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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance
- Sprache: Englisch
Expert real-world insight on the intricacies of quantitative trading before, during, and after the trade
The Elements of Quantitative Investing is a comprehensive guide to quantitative investing, covering everything readers need to know from inception of a strategy, to execution, to post-trade analysis, with insight into all the quantitative methods used throughout the investment process. This book describes all the steps of quantitative modeling, including statistical properties of returns, factor model, portfolio management, and more. The inclusion of each topic is determined by real-world applicability. Divided into three parts, each corresponding to a phase of the investment process, this book focuses on well-known factor models, such as PCA, but with essential grounding in financial context. This book encourages the reader to think deeply about simple things.
The author, Giuseppe Paleologo, has held senior quantitative research and risk management positions at three of the four biggest hedge fund platforms in the world, and at one of the top three proprietary trading firms. Currently, he serves as the Head of Quantitative Research at Balyasny Asset Management with $21 billion in assets under management. He has held teaching positions at Cornell University and New York University and holds a Ph.D. and two M.S. from Stanford University. This book answers questions that every quantitative investor has asked at some point in their career, including:
- How do I model multivariate returns?
- How do I test these models, either developed by me or by commercial vendors?
- How do I incorporate asset-specific data in my model?
- How do I convert risk appetite and expected returns into a portfolio?
- How do I account for transaction costs in portfolio management?
The Elements of Quantitative Investing earns a well-deserved spot on the bookshelves of financial practitioners seeking expert insight from a leading financial executive on quantitative investment topics—knowledge which is usually accessible to few and transmitted by one-on-one apprenticeship.
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Seitenzahl: 507
Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
Acknowledgments
Introduction
Notation
Chapter 1: The Map and the Territory
1.1 The Securities
1.2 Modes of Exchange
1.3 Who Are the Market Participants?
1.4 Where Do Excess Returns Come From?
1.5 The Elements of Quantitative Investing
Chapter 2: Univariate Returns
2.1 Returns
2.2 Conditional Heteroskedastic Models
2.3 State-Space Estimation of Variance
2.4 ⋆Appendix
2.5 Exercises
Chapter 3: Interlude: What Is Performance?
3.1 Expected Return
3.2 Volatility
3.3 Sharpe Ratio
3.4 Capacity
Chapter 4: Linear Models of Returns
4.1 Factor Models
4.2 Interpretations of Factor Models
4.3 Alpha Spanned and Alpha Orthogonal
4.4 Transformations
4.5 Applications
4.6 Factor Models Types
4.7 ⋆Appendix
4.8 Exercises
Chapter 5: Evaluating Risk
5.1 Evaluating the Covariance Matrix
5.2 Evaluating the Precision Matrix
5.3 Ancillary Tests
5.4 ⋆Appendix
Chapter 6: Fundamental Factor Models
6.1 The Inputs and the Process
6.2 Cross-Sectional Regression
6.3 Estimating the Factor Covariance Matrix
6.4 Estimating the Idiosyncratic Covariance Matrix
6.5 Winsorization of Returns
6.6 ⋆Advanced Model Topics
6.7 A Tour of Factors
Chapter 7: Statistical Factor Models
7.1 Statistical Models: The Basics
7.2 Beyond the Basics
7.3 Real-Life Stylized Behavior of PCA
7.4 Interpreting Principal Components
7.5 Statistical Model Estimation in Practice
7.6 ⋆Appendix
Chapter 8: Evaluating Excess Returns
8.1 Backtesting Best Practices
8.2 The Backtesting Protocol
8.3 The Rademacher Anti-Serum (RAS)
8.4 Some Empirical Results
8.5 ⋆Appendix
Chapter 9: Portfolio Management: The Basics
9.1 Why Mean-Variance Optimization?
9.2 Mean-Variance Optimal Portfolios
9.3 Trading in Factor Space
9.4 Trading in Idio Space
9.5 Drivers of Information Ratio: Information Coefficient and Diversification
9.6 Aggregation: Signals versus Portfolios
9.7 ⋆Appendix
Chapter 10: Beyond Simple Mean-Variance
10.1 Shortcomings of Naïve MVO
10.2 Constraints and Modified Objectives
10.3 How Does Estimation Error Affect the Sharpe Ratio?
10.4 ⋆Appendix
Chapter 11: Market-Impact-Aware Portfolio Management
11.1 Market Impact
11.2 Finite-Horizon Optimization
11.3 Infinite-Horizon Optimization
11.4 ⋆Appendix
Chapter 12: Hedging
12.1 Toy Story
12.2 Factor Hedging
12.3 Hedging Tradeable Factors with Time-Series Betas
12.4 Factor-Mimicking Portfolios of Time Series
12.5 ⋆Appendix
Chapter 13: Dynamic Risk Allocation
13.1 The Kelly Criterion
13.2 Mathematical Properties
13.3 The Fractional Kelly Strategy
13.4 Fractional Kelly and Drawdown Control
Chapter 14: Ex-Post Performance Attribution
14.1 Performance Attribution: The Basics
14.2 Performance Attribution with Errors
14.3 Maximal Performance Attribution
14.4 Selection versus Sizing Attribution
14.5 Appendix⋆
Chapter 15: A Coda about Leitmotifs
References
Index
End User License Agreement
List of Illustrations
Introduction
Figure 1 Punk fanzine Sideburn #1, page 2 (1977).
Figure 2 Chapter dependencies.
Chapter 1
Figure 1.1 The components of the investment process.
Chapter 2
Figure 2.1 Autocorrelation plot of daily log returns (range: 1/3/2000–12/8/2017)...
Figure 2.2 Quantile-Quantile plot for daily log returns (light gray dots) and GA...
Figure 2.3 Relationship between and .
Chapter 4
Figure 4.1 A typical loadings matrix, partitioned into different blocks. The st...
Figure 4.2 Factor models as graphical models.
