1 Moment Contribution Example: Long-Term Treasuries Added to a US E...

FIGURE 3.2 MPTE Example: Fixed Income

FIGURE 3.3 Payoffs of Concave and Convex ARP

FIGURE 3.4 Preeminent Traditional and Alternative Risk Premia

FIGURE 3.5 Workflow for Creating an Asset Class Menu

FIGURE 3.6 A New Asset Class Taxonomy

FIGURE 3.7 ARP Moment Contributions

Chapter 4

FIGURE 4.1 Bootstrap Estimates of Average Monthly Return for US Equities

FIGURE 4.2 Standard Error of First Four Moment Estimates for US Equities as ...

FIGURE 4.3 Standard Error of First Four Moment Estimates for US Equities as ...

FIGURE 4.4 Stationarity Test Results (historical data from 1972 to 2018)10

FIGURE 4.5 Reasons to Modify Historical Estimates

FIGURE 4.6 Calculation Steps for Return Distribution Shifting and Scaling

Chapter 5

FIGURE 5.1 Optimization Results for Selected

,

, and

FIGURE 5.2 Comparison with Mean-Variance and Mean-Semivariance Frameworks Wh...

FIGURE 5.3 Comparison with Mean-Variance and Mean-Semivariance Frameworks

FIGURE 5.4 Error Bars on Optimization Results for Selected

,

, and

FIGURE 5.5 Error Bars on Utility Optimization vs. Risk Parity

FIGURE 5.6 Error Bars on Optimization Results as a Function of Sample Size (

FIGURE 5.7 Error Bars on Optimization Results as a Function of Asset Univers...

Guide

Cover

Table of Contents

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Modern Asset Allocation for Wealth Management

DAVID M. BERNS, PhD

Copyright © 2020 by David Berns.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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Preface

Modern portfolio theory (MPT) is one of the most insightful tools of modern finance. It introduced the world to the first intuitive framework for portfolio risk and how one can optimally combine investable assets to form portfolios with high return and low volatility. The elegance and power of mean-variance (M-V) optimization garnered its inventor Harry Markowitz a well-deserved Nobel Memorial Prize in Economics and has always been a great personal inspiration for how quantitative insights can assist us all in our daily life.

The actual process of implementing MPT for clients can be challenging in practice, though. Setting client risk preferences, accounting for client financial goals, deciding which assets to include in the portfolio mix, forecasting future asset performance, and running an optimization routine all sound simple enough conceptually, but when you actually sit down to implement these tasks, the true complexity of the problem becomes apparent. This implementation hurdle forces many advisors either to outsource the asset allocation component of their process or deploy simple portfolio construction heuristics (rules of thumb) that are sub-optimal and lack connection to client preferences.

The financial ecosystem has also seen tremendous evolution since MPT was first introduced in 1952. The world has been introduced to non-linear investable assets such as options and certain alternative risk premia (AKA style premia, factor investing, or smart beta), which have rapidly become more available to retail investors over the past two decades. Additionally, our understanding of human behavior when it comes to decision-making under uncertainly has markedly shifted with the discovery of prospect theory (PT) in the 1970s. Homo economicus, the perfectly rational investor, is no longer the client we are building portfolios for. These evolutions cannot be handled in the MPT framework: non-linear assets cannot be represented by mean and variance and the M-V approach cannot capture the nuances of behavioral risk preferences.

While MPT is both practically challenging and theoretically antiquated, there are wonderful new methods available for both simplifying the challenging tasks in the asset allocation process and addressing the realities of human decision-making in today's markets. Unfortunately, this progress has not been widely assimilated by the wealth management community, which includes both traditional advisors and robo-advisors. Most advisors still utilize the original formulation of MPT or deploy heuristic models that help avoid the challenges of implementation altogether. This book is a first step to bridging the gap between the original formulation of MPT and a more modern and practical asset allocation framework.

This book was written to enable advisors to more accurately design portfolios for real-world client preferences while conquering the complexities of the asset allocation process that often push advisors into sub-optimal heuristics or outsourcing. To empower advisors fully in being able to implement the framework catalogued in this book, the complete machinery is available as a cloud-based SaaS: www.portfoliodesigner.com. Just as the book is meant to provide a modern and intuitive system for creating portfolios, the software is also intended to provide an accurate and scalable solution for real-world asset allocation based on the methods presented here. And for those who don't want to deploy the primary framework of the book, the hope is that the materials presented here can minimally help advisors navigate the wide world of asset allocation solutions out there in a more informed and fiduciary manner.

