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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
You have great investment ideas. If you turn them into highly profitable portfolios, this book is for you. Advanced Portfolio Management: A Quant's Guide for Fundamental Investors is for fundamental equity analysts and portfolio managers, present, and future. Whatever stage you are at in your career, you have valuable investment ideas but always need knowledge to turn them into money. This book will introduce you to a framework for portfolio construction and risk management that is grounded in sound theory and tested by successful fundamental portfolio managers. The emphasis is on theory relevant to fundamental portfolio managers that works in practice, enabling you to convert ideas into a strategy portfolio that is both profitable and resilient. Intuition always comes first, and this book helps to lay out simple but effective "rules of thumb" that require little effort to implement and understand. At the same time, the book shows how to implement sophisticated techniques in order to meet the challenges a successful investor faces as his or her strategy grows in size and complexity. Advanced Portfolio Management also contains more advanced material and a quantitative appendix, which benefit quantitative researchers who are members of fundamental teams. You will learn how to: * Separate stock-specific return drivers from the investment environment's return drivers * Understand current investment themes * Size your cash positions based on * Your investment ideas * Understand your performance * Measure and decompose risk * Hedge the risk you don't want * Use diversification to your advantage * Manage losses and control tail risk * Set your leverage Author Giuseppe A. Paleologo has consulted, collaborated, taught, and drank strong wine with some of the best stock-pickers in the world; he has traded tens of billions of dollars hedging and optimizing their books and has helped them navigate through big drawdowns and even bigger recoveries. Whether or not you have access to risk models or advanced mathematical background, you will benefit from the techniques and the insights contained in the book--and won't find them covered anywhere else.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Dedication
Chapter 1: For Whom? Why? And How?
1.1 What You Will Find Here
1.2 Asterisks; Or, How to Read This Book
1.3 Acknowledgments
Chapter 2: The Problem: From Ideas to Profit
2.1 How to Invest in Your Edge, and Hedge the Rest
2.2 How to Size Your Positions
2.3 How to Learn from Your History
2.4 How to Trade Efficiently
2.5 How to Limit Factor Risk
2.6 How to Control Maximum Losses
2.7 How to Determine Your Leverage
2.8 How to Analyze New Sources of Data
Notes
Chapter 3: A Tour of Risk and Performance
3.1 Introduction
3.2 Alpha and Beta
3.3 Where Does Alpha Come From?
3.4 Estimate Risk in Advance
3.5 First Steps in Risk Decomposition
3.6 Simple Hedging
3.7 Separation of Concerns
3.8 Takeaway Messages
Notes
Chapter 4: An Introduction to Multi-Factor Models
4.1 From One Factor to Many
4.2 ★Frequently Asked Questions About Risk
4.3 ★The Machinery of Risk Models
4.4 Takeaway Messages
Notes
Chapter 5: Understand Factors
5.1 The Economic Environment
5.2 The Trading Environment
5.3 The Company: Valuation Factors
5.4 Takeaway Messages
Notes
Chapter 6: Use Effective Heuristics for Alpha Sizing
6.1 Sharpe Ratio
6.2 Estimating Expected Returns
6.3 Risk-Based Sizing
6.4 ★Empirical Analysis of the Sizing Rules
6.5 From Ideas to Positions
6.6 Time-Series Risk-Based Portfolio Targeting
6.7 ★Frequently Asked Questions About Performance
6.8 Takeaway Messages
Notes
Chapter 7: Manage Factor Risk
7.1 Tactical Factor Risk Management
7.2 Strategic Factor Risk Management
7.3 Systematic Hedging and Portfolio Management
7.4 Takeaway Messages
Notes
Chapter 8: Understand Your Performance
8.1 Factor
8.2 Idiosyncratic
8.3 Trade Events Efficiently
8.4 ★Use Alternative Data!
8.5 ★Frequently Asked Questions About Performance
8.6 Takeaway Messages
Notes
Chapter 9: Manage Your Losses
9.1 How Stop-Loss Works
9.2 Why a Stop-Loss Policy?
9.3 The Costs and Benefits of Stop-Loss
9.4 Takeaway Messages
Notes
Chapter 10: ★Set Your Leverage Ratio for a Sustainable Business
10.1 A Framework for Leverage Decisions
10.2 Takeaway Messages
Notes
Chapter 11: ★★Appendix
11.1 Essential Risk Model Formulas
11.2 Diversification
11.3 Mean-Variance Formulations
11.4 Proportional-Rule Formulations
11.5 Generating Custom Factors
11.6 Optimization Formulations
11.7 Tactical Portfolio Optimization
11.8 Hedging Formulations
11.9 Optimal Event Trading
Notes
References
Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1 Parameter estimates for Synchrony's returns regressed against SP500...