Figure 4.3 A factor model as the superposition of weighted factor loadings.
Figure 4.4 Factor models as scalar products of per-stock loadings and factor re...
Figure 4.5 Singular Value Decomposition, full form.
Figure 4.6 Singular Value Decomposition as a sequence of steps: rotation, scali...
Chapter 5
Figure 5.1 QLIKE and MSE comparison. Notice that QLIKE is skewed, with higher l...
Chapter 6
Figure 6.1 Clusters for idiosyncratic matrix.
Figure 6.2 Left: credit-equity-linked factor covariance matrix. Right: country-...
Chapter 7
Figure 7.1 The eigenvectors associated with identical eigenvalues are not uniqu...
Figure 7.2 (a) Probabilistic PCA for a universe of 1000 assets, with 10 factors...
Figure 7.3 We estimate the risk model parameters using data in an interval of w...
Figure 7.4 (a) 1000 assets, normally distributed returns; (b) 1000 assets, t-di...
Figure 7.5 Variances of the eigenfactors (normalized to the variance of the fir...
Figure 7.6 Cumulative percentage of variance described by the first factors, ...
Figure 7.7 Eigenfactor turnover for different covariance matrices. Top: total re...
Figure 7.8 Distance between column subspaces of the first eight eigenfactors in...
Figure 7.9 Factor returns for the first four eigenvectors. The eigenfactors are...
Chapter 8
Figure 8.1 A scheme of the cross-validation procedure. Darker boxes are validat...
Figure 8.2 A scheme of the cross-validation procedure. Data are split into two ...
Figure 8.3 Cross-validated Sharpe for (a) Scenario 1, (b) Scenario 2.
Figure 8.4 Two common walk-forward schemes. The top one uses fixed-length train...
Figure 8.5 Rademacher complexity for 5000 strategies, with iid Gaussian returns...
Chapter 9
Figure 9.1 Left: the decentralized solution to portfolio combination. Right: th...
Chapter 10
Figure 10.1 Level plots of the loss of PnL (and Sharpe Ratio) as a function of t...
Figure 10.2 Level plots of the loss of PnL (and Sharpe Ratio) as a function of t...
Figure 10.3 Fraction loss in Sharpe Ratio for two strategies with Sharpe Ratios ...
Chapter 11
Figure 11.1 Market impact over time for a single trade executed at time ...
Figure 11.2 Market impact over time. The dashed line is the permanent market imp...
Chapter 13
Figure 13.1 Cumulative returns under the dynamic and static policies. All the cu...
Figure 13.2 Expected value of the log of the single-period growth, which is maxi...
Figure 13.3 (a) Time series of cumulative returns for different fractions of the...
Figure 13.4 The optimal Kelly size in the presence of parameter uncertainty is a...
Figure 13.5 Percentage reduction factor .
Figure 13.6 Comparison of fractional Kelly and Grossman-Zhou strategies. Both st...
Chapter 14
Figure 14.1 Top: PnL base factor performance attribution. Bottom: Maximal attrib...
Figure 14.2 A taxonomy of performance attribution.
List of Tables
Chapter 2
Table 2.1 Sample skewness and kurtosis of daily log returns and confide...
Table 2.2 Distances between the theoretical normal distribution and the empiri...
Table 2.3 Estimated for left and right tail of probability density function ...
Chapter 6
Table 6.1 Ticker and company names of cluster components in Figure 6.1
Chapter 7
Table 7.1 Summary of impact of high factor turnover
Table 7.2 Regression coefficients for the first principal component
Table 7.3 Regression coefficients for the second principal component
Chapter 8
Table 8.1 Frequency histograms for the two simulated scenarios; the conversion...
Table 8.2 Comparison of and Massart’s bound
Table 8.3 Simulations for normally distributed returns
Table 8.4 Simulations for t-distributed returns
Table 8.5 Summary data for the factors in Jensen et al.’s database
Table 8.6 Summary data for the factors in Zimmerman and Chen’s database
Guide
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
Acknowledgments
Introduction
Notation
Begin Reading
References
Index
End User License Agreement
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The Elements of Quantitative Investing
Giuseppe A. Paleologo
Copyright © 2025 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) 750-4470, 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, or online at http://www.wiley.com/go/permission.
