This five-volume set of 114 articles, edited by the prominent financial economist Andrew Lo, brings together many of the most important academic studies of the past four and a half decades in the growing field of financial econometrics. Like the field itself, the scope of this collection is quite wide, touching nearly every issue in empirical finance. The work is divided into five themes:
- Statistical models of asset prices
- Static asset-pricing models
- Dynamic asset-pricing models
- Continuous-time methods and market microstructure
- Statistical methods and non-standard finance
Lo’s ambitious project provides an intellectual history of financial econometrics. An examination of this compendium reveals the remarkable extent to which these five themes have been embraced by the money management profession. Although most of the articles collected by Lo have been influential in the realm of academic research, it is odd that certain aspects of financial economics have not yet materially influenced practitioners. Also curious is the fact that some areas that academic researchers initially regarded as relevant later turned out to be fads that did not change money managers’ long-term behavior.
Volume 1. Statistical Models of Asset Prices
The first volume explores the foundations of statistical models under the simple premise that we need to understand the distributional properties of assets in order to form a foundation for finance. These articles set the stage for the other volumes by asking the simple question, how do prices behave? The volume is divided into the following four sections.
Philosophical Background.
This section assembles some of the most important methodological articles on financial econometrics. It could be a book by itself if it fully explored all the important econometric issues it raises. Statistical analysis is not merely about running numbers; rather, it is about understanding the inputs and outputs in order to eliminate garbage in the process. All researchers should be required to read such articles as “Let’s Take the Con out of Econometrics” and “R-Squared” before being handed a computer and dataset.
Random Walk.
This section is an interesting history of scientific advancement. Early studies that “proved” the random walk hypothesis actually did no such thing. A close reading of Eugene Fama’s early work reveals a careful writer and a brilliant researcher who grappled with concepts of efficiency. Lo then takes a great leap in time from the 1960s to the late 1980s, when the religion of efficient markets began to be attacked. Enhanced statistical tools enabled more subtle econometric analysis and the movement to search for behavioral anomalies. What happened in between and how the shift in research focus occurred would have been interesting topics for discussion. In addition, the reader would have been better served if Lo had examined the econometric community’s stance on these issues.
Time-Varying Movements.
This section discusses the techniques of GARCH (generalized autoregressive conditional heteroscedasticity) and regime-switching models, which have been the subject of a major explosion in econometric research. Volatility changes are now a foundation for financial econometricians’ thinking about asset prices, yet practitioners do not use GARCH approaches universally. Model complexity has increased, but our understanding of pricing behavior has not always matched the empirical work.
The practitioner’s trade-off between precise research and simplicity of implementation is an issue that is not often addressed in connection with this work. Although long-memory model structures and fat tails in asset-price distributions have been studied for some time, they have not received their due from money managers. Long memory is central to long-term portfolio management and asset allocation, but it is rarely explored in depth by money managers. Fat tails are often discussed conceptually—most recently in connection with risk management and “black swan” events—but are seldom included directly in models. The mathematics is too difficult for most practitioners. Figuring out how to make these complex topics more accessible to practitioners is an important challenge.
Stationarity Issues.
As measured through unit root and cointegration analysis, stationarity issues are essential for any work in financial econometrics. Once again, however, this research has not passed into general use by practitioners. These important issues of time-series analysis have often not been made accessible to practitioners who serve on investment committees. Investment organizations’ resulting lack of attention to stationarity leads to all sorts of model flaws and false conclusions in Wall Street research.
Volume 2. Static Asset-Pricing Models
This volume is a tight presentation of three major topics: the capital asset pricing model (CAPM), the arbitrage pricing model, and performance attribution. It explores asset returns not through distribution properties but through the static models that form the central thesis of financial economics: the trade-off between return and risk. Static models are the foundation for portfolio managers’ current thinking, but measuring even the simplest risk–return trade-off poses difficulties. These articles tell the unfortunate tale of how pinning down the return incentives for bearing risk is not as easy as one might expect. The empirical evidence is simply not that clear. The body of knowledge taught to MBA students does not stand up well to testing.