Table 3.2 Parameter estimates for Synchrony's returns regressed against SP500...
Table 3.3 Probabilities of occurrence of rare events under the normal distrib...
Table 3.4 Synchrony's risk parameters for the year 2019.
Table 3.5 Synchrony, Wal-Mart and SP500 risk parameters, together with holdin...
Table 3.6 Portfolio example, with increasing number of stocks. Each stock has...
Table 3.7 Synchrony, Wal-Mart and SP500 risk parameters, together with holdin...
Chapter 4
Table 4.1 Comparison of different approaches to modeling risk.
Chapter 5
Table 5.1 Country and industry loadings for a sample of US and Canadian compa...
Table 5.2 Performance of stock and hypothetical portfolios, for trend-followi...
Chapter 6
Table 6.1 Sharpe Ratio for different rules based on
predicted
volatility, for ...
Table 6.2 Sharpe Ratio of different strategies using
realized
volatility, for ...
Table 6.3 Results of simulated strategies using different sizing methods.
Table 6.4 Expected returns and NMV.
Table 6.5 Sharpe Ratio of unit-GMV and unit-dollar volatility scaling, with o...
Table 6.6 Sharpe Ratio of unit-GMV and unit-dollar volatility scaling, with o...
Chapter 7
Table 7.1 An example of risk decomposition for a technology sector portfolio.
Table 7.2 Per-stock Net Market Value (in $M), Marginal Contribution to Factor...
Table 7.3 Risk-adjusted losses for keeping a percentage of idio variance belo...
Table 7.4 Single-Stock Limit, based on coverage breadth and ratio between ret...
Chapter 8
Table 8.1 Portfolio Factor exposures.
Table 8.2 A list of position/dates/NMV.
Table 8.3 A list of position/dates/NMV, rearranged in matrix form.
Table 8.4 A list of position / dates / nmv, rearranged in matrix form with eq...
Table 8.5 A list of position/date/nmv, rearranged in matrix form.
Chapter 9
Table 9.1 Efficiency for different values of the PM Sharpe Ratio and the loss...
Chapter 10
Table 10.1 Ranges for Leverage Ratio. Values of max leverage are highlighted ...
List of Illustrations
Chapter 3
Figure 3.1 Linear regression of Synchrony's (SYF) and Wal-Mart's (WMT) daily...
Figure 3.2 Flowchart illustrating the relationships between market, idio and...
Figure 3.3 The variance of the sum of two independent random variables is eq...
Chapter 4
Figure 4.1 Analogous to Figure 3.2 but for two factors.
Figure 4.2 Steps needed to generate a risk model.
Chapter 5
Figure 5.1 Summary correlation matrix between the factor returns of a US mod...
Figure 5.2 Time Series of the country factor cumulative returns, 2007–2017.
Figure 5.3 Time Series of the Beta factor cumulative returns, 1998–2020.
Figure 5.4 Beta compression phenomenon.
Figure 5.5 Time Series of the Volatility factor cumulative returns, 2007–201...
Figure 5.6 Time Series of the Short Interest factor cumulative returns, 2007...
Figure 5.7 The deleveraging cycle.
Figure 5.8 Time Series of the Active Manager Holdings factor cumulative retu...
Figure 5.9 Time Series of the medium-term momentum factor cumulative returns...
Figure 5.10 Quantile-Quantile plot of the medium-term momentum factor cumula...
Figure 5.11 A quartet of value factors.
Chapter 6
Figure 6.1 Position sizes in a simulated portfolio.
Figure 6.2 Realized Sharpe Ratios for sectors-based portfolio for portfolios...
Figure 6.3 Realized Sharpe Ratios for sectors-based portfolio for portfolios...
Figure 6.4 Realized Sharpe for the case of normally distributed signals.
Figure 6.5 Realized Sharpe for the case of buy/sell signals.
Chapter 7
Figure 7.1 Relationship between percentage idio var and risk-adjusted perfor...
Chapter 8
Figure 8.1 Performance Attribution example. The figure shows total PnL, idio...
Figure 8.2 Performance Attribution example. The figure shows total PnL ex ma...
Figure 8.3 Performance Attribution example. The figure shows some of the lar...