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Library of Congress Cataloging-in-Publication Data Applied for:
Print ISBN: 9781394265459
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Cover Image: Courtesy of Giuseppe A. Paleologo
Cover Design: Wiley
To Tofu, again
Acknowledgments
The following people have proofread, commented on, discussed or supported the development of this book. Some of them are old friends, most are strangers who spontaneously offered to help. Meeting them (usually on X or on LinkedIn) has been an unforeseen pleasure in the writing of the book, and I am grateful for their generosity and the many corrections they sent my way. Unfortunately all the remaining errors are my responsibility.3
@0xfdf, Rashad Ahmed, Amir Aliev, Sandro C. Andrade, Samuel Babichenko, Ashish Bajpaj, Soumyadipta Banerjee, Rayan Ben Redjeb, Jerome Benveniste, Igor Berman, Jon Beyer, Victor Bomers, David Bonnerot, Thomas Byrne, Ben Chaddha, Yuyao Che, Leif Cussein, Vladimir Cvetkovic, Drake Daly, Alex Darby, Ruolag Deng, Jane Doe, John Doe (Jane’s occasionally hostile brother), Saarialho Eero, Bill Falloon, Frank Fan, Marta Filizola, Tom Fleming, Claudio Fontana, Fan Gao, Ernesto Guridi, Touko Haapanen, Victor Haghani, Leila Hardy, Levon Haykazyan, Erik Hellgren, Alex Hermeneanu, Leonhard Hochfilzer, Clint Howard, Jack Huang, Kevin Jacobs, Fredrik Jäfvert, Bob Jansen, Amanda Jiménez, Yassine Kachrad, Abhinav R. Kannan, Shahin Khobahi, D. K., Marco Kuhlen, Markku Kurtti, Kofi Kwapong, Jessie Li, Vitoria Lima, @jesse_livermore, Samuel Londner, Dustin Lorshbough, Marco Lucchesi, Joseph Maestri, Baridhi Malakar, Emanuel Malek, Paul-Henri Memin, Francesco Mina, Simon Minovitsky, Caroline Moon, Roberto Moura, Abhijit Naik, Graeme Newby, Juntunen Nikolaus, Mikhail Novichkov, Andrew Novotny, Adam Nunes, Tom Ó Nualláin, Yogesh Padmanabhan, Jeff Park, Damon Petersen, Henrik Hiro Pettersson, Saharat Phomthong, Alexis Plascencia, Gabriele Pompa, David Popovic, Akshay Prasadan, Miika Purola, Siddhant Pyasi, Cas Rijnierse, Viktor Salihu, Mateus Sampaio, Ali Sanjari, Douglas Ricardo Sansão, Tanmay Satpathy, Guilherme Saturnino, Abishek Saxena, Christian Schmitz, Maarten Scholl, Timothy Shchetilin, Shawn Sheng, Nakul Shenoy, Marco Signoretto, Ashutosh Singh, Matt Smith, Richárd Süveges, @systematicls, Samer Takriti, Gianmario Tamagnone, Xiaolong Tan, Kaspar Thommen, Maxim Tishin, Shahpour Turkian, Nathan Ueda, Carlos Ungil, Sinan Unver, Ricardo Valdez, Derrick VanGennep, Paul Vriend, Jay Vyas, Andrew Wang, Shida Wang, Simon Xiang, Jeremy Young, Alvin Zhang, Howard Zhang, Siqi Zheng.
I owe special thanks to Brandon DiNunno, Denis Dmitriev, Jean-François Fortin, Antoine Liutkus, Dustin Lorshbough, Tom Mainiero, Krutarth Satoskar, and Trent Spears for their deep and wide reading of the manuscript.
G.A.P.
Note
3
And my cat’s.
Introduction
This book originates from notes I wrote for two university courses. The first is ORIE5256 - Topics in Risk Management and Portfolio Construction, a course offered in the program for M.S. in Financial Engineering at Cornell University. The second is MATH-GA 2708.001 - Algorithmic Trading & Quantitative Strategies, offered in the Mathematics Department at New York University. When I set out to write this book, my objective was to write the quantitative introduction I had wanted to read at the beginning of my journey in finance. Given the scope and goals of quantitative investing, it is only possible to cover a small fraction of it in a course, or even in a book. To address this problem, I made three choices.
First and most important, I aim for synthesis. A book is, first of all, a knowledge filter. In the preface to his classic (Kelley, 1955), Kelley wrote that he wanted to title his book “What Every Young Analyst Should Know”; that book was barely three hundred pages long. It still feels fresh and necessary today. In order to keep my book of manageable length, my working principle has been to focus on real-world problems and then use the simplest techniques that allow me to address the problem at hand. A recurrent theme in the book is that almost everything in it is either linear or quadratic. In the process of writing, I have ruthlessly eliminated topics of secondary importance, material that was too hard for the payoff that it gave the readers, and also topics or ideas that are not sufficiently well-formed, or too experimental. Even if you choose not to read my book, I implore you to internalize the following lesson, learned by practitioners through sweat and tears: theory is cheap. There are thousands and thousands of theory papers, in love with technical virtuosity but oblivious of reality. Do not fall into temptation; by applications be driven.1
Second, I consider risk management and portfolio management as intrinsically connected. Asset return modeling, volatility estimation, portfolio optimization, ex-ante and ex-post performance analytics are all linked. For example, hedging belongs to risk and portfolio optimization, and analysis of performance feeds back into portfolio construction. I have avoided redundancy as much as possible. Sections often refer to earlier ones or are linked to later ones. As I was revising my book draft, whenever I found I had introduced some topic (often because I was infatuated with it) and then never used it, I exiled it to a long file made out of “rejected sections” that lives in my laptop. That is the sad part. The happy part: it’s surprising how tall a tree can grow with a bit of pruning. Out of metaphor, there is a lot of material in this book, and it gets challenging at times.
Third, I occasionally integrate some standard financial results approaches with tools from the field of statistical learning. The former is applied in fundamental factor modeling, portfolio optimization, and performance attribution. I use the latter for the estimation of statistical models and backtesting. My hope is that the integration of these different approaches is seamless.
The questions that I address in this book are:
How do I model returns in a way that allows me to generate risk and return forecasts?
What are excess returns?
How do I model multivariate returns?
How do I describe and forecast risk?
How do I test risk forecasts and return forecasts?
How do I backtest alphas?
How do I monetize these signals?
How do I optimize a portfolio?
What is the impact of risk and alpha errors on performance?
How do I account for transaction costs in portfolio management?
How do I hedge a portfolio?
How do I improve?
How do I allocate risk over time?
How do I distinguish skill from luck?
The style of the book is also, I hope, a bit different. I have kept in mind the six values that Italo Calvino (Calvino, 1999) hoped to preserve in the current millennium: Lightness, Quickness, Exactitude, Visibility, Multiplicity, and Consistency. My aversion to advanced mathematics notwithstanding, I must warn the reader that the book is not easy. During my lectures, I have induced more than one student into a comatose stupor. Afterwards, a few students left finance altogether and successfully pursued careers in entertainment. Another student keeps sending me postcards from Ibiza. A handful have become portfolio managers at hedge funds and risk managers. Yet, it is the easiest book I could write for the task at hand, and it is written in the friendliest style I am capable of. Also, I would be lying—and conveying the wrong message—if I claimed that the problems I present are now settled, and that the book is the last word on the subject. On the contrary, you and I are in this book together, and together we shall keep a beginner’s mind (Suzuki, 1970): a spirit of openness and curiosity, even when facing advanced topics. I will point out the limits of my theories and the open problems for you to work on. If you are old enough to have lived in the seventies and liked punk music, you may remember a cyclostyled zine (Figure 1). On its second page it showed three open chords; below them, a command: “NOW FORM A BAND.” May this book be your field guide to being a punk quantitative researcher. It will be a life well lived.