The intellectual journey with static models takes us from simple tests to higher levels of inference to explain market anomalies in the risk–return trade-off. The CAPM—the theoretical bulwark of finance—encounters difficulties with the power of tests, issues of small sample size, and factor construction. Consequently, research has moved beyond the market risk model to account for small-capitalization and market-to-book effects in explaining return behavior.
Describing returns in terms of different factors is the underlying notion of arbitrage pricing theory (APT). APT has proved to be a battleground of both theoretical justification and empirical testing. These battles have been crucial to the development of pricing models, but they have presented a barrier to practitioners’ fully embracing the APT approach to pricing individual assets.
In contrast, practitioners have eagerly adopted theorists’ work on performance attribution. This research strives to assess whether a portfolio manager has market-timing skill or security selection ability or is merely taking on higher-than-market risk. The literature on performance attribution has provided good, simple tests—albeit not very powerful ones—that can answer questions on manager quality. Even such simple measures of performance as the Sharpe ratio, however, can be gamed and/or biased by serial correlation and nonsynchronous trading.
Volume 3. Dynamic Asset-Pricing Models
This volume deals with complex models of price dynamics over time. The first section focuses on tests of rationality that measure variance bounds. In the 1980s, this area was one of the most widely discussed topics in financial econometrics. Today, however, it appears to be an interesting methodological fad rather than a topic that has led to a major adjustment in practitioners’ modeling approaches.
In a simple pricing model, assumptions about an asset’s payout stream set the upper bound for price variance, which determines whether financial markets are too volatile relative to the fundamentals. The objective of these tests moves beyond the simple properties of a random walk and adds structure to tests of rationality. Unfortunately, the debate concerning the establishment of rationality on the basis of these tests has not been resolved, because modeling is difficult and evidence of rationality can be mistakenly rejected. The validity of findings has been questioned in light of potential bias from small sample size, the power of the test, and the test’s underlying assumptions. Given the uncertain usefulness of this work, one might well wonder why Lo has included these articles. The topic may still excite academics, but most practitioners will not find it interesting.
Dynamic pricing models have also tried to explain return behavior over time by using consumption-based pricing approaches. These models explore asset returns over the business cycle and the fact that the equity premium appears higher than one would expect. Unfortunately, such models fail to fully provide an empirically justified, useful framework for explaining either returns or the equity premium puzzle. Although consumption-based models establish the critical link between financial returns and macroeconomic behavior, we are still left with no clear answers concerning the equity premium puzzle. Nevertheless, this topic remains an important area of research at the intersection of finance and macroeconomics.
The third part of dynamic modeling focuses on the behavior of interest rates and the yield curve. These articles present a good historical perspective. The narrative begins with simple models that try to fit a curve by using exponential splines throughout the term structure. It moves on to general equilibrium models (e.g., the Cox–Ingersoll–Ross model) that explain the behavior of rates in terms of such factors as inflation and default risk. These models have greatly influenced swap pricing, but the lack of a strong link between equity and bond pricing models is notable. The research on the dynamics of interest rates often uses a language separate from that of equity approaches, which creates language and research barriers between equity and fixed-income managers.
Volume 4. Continuous-Time Methods and Market Microstructure
The fourth volume focuses on continuous-time methods and the microstructure of markets. The microstructure articles deal with the complexities of price behavior. Some of this work is a natural extension of the statistical modeling in Volume 1. The problems of nonsynchronous timing, the bid–ask spread, and serial correlation in pricing all affect return patterns for assets. In addition, the institutional structure for determining prices sheds light on how returns are generated and what is meant by following a random walk.
Over the last decade, market microstructure has become one of the most exciting areas in finance. This volume covers the subdiscipline’s major pricing topics: the impact of nonsynchronous and infrequent trading, the behavior of dealer spreads and transaction information, and the limit order book and its effect on higher-frequency prices.