Figure 8.4 Top: Idiosyncratic performance of equal-sized vs. actual-sized po...
Figure 8.5 Liquidity-constrained simulation.
Figure 8.6 Flowchart describing the process connecting alternative data to s...
Chapter 9
Figure 9.1 Deployed Capital as a function of drawdown for Grossman-Zhou opti...
Figure 9.2 Impact of stop-loss on performance. We visualize five- and ten-ye...
Figure 9.3 Relationship between efficiency of a strategy and stop-loss, base...
Guide
Cover Page
Table of Contents
Title Page
Copyrigt
Dedication
Begin Reading
References
Index
End User License Agreement
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Advanced Portfolio Management
A Quant’s Guide for Fundamental Investors
Giuseppe A. Paleologo
Copyright © 2021 by Giuseppe A. Paleologo. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
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Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format.
Library of Congress Cataloging-in-Publication Data is Available:
ISBN 9781119789796 (Hardback)ISBN 9781119789819 (epdf)ISBN 9781119789802 (epub)
Cover Design: WileyCover Image: © Giovani Battista Piranesi, Public Domain
To Tofu
Chapter 1For Whom? Why? And How?
I wrote this book for equity fundamental analysts and portfolio managers, present and future. I am addressing the reader directly: I am talking to you, the investor who is deeply in the weeds of the industry and the companies you cover, investigating possible mispricings or unjustified divergences in valuation between two companies. You, the reader, are obsessed with your work and want to be better at it. If you are reading this, and think, that's me!, rest assured: yes, it's probably you. You were the undergraduate in Chemical Engineering from Toronto who went from a summer job at a liquor store to founding an $8B hedge fund. The deeply thoughtful Norwegian pension fund manager who kept extending our meeting asking questions. The successful energy portfolio manager who interviewed me for my first hedge fund job, and the new college graduate from a large state university in Pennsylvania taking a job as an associate in a financials team.
I imagine that these readers are at different stages in their careers. Since the companies they cover are fundamentally different, they do think in different ways. But they all share a feature: they all have valuable trading ideas but realize that having good ideas is useless without the knowledge of how to turn them into money. This is the objective of portfolio construction and risk management: how to put together a portfolio of holdings that will be profitable over time and will survive adversities. This book is a short, incomplete guide toward investment enlightenment.
There is a second group of readers who will benefit from this book: the quantitative researchers who are, more and more, essential members of fundamental teams. There is not a strict separation between PMs and quantitative researchers. The quantitive researchers will find the appendix useful, if they want to implement programmatically the advanced tools the book describes.
1.1 What You Will Find Here
The book introduces a few themes, and then revisits them by adding details. You will learn how to:
Separate stock-specific return drivers from the investment environment's return drivers;
Size your positions;
Understand your performance;
Measure and decompose risk;
Hedge the risk you don't want;
Use diversification to your advantage;
Manage losses;
Set your leverage
.
The approach I follow is to offer recommendations and best practices that are motivated by theory and confirmed by empirical evidence and successful practice. While I rely heavily on the framework of factor modeling, I believe that even a reader who does not currently have access to a risk model can still get a lot out of it. Day-to-day, several portfolio managers run very successful books without checking their factor risk decomposition every minute. The reason is that they have converted insights into effective heuristics. Wherever I can, I will flesh out these rules of thumb, and explain how and when they work.
1.2 Asterisks; Or, How to Read This Book
The mathematical requirements are minimal. Having taken an introductory course in Statistics should give the tools necessary to follow the text. Different readers have different objectives. Some want to get the gist of a book. Time is precious, only the thesis matters, its defense doesn't. Gettysburg Address: This new nation was conceived in Liberty, and dedicated to the proposition that all men are created equal. Hamlet: revenge is a futile pursuit. Moby Dick: please, don't hunt whales. To the CliffsNotes-oriented reader, to the secret agent perusing a book between Martinis: there is hope. Just read the sections that are not marked by a “”. Then there is the detail-oriented reader.
If you always collect all the trophies when playing a video game, or if you felt compelled to finish War and Peace in high school and didn't regret it: please read all the chapters and sections marked by “”, but skip the double-starred chapter “”. You will learn the “Why” of things, not only the “How”. These sections contain empirical tests and more advanced material and their results are not used in the remainder of the book. Finally, for the quantitative researcher and the risk manager, there is the double-starred appendix. Think of this as eleven on the volume knob of a guitar amplifier, as the “Chuck Norris Guide to Portfolio Construction.” If you can read it, you should.