Figure 1 Punk fanzine Sideburn #1, page 2 (1977).
Source:Flickr.com/Dunk.
Prerequisites
The book should be accessible to a beginning graduate or advanced undergraduate student in Physics, Mathematics, Statistics, or Engineering. This means having a working relationship, and if possible a romantic one, with advanced linear algebra, probability theory, and statistics. Even more important is to have a deep interest in quantitative modeling of real-life phenomena. Many readers will be either members of a systematic trading team, or work as quantitative researchers in the central team of a hedge fund or a quantitative asset manager.
The book’s material is organized in such a way that you do not need to go through mathematical proofs. You can rely only on informal statements of mathematical results in the main body of the chapters, and that will suffice to understand the main points. The appendices at the end of the chapters contain more rigorous statements, proofs, and background material. If you plan on actively doing research, you should study them, eventually.
Even if you read only the main body, you should be used to thinking in mathematical models. The Book of Nature is written in a mathematical language.2 Be comfortable with:
Working with linear algebra, at least at the level of Strang (2019) and Trefethen and Bau (1997).
Some applied probability, at the level of Ross (2023). Exposure to some simple control theory and state-space models helps. You can come to this from econometrics (Harvey, 1990; Shumway and Stoffer, 2011), control theory (Simon2006), or statistics (Hyndman et al., 2008).
Some optimization modeling is a plus. The first few chapters of Boyd and Vandenberghe (2004) would be ideal. However, I will cover the basic theory in an appendix.
Organization
Like Caesar’s Gaul, the book is broadly divided into three parts. The first part focuses on returns modeling. I cover the basics of GARCH early on because they are needed for factor modeling, and then I cover factor models because they are necessary for everything. I have separate chapters for fundamental and statistical models. These topics are covered in depth, and both the treatment and some of the modeling approaches are novel. Finally, I cover data snooping/backtesting as a separate chapter, since it is a central element of the investment process.
The second part is devoted to portfolio construction and performance analysis, both ex ante and ex post. The focus is on mean-variance optimization (MVO). I emphasize the geometric intuition behind much of mean-variance optimization. Rotations, projections, and angles are prevalent throughout. This allows for a synthetic, elegant characterization of performance and for concise proofs. The statistics of the Sharpe Ratio are covered in some detail. The decomposition of payoffs into timing components, factor and idiosyncratic Profit and Loss (PnL), and stock selection versus sizing of positions is rigorously demonstrated. Model error plays an important role in this part. If an optimization problem is Othello, then model error must be Iago: it can drive the optimization insane. Unlike in Shakespeare’s tragedies, we can try to rewrite the endings and turn them into comedies.
The third part is the shortest. It contains results about intertemporal volatility allocation and performance attribution. These are essential components of the investment process and belong in a book with the word “Elements” in its title.
Each chapter is organized like an onion. The first sections convey the essential ideas using simple quantitative methods and are aimed at a broad audience. Sections marked with a star “” are more advanced and can be skipped on a first reading. Proofs of new results or basic technical material are relegated to the appendices at the end of the chapters. The goal is not to disrupt the flow of learning. As mentioned at the beginning of this preface, the content of this book was taught first and written later. It is meant to be read aloud and discussed, but it should be suitable for self-study. The dependencies among the chapters are shown in Figure 2.
Figure 2 Chapter dependencies.
Giuseppe “gappy” A. Paleologo
Riverdale, New York
March 21, 2025
Notes
1
References to “By Demons be Driven” by Pantera and to Warcraft 3 are intentional.
2
“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth” (Galilei, 1623).
Notation
field of real numbers
set of natural numbers
scalars
vectors (assumed to be )
matrices
vector or matrix transpose
Moore–Penrose pseudo-inverse
covariance matrix
diagonal matrix with scalars on the main diagonal
th element of a vector
element of a matrix on th row and th column
or
th row of matrix
or
th column of matrix
trace operator:
determinant of a matrix
Kroneker’s delta: if , 0 otherwise
Dirac’s delta function: for , and
vector whose elements are all ones: for all
indicator function, equal to 1 if is true, 0 otherwise
vector whose th element is 1 and the others are zero:
identity matrix of size
-norm, for :
2-norm of a vector
, for a positive-definite matrix
operator norm for a positive-definite matrix :
largest integer that is less than, or equal to,
scalar product of two vectors, i.e.,
scalar product of two matrices:
cosine similarity
,
Hadamard (element-wise) product of two vectors (matrices):
,
random variables and are independent
expectation of random variables or random vectors
expectation of a function of random variable
average of a vector
variance of a random variable
shift operator: , i.e.,
rv
random variables
iid rv
independent, identically distributed random variables
equality in distribution of two random variables
rv distributed according to a distribution, e.g.,
of the same order: if for some
convergence in distribution
equivalence of optimization problems: for constants ,
Chapter 1The Map and the Territory
The Questions
What are the essential components of quantitative investing?
What types of securities are involved and how are they traded?
Who are the main market participants and what roles do they play?
Where do excess returns in investing come from?
What are the key elements that form the analytical framework of a quantitative portfolio manager?