While a primary goal of this writing is to provide a practical solution to asset allocation, I must warn you that the final framework falls short of being a simple solution. Any asset allocation solution that truly respects client preferences and the foundations of modern financial economics will require a certain foundation of knowledge and measured care for proper implementation. My hope is that, with education and practice, the refined perspective presented here will quickly become second nature to wealth management practitioners and ultimately lead to a scalable process that financial advisors can truly stand behind. To help streamline this education, I have decided not to present an encyclopedic review of asset allocation tools, but instead to focus on a limited number of tools for each step of the asset allocation process. To this end, I have consciously focused on the most accurate methods that were simultaneously practical, which includes elements that are undeniably optimal (and need never be replaced) and others that are clearly not optimal (and may warrant replacement). While the ultimately singular framework presented here indeed has its limitations, my truest intention was to create a modern yet practical process that the wealth management community could readily and confidently deploy today.

For the purposes of this book, asset allocation is defined as anything related to creating an investment portfolio from scratch. This includes setting client risk preferences, deciding which assets to include in client portfolios, forecasting future asset performance, and blending assets together to form optimal client portfolios. Following the first chapter, which reviews some key preliminary concepts and presents the general framework pursued here, this book is organized in the order in which each asset allocation task is carried out when creating a client's portfolio in practice. Hence, Chapters 2–5 are meant to serve as a step-by-step guidebook to asset allocation, where the aforementioned software follows the exact same workflow. Below is a brief overview of what will be covered in each chapter.

Chapter 1. Preliminaries. Utility theory and estimation error, two key concepts that underlie much of the book's discussions, are introduced. Asset allocation is then defined as the maximization of expected utility while minimizing the effects of estimation error, which will ultimately lead to the book's modern yet practical process for building portfolios. MPT and other popular models are shown to be approximations to the full problem we would like to solve. Key concepts from behavioral economics are also introduced, including a modern utility function with three (not one) risk parameters, that can capture real-world client preferences. We then review how to minimize estimation error and its consequences to create a practical framework that advisors can actually implement. The chapter ends with a formal definition of the overall framework that is pursued in the remainder of the book.

Chapter 2. The Client Risk Profile. The chapter begins with a review of how to measure the three dimensions of client risk preferences (risk aversion, loss aversion, and reflection) via three lottery-based questionnaires. The concept of standard of living risk (SLR) is introduced to help determine whether these preferences should be moderated to achieve the long-term cash flow goals of the portfolio. SLR is then formally assessed with a comprehensive yet simple balance sheet model, which goes far beyond the generic lifecycle investing input of time to retirement, and leads to a personalized glidepath with a strong focus on risk management. The final output of the chapter is a systematic and precise definition of a client's utility function that simultaneously accounts for all three dimensions of risk preferences and all financial goals.

Chapter 3. Asset Selection. The third chapter presents a systematic approach to selecting assets for the portfolio that are simultaneously accretive to a client's utility and minimally sensitive to estimation error. By combining this asset selection process with the concept of risk premia, the chapter also introduces a new paradigm for an asset class taxonomy, allowing advisors to deploy a new minimal set of well-motivated asset classes that is both complete and robust to estimation error sensitivity.

Chapter 4. Capital Market Assumptions. This chapter justifies the use of historical return distributions as the starting point for asset class forecasts. We review techniques that help diagnose whether history indeed repeats itself and whether our historical data is sufficient to estimate accurately the properties of the markets we want to invest in. A system is then introduced for modifying history-based forecasts by shifting and scaling the distributions, allowing advisors to account for custom forecasts, manager alpha, manager fees, and the effects of taxes in their capital market assumptions.

Chapter 5. Portfolio Optimization. In the fifth and final chapter, we finally maximize our new three-dimensional utility function over the assets selected and capital market assumptions created in the previous chapters. Optimizer results are presented as a function of our three utility function parameters, showcasing an intuitive evolution of portfolios as we navigate through the three-dimensional risk preference space. By comparing these results to other popular optimization frameworks, we will showcase a much more nuanced mapping of client preferences to portfolios. The chapter ends with a review of the sensitivity of our optimal portfolios to estimation error, highlighting generally robust asset allocation results.

There are three key assumptions made throughout this book to simplify the problem at hand dramatically without compromising the use case of the solution too severely: (1) we are only interested in managing portfolios over long-term horizons (10+ years); (2) consumption (i.e. withdrawals) out of investment portfolios only occurs after retirement; and (3) all assets deployed are extremely liquid. Let's quickly review the ramifications of these assumptions so the reader has a very clear perspective on the solution being built here.