1.3 Acknowledgments
I thank Qontigo (formerly Axioma) for making available its US risk model; special thanks to Chris Canova and Sebastian Ceria. Samantha Enders, Purvi Patel, and Bill Falloon at Wiley guided the book composition from the first phone call to its publication. The following people read the book and provided corrections and feedback: Ashish Bajpai, Victor Bomers, Omer Cedar, Phil Durand, François Drouin, Ross Fabricant, Tom Fleming, Izabella Goldenberg, Ernesto Guridi, Dimitrios Margaritis, Chris Martin, Michael Medeiros, Gurraj Singh Sangha, Ashutosh Singh, David Stemerman, Thomas Twiggs, Davide Vetrale, and Bernd Wuebben. I also owe much to people with whom I discussed – and from whom I learned about – several of these topics. Although they are too many to mention them all, Ravi Aggarwal, Brandon Haley, Gustav Rydbeck, Fabian Blohm, Costis Maglaras, Sai Muthialu, Vishal Soni and Samer Takriti, and, again, Sebastian Ceria have taught me most of what I know. All remaining errors are mine.
Chapter 2The Problem: From Ideas to Profit
For those of you who are starting now, you are entering an industry in transition. If you could travel in time to 1995 and visit a portfolio manager's desk, you would have seem him or her using the same tools, processes and data they are using in 2020: Microsoft Excel, to model company earnings; a Bloomberg terminal; company-level models of earnings (also written in Excel), quarterly conferences where one meets with company executives. All of this is changing. Aside from the ever-present game of competition and imitation, two forces are moving the industry. The first is the availability of new data sources. “New”, because storage and computational advances make it possible to collect and process unstructured, transactional data sets that were not collected before. And “available”, because networking and cloud computing reduce dramatically the cost of consuming and managing these data. The second driving force is the transition of new analytical tools from mathematics to technology. Optimization, Factor Models, Machine Learning methods for supervised and unsupervised prediction: these were once advanced techniques that required expertise and relied on immature software prototypes. Now we have tools – technologies, really – that are robust, easy-to-use, powerful and free. Bloomberg and Excel are no longer sufficient, and with that, the toolkit that served the industry for so many years is suddenly incomplete. To meet the new challenges, fundamental teams are hiring “data scientists”. Don't be fooled by the generic title. These are people who need to combine quantitative rigor and technical expertise with the investment process. Very often, they test new data sources; they run optimizations; they test hypotheses that the portfolio manager formulated. Ultimately, however, it is the portfolio manager who constructs the portfolio and supervises the action of the data scientist. The portfolio manager knows alphas, portfolio construction, risk management and data, and these are deeply connected. The success of a strategy is up to her competency and knowledge of these topics. A good portfolio manager can be – and should be! – a good risk manager, too. I believe it is possible to explain the basics of a systematic approach to portfolio construction without resorting to advanced mathematics and requiring much preexisting knowledge. This book is an elementary book in the sense that it assumes very little. I hope most readers will find in it something they already know, but that all readers will find something they did not know.
It seems inevitable that many books on this important subject must exist. In my years spent working as a quantitative researcher and consultant for the sell- and the buy-side, I have never been able to wholeheartedly recommend a book to my clients and colleagues that would help them in their endeavors. Like Italian art during the Renaissance, real-world finance works through a system of apprenticeship. Finance practitioners acquire most of their knowledge by doing and experiencing things. They talk and listen to risk-takers like themselves. They believe portfolio managers more than “managers” who have never managed a portfolio. They have a strong incentive not to share knowledge with outsiders, in order to protect their edge. All of this conspires against the existence of a good book on portfolio construction. Although the distance between professionals and academics is smaller in Finance than in other disciplines, it is still wide; the specific subject of portfolio management is covered by only a handful of journals.1
Summing up, there is no master theory yet of portfolio management. There are problems and technologies to solve in part these problems. Theories come and go; but a solution to a real problem is forever. As you explore portfolio management, you will find papers on optimization, position sizing, exploratory analysis of alternative data, timing of factors. Keep in mind the following maxim, which I paraphrase from a seminal paper on reproducible research:
An article about the theory of portfolio management is not the scholarship itself, it is merely advertising of the scholarship.
[Buckheit and Donoho, 1995]
Always look for simulation-based validations of a theory, and question the soundness of the assumptions in the simulation; and always look for empirical tests based on historical data, while being aware that these historical tests are most interesting when they show the limits of applicability of the theory, not when they confirm it [López de Prado, 2020].
