Market anomaly

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A market anomaly in a financial market is predictability that seems to be inconsistent with (typically risk-based) theories of asset prices.[1] Standard theories include the capital asset pricing model and the Fama-French Three Factor Model, but a lack of agreement among academics about the proper theory leads many to refer to anomalies without a reference to a benchmark theory (Daniel and Hirschleifer 2015[2] and Barberis 2018,[3] for example). Indeed, many academics simply refer to anomalies as "return predictors", avoiding the problem of defining a benchmark theory.[4]

Academics have documented more than 150 return predictors (see List of Anomalies Documented in Academic Journals). These "anomalies", however, come with many caveats. Almost all documented anomalies focus on illiquid, small stocks.[4] Moreover, the studies do not account for trading costs. As a result, many anomalies do not offer profits, despite the presence of predictability.[5] Additionally, return predictability declines substantially after the publication of a predictor, and thus may not offer profits in the future.[4] Finally, return predictability may be due to cross-sectional or time-variation in risk, and thus does not necessarily provide a good investment opportunity. Relatedly, return predictability by itself does not disprove the efficient market hypothesis, as one needs to show predictability over and above that implied by a particular model of risk.[6]

The four primary explanations for market anomalies are (1) mispricing, (2) unmeasured risk, (3) limits to arbitrage, and (4) selection bias.[4] Academics have not reached a consensus on the underlying cause, with prominent academics continuing to advocate for selection bias,[7] mispricing,[3] and risk-based theories.[8]

Anomalies can be broadly categorized into time-series and cross-sectional anomalies. Time-series anomalies refer to predictability in the aggregate stock market, such as the often-discussed Cyclically Adjusted Price-Earnings (CAPE) predictor.[9] These time-series predictors indicate times in which it is better to be invested in stocks vs a safe asset (such as Treasury bills). Cross-sectional anomalies refer to the predictable out-performance of particular stocks relative to others. For example, the well-known size anomaly[10] refers to the fact that stocks with lower market capitalization tend to out-perform stocks with higher market capitalization in the future.

Explanations for Anomalies[edit]

Mispricing[edit]

Many, if not most, of the papers which document anomalies attribute them to mispricing (Lakonishok, Shelifer, and Visny 1994,[11] for example). The mispricing explanation is natural, as anomalies are by definition deviations from a benchmark theory of asset prices. "Mispricing" is then defined as the deviation relative to the benchmark.

The most common benchmark is the CAPM (Capital-Asset-Pricing Model). The deviation from this theory is measured by a non-zero intercept in an estimated security market line. This intercept is commonly denoted by the Greek letter alpha:

where is the return on the anomaly, is the return on the risk-free rate, is the slope from regressing the anomaly's return on the market's return, and is the return on the "market", often proxied by the return on the CRSP index (an index of all publicly traded U.S. stocks).

The mispricing explanations are often contentious within academic finance, as academics do not agree on the proper benchmark theory (see Unmeasured Risk, below). This disagreement is closely related to the "joint-hypothesis problem" of the efficient market hypothesis.

Unmeasured Risk[edit]

Among academics, a common response to claims of mispricing was the idea that the anomaly captures a dimension of risk that is missing from the benchmark theory. For example, the anomaly may generate expected returns beyond those measured using the CAPM regression because the time-series of its returns are correlated with labor income, which is not captured by standard proxies for the market return.[12]

Perhaps the most well-known example of this unmeasured risk explanation is found in Fama and French's seminar paper on their 3-factor model: "if assets are priced rationally, variables that are related to average returns ... ..., must proxy for sensitivity to common (shared and thus undiversifiable) risk factors in returns. The [3-factor model] time-series regressions give direct evidence on this issue."[13]

The unmeasured risk explanation is closely related to the shortcomings of the CAPM as a theory of risk as well as shortcomings of empirical tests of the CAPM and related models. Perhaps the most common critique of the CAPM is that it is derived in a single period setting, and thus is missing dynamic features like periods of high uncertainty. In a more general setting, the CAPM typically implies multiple risk factors, as shown in Merton's Intertemporal CAPM theory. Moreover, the ICAPM generally implies the expected returns vary over time, and thus time-series predictability is not clear evidence of mispricing. Indeed, since the CAPM cannot at all capture dynamic expected returns, evidence of time-series predictability is less often regarded as mispricing as compared to cross-sectional predictability.