This chapter is a guide to the essential components of quantitative investing. When considering the meaning of a word, it’s often instructive to go back to its etymology, so let’s play this game. Despite being a Germanic language, English adopted many words from Latin, sometimes by way of French. “Investing” comes from “Investire”, which in Latin meant “to cover with a vest”, or “to put in a vest”. So it should be hardly surprising that two thousand years later, vests would become the favorite garment of hedge fund managers. In the Middle Ages, the verb took on the additional meaning “to surround, to have ownership of”. It is also possible that the modern meaning overtook the old because, in ceremonies in which ownership was transferred, the new owner was “invested” with a cloak and other regalia. In Italian—the direct successor to Latin—the old meaning is gone, and “investire” only means “to receive possession of something”. As for “quantitative”, that is Latin too: “quantum”, a noun denoting something that can be measured, increased, and decreased. We will deal with ownership, sold and bought in units that can be measured, increased and decreased. This is, unfortunately, the whole of finance. You can own a house, a painting, a bet on the survival of humankind, or even an idea. Each one of these investment topics deserves its own book, written by a competent author. In writing this book, I have chosen to trade off generality in favor of detail. I have covered each subject with the goal in mind that you would have sufficient information to understand it, implement it, and critique it. However, even an analytical book needs an introduction that puts things in their proper context. In this chapter, I aim to provide that context. You will have a broad understanding of the classes of securities to which these methods apply; and of the way these securities are traded, and by whom. This is a necessary prerequisite to explore fundamental questions: Where are excess returns coming from? What causes these trading opportunities? Finally, I will present the essential components that make up the analytical framework of a quantitative portfolio manager. The underlying message is that to be successful, an investor must understand how things work. A seminal early book on investing is titled “The Intelligent Investor” (Graham, 2006). To double down on Latin, the original meaning of “intelligent” is “to read into something”, similar to “insightful” in the English language. Your success will come from reasoning about the behavior of your counterparties, the rules governing the trading of your assets, and the functioning of exchanges. Many budding quants focus on quantitative methods. The fact is that theory is cheap and is often not hard. What is hard is putting the right tool at the service of the right insight.
Finally, this is the only chapter without mathematics. You should enjoy it while it lasts.
1.1 The Securities
We will be concerned with standardized products that are liquid. We explain these concepts in more detail.
To “own” an object is effectively to own claims on that object in the future. If you own a house, you can live in it or rent it out (your claim) and it is yours. This claim is not absolute, however. In most countries, the local or central government may need your property for reasons of public welfare and can require you to exchange your claim for cash at a fair price. If you own a painting, you may enjoy it in the confines of your house, but may not necessarily own its reproduction rights. If you own a bet on the future of humanity, your counterparty may have some force majeure clauses that prevent it from paying (e.g., consider a zombie apocalypse scenario). Defining ownership of an “idea” is especially challenging and prone to be treated on an ad hoc basis. Compared to the infinite and ever-changing nature of the meaning of property rights, our coverage is very narrow. Specifically, we focus on the subset of contracts that are standardized and liquid. We buy and sell standardized claims. These claims come in a few varieties, and their attributes are clearly defined and known to all potential buyers and sellers. Examples are:
Equities and Exchange-Traded Funds (ETFs)
. These give us partial ownership in companies, or groups of companies, and entitle us to receive future cash payments generated by the economic activities of these companies.
Futures
. These contracts deliver a physical commodity or a cash payment contingent on the state of the world at a future date, at a price determined today.
Bonds
. These are contracts that allow the transfer of debt claims among parties. An investor lends money to a borrower, in exchange for a fixed cash flow in the future (e.g., periodic interest payments and a final payment). A bond makes this claim transferable to other lenders.
Vanilla options
. These are claims that depend on the future value of some underlying asset; for example, you may receive the right (but not the obligation) to buy a stock at a future date, at a price determined today. The nature of these claims is standardized, hence the term “vanilla”.
Interest Rate Swaps (IRSs)
. These contracts allow the exchange of a certain, deterministic cash flow stream for an uncertain one, which depends on interest rates at future dates.
Credit Default Swaps (CDSs)
. These contracts insure the buyer against the failure of a company at a future date, in exchange for recurring fixed payments.
Further these contracts are liquid. For our purposes, a liquid contract is one that can be bought and sold at large enough sizes, and at sufficiently short time horizons, to enable quantitative strategies to be implemented. This means that if we plan to buy or sell a contract, we should be able to do so without incurring a transaction cost so high that our strategy is not economically attractive even for small trading sizes, and that the waiting time due to searching for a counterparty should not be so long as to make the transaction economically unattractive.
The properties of standardization and liquidity are closely intertwined. Increased standardization tends to enhance liquidity by consolidating demand, as it aggregates dispersed demand from bespoke products toward a smaller set of standardized ones. Furthermore, standardization streamlines the trading process, reducing transaction costs and simplifying contracts, thereby fostering investor trust and attracting more participants, thus enhancing liquidity. However, the downside is that customers may sacrifice the ability to trade certain useful product characteristics. Determining the optimal level of customization, even at the expense of liquidity, remains an ongoing process of learning and adaptation. For instance, prior to the 2008 financial crisis, CDSs exhibited greater variety. However, the “Big Bang” initiated by the International Swaps and Derivatives Association (ISDA) on April 8, 2009, simplified contract terms, including standardizing coupon rates (100 bps and 500 bps) and introducing a standard upfront payment, which played a pivotal role in restoring confidence in this asset class (Vause, 2010).
Trading and liquidity are at the core of the book. In order to better understand the trading process and the nature of liquidity, we should describe in some detail how trading on-exchange and over-the-counter happens.
1.2 Modes of Exchange
At any given time, economic agents want to buy or sell contracts. They want to do so quickly, securely, and cheaply. The three options around which trading is currently organized are exchanges, over-the-counter, and dark pools. Exchanges are venues in which the orders of buyers and sellers are anonymized and matched against each other. Orders are characterized by size, the number of contracts, direction (buy or sell), and price. They represent requests to buy or sell a number of contracts. The exchange records such active orders on a ledger, known as the limit-order book (LOB), and employs a set of priority rules to match buy and sell orders in the exchanges—aptly named a matching engine. In order to trade on an exchange, one must be a member of that exchange. Membership entails apparent benefits and less-apparent responsibilities. Market participants must maintain sound governance, risk processes, and capital structure.