Now, what are the problems?
2.1 How to Invest in Your Edge, and Hedge the Rest
Perhaps the simplest and deepest challenge is to understand the limits of your knowledge. If you develop a thesis with regard to the value of a company, you implicitly have a thesis on the peers of that company. All valuation judgements are relative. The question is, relative to what? The goal is to understand the drivers of pervasive returns, i.e., not of returns that we can forecast through deep investigation of a specific company, but rather that have a common explanatory factor; and then measure performance relative to those factors. There are at least two payoffs from following this process:
The first is an improvement in the alpha research process. If you know what the environment is, then you know if a bet on a particular company carries with it unintended bets. Separating the stock from the environment gives you
clarity of thought
.
The second is an improvement in the risk management process. If you know your environment, you can control your risk much more effectively; specifically, you can effectively reduce the environmental risk and keep only your intended bets; you can
hedge out what you don't know
.
2
This subject is covered throughout the book, and is the main subject of Chapters 3, 4, and 5.
2.2 How to Size Your Positions
Once you have effectively estimated the true stock-specific return, your next problem is converting a thesis into an investment. It stands to reason that, the stronger the conviction, the larger the position should be. This leaves many questions unanswered. Is conviction the only variable? How does stock risk enter the sizing decision? What is the role played by the other stocks in the portfolio?
This is the subject of Chapter 6.
2.3 How to Learn from Your History
According to Plato, Socrates famously told the jury that sentenced him to death that “the unexamined life is not worth living”. He was probably referring to portfolio managers. Billions of people happily live their unexamined yet worthy lives, but not many portfolio managers survive for long without examining their strategies. If you want to remain among the (professionally) living, you must make a habit of periodically revisiting your decisions and learning from them. The life of the good portfolio manager is one marked by continuous self-doubt and adaptation. The distinctive features of a strategy's performance are stock selection, position sizing, and timing skills. The challenge is how to quantify them and improve upon them.
This is the subject of Chapter 8.
2.4 How to Trade Efficiently
Transaction costs play a crucial role in the viability of a trading strategy. Often, portfolio managers are not fully aware of the fact that these costs can eat up a substantial fraction of their revenues. As a result, they may over-trade, either by opening and closing positions more aggressively than needed, or by adjusting too often the size of a position over the lifetime of the trade. Earning events and other catalysts like product launches, drug approvals, sell-side upgrades/downgrades are an important source of revenue for fundamental PMs; how should one trade these events in order to maximize revenues inclusive of costs? Finally, what role should risk management play in event (and, in particular, earnings) trades? Positioning too early exposes the PM to unwanted risk in the days preceding the event.
This is the subject of Sections 8.2.1 and 8.3.
2.5 How to Limit Factor Risk
The output of your fundamental research changes continuously. The rules of your risk management process should not. They should be predictable, implementable, effective. These usually come in the form of limits: on your deployed capital, on your deployed portfolio risk, but also on less obvious dimensions of your strategy; for example, single-position maximum size is an important aspect of risk management. The challenge is to determine the rules that allow a manager to fully express her ideas while controlling risk.
This is the subject of Section 7.2.
2.6 How to Control Maximum Losses
An essential mandate of a manager is to protect capital. The Prime Directive, in almost everything, is to survive. A necessary condition for survival is not to exceed a loss threshold beyond which the future of the firm or of your strategy would be compromised. This is often implemented via explicit or implicit stop-loss policies. But how to set these policies? And how does the choice of a limit affect your performance?
This is the subject of Chapter 9.
2.7 How to Determine Your Leverage
This challenge is not faced by all portfolio managers. When they are working for a multi-PM platform, leverage decisions are the responsibility of the firm. However, a few independent investors do start their own hedge funds, and choosing a leverage that makes the firm viable, attractive to investors, and prudent is perhaps the most important decision they face.
This is the subject of Chapter 10.
2.8 How to Analyze New Sources of Data
New sources of data that go far beyond standard financial information become available every day. The portfolio manager faces the challenge of evaluating them, processing them and incorporating them into their investment process. The ability to transform data and extract value from them will become an important competitive advantage in the years to come. The range of methods available to an investor is as wide as the methods of Statistics, Machine Learning and Artificial Intelligence, and experimenting with them all is a daunting task. Are there ways to screen and learn from data so that the output is consistent with and complementary to your investment process?
This is the subject of Section 8.4.
Notes
1
Among them,
The Journal of Portfolio Management
,
The Journal of Financial Data Science
, and the
Financial Analysts Journal
.