Assumption 1 implies that we will not be focused on exploiting short-term (6–12 month) return predictability (AKA tactical asset allocation) or medium-term (3–5 year) return predictability (AKA opportunistic trading). Given the lack of tactical portfolio shifts, it is expected that advisors will typically hold positions beyond the short-term capital gains cutoff, and it can be assumed that taxes are not dependent on holding period, allowing us to account completely for taxes within our capital market forecasts. One can then assume there is little friction (tax or cost) to rebalancing at will, which leads to the following critical corollary: the long-term, multi-period portfolio decision can be reduced to the much simpler single period problem. Finally, the long horizon focus will help justify the deployment of historical distribution estimates as forecast starting points.

The first key ramification of assumption 2 is that we only need to consider “asset only” portfolio construction methods, i.e. asset-liability optimization methods with regular consumption within horizon (common for pension plans and insurance companies) are not considered. Additionally, it allows us to focus on the simpler problem of maximizing utility of wealth, rather than the more complex problem of maximizing utility of consumption.

Assumption 3 has two main consequences: (1) liquidity preferences can be ignored while setting the client risk profile; and (2) the liquidity risk premium need not be considered as a source of return. This assumption also keeps us squarely focused on the average retail client, since they don't have access to less-liquid alternative assets (like hedge funds and private equity/real estate) that are commonly held by ultra-high-net-worth individuals.

I hope this book and the accompanying software empowers advisors to tackle real-world asset allocation confidently on their own, with a powerful yet intuitive workflow.

David Berns

New York

January 10, 2020

Acknowledgments

First and foremost, thank you to my amazing family and friends for all their love and support throughout the writing of this book. Carolee, thank you for selflessly taking care of me and our family through all of the anxiety-laden early mornings, late nights, and weekend sessions; I couldn't have done this without you. Craig Enders, thank you for keeping me sane through this endeavor and being so helpful on just about every topic covered. Thank you to my trusted friends in the advisory space—Alex Chown, Jeff Egizi, Zung Nguyen, and Erick Rawlings—for all your thoughtful input. Thank you to Chad Buckendahl, Susan Davis-Becker, John Grable, Michael Guillemette, Michael Kitces, Mark Kritzman, Thierry Roncalli, and Jarrod Wilcox for helpful feedback on special topics. And thank you to Bill Falloon and the rest of the Wiley team for their gracious support and encouragement all along the way. I'd additionally like to thank Mark Kritzman, who through his lifelong commitment to rigorous yet elegant approaches in asset allocation, has inspired me to continue to advance a modern yet practical solution for our wealth management community. And finally, to my science teachers, Peggy Cebe, Leon Gunther, Will Oliver, and Terry Orlando, thank you for the lessons in research that I carry with me every day.

CHAPTER 1Preliminaries

The chapter begins with a review of two topics that will serve as the foundations of our asset allocation framework: expected utility and estimation error. Asset allocation is then defined as the process of maximizing expected utility while minimizing estimation error and its consequences—a simple yet powerful definition that will guide us through the rest of the book. The chapter concludes with an explicit definition of the modern yet tractable asset allocation framework that is recommended in this book: the maximization of a utility function with not one but three dimensions of client risk preferences while minimizing estimation error and its consequences by only investing in distinct assets and using statistically sound historical estimates as our forecasting foundation.

Key Takeaways:

Individual investors look to maximize their future utility of wealth, not their future wealth.

Mean-variance optimization is just an approximation to the full utility maximization problem we will tackle.

Maximizing the full utility function allows for a transparent and precise mapping of client preferences to portfolios.

A utility function with three risk preferences, accounting for both neoclassical and behavioral risk preferences, will be maximized in a returns-based framework.

Estimation error and the associated sensitivity to asset allocation recommendations can't be avoided or removed via a holy grail solution.

Estimation error will be managed by deploying non-parametric historical estimation of stationary assets with large sample sizes; and sensitivity to estimation error will be managed by only investing in easily distinguishable assets.

EXPECTED UTILITY

Introduction

When deciding whether to invest in an asset, at first glance one might think that the decision is as simple as calculating the expected value of the possible payoffs and investing if the expected payoff is positive. Let's say you are offered the opportunity to invest in a piece of property and the possible outcomes a year from now are a drop of $100,000 and a rise of $150,000, both with a 50% chance of occurring. The expected payoff for the investment is , so if you only care about expected return, then you would certainly invest.

But are you really prepared to potentially lose $100,000? The answer for many people is no, because $100,000 is a substantial fraction of their assets. If $100,000 represented all of your wealth, you certainly wouldn't risk losing everything. What about an extremely wealthy person? Should they necessarily be enthusiastic about this gamble since the potential loss represents only a small fraction of their wealth? Not if they are very averse to gambling and would much prefer just sitting tight with what they have (“a bird in the hand is worth two in the bush”). When making decisions regarding risky investments one needs to account for (1) how large the potential payoffs are relative to starting wealth; and (2) preferences regarding gambling.