Exchanges evolve continuously due to two driving forces. On one side, there is a push toward consolidation, which reduces operating costs and gives the owner pricing power. On the other side, technical and process innovations introduce new competitors into the market. In the United States alone, there are more than a dozen equity stock exchanges. Exchange-traded assets, such as stocks, options, and future contracts (including Forex Futures), are often liquid, although this condition is neither necessary nor sufficient: some exchange-traded assets are traded in minimal volumes and, therefore, are not liquid, and some very liquid products are traded off-exchange.
Other assets are not traded on exchanges, but over-the-counter (OTC). In this case, the buyer or seller transacts through an institutional market participant, the broker-dealer, which is connected to other broker-dealers and facilitates the matching of orders. Bonds, IRSs, Forex spot currencies, Forex Forwards, and CDSs are examples of contracts traded OTC. Some of these, like currencies, are among the world’s most liquid contracts. A precondition for liquidity is standardization. Think of a house. “The New York housing market” is very different from the stock market in that each of the 15.4 billion outstanding Apple shares (as of July 2024) is indistinguishable from the other and sells in a matter of seconds. In contrast, a house has many attributes that make it unique: location, size, age, blueprint, and condition. Another characteristic of liquid markets is the large number of participants. When numerous participants are involved in a market, competing for a relatively low number of contracts, transactions become more frequent, and the necessity for bilateral bargaining diminishes. The ability of any individual participant to influence the price is significantly reduced. To illustrate, consider the housing market as a counterpoint: when selling a house, you typically negotiate with one specific buyer (out of a few eligible ones), who may spend many hours searching for the right property and may engage in intense bargaining, sometimes to the point of contention, to secure the best possible price.
Finally, Dark Pools (a type of ATS, or Alternative Trading System, which does not make its LOB transparent) are additional venues that are distinct from exchanges (although sometimes owned by them). Dark Pools address the needs of certain institutional investors to execute orders without displaying their trading intentions. By design, Dark Pools hide order details and only make trades details available after execution. As of 2024, approximately 16% of U.S. shares are traded on Dark Pools.
1.3 Who Are the Market Participants?
It is convention to partition traders into the sell side and the buy side. The former facilitates trading by providing services; the latter receives trade for their own benefit. Below I describe the participant types. For a more detailed description, see Harris (2003).
1.3.1 The Sell Side
The sell side comprises brokers, dealers, and broker-dealers.
Dealers
1
fulfill their clients’ demands, thus providing liquidity. They take the opposite side of the trade; they are profitable if, on average, they sell (buy) at a price higher (lower) than what they initially paid to buy (sell) the asset. The difference between buy and sell prices is the
spread
. When dealers interact with clients, they quote the buy price (the
bid price
) and the sell price (the
ask price
) for a contract. They are effectively
making a market
, since these quotes make transactions possible. In OTC markets, dealers are the primary liquidity providers. The most sophisticated among such markets allow the dealers to quote prices, quantities, and other attributes continuously. For example, fixed-income products can be traded on Dealerweb or Bloomberg. In order markets or for highly bespoke products, the dealers quote on request, possibly one-sided only, for a specific quantity and with an expiration time. The quote, or the spread if the quote is two-sided, depends on the quantity. Similarly to speculators, dealers trade on their own behalf. Like speculators, they hold a portfolio (or an
inventory
of positions) and face the issue of trading counterparties that may be more informed than themselves. Unlike speculators, dealers are passive traders, in that they respond to their clients. Also, unlike speculators, dealers enjoy special regulatory status. Because dealers observe the demand flow of their clients, they are informed agents, often serving the needs of informed clients. The dealers’ profit originates from the realized spread of their trade (which is usually lower than the quoted spread) but also from the specific information the dealer derives from the order flow. One specific type of flow originates from retail investors (who we introduce later in the chapter). These investors access the market indirectly through brokers. Brokers have special arrangements to direct market orders to dealers, who commit to executing them while offering certain price guarantees on the trade.
In summary, dealers are liquidity providers, and they are compensated for services through trading profits.
Brokers
2
trade on behalf of their clients. When the broker receives an order from a client, together with information about the client’s time and price preferences, it searches for the most effective channel to execute it in accordance with these preferences. For example, a client sends a broker an order to buy a certain number of shares of a company. The broker is a member of all major exchanges. It splits the large order into smaller orders and routes them to the various markets at times that meet the execution horizon of the client or its expected cost. Unlike dealers, brokers are intermediaries who take no risk by holding contract positions at any given time. The intermediation service they provide is beneficial; however, it comes with its own risks. First, brokers provide exchange access to non-member clients and they provide OTC dealer access to non-institutional clients. Institutional clients, too, may want to enlist a broker when interacting with dealers, since the broker anonymizes the clients. Further, broker intermediation solves bilateral settlement risk: money is exchanged for contracts after the trade occurs. Clients need to know and trust their counterparty to protect themselves from insolvency, reneging, or non-compliance. There is a small number of brokers compared to the number of traders, so that clients need to approve (and be approved by) only a few counterparties; a reduction in time, cost, and risk. This, of course, does not eliminate counterparty risk. It transfers it to the brokers. The brokers manage it by vetting the clients, and by requiring that clients deposit capital at the broker, which the broker uses in case of client insolvency. The brokers also
clear
and
settle
trades on behalf of the client. In addition to these services, brokers, and especially
prime brokers
, the subclass of brokers servicing hedge funds and other sophisticated investors, offer their clients other services:
Custodial services
. Brokers ensure receipt, recording, and safekeeping of securities.
Rehypothecation
. Clients may allow the brokers to use their securities for the brokers’ own needs in exchange for fees or rebates. For example, brokers may use client securities as collateral for their own transaction or lend them to other clients.
