© Michael Isichenko
Preface
This book describes the process used by quantitative traders, or quants, a community the author has belonged to for a number of years. Quants are not usually trained as quants, but often come from one of the “hard sciences” such as mathematics, statistics, physics, electrical engineering, economics, or computer science. The author, a physicist by training, feels guilty for (ab)using the word describing a fundamental concept of quantum physics in the context of quantitative trading, but this slang is too rooted in the industry to be avoided. Having quantitative finance professionals in mind, the intended audience is presumed interdisciplinary, fluent in mathematical notation, not foreign to algorithmic thinking, familiar with basic financial concepts such as market-neutral strategies, and not needing a definition of pnl. This book could be also interesting to those readers who are thinking of joining the quant workforce and wondering if it is worth it.
The quant trading business, especially its alpha part, tends to be fairly secretive, but the traffic of portfolio managers and analysts between quant shops has created a body of common knowledge, some of which has been published in the literature. The book is an attempt to cover parts of this knowledge, as well as to add a few ideas developed by the author in his own free time. I appreciate the concern of some of the more advanced colleagues of mine about letting the tricks of the trade “out in the wild.” Those tricks, such as machine learning and optimization algorithms, are mostly in the public domain already but are spread over multiple fields. In addition to academic research, Wall Street can learn a lot from Silicon Valley, whose inhabitants have generated a tremendous and less secretive body of knowledge. Using an analogy with cryptography, sec urity through obscurity is a popular approach in quantitative trading, but it gradually gives way to security by design ultimately rooted in the increasingly difficult forecasting of future asset prices, the holy skill and grail of quantitative portfolio management. The rest of the quant trading process, while not exactly trivial in scope, is within the reach of a reasonably trained scientist, this author included, who is willing and able to read Wikipedia,1 and learn better coding.
The choice of topics for this book is aligned with the author's personal interests in the field, although an honest attempt is made to cover, in depth or in passing, all relevant parts of statistical arbitrage, a quantitative approach to equity trading. Whether or not a particular formula or approach is expected to help make money (or avoid losses) is not disclosed or opined upon, in part because any application success is data- and implementation-dependent, and in part to keep the reader in suspense. The book is also an attempt to strike a balance between what the author could say and is comfortable saying. In the field of quantitative trading, the more interesting stuff doesn't usually get published. In this book, the reader will hopefully find a few things that might be interesting or at least entertaining.
Any resemblance of described quantitative practices to past or existing firms is coincidental and may not be statistically significant. As Kurt Vonnegut admitted in Slaughterhouse-Five, All this happened, more or less. This book is for quants and, occasionally, about quants.
A lot of the quantitative portfolio management process involves data and code. The exposition style adopted in this book does not include too many charts, tables, or code snippets, although there are some. Instead, the focus is on ideas, motivation for various approaches, and mathematical description seeking a terse and elegant exposition whenever possible. Mathematical formulas tend to be more compact and expressive than code written in any programming language. In addition, and quoting Eugene Wigner,2 the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and ... there is no rational explanation for it.
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1 1 Accordingly, and for the reader's convenience, the electronic version of this book has multiple hyperlinks to Wikipedia and other URLs.
This book is an unlikely result of some 20 years of trial-and-error discovery. It is also a work in progress. The author will appreciate indication of any omission or error, as well as any feedback from the reader, whose comments are most welcome at [email protected].
M.I.
New York-Montauk, June 2020–May 2021.
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1 2 E. Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Communications in Pure and Applied Mathematics, 13(I), February 1960.
About this Book
Quantitative trading of financial securities is a multi-billion dollar business employing thousands of portfolio managers and quantitative analysts (“quants”) trained in mathematics, physics, or other “hard” sciences. The quants trade stocks and other securities creating liquidity for investors and competing, as best they can, at finding and exploiting any mispricings with their systematic data-driven trading algorithms. The result is highly efficient financial markets, which nonetheless are not immune to events of crowding, bubbling, occasional liquidation panic, and “cobra effects” including the high-frequency trading (HFT) arms race. This book attempts a systematic description of the quant trading process by covering all its major parts including sourcing financial data, “learning” future asset returns from historical data, generating and combining forecasts, diversification and its limitations, risk and leverage management, building optimal portfolios of stocks subject to risk preferences and trading costs, and executing trades. The book highlights the difficulties of financial forecasting due to quantitative competition, the curse of dimensionality, and the propensity to overfitting. Some of the topics included in the book have not been previously discussed in the literature. The exposition seeks a balance between financial insight, mathematical ideas of statistical and machine learning, practical computational aspects, actual stories and thoughts “from the trenches,” as observed by a physicist turned a quant, and even tough or funny questions asked at countless quant interviews. The intended audience includes practicing quants, who will encounter things both familiar and novel (such as lesser-known ML algorithms, combining multiple alphas, or multi-period portfolio optimization), students and scientists thinking of joining the quant workforce (and wondering if it's worth it), financial regulators (mindful of the unintended cobra effects they may create), investors (trying to understand their risk-reward tradeoff), and the general public interested in quantitative and algorithmic trading from a broad scientific, social, and occasionally ironic standpoint.
Abstract
The book presents a systematic review of the quantitative equity trading process, aka statistical arbitrage, including market and other financial data, alpha generation, risk, trading costs, and portfolio construction. Financial forecasting involves statistical learning of future asset returns on features extracted from relevant current and past data, including price-volume, fundamental and analyst, holdings and flows, news, alternative, and other publicly available datasets. Both theoretical and algorithmic machine learning (ML) aspects of financial
