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

Chapter 2 Financial Data: Stylized Facts

“If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.”

— James Whitcomb Riley

Different domains in science and engineering are deeply rooted on the specifics of the data. For instance, Sir Isaac Newton formulated the laws of motion and universal gravitation based on the observations of the motion of planets and other objects on Earth. As another example, Claude Shannon—the “father of information theory” and inventor of the concept of “bit” as a measure of information—developed a groundbreaking mathematical theory of communication based on probabilistic models of wireless and wireline transmission channels.

Likewise, the first step in any endeavor in finance or financial engineering should be to understand financial data. The study and characterization of financial data started flourishing as early as the 1960s (Fama, 1965; Mandelbrot, 1963) and it is now a mature topic in which academics and practitioners have exposed some particularities of the data commonly referred to as “stylized facts.” This chapter takes us on a rather visual exploratory analysis of financial data based on empirical market data.

This material will be published by Cambridge University Press as Portfolio Optimization: Theory and Application by Daniel P. Palomar. This pre-publication version is free to view and download for personal use only; not for re-distribution, re-sale, or use in derivative works. © Daniel P. Palomar 2024.

References

Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38(1), 34–105.

Mandelbrot, B. B. (1963). The variation of certain speculative prices. The Journal of Business, 36(4), 394–419.