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Chapter 1
Conceptual Foundations of Capital Market Anomalies
Mozaffar Khan
This book describes unexpected price behavior in equity markets, termed Anomalies, that can potentially be exploited by investors to earn abnormal returns. In capital markets, an anomaly is a deviation from the prediction of the efficient markets theory. The purpose of this chapter is to provide a conceptual framework for understanding the academic research on anomalies and to evaluate whether certain anomalies can be profitably exploited. The chapter begins with a discussion of efficient markets theory, which specifies how assets (specifically stocks) are expected to be priced under a set of ideal or theoretical conditions. The discussion then moves on to anomalies, or price behavior, that is unexpected if markets are efficient. The chapter defines anomalies, discusses explanations for anomalies that have been examined in the academic literature, and concludes by weighing the evidence for these different explanations. Since anomalies yield predictable positive risk-adjusted returns, proper risk measurement is critical to the identification of anomalies. Hence, the appendix to this chapter provides a detailed review of risk measurement and expected return models.1
No specific anomaly is discussed in this chapter, because the discussion here is intended to be applicable to all anomalies. It is hoped that, at the end of this chapter, investors will have the conceptual tools necessary to evaluate and understand observed price behavior in general, and the anomalies discussed in the subsequent chapters in particular.
Efficient Markets
The efficient markets theory is usually credited to Fama (1965, 1970), and also has theoretical roots in Samuelson (1965) and Mandelbrot (1966). A market is informationally efficient if prices are, on average, correct, given the publicly available information. Prices react rapidly to new events, and, on average, correctly impound the new information. This characterizes an equilibrium in a competitive market if the following conditions, among others, hold:
- Structural Knowledge. Investors are assumed to have complete information about the underlying structure of the return-generating process. For example, investors know the parameters and functional form of the model that governs the stock's returns. Consider what happens when this information is not known for a given stock S. An event may change the risk or expected cash flows of S, but if there is preexisting uncertainty about the parameters of the pricing equation for S, it is difficult to revise the price so that it correctly impounds the new information.
- Rational Information Processing. Investors, on average, are assumed to process information in a cognitively unbiased, Bayesian fashion. They are not subject to psychological biases that cause them to over- or underreact to information. Although there may be some investors who are not rational, their trades are unlikely to be correlated, so their irrational trades essentially cancel each other out (noise trading).
- No Limits to Arbitrage. Even if the trades of irrational investors are correlated and result in mispricing, rational investors will quickly step in and arbitrage away the mispricing. Absent frictions, arbitrage facilitates market efficiency by quickly eliminating deviations from fundamental values. Frictions that limit arbitrage include transaction costs, short-sale constraints, a limited number of arbitrageurs combined with specialization among arbitrageurs, the absence of close substitutes for the mispriced stock, lingering heterogeneity of investor opinion about the “correct” price for the stock, and bounded investment scalability.
It is useful to keep the preceding assumptions in mind because, when they are violated, they become potential explanations for observed mispricing. A stock may be mispriced if any combination of these assumptions does not hold. The efficient markets theory is perhaps the single most pervasive organizing principle in finance. Its power lies in:
- The range of phenomena it is capable of explaining and predicting. The average stock at a random point in time is likely fairly priced. If mispricing were rampant and easily identifiable by the average investor, paid investment professionals might be obsolete. Paid investment professionals are more likely needed when mispricing has to be ferreted out of dark corners, than when mispricing exists out in the open.
- The discipline it forces on our thinking. When an ostensibly mispriced stock is identified, it forces us to understand why it is mispriced, or in other words, it forces us to ask why the mispricing signal is expected to be reliable. Investment decisions attempt to anticipate future outcomes, and these outcomes are difficult to predict absent understanding of the reasons for the mispricing.
- The guide it provides to understanding why a stock may be mispriced. This guide is the set of assumptions of the theory outlined previously. The theory then, in essence, tells us which explanations (i.e., assumptions) to explore in attempting to understand why a given stock may be mispriced.
Respect for the efficient markets theory, and an acknowledgement that it sometimes fails (i.e., that mispriced stocks can be identified), can coexist. One need not disdain the theory in the pursuit of anomalies, to which we turn next.
Identifying Anomalies in Capital Markets
Capital market anomalies are deviations from the prediction of efficient markets theory. Such anomalies manifest in predictable nonzero risk-adjusted returns (RAR). A stock with zero risk-adjusted returns provides a fair return for its risk. A stock with positive (negative) risk-adjusted returns provides a more-than-fair (less-than-fair) return for its risk. Investors would like to be long the former and short the latter.