Empirical shortcomings primarily regard the difficulty in measuring wealth or marginal utility. Theoretically, wealth includes not only stock market wealth, but also non-tradable wealth like private assets and future labor income. In the consumption CAPM, (which is theoretically equivalent to Merton's ICAPM), the proper proxy for wealth is consumption, which is difficult to measure (Savov 2011,[14] for example).

Despite the theoretical soundness of the unmeasured risk explanation, there is little consensus among academics about the proper risk model over and above the CAPM. Propositions include the well-known Fama-French 3-Factor Model, Fama-French-Carhart 4-factor model, Fama-French 5-factor model, and Stambaugh and Yuan's 4-factor model.[15][16][17] These models are all empirically-oriented, rather than derived from a formal theory of equilibrium like Merton's ICAPM.

Limits to Arbitrage[edit]

Anomalies are almost always documented using closing prices from the CRSP dataset. These prices do not reflect trading costs, which can prevent arbitrage and thus the elimination predictability. Moreover, almost all anomalies are documented using equally-weighted portfolios,[4] and thus require trading of illiquid (costly-to-trade) stocks.

The limits to arbitrage explanation can be thought of as a refinement of the mispricing framework. A return pattern only offers profits if the returns it offers survives trading costs, and thus should not be considered mispricing unless trading costs are accounted for.

A large literature documents that trading costs greatly reduce anomaly returns. This literature goes back to Stoll and Whaley (1983) and Ball, Kothari, and Shanken (1995).[18][19] A recent paper that studies dozens of anomalies finds that trading costs have a massive effect on the average anomaly (Novy-Marx and Velikov 2015).[5]

Selection Bias[edit]

The documented anomalies are likely the best performers from a much larger set of potential return predictors. This selection creates a bias and implies that estimates of the profitability of anomalies is overstated. This explanation for anomalies is also known as data snooping, p-hacking, data mining, and data dredging, and is closely related to the multiple comparisons problem. Concerns about selection bias in anomalies goes back at least to Jensen and Bennington (1970).[20]

Most research on selection bias in market anomalies focuses on particular subsets of predictors. For example, Sullivan, Timmermann, and White (2001) show that calendar-based anomalies are no longer significant after adjusting for selection bias.[21] A recent meta-analysis of the size premium shows that the reported estimates of the size premium are exaggerated twofold because of selection bias [22].

Research on selection bias for anomalies more generally is relatively limited and inconclusive. McLean and Pontiff (2016) use an out-of-sample test to show that selection bias accounts for at most 26% of the typical anomaly's mean return during the sample period of the original publication. To show this, they replicate almost 100 anomalies, and show that the average anomaly's return is only 26% smaller in the few years immediately after the end of the original samples. As some of this decline may be due to investor learning effects, the 26% is an upper bound.[4] In contrast, Harvey, Liu, and Zhu (2016) adapt multiple testing adjustments from statistics such as the False Discovery Rate to asset pricing "factors". They refer to a factor as any variable that helps explain the cross-section of expected returns, and thus include many anomalies in their study. They find that multiple-testing statistics imply that factors with t-stats < 3.0 should not be considered statistically significant, and conclude that most published findings are likely false.[23]

List of Anomalies Documented in Academic Journals[edit]

