Just like it is difficult to make forecasts in efficient markets, it is also difficult, but not impossible, to optimally combine forecasts due to their correlation and what is known as the curse of dimensionality. To break the never ending cycle of quantitative trial and error, it is important to understand fundamental limitations on what can and what can't be done.
The book is structured as follows. Chapter 1 briefly reviews raw and derived market data used by quants. Alpha generation, the central part of the quant process, is discussed in Chapter 2. This chapter starts with additional financial data usable for forecasting future asset returns. Both theoretical and algorithmic aspects of machine learning (ML) are discussed with an emphasis on challenges specific to financial forecasting. Once multiple alphas have been generated, they need to be combined to form the best possible forecast for each asset. Good ways of combining alphas is an alpha in itself. ML approaches to forecast combining are discussed in Chapter 3. A formal view of risk management, as relevant to portfolio construction, is presented in Chapter 4. Trading costs, with an emphasis on their mathematical structure, are reviewed in Chapter 5. There a case is made for a linear impact model that, while approximate, has a strong advantage of making several closed-form multi-period optimization solutions possible. Impact of a net flow of funds at a macro scale is also discussed with implications for stock market elasticity and bubbles. Chapter 6 describes the construction of a portfolio optimized for expected future profits subject to trading costs and risk preferences. This part tends to use the most math and includes previously unpublished results for multi-period portfolio optimization subject to impact and slippage costs. Related questions of portfolio capacity and optimal leverage, including the Kelly criterion, are also discussed. Chapter 7 concerns the purpose and implementation of a trading simulator and its role in quant research. A few auxiliary algorithmic and mathematical details are presented in appendices.
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1 11 X. Gabaix, R.S.J. Koijen, In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis, Swiss Finance Institute Research Paper No. 20-91, Available at SSRN: https://ssrn.com/abstract=3686935, 2021.
2 12 J.-P. Bouchaud, J.D. Farmer, F. Lillo, How markets slowly digest changes in supply and demand, arXiv:0809.0822 [q-fin.TR], 2008.
Computation is a primary tool in most parts of the quantitative trading process and in machine learning. Several aspects of computing, including coding style, efficiency, bugs, and environmental issues are discussed throughout the book. A few important machine learning concepts, such as bias-variance tradeoff (Secs. 2.3.5 and 2.4.12) and the curse of dimensionality (Sec. 2.4.10), are supported by small self-contained pieces of Python code generating meaningful plots. The reader is encouraged to experiment along these lines. It is often easier to do productive experimental mathematics than real math.
Some of the material covering statistics, machine learning, and optimization necessarily involves a fair amount of math and relies on academic and applied research in various, often disjoint, fields. Our exposition does not attempt to be mathematically rigorous and mostly settles for a “physicist's level of rigor” while trying to build a qualitative understanding of what's going on. Accordingly, the book is designed to be reasonably accessible and informative to a less technical reader who can skip over the more scary math and focus on the plain English around it. For example, the fairly technical method of boosting in ML (Sec. 2.4.14) is explained as follows: The idea of boosting is twofold: learning on someone else's errors and voting by majority.
The field of quantitative portfolio management is too broad for a single paper or book to cover. Important topics either omitted here or just mentioned in passing include market microstructure theory, algorithmic execution, big data management, and non-equity asset classes. Several books cover these and related topics.13,14,15,16,17 While citing multiple research papers in various fields, the author could not possibly do justice to all relevant or original multidisciplinary contributions. The footnote references include work that seemed useful, stimulating, or just fascinating when developing (or explaining) forecasting and optimization ideas for quantitative portfolio management. Among the many destinations where Google search brings us, the arXiv,18 is an impressive open source of reasonably high signal-to-noise ratio19 publications.
A note about footnotes. Citing sources in footnotes seems more user-friendly than at the end of chapters. Footnotes are also used for various reflections or mini stories that could be either meaningful or entertaining but often tangential to the main material.
Finally, in the spirit of the quant problem-solving sportsmanship, and for the reader's entertainment, a number of actual interview questions asked at various quant job interviews are inserted in different sections of the book and indexed at the end, along with the main index, quotes, and the stories.
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1 13 R.C. Grinold, R.N. Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk. McGraw-Hill, New York, 2000.
2 14 R.K. Narang, Inside the Black Box: A Simple Guide to Quantitative and High Frequency Trading, 2nd Edition, Wiley, 2013.
3 15 J.-P. Bouchaud, J. Bonart, J. Donier, M. Gould, Trades, Quotes and Prices. Financial Markets Under the Microscope, Cambridge University Press, 2018.
4 16 Z. Kakushadze, J.A. Serur, 151 Trading Strategies, Available at SSRN: https://ssrn.com/abstract=3247865, 2018.