A theory is an approximation of reality. Zero approximation errors are unheard of in practice. According to Kuhn (1962), anomalies are common and expected in every field, and they are an integral part of the routine “puzzle-solving” process of science. Scientists are reluctant to discard a broad theory or paradigm upon discovery of some instances of its falsification (i.e., significant approximation errors). To discard a paradigm, a replacement candidate that better explains at least as wide a range of phenomena is needed. This burden of competition is necessary for robust strains of theory to emerge. Therefore, subjecting anomalies to healthy skepticism should be seen as part of the normal discovery process of science in which the objective is to develop robust theories (Kuhn 1962), in our case, a robust theory of asset pricing.
There are essentially two steps in identifying anomalies. The first step is identifying a mispricing signal. An example of a mispricing and, hence, an investment signal is the magnitude of a firm's earnings surprise. Firms with extreme positive (negative) quarterly earnings surprise have predictably higher (lower) future returns, so the investment strategy is to go long (short) on stocks of firms with an extreme positive (negative) earnings surprise in order to earn positive returns. This is known as the post-earnings announcement drift (PEAD) anomaly. In subsequent chapters, a number of different mispricing signals (or anomalies) are described.
The second step is evaluating the economic significance and statistical reliability of the mispricing signal. The typical approach is to sort the cross-section of firms into, for example, deciles based on a mispricing signal. For example, firms would be sorted into deciles of earnings surprise in the PEAD strategy, with the top (bottom) decile containing firms with the highest positive (most negative) earnings surprise. The magnitude of the average risk-adjusted return, or alpha, on a portfolio that is long on stocks in one extreme decile, and short stocks in the other extreme decile, is a measure of the economic significance of the mispricing signal. The alpha is the raw return on the portfolio minus the expected return based on the risk of the portfolio.2 A long-short portfolio is not necessarily risk-neutral, and, therefore, it is more common to examine alphas, rather than raw returns, to the long-short portfolio. Many anomalies described in the subsequent chapters typically yield alphas of about 10% per year. The costs, such as information, search, and trading costs of the strategy are also typically subtracted from the alpha in practice to arrive at an estimate of the economic significance of an implementable trading strategy based on the mispricing signal.
The statistical reliability of the mispricing signal is measured by how reliably different the trading strategy's alpha is from zero. Consider a strategy that is implemented annually and can be back-tested on 40 years of data. In this case, we would have 40 separate risk-adjusted returns, one for each year the strategy is implemented. We would expect some variation in risk-adjusted returns across the 40 years. If the variation is low relative to the mean risk-adjusted return, the strategy would be considered statistically reliable. In particular, a t-statistic with a p-value less than 5% is the typical criterion for statistical reliability of an alpha.
Explaining Anomalies
The academic literature has pursued several potential explanations for capital markets anomalies.
- One subset of the literature explores whether the anomaly in question is real. The ostensible anomaly may be: an artifact of mismeasured risk; a result of mismeasured statistical reliability; or a result of data snooping.
- Another subset of the literature explores whether anomalies can be explained by rational structural uncertainty, whereby mispricing is a result of uncertainty about the underlying return-generating process (a violation of the first assumption of efficient markets identified in the previous section).
- A third subset of the literature explores whether investors’ psychological biases are responsible for mispricing (a violation of the second assumption of efficient markets identified in the previous section).
- A fourth subset of the literature explores whether limits to arbitrage can explain the persistence of mispricing (a violation of the third assumption of efficient markets identified in the previous section).
These explanations are discussed in the following section.
Is the Anomaly Real?
A real anomaly is one that can be profitably exploited by investors to earn statistically reliable and positive risk-adjusted returns. Identifying a real anomaly, therefore, requires ensuring that the risk of the investment strategy is correctly measured (for proper risk adjustment), and that the RARs are statistically reliable and expected to persist out of sample, as discussed in the next section.
RISK MISMEASUREMENT
The expected return on a stock is determined in theory by its risk, so if the theory holds, a stock is not expected to have predictably nonzero alphas. Alpha is the difference between the realized return and a model-implied expected return or benchmark. If the benchmark is too low (high), the alpha can appear positive (negative). This is known as the joint hypothesis problem: any test of market efficiency (the proposition that risk-adjusted returns are zero on average) is also jointly a test of the assumed equilibrium model for expected returns. Therefore, a ...