Description Author(s) Year Journal Broad Category
Change in capital investment, industry adjusted Abarbanell and Bushee 1998 The Accounting Review Cross-Sectional
Gross Margin growth over sales growth Abarbanell and Bushee 1998 The Accounting Review Cross-Sectional
Sales growth over inventory growth Abarbanell and Bushee 1998 The Accounting Review Cross-Sectional
Sales growth over overhead growth Abarbanell and Bushee 1998 The Accounting Review Cross-Sectional
Operating Cash flows to price Desai, Rajgopal, and Benkatachalam 2004 The Accounting Review Cross-Sectional
Earnings Forecast Elgers, Lo, and Pfeiffer 2001 The Accounting Review Cross-Sectional
Growth in Long term net operating assets Fairfield, Whisenant and Yohn 2003 The Accounting Review Cross-Sectional
Earnings Surprise Foster, Olsen and Shevliln 1984 The Accounting Review Cross-Sectional
Percent Operating Accruals Hafzalla, Lundholm, and Van Winkle 2011 The Accounting Review Cross-Sectional
Percent Total Accruals Hafzalla, Lundholm, and Van Winkle 2011 The Accounting Review Cross-Sectional
Real dirty surplus Landsman et al. 2011 The Accounting Review Cross-Sectional
Taxable income to income Lev and Nissim 2004 The Accounting Review Cross-Sectional
Piotroski F-score Piotroski 2000 The Accounting Review Cross-Sectional
Accruals Sloan 1996 The Accounting Review Cross-Sectional
Asset Turnover Soliman 2008 The Accounting Review Cross-Sectional
Change in Asset Turnover Soliman 2008 The Accounting Review Cross-Sectional
Change in Noncurrent Operating Assets Soliman 2008 The Accounting Review Cross-Sectional
Change in Net Working Capital Soliman 2008 The Accounting Review Cross-Sectional
Change in Profit Margin Soliman 2008 The Accounting Review Cross-Sectional
Profit Margin Soliman 2008 The Accounting Review Cross-Sectional
Abnormal Accruals Xie 2001 The Accounting Review Cross-Sectional
Earnings Consistency Alwathainani 2009 British Accounting Review Cross-Sectional
Deferred Revenue Prakash and Sinha 2012 Contemporary Accounting Research Cross-Sectional
Sales-to-price Barbee, Mukherji, and Raines 1996 Financial Analysts' Journal Cross-Sectional
earnings / assets Balakrishnan, Bartov, and Faurel 2010 Journal of Accounting and Economics Cross-Sectional
Net debt financing Bradshaw, Richardson, and Sloan 2006 Journal of Accounting and Economics Cross-Sectional
Net equity financing Bradshaw, Richardson, and Sloan 2006 Journal of Accounting and Economics Cross-Sectional
Net external financing Bradshaw, Richardson, and Sloan 2006 Journal of Accounting and Economics Cross-Sectional
Net Operating Assets Hirschleifer, Hou Teoh, and Zhang 2004 Journal of Accounting and Economics Cross-Sectional
Change in depreciation to gross PPE Holthausen Larcker 1992 Journal of Accounting and Economics Cross-Sectional
Change in equity to assets Richardson, Sloan Soliman and Tuna 2005 Journal of Accounting and Economics Cross-Sectional
Change in current operating assets Richardson, Sloan Soliman and Tuna 2005 Journal of Accounting and Economics Cross-Sectional
Change in current operating liabilities Richardson, Sloan Soliman and Tuna 2005 Journal of Accounting and Economics Cross-Sectional
Change in financial liabilities Richardson, Sloan Soliman and Tuna 2005 Journal of Accounting and Economics Cross-Sectional
Change in long-term investment Richardson, Sloan Soliman and Tuna 2005 Journal of Accounting and Economics Cross-Sectional