Margin loans
. Brokers lend clients short-term capital to buy securities. They charge them SOFR
3
plus a spread.
Location of short positions
. Clients may want to
short
stocks (i.e., sell shares first, and buy them back at a later time), with the expectation that future prices will be lower than current ones. Brokers enable these transactions by lending shares from a third party and making them available to clients. The clients then sell them in the open market, buy them back at a later time, and return them to the broker. After the initial sale, but before the buyback, the broker invests the cash proceeds at SOFR plus a spread. The client receives from the broker SOFR minus a spread.
Research reports and services
, as well as broker-specific data. These services used to be bundled in broker commissions but after the implementation of MIFID II regulation, they are now charged separately.
Capital introductions
, in which brokers facilitate the connection between hedge funds and potential investors.
In summary, brokers offer diversified services, the most important of which is to facilitate clients’ transactions. They are compensated by commissions, interest on cash balances, interest on lending, and payment for order flow (PFOF), which is the compensation brokers receive from market makers for routing orders to them.
Broker-dealers, also called dual traders, combine the previous two functions in a single entity. They act both on behalf of the client and on their own behalf. This introduces a tension. The dealer’s arm is incentivized to use the broker’s information in trading to its advantage. Maybe the simplest action is front-running: the dealer is aware of incoming buying or selling demand for a security, and buys it in advance before this demand manifests in the market and is reflected in prices. To mitigate this type of behavior, regulations are in place to safeguard the interest of the client. The most important law regulating brokers, dealers, and broker-dealers is the Securities Exchange Act of 1934 (or “1934 Act”).
1.3.2 The Buy Side
The buy side usually trades with the sell side. You (the reader of this book) are likely to be a member of this group, even though certain dealers face quantitative challenges similar to yours. It is important to understand who the actors in the buy-side drama are, because you will continuously interact with them, and your excess returns will be the outcome of this interaction. We could classify the buy-side actors according to several criteria. For example, the sub-industry to which they belong: life insurers, mutual funds, hedge funds, and so on. I opt to classify them (subjectively!) based on the type of investing they perform.
Indexers
are passive investors. Their portfolios replicate the compositions of the benchmarks, or indices, generated by data providers like MSCI, S&P, Russell, CRSP, or from exchanges like FTSE 100, TOPIX, and Deutsche Börse. These indices are updated on a quarterly or biannual basis, and they comprise bond indices as well, like the Bloomberg Agg (until 2016 owned by Barclays). Several investment vehicles track indices; mutual funds and exchange-traded funds are the largest in terms of size. Large firms in this group are Blackrock, Vanguard, and State Street. Indexers make up a large and growing share of the total asset base. According to estimates by Chinco and Sammon (2023), they represent over 37% of the U.S. stock market capitalization as of 2020.
Hedgers
are firms participating in markets with the primary objective of reducing financial risk originating from their core businesses. For example, currency risk is faced by any firm doing business internationally. Firms such as airlines and manufacturing companies purchase fossil fuels (gas, Brent, and West Texas Intermediate), whose price variability can be very disruptive. Hedgers primarily participate in derivative markets: futures, swaps, and options. Hedgers differ from other participants who also hedge, such as dealers or hedge funds, in that hedging is the primary activity they perform.
Institutional active managers
are firms investing on behalf of their clients. They run strategies that are sometimes benchmarked to commercial indices and hope to beat them. There is some evidence of underperformance of funds serving retail investors; see S&P SPIVA report
4
or the Refinitiv study (Glow, 2023). Both show that over 60% of funds underperform their benchmarks over a one-year trailing basis. The outperformance of funds over one year is not persistent: as of January 2024, 91% of funds trail the performance of the S&P500 over the previous 15 years. On the other side, funds serving institutions seem to beat their benchmarks (Gerakos and Linnainmaa, 2021). The
tracking error
is a measure of the risk they can take when differing from their reference benchmarks. Otherwise stated, their portfolios can be expressed as the sum of the positions in a benchmark, and of discretionary positions of a “tracking portfolio”. A large tracking error gives the funds much discretion; a low one places their returns close to the indices, and makes them “index huggers,” or “closet indexers” (i.e., index funds in disguise).
Asset allocators
manage portfolios composed of securities in multiple asset classes. Within an asset class, the portfolio closely follows a representative benchmark. One can view asset allocators as managers of a portfolio of asset classes. The relative weight of these asset classes in the portfolio is either constant or changes slowly. Common asset classes are equities, bonds, commodities, and cash equivalents.
5
In addition, asset allocators invest in alternative asset managers like private equity firms, venture capital, hedge funds, and real estate.
Informed traders
include primarily hedge funds and principal trading firms. These firms are usually organized as partnerships, although a few are public companies. They face fewer constraints than institutional managers. Whereas principal trading firms only have general partners (GPs, the principals) investing their own money, hedge funds also have limited partners (LPs) who do not invest actively.
6
These firms pursue absolute returns (i.e., not tracking a benchmark), which exhibit low correlation to the indices of major asset classes.
7
Informed traders invest heavily in human capital, technology, and data to achieve this goal. They fulfill two major functions. The first one is
price discovery
. By using all information available to them, they generate estimates of the true value of securities. If the security prices differ from their estimates, they trade to exploit the mispricing. If the price is lower than their estimate, they buy the security. In the process, they increase its price and bring it closer to equilibrium. Mispricing can take many forms. If the same security is offered at different prices on different exchanges,
arbitrageurs
(a subset of informed traders) will try to exploit the difference; of course, this may not be easy to do, so the difference either persists, or disappears very quickly due to technology investment in low-latency trading. The second role of informed traders is
liquidity provisioning
. Supply and demand of certain assets is predictable to a certain degree. I provide examples in
Section 1.4
; hedge funds and market makers develop specialized strategies that predict imbalances, hold (or short) securities before the liquidity need materializes, and meet the liquidity needs at the event. The range of possible intervals between prediction and event can be vast—from sub-second for high-frequency market makers to weeks or months for hedge funds.