These topics are important methodological and empirical issues that have led to greater realism in our empirical testing—as well as in our understanding of returns—and have greatly influenced active trading methods. Both short-term trading and algo execution studies have experienced explosive growth on Wall Street as part of the research on market microstructure.
The second portion of this volume deals with the complex topics of derivatives and continuous-time econometrics. The pioneering work on option pricing has fostered a rich set of derivatives-testing procedures, ranging from measuring volatility to nonparametric estimation. These articles present volatility estimation by a wide range of methods, as well as issues of discontinuous price jumps. This empirical work has significantly influenced the behavior of option-trading practitioners. Lo includes a discussion of nonparametric methods for pricing derivatives, but this area of finance has become quite specialized and does not represent mainstream research. Much research has been done on the testing of option models, but this area is not addressed in this volume.
Volume 5. Statistical Methods and Non-Standard Finance
The final volume focuses on statistical techniques and what is described as “non-standard finance,” although many of the approaches are actually part of our normal investment research lexicon. This volume is divided into four sections: anomalies and selection bias, Bayesian methods, event studies and statistical tools, and non-standard finance.
The articles on statistical methods have provided the foundation for significant new directions in financial research. These techniques have enhanced our ability to tease information from data.
A huge benefit of conducting research in financial markets is the abundance of data, yet this characteristic leads to significant issues of selection bias, data snooping, and backtest problems. Interestingly, the wealth of data in financial markets is still not nearly sufficient, given the significant potential for survivorship bias. This statement is simply another way to describe the fundamental flaw of testing when the experimental design is limited. Nevertheless, Monte Carlo methods and sampling techniques have been developed to minimize such design issues.
The articles on Bayesian methods bring together the most important research on using these techniques for portfolio structure and asset pricing. Although these methods are compelling, Bayesian statistics have yet to be embraced by most portfolio managers. This lack of acceptance is mainly a result of difficulties with implementing the statistical procedures. From a theoretical view, the main conceptual hurdle has been setting up priors for the distributions. Nevertheless, Bayesian inference is an area with significant potential for money management in light of the strong intuition of using priors to set model parameters.
A backbone of research during the 1970s and 1980s, event studies are not as widely used today, because the analysis of many events has been exhausted. The technique of generalized method of moments has become a statistical workhorse in finance but is misplaced in this section.
The volume’s final section examines non-standard financial analysis involving technical trading and nonlinear dynamics. Misclassified as non-standard finance, these topics are properly part of the ongoing discussion of efficient markets. The test of efficiency is a joint test of market behavior and the model to be tested. Advances in the field of finance need to focus on the nonlinear dynamics of price. Research in this area has significant potential for application by practitioners; thus, stigmatizing it as a backwater is unwarranted.
Conclusion
Any book constructed from a set of articles has certain limitations. Articles of varying quality were written during periods of varying knowledge. Disputes inevitably arise regarding why certain articles are included or omitted. Many of this volume’s articles have had substantial influence, but others represent the editor’s idiosyncratic interests.
Andrew Lo should be commended for his attempt to provide a complete picture of financial econometrics. Readers would benefit, however, from more context on why particular articles are important and how they have shaped thinking on finance. Although Lo provides some insightful comments, the 9-page introduction is sparse relative to the more than 3,200 pages of articles. Readers are left to infer why the chosen studies are the most important. One wishes for a more extensive description of the development of the book’s topics and why certain topics have ceased to generate interesting research.
The primary market for this costly publication is academics, most of whom have already read many of its articles. Regrettably, those who could benefit most from the collection have not been exposed to its articles in their original form. Rather than spending more than $1,000 for this five-volume set, most readers would be better off purchasing The Econometrics of Financial Markets and A Non-Random Walk Down Wall Street, both coauthored by Lo. Although these two books do not contain the original source material, they provide a complete review of the important work at a low cost and in an integrated framework. Having the original work as a reference is important, but a good synthesis carries a premium in a busy world.
—M.S.R.