Enterprise component of BM Penman, Richardson, and Tuna 2007 Journal of Accounting Research Cross-Sectional
Leverage component of BM Penman, Richardson, and Tuna 2007 Journal of Accounting Research Cross-Sectional
Net debt to price Penman, Richardson, and Tuna 2007 Journal of Accounting Research Cross-Sectional
Change in Taxes Thomas and Zhang 2011 Journal of Accounting Research Cross-Sectional
IPO and no R&D spending Gou, Lev, and Shi 2006 Journal of Business, Finance and Accounting Cross-Sectional
Change in capex (two years) Anderson and Garcia-Feijoo 2006 Journal of Finance Cross-Sectional
Idiosyncratic risk Ang, Hodrick, Xing, and Zhang 2006 Journal of Finance Cross-Sectional
Junk Stock Momentum Avramov, Chordia, Jostova, and Philipov 2007 Journal of Finance Cross-Sectional
Maximum return over month Bali, Cakici, and Whitelaw 2010 Journal of Finance Cross-Sectional
Consensus Recommendation Barber, Lehavy, McNichols, and Trueman 2001 Journal of Finance Cross-Sectional
Down forecast EPS Barber, Lehavy, McNichols, and Trueman 2001 Journal of Finance Cross-Sectional
Up Forecast Barber, Lehavy, McNichols, and Trueman 2001 Journal of Finance Cross-Sectional
Earnings-to-Price Ratio Basu 1977 Journal of Finance Cross-Sectional
Price Blume and Husic 1972 Journal of Finance Cross-Sectional
Net Payout Yield Boudoukh, Michaely, Richardson, and Roberts 2007 Journal of Finance Cross-Sectional
Payout Yield Boudoukh, Michaely, Richardson, and Roberts 2007 Journal of Finance Cross-Sectional
Failure probability Campbell, Hilscher, and Szilagyi 2008 Journal of Finance Cross-Sectional
Earnings announcement return Chan, Jegadeesh, and Lakonishok 1996 Journal of Finance Cross-Sectional
Earnings forecast revisions Chan, Jegadeesh, and Lakonishok 1996 Journal of Finance Cross-Sectional
Advertising Expense Chan, Lakonishok, and Sougiannis 2001 Journal of Finance Cross-Sectional
R&D over market cap Chan, Lakonishok, and Sougiannis 2001 Journal of Finance Cross-Sectional
Asset Growth Cooper, Gulen and Schill 2008 Journal of Finance Cross-Sectional
Intangible return Daniel and Titman 2006 Journal of Finance Cross-Sectional
Share issuance (5 year) Daniel and Titman 2006 Journal of Finance Cross-Sectional
Momentum-Reversal De Bondt and Thaler 1985 Journal of Finance Cross-Sectional
Long-run reversal De Bondt and Thaler 1985 Journal of Finance Cross-Sectional
Exchange Switch Dharan Ikenberry 1995 Journal of Finance Cross-Sectional
Credit Rating Downgrade Dichev Piotroski 2001 Journal of Finance Cross-Sectional
EPS Forecast Dispersion Diether et al. 2002 Journal of Finance Cross-Sectional
Unexpected R&D increase Eberhart et al. 2004 Journal of Finance Cross-Sectional
Organizational Capital Eisfeldt and Papanikolaou 2013 Journal of Finance Cross-Sectional
Pension Funding Status Franzoni and Martin 2006 Journal of Finance Cross-Sectional
52 week high George and Hwang 2004 Journal of Finance Cross-Sectional
Tangibility Hahn and Lee 2009 Journal of Finance Cross-Sectional
Industry concentration (Herfindahl) Hou and Robinson 2006 Journal of Finance Cross-Sectional
Momentum (12 month) Jegadeesh and Titman 1993 Journal of Finance Cross-Sectional
Momentum (6 month) Jegadeesh and Titman 1993 Journal of Finance Cross-Sectional
Change in recommendation Jegadeesh et al. 2004 Journal of Finance Cross-Sectional
Short term reversal Jegedeesh 1989 Journal of Finance Cross-Sectional
Long-term EPS forecast La Porta 1996 Journal of Finance Cross-Sectional