Retail investors
trade for their own account via retail brokers. In 2020, retail investors made up approximately 20% of total volume; the share was slightly more than 10% in 2011. Several studies, across different national markets and periods, have shown that retail traders are consistently unprofitable (Barber and Odean, 2013); retail trader flow is uninformed. This is one of the reasons why it is highly sought after by dealers, who will pay the retail brokers for routing it to them (payment for order flow).
1.4 Where Do Excess Returns Come From?
Now that we have introduced the main actors in the play (usually a tragedy, rarely a comedy, and occasionally a farce) of investing, we can discuss the sources of excess returns. The “excess” qualifier means “in excess of portfolio invested in risk-free assets, such as short-dated U.S. treasuries.” This topic is central both to academic financial research and to practitioners. Academic finance is primarily concerned with the question of efficiency. In the words of Malkiel (1987):
A capital market is said to be efficient if it fully and correctly reveals all available information in determining security prices. Formally, the market is said to be efficient with respect to some information set,, if security prices would be unaffected by revealing that information to all participants. Moreover, efficiency with respect to an information set,, implies that it is impossible to make economic profits by trading on the basis of.
An exceptionally concise definition, if there ever was one. At its core is the “information set ”. This could be, for example, the set of all historical prices of the traded securities. Nowadays, this information can be obtained with relatively8 little effort. A different type of information set is publicly available information,9 defined in the United States as “any information that you reasonably believe is lawfully made available to the general public from: (i) federal, state, or local government records; (ii) widely distributed media; or (iii) disclosures to the general public that are required to be made by federal, state, or local law.” An even finer information set is the set of all information available to any investor. Academic research tries to determine the validity of the statement that “security prices would be unaffected by revealing that information to all participants.” Note that this does not mean that is not helpful to predict future prices. Indeed, there is empirical evidence that asset prices are predictable. However, the hypothesis is that current prices may not be affected. We do not trade in the direction of returns, up to the point that the investing opportunity disappears. This is unintuitive. Why would we not take advantage of an informative prediction? One reason is risk. Even if we have some information about the future return of an asset, the uncertainty around the prediction is too high for us to take advantage of it. For example, say that, to the best of our knowledge of , we expect the U.S. market to appreciate 8% next year, while our cash custodied at the broker will return a measly 2%. Does this imply that we will rebalance our portfolio to 100% a market-tracking asset like SPY? Hardly. The reason is that the standard deviation of market returns is 20%, a little too high for comfort. Risk, however, is not the only reason. Another one is liquidity. Indeed, the road to hell of an investor is littered with quite accurate predictions of assets that barely trade or do not trade at all. A famous example is the spin-off of Palm (a now-defunct mobile device company) by 3Com (a telecom equipment maker, also defunct) in 2000. 3Com floated on the public market 5% of the shares of Palm, while retaining the other 95%. Right after the initial public offering (IPO), Palm had a market value of $54B, while 3Com had a market capitalization of $28B. The implied value of 3Com assets was –$22B, even though the company had no debt, $1B in cash, and positive cash flow. Either 3Com was dramatically undervalued, or Palm was dramatically overvalued. An investor could have therefore bought 3Com shares and shorted Palm for an equal amount. The portfolio comprising these two assets was a synthetic asset whose return could be predicted. There was a problem, however. Palm shares were in short (pun intended) supply. In order to short a share, the investor must first borrow it, at a rate decided by the lender. If quoted at all, these rates were so high as to make the trade either unattractive or impossible.
Risk and liquidity are not the only two factors limiting the exploitation of information. We list three more. The first one is funding. Consider a scenario in which certain assets, or certain portfolios,10 have lost much of their value due to market distress. We are managing a small hedge fund, which has also lost money in this environment. Based on historical examples, we have a strong belief that such assets will rebound. Such scenarios occur quite regularly, especially in “deleveraging spirals”. However, we do not have much capital available to post as margin. In addition, we need a capital buffer in order to withstand a possible additional loss in the very short term. Funding constraints prevent us from buying the asset, in spite of our accurate forecast.
A significant source of excess returns arises from flow predictability. Some agents, notably institutional investors and market makers, but not only these, will trade known securities on known dates. Speculators can then take advantage of this information by providing liquidity beforehand.11 One of the most important instances of this is index rebalancing. Several index providers update the weights of their indices on predetermined dates using well-defined rules. Some securities are added to the index, others are removed, and finally most of the remaining ones have an updated weight. The term used for this process is index reconstitution. For example, TSLA was added to the NASDAQ 100, effective July 15, 2013. The announcement was made on July 10, 2013; but several investors could have forecasted the event well before that date. These investors would then purchase TSLA shares and sell them at the closing auction of July 15, 2013. The ETF, mutual funds, and bespoke products that track the index have an obligation to buy TSLA on the close of that day, and the resulting demand is likely to push up the stock price. The informed investors providing liquidity do not do so risk-free. They hold the stocks until the effective date, and over these days are exposed to the risk that TSLA may suffer from company-specific or industry-specific losses. Moreover, there is the remote risk that the reconstitution be cancelled or postponed. The size of passive investing is large and its estimate ranges from 17.5% (Novick, 2017) to 38% (Chinco and Sammon, 2023) of total assets under management. The buyer of index products bears the indirect cost of such rebalancing (Li, 2021). This is just one prominent example of predictable flows, but several others exist, usually smaller in size, but also not as widely known as index rebalancing. Their common feature is the existence of institutional or procedural constraints (sometimes driven by internal processes, other times by regulatory requirements) that introduce predictability in the demand of securities.
Finally, we consider a last source of excess returns: informational advantage