2
Joe Armstrong, a leading computer scientist and the inventor of the computer language Erlang, uses an effective metaphor for the lack of separation between the object of interest and its environment:
You wanted a banana but what you got was a gorilla holding the banana and the entire jungle
[Seibel,
2009
].
Chapter 3A Tour of Risk and Performance
What will you learn here:
A very gentle introduction to factor models, starting with the simplest example of a model, which you probably already know. And how risk estimation, performance attribution and hedging can be performed using this simple approach.
Why do you need it:
Because the themes I introduce here will return over and over again throughout the book, from simple heuristics to advanced optimizations.
When will you need this:
Always. This will become your second nature. You will break the ice at cocktail parties mentioning how much risk decomposition helped you in your life.
3.1 Introduction
On July 3, 1884, the Customer's Afternoon Letter (owned by Dow Jones & Co.) began publishing the first stock index: a simple price average of nine transportation companies and two industrial ones. In 1886 it published the first Dow Jones Industrial Average. In 1889, the newspaper became The Wall Street Journal, and over time more indices were created. Indices provided a benchmark against which to compare one's investment; and they are a summary of the overall behavior of the market or of a specific sector. A typical benchmarking exercise: if we hold a stock, on any given day we first look at the overall market return, as provided by the index, and then we compute the out- or underperformance of the stock compared to the market. When we look at indices as market summaries, we implicitly know that they describe most, or at least some, of the stock returns for that market segment. In a very real way, having an index gives us a way to describe performance and variation of stock returns. Factor models capture these two intuitive facts, make it rigorous, and extend them in many directions.
A first extension aims to offer more flexibility in the relationship between stock and benchmark. For example, a cyclical stock in the financial sector like Synchrony Financial (ticker: SYF) moves more in sync (lame pun) with the market than, say, Walmart (ticker: WMT), a large, stable, defensive stock. Figure 3.1 bears this out. We take the daily returns of Synchrony and Wal-Mart and regress them against the daily returns of SPY.1 The regression coefficient is denoted “beta”. If the market returns an incremental 1%, the stock returns an incremental (beta) * (1%), everything else being equal. It is a measure of market sensitivity that differs from stock to stock. Figure 3.1 shows the regression of SYF daily returns against SP500 futures returns, for the period January 2, 2018, to December 31, 2019. Let us go with the assumption that we can estimate the true beta of a stock to the market; i.e., the estimation error of the beta doesn't really matter. Then a simple decomposition of market return + stock-specific return gives us a great deal of information. On the benchmarking side, we now know what fraction of the return is attributable to the market. It may seem that SYF is outperforming the market in a bull market and Wal-Mart is underperforming. However, after decomposing returns, it may be the other way around: SYF is just a leveraged bet on the market, and after we remove the market contribution, SYF has underperformed, and WMT has outperformed. Another benefit from the linear relationship between market and stock returns is that it establishes a relationship among all stock returns. The market is the common link. For the overwhelming majority of stocks, the beta to the market is positive, but it can take values in a wide interval; several stocks exhibit betas higher than two. This relationship has implications for expected returns and risk as well. We will delve deeper into both later in this chapter. But before we proceed, we introduce a new term, “alpha”. In your daily job, it's alpha that will pay your salary. Beta, on the other hand, can get you fired. This explains why so many portfolio managers have the symbol tattooed on their bodies, while no one ever thought of getting a tattoo with the symbol . Not even risk managers.
Figure 3.1 Linear regression of Synchrony's (SYF) and Wal-Mart's (WMT) daily returns against the SPY daily returns, using daily returns for the years 2018 and 2019.
3.2 Alpha and Beta
Consider the regression line for SYF again. The complete formula for a linear regression includes an intercept and an error term, or residual. We write this explicitly. For a given stock,
Visually, this relationship is shown in Figure 3.2. We already introduced the term . This market component of the stock return is also called the systematic return of a stock. The first term on the left is the intercept ; it is a constant. When the market return is zero, the daily stock return is in expectation equal to alpha. No one observes expected returns, however. Even in the absence of market returns, the realized return of the stock would be . The last term is the “noise” around the stock return; it is also called idiosyncratic return of the stock. The terms specific and residual are also common, and we use all of them interchangeably. We would like to believe that this nuisance term is specific to the company: every commonality among the stocks comes the beta and the market return. The simple model of Equation (3.1), with a single systematic source of return for all the stocks, is called a single-factor model.
Figure 3.2