Cash flow to market Lakonishok, Scheifer, and Vishny 1994 Journal of Finance Cross-Sectional
Revenue Growth Rank Lakonishok, Scheifer, and Vishny 1994 Journal of Finance Cross-Sectional
Momentum and Volume Lee Swaminathan 2000 Journal of Finance Cross-Sectional
Public Seasoned Equity Offerings Loughran Ritter 1995 Journal of Finance Cross-Sectional
Dividend Initiation Michaely et al. 1995 Journal of Finance Cross-Sectional
Dividend Omission Michaely et al. 1995 Journal of Finance Cross-Sectional
Institutional ownership interactions with anomalies Nagel 2005 Journal of Finance Cross-Sectional
Dividend Yield Naranjo et al. 1998 Journal of Finance Cross-Sectional
Share issuance (1 year) Pontiff and Woodgate 2008 Journal of Finance Cross-Sectional
Initial Public Offerings Ritter 1991 Journal of Finance Cross-Sectional
Firm Age - Momentum Zhang 2004 Journal of Finance Cross-Sectional
Book to market Stattman 1980 The Chicago MBA Cross-Sectional
Bid-ask spread Amihud and Mendelsohn 1986 Journal of Financial Economics Cross-Sectional
Institutional Ownership for stocks with high short interest Asquith, Pathak, and Ritter 2005 Journal of Financial Economics Cross-Sectional
Cash-based operating profitability Ball, Gerakos, Linnainmaa, and Nikolaev 2016 Journal of Financial Economics Cross-Sectional
Size Banz 1981 Journal of Financial Economics Cross-Sectional
Market leverage Bhandari 1988 Journal of Financial Economics Cross-Sectional
Past trading volume Brennan, Chordia, and Subrahmanyam 1998 Journal of Financial Economics Cross-Sectional
Breadth of ownership Chen Hong Stein 2002 Journal of Financial Economics Cross-Sectional
Turnover volatility Chordia, Subrahmanyam, and Anshuman 2001 Journal of Financial Economics Cross-Sectional
Volume Variance Chordia, Subrahmanyam, and Anshuman 2001 Journal of Financial Economics Cross-Sectional
Conglomerate return Cohen and Lou 2012 Journal of Financial Economics Cross-Sectional
Spinoffs Cusatis et al. 1993 Journal of Financial Economics Cross-Sectional
Short Interest Dechow, Hutton, Meulbroek, and Sloan 2001 Journal of Financial Economics Cross-Sectional
O Score Dichev 1998 Journal of Financial Economics Cross-Sectional
Altman Z-Score Dichev 1998 Journal of Financial Economics Cross-Sectional
operating profits / book equity Fama and French 2006 Journal of Financial Economics Cross-Sectional
Industry Momentum Grinblatt Moskowitz 1999 Journal of Financial Economics Cross-Sectional
Dividends Hartzmark Salomon 2013 Journal of Financial Economics Cross-Sectional
net income / book equity Haugen and Baker 1996 Journal of Financial Economics Cross-Sectional
Cash-flow variance Haugen and Baker 1996 Journal of Financial Economics Cross-Sectional
Volume to market equity Haugen and Baker 1996 Journal of Financial Economics Cross-Sectional
Volume Trend Haugen and Baker 1996 Journal of Financial Economics Cross-Sectional
Return Seasonality Heston and Sadka 2008 Journal of Financial Economics Cross-Sectional
Sin Stock (selection criteria) Hong Kacperczyk 2009 Journal of Financial Economics Cross-Sectional
Share repurchases Ikenberry et al. 1995 Journal of Financial Economics Cross-Sectional
Revenue Surprise Jegadeesh and Livnat 2006 Journal of Financial Economics Cross-Sectional
Option Volume relative to recent average Johnson So 2012 Journal of Financial Economics Cross-Sectional
Option Volume to Stock Volume Johnson So 2012 Journal of Financial Economics Cross-Sectional
