The past few decades have seen first a trickle and then a steady stream of science quants forsaking academe for the challenges and rewards of Wall Street. The information technology revolution created the means, and scientists had the quantitative chops. But even a gifted mathematician may be at a loss trying to make sense of financial data absent a grounding in rudimentary economic concepts, without which the most ingenious model will mislead—with potentially disastrous consequences.
The Elements of Financial Econometrics is a compact guide for such scientific migrants. More significantly, it is a toolbox for investment practitioners who want to hone their ability to investigate intuitive or theory-based hunches with empirical rigor and broaden the scope of analytical tools available to them. The book—by Qiwei Yao, a professor of statistics at the London School of Economics, and Jianqing Fan, a statistician and financial econometrician at Princeton University—grew out of a master’s-level course in quantitative finance at Princeton.
Financial practitioners are aware that asset prices are not normally distributed, with important implications for portfolio construction and risk management. But how significant is the deviation from normality for different time intervals or different packages of securities? The authors show how to run the tests using prices of such familiar instruments as Apple and Disney stocks and such indexes as the S&P 500 Index and the Chicago Board Options Exchange Volatility Index (VIX).
That deviations from normality are inversely proportional to the length of the interval between returns has critical implications for the suitability of different investment strategies for different time horizons. Analysts searching for profit opportunities may wish to determine whether a series is a random walk; the book illustrates tests for random walks and their relative merits.
Case studies in the book use readily available data, often downloadable from Yahoo! Finance. They enable practitioners to deploy the techniques explained in the book to reproduce its charts and figures and to apply these techniques to their own projects. The authors have helpfully put all the datasets and codes used in the book on an openly accessible website. They also provide guidance on using R—the language and environment widely used in statistical computing and graphics—to replicate the case studies.
Practitioners know that the past may be an unreliable guide to the future, but some degree of stationarity in a data series is necessary for a forecast to work. The authors discuss strong and weak stationarity and show the uses of alternative models depending on the degree of stationarity (e.g., autoregressive moving average [ARMA], autoregressive integrated moving average [ARIMA], and fractional autoregressive integrated moving average [FARIMA]).
The book contains explanations of time-series models, including time series with trends, exponential smoothing, heteroskedastic volatility models (autoregressive conditional heteroskedasticity [ARCH], generalized autoregressive conditional heteroskedasticity [GARCH], etc.), and state-space models (e.g., the Kalman filter). The more advanced material is relegated to the ends of chapters and is not essential to understanding the core topics.
Most practitioners are familiar with the capital asset pricing model; the authors show both how to derive it and how to use statistical tools to test it. Moving to contemporary topics in the midsection of the book, they explore multi-factor models—the basis of the current explosion of “smart beta” products—and econometric techniques for validating them. Of greater relevance to practitioners is the authors’ discussion of how to use the models to forecast a firm’s expected returns, how to use factors for hedging, and how to apply shocks to the factors to determine a portfolio’s performance under various forms of stress.
The latter portions of the book cover portfolio allocation and risk assessment issues, such as how to assess the risk of a large portfolio, problems with large covariance matrices (needed to assemble an optimal portfolio), and how to select individual securities from a large pool for investment. The discussion continues with pricing models based on dividends, including dividend discount models, and concludes with an examination of “rational bubbles.”
One topic of growing importance discussed in the book is the analysis of high-frequency financial data. Big-data analysis is driven not only by investment managers seeking profit opportunities but also by regulators tasked with determining the underlying cause of flash crashes, such as the one in 2010 and similar, more recent events around the world.
A note to the unwary: Even experienced professionals will struggle to follow the text if they lack a solid foundation in math and statistics. Readers are assumed to be proficient in undergraduate-level calculus, linear algebra, statistics, and probability. Unfortunately, there is no answer section for the end-of-chapter problems, a missed opportunity to make the book more practical for practitioners wanting to check their understanding of the material. But for those willing and able to do the hands-on work, The Elements of Financial Econometrics is a compact how-to guide, useful for raising one’s game with an array of basic quantitative analytical tools.