\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \newcommand{\textnormal}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

1.4 Comparison with Existing Books

The financial literature on data modeling and portfolio design is extensive and diverse. This book aims to provide a unique perspective on these topics, and it is instructive to compare it with some of the existing textbooks.

  • Financial data modeling: Many excellent textbooks cover financial data modeling, such as Campbell et al. (1997), Meucci (2005), Tsay (2010), Ruppert and Matteson (2015), Lütkepohl (2007), Tsay (2013), Fabozzi et al. (2007), Fabozzi et al. (2010), and Feng and Palomar (2016). In this book, Chapters 3 and 4 provide a succinct overview of i.i.d. models and models with temporal structure, respectively. Particular emphasis is placed on heavy-tailed models and estimators (as opposed to the more traditional methods based on the Gaussian assumption), stochastic volatility models (usually not receiving their deserved attention), and the use of state-space models with Kalman filtering as a unified approach with efficient algorithms.

  • Modern portfolio theory: Traditional books that focus primarily on portfolio foundations and mean–variance portfolios include Grinold and Kahn (2000), Meucci (2005), Cornuejols and Tütüncü (2006), Fabozzi et al. (2007), Prigent (2007), Michaud and Michaud (2008), Bacon (2008), and Fabozzi et al. (2010). In this book, Chapters 6 and 7 cover this material with an optimization perspective, including utility-based portfolios, a recent derivation of the otherwise heuristic quintile portfolio as a robust solution, and particularly delving in detail into the nonconvex formulation of the maximum Sharpe ratio portfolio. It also provides a recently proposed universal algorithm for all these portfolios based on different trade-offs of the mean and variance.

  • Risk parity portfolios: Roncalli’s book (Roncalli, 2013b) provides a detailed mathematical treatment (see also Feng and Palomar (2016)), while Qian’s book (Qian, 2016) covers the fundamentals. In this book, Chapter 11 covers risk parity portfolios from an optimization perspective, progressively covering the naive solution, the vanilla convex formulations, and the more practical and general nonconvex formulations, with emphasis on the numerical algorithms.

  • Backtesting: López de Prado’s book (López de Prado, 2018a) covers backtesting and its dangers in great detail from the perspective of machine learning, while Pardo (2008) focuses on the walk-forward backtest. In this book, Chapter 8 explores the many dangers of backtesting and the different forms of executing backtesting based on market data, as well as synthetic data, with abundant figures.

  • Index tracking: The topic of index tracking is treated in detail in Prigent (2007) and Benidis et al. (2018a), with shorter treatments in Cornuejols and Tütüncü (2006) and Feng and Palomar (2016). In this book, Chapter 13 provides a concise yet broad state-of-the-art exposure, offering new formulations and a cutting-edge algorithm that automatically selects the right level of sparsity.

  • Robust portfolios: Robust optimization is widely explored within the context of portfolio design, with standard references including Fabozzi et al. (2007) and Cornuejols and Tütüncü (2006) (see also Feng and Palomar (2016)). In this book, Chapter 14 gives a concise presentation of these techniques for obtaining robust portfolios with illustrative numerical experiments.

  • Pairs trading: The standard reference to this topic is Vidyamurthy (2004); see also Feng and Palomar (2016). In this book, Chapter 15 provides full coverage of the basics and presents a more sophisticated use of the Kalman filter for better adaptability over time.

  • High-frequency trading: High-frequency data and trading based on the limit order book require a completely different treatment than what is covered in this book. Some key references include Abergel et al. (2016), Lehalle and Laruelle (2018), Bouchaud et al. (2018), and Kissell (2020).

  • Machine learning in finance: Recent textbooks that give a broad account of the use of machine learning in financial systems include López de Prado (2018a) and Dixon et al. (2020). In this book, Chapter 16 briefly discusses machine learning and deep learning techniques in the context of portfolio design.

References

Abergel, F., Anane, M., Chakraborti, A., Jedidi, A., and Toke, I. M. (2016). Limit Order Books. Cambridge University Press.
Bacon, C. (2008). Practical Portfolio Performance Measurement and Attribution. John Wiley & Sons.
Benidis, K., Feng, Y., and Palomar, D. P. (2018a). Optimization methods for financial index tracking: From theory to practice. Foundations and Trends in Optimization, Now Publishers, 3(3), 171–279.
Bouchaud, J.-P., Bonart, J., Donier, J., and Gould, M. (2018). Trades, Quotes and Prices: Financial Markets Under the Microscope. Cambridge University Press.
Campbell, J. Y., Lo, A. W., and MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.
Cornuejols, G., and Tütüncü, R. (2006). Optimization Methods in Finance. Cambridge University Press.
Dixon, M. F., Halperin, I., and Bilokon, P. (2020). Machine Learning in Finance. Springer.
Fabozzi, F. J., Focardi, S. M., and Kolm, P. N. (2010). Quantitative Equity Investing: Techniques and Strategies. John Wiley & Sons.
Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., and Focardi, S. M. (2007). Robust Portfolio Optimization and Management. John Wiley & Sons.
Feng, Y., and Palomar, D. P. (2016). A signal processing perspective on financial engineering. Foundations and Trends in Signal Processing, Now Publishers, 9(1–2), 1–231.
Grinold, R. C., and Kahn, R. N. (2000). Active Portfolio Management. McGraw Hill.
Kissell, R. (2020). Algorithmic Trading Methods: Applications Using Advanced Statistics, Optimization, and Machine Learning Techniques. Academic Press.
Lehalle, C.-A., and Laruelle, S. (Eds.). (2018). Market Microstructure in Practice. World Scientific Publishing Co. Pte. Ltd.
López de Prado, M. (2018a). Advances in Financial Machine Learning. John Wiley & Sons.
Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer.
Meucci, A. (2005). Risk and Asset Allocation. Springer.
Michaud, R. O., and Michaud, R. O. (2008). Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation. Oxford University Press.
Pardo, R. (2008). The Evaluation and Optimization of Trading Strategies. John Wiley & Sons.
Prigent, J. L. (2007). Portfolio Optimization and Performance Analysis. CRC Press.
Qian, E. (2016). Risk Parity Fundamentals. CRC Press.
Roncalli, T. (2013b). Introduction to Risk Parity and Budgeting. Chapman & Hall/CRC.
Ruppert, D., and Matteson, S. D. (2015). Statistics and Data Analysis for Financial Engineering: With R Examples. Springer.
Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons.
Tsay, R. S. (2013). Multivariate Time Series Analysis: With R and Financial Applications. John Wiley & Sons.
Vidyamurthy, G. (2004). Pairs Trading: Quantitative Methods and Analysis. John Wiley & Sons.