Days with zero trades Liu 2006 Journal of Financial Economics Cross-Sectional
Intermediate Momentum Novy-Marx 2012 Journal of Financial Economics Cross-Sectional
gross profits / total assets Novy-Marx 2013 Journal of Financial Economics Cross-Sectional
Cash to assets Palazzo 2012 Journal of Financial Economics Cross-Sectional
Debt Issuance Spiess Affleck-Graves 1999 Journal of Financial Economics Cross-Sectional
Slope of smile Yan 2011 Journal of Financial Economics Cross-Sectional
Amihud's illiquidity Amihud 2002 Journal of Financial Markets Cross-Sectional
Share Volume Datar, Naik, and Radcliffe 1998 Journal of Financial Markets Cross-Sectional
Enterprise Multiple Loughran and Wellman 2011 Journal of Financial and Quantitative Analysis Cross-Sectional
Efficient frontier index Nguyen Swanson 2009 Journal of Financial and Quantitative Analysis Cross-Sectional
Investment Titman, Wei, and Xie 2004 Journal of Financial and Quantitative Analysis Cross-Sectional
Convertible debt indicator Valta 2016 Journal of Financial and Quantitative Analysis Cross-Sectional
Volatility smirk Xing Zhang Zhao 2010 Journal of Financial and Quantitative Analysis Cross-Sectional
Sustainable Growth Lockwood Prombutr 2010 Journal of Financial Research Cross-Sectional
Momentum and LT Reversal Chan and Kot 2006 Journal of Investment Management Cross-Sectional
Employment growth Belo, Lin, and Bazdresch 2014 Journal of Political Economy Cross-Sectional
CAPM beta squared Fama and MacBeth 1973 Journal of Political Economy Cross-Sectional
Number of consecutive earnings increases Loh Warachka 2012 Management Science Cross-Sectional
Governance Index Gompers, Ishii and Metrick 2003 Quarterly Journal of Economics Cross-Sectional
Change in Forecast and Accrual Barth and Hutton 2004 Review of Accounting Studies Cross-Sectional
Excluded Expenses Doyle et al. 2003 Review of Accounting Studies Cross-Sectional
Mohanram G-score Mohanram 2005 Review of Accounting Studies Cross-Sectional
Order backlog Rajgopal, Shevlin and Venkatachalam 2003 Review of Accounting Studies Cross-Sectional
Inventory Growth Thomas and Zhang 2002 Review of Accounting Studies Cross-Sectional
Operating Leverage Novy-Marx 2010 Review of Finance Cross-Sectional
Decline in Analyst Coverage Scherbina 2008 Review of Finance Cross-Sectional
Earnings surprise of big firms Hou 2007 Review of Financial Studies Cross-Sectional
Industry return of big firms Hou 2007 Review of Financial Studies Cross-Sectional
Price delay Hou and Moskowitz 2005 Review of Financial Studies Cross-Sectional
Tail risk beta Kelly and Jiang 2014 Review of Financial Studies Cross-Sectional
Kaplan Zingales index Lamont, Polk, and Saa-Requejo 2001 Review of Financial Studies Cross-Sectional
Growth in advertising expenses Lou 2014 Review of Financial Studies Cross-Sectional
Composite debt issuance Lyandres, Sun and Zhang 2008 Review of Financial Studies Cross-Sectional
Real estate holdings Tuzel 2010 Review of Financial Studies Cross-Sectional
Book-to-market and accruals Bartov and Kim 2004 Review of Quantitative Finance and Accounting Cross-Sectional
Weekend Effect Smirlock and Starks 1986 Journal of Financial Economics Time-Series
January Effect Keims 1985 Journal of Financial Economics Time-Series
Turn of the Month Effect Agrawal and Tandon 1994 Journal of International Money and Finance Time-Series

References[edit]

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External links[edit]