In 1738 Daniel Bernoulli, one of the world's most gifted physicists and mathematicians at the time, posited that rational investors do not choose investments based on expected returns, but rather based on expected utility.1 Utility is exactly what it sounds like: it is a personalized value scale one ascribes to a certain amount of wealth. For example, a very affluent person will not place the same value on an incremental $100 as someone less fortunate. And a professional gambler will not be as afraid of losing some of his wealth as someone who is staunchly opposed to gambling. The concept of utility can therefore account for both effects described in the previous paragraph: potential loss versus total wealth and propensity for gambling. The expected utility (EU) one period later in time is formally defined as

Equation 1.1 Expected Utility

where pi is the probability of outcome i, is the utility of outcome i, and O is the number of possible outcomes.

Let's now return to our real estate example. Figure 1.1 shows an example utility function for a person with total wealth of $1 million. For the moment, don't worry about the precise shape of the utility function being used; just note that it is a reasonable one for many investors, as will be discussed later in the chapter. Initially the investor's utility is 1 (the utility units are arbitrary and are just an accounting tool2). Given the precise utility function being used and the starting wealth level relative to the potential wealth outcomes, the utility for the positive payoff outcome is 1.5 while the loss outcome has a utility of 0.29, and the expected utility of the investment is 0.9. Since the EU is less than the starting utility of 1, the bet should not be accepted, disagreeing with the decision to invest earlier based purely on expected payoff. If the utility function were a lot less curved downward (imagine more of a straight line at 45 degrees), indicative of an investor with greater propensity to gamble, the expected utility would actually be greater than 1 and the investor would choose to make the investment. Additionally, if the starting wealth of the investor were much less than $1 million, the bet would become less appealing again, as the assumed utility function drops increasingly fast as wealth shrinks, bringing the expected utility well below the starting utility level. Hence, this simple utility construction can indeed account for both gambling propensity as well as the magnitude of the gamble relative to current wealth, as promised.

FIGURE 1.1 Choice Under Uncertainty: Expected Return vs. Expected Utility

The concept of EU is easily extended to a portfolio of assets:

Equation 1.2 Portfolio Expected Utility

where we now first sum over all N assets in the portfolio according to their weights wj, before summing over all O possible outcomes, which ultimately leads to the same formula as Eq. (1.1) except that each outcome is defined at the portfolio level .

How can this help us choose an asset mix for clients? Since utility of wealth is what is important to clients, the goal of wealth management is to maximize the expected utility one period from now.3,4 This is done by starting with Eq. (1.2) and filling in the blanks in four sequential steps: (1) specify the client's utility function; (2) choose assets to include in the portfolio; (3) delineate all possible outcomes and their probability over the next time period; and (4) find the portfolio weights that maximize future EU. These four steps are precisely what is covered in Chapters 2 through 5.

Before moving on, let's take stock of how incredibly insightful this succinct formulation is. The right side of Eq. (1.2) tells us that the advisor's entire mission when building a client's portfolio is to invest in a set of assets that have high probabilities of utility outcomes higher than starting utility (the higher the better) while having as low a probability as possible of outcomes below starting utility (again, the higher utility the better). Just how aggressive we must be in accessing outcomes on the right side of the utility curve and avoiding those on the left is set by the shape of the utility function. For example, utility functions that fall off quickly to the left will require more focus on avoiding the negative outcomes while flatter functions will require less focus on negative outcome avoidance. If we can create an intuitive perspective on the shape of our client's utility function and the return distributions of the assets we invest in, we can build great intuition on the kinds of portfolios the client should have without even running an optimizer. This simple intuition will be a powerful guiding concept as we transition from modern portfolio theory (MPT), which is generally presented without mention of a utility function, to a completely general EU formulation of the problem.

MPT Is an Approximation

A key proposition of this book is to build client portfolios that have maximal EU as defined by Eq. (1.2). Conceptually, this is a very different approach than the popular mean-variance (M-V) framework, where portfolios are built by maximizing return while minimizing variance, without ever mentioning the client's utility. It is thus imperative to show how deploying the full utility function in the process of building portfolios relates to the MPT framework. It is also time to introduce the most complicated mathematical formula in the book. I promise that the temporary pain will be worth it in the long run and that the reader will not be subjected to any other formulas this complex for the remainder of the book.

The expected utility in our simple real estate example was a function of next period wealth. We will now transition to writing our next period utility outcomes in Eq. (1.2) in terms of return r rather than wealth, by writing the next period wealth associated with an outcome i as