University of Rochester William E.Simon Graduate School of Business Administration The Bradley Policy Research Center Financial Research and Policy Working Paper No. FR02-13 October 2002 Anomalies and Market Efficiency G.William Schwert Simon School of Business,University of Rochester This paper can be downloaded from the Social Science Research Network Electronic Paper Collection: http://papers.ssrn.com/abstract=
University of Rochester William E. Simon Graduate School of Business Administration The Bradley Policy Research Center Financial Research and Policy Working Paper No. FR 02-13 October 2002 Anomalies and Market Efficiency G. William Schwert Simon School of Business, University of Rochester This paper can be downloaded from the Social Science Research Network Electronic Paper Collection: http://papers.ssrn.com/abstract=
Anomalies and Market Efficiency G.William Schwert University of Rochester,Rochester,NY 14627 and National Bureau of Economic Research October 2002 Anomalies are empirical results that seem to be inconsistent with maintained theories of asset-pricing behavior.They indicate either market inefficiency (profit opportunities)or inadequacies in the underlying asset-pricing model. The evidence in this paper shows that the size effect,the value effect,the weekend effect, and the dividend yield effect seem to have weakened or disappeared after the papers that highlighted them were published.At about the same time,practitioners began investment vehicles that implemented the strategies implied by some of these academic papers. The small-firm turn-of-the-year effect became weaker in the years after it was first documented in the academic literature,although there is some evidence that it still exists. Interestingly,however,it does not seem to exist in the portfolio returns of practitioners who focus on small-capitalization firms. All of these findings raise the possibility that anomalies are more apparent than real.The notoriety associated with the findings of unusual evidence tempts authors to further investigate puzzling anomalies and later to try to explain them.But even if the anomalies existed in the sample period in which they were first identified,the activities of practitioners who implement strategies to take advantage of anomalous behavior can cause the anomalies to disappear (as research findings cause the market to become more efficient). Key words:Market efficiency,anomaly,size effect,value effect,selection bias,momentum JEL Classifications:G14,G12.G34.G32 Corresponding author:G.William Schwert,William E.Simon Graduate School of Business Administration,University of Rochester. Email:Schwert@schwert.ssb.rochester.edu Forthcoming in the Handbook of the Economics of Finance,edited by George Constantinides,Milton Harris,and Rene M.Stulz.The Bradley Policy Research Center,William E.Simon Graduate School of Business Administration,University of Rochester,provided support for this research.I received helpful comments from Yakov Amihud,Brad Barber,John Cochrane,Eugene Fama,Murray Frank,Ken French,David Hirshleifer,Tim Loughran,Randall Morck,Jeff Pontiff,Jay Ritter,Rene Stulz,A.Subrahmanyam,Sheridan Titman,Janice Willett, and Jerold Zimmerman.The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. G.William Schwert,2002.All rights reserved.Short sections of text,not to exceed two paragraphs,may be quoted without explicit permission provided that full credit,including notice,is given to the source
Anomalies and Market Efficiency G. William Schwert University of Rochester, Rochester, NY 14627 and National Bureau of Economic Research October 2002 Anomalies are empirical results that seem to be inconsistent with maintained theories of asset-pricing behavior. They indicate either market inefficiency (profit opportunities) or inadequacies in the underlying asset-pricing model. The evidence in this paper shows that the size effect, the value effect, the weekend effect, and the dividend yield effect seem to have weakened or disappeared after the papers that highlighted them were published. At about the same time, practitioners began investment vehicles that implemented the strategies implied by some of these academic papers. The small-firm turn-of-the-year effect became weaker in the years after it was first documented in the academic literature, although there is some evidence that it still exists. Interestingly, however, it does not seem to exist in the portfolio returns of practitioners who focus on small-capitalization firms. All of these findings raise the possibility that anomalies are more apparent than real. The notoriety associated with the findings of unusual evidence tempts authors to further investigate puzzling anomalies and later to try to explain them. But even if the anomalies existed in the sample period in which they were first identified, the activities of practitioners who implement strategies to take advantage of anomalous behavior can cause the anomalies to disappear (as research findings cause the market to become more efficient). Key words: Market efficiency, anomaly, size effect, value effect, selection bias, momentum JEL Classifications: G14, G12, G34, G32 Corresponding author: G. William Schwert, William E. Simon Graduate School of Business Administration, University of Rochester. Email: Schwert@schwert.ssb.rochester.edu Forthcoming in the Handbook of the Economics of Finance, edited by George Constantinides, Milton Harris, and René M. Stulz. The Bradley Policy Research Center, William E. Simon Graduate School of Business Administration, University of Rochester, provided support for this research. I received helpful comments from Yakov Amihud, Brad Barber, John Cochrane, Eugene Fama, Murray Frank, Ken French, David Hirshleifer, Tim Loughran, Randall Mørck, Jeff Pontiff, Jay Ritter, René Stulz, A. Subrahmanyam, Sheridan Titman, Janice Willett, and Jerold Zimmerman. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. © G. William Schwert, 2002. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source
Schwert--Anomalies and Market Efficiency 1 Introduction Anomalies are empirical results that seem to be inconsistent with maintained theories of asset-pricing behavior.They indicate either market inefficiency (profit opportunities)or inadequacies in the underlying asset-pricing model.After they are documented and analyzed in the academic literature,anomalies often seem to disappear,reverse,or attenuate.This raises the question of whether profit opportunities existed in the past,but have since been arbitraged away, or whether the anomalies were simply statistical aberrations that attracted the attention of academics and practitioners. Surveys of the efficient markets literature date back at least to Fama(1970),and there are several recent updates,including Fama (1991)and Keim and Ziemba (2000),that stress particular areas of the finance literature.By their nature,surveys reflect the views and perspectives of their authors,and this one will be no exception.My goal is to highlight some interesting findings that have emerged from the research of many people and to raise questions about the implications of these findings for the way academics and practitioners use financial theory.I There are obvious connections between this chapter and earlier chapters by Ritter(10- Investment Banking and Securities Issuance)and Ferson (16-Multifactor Pricing Models),as well as later chapters by Barberis and Thaler (18-Behavioral Issues),Cochrane (20-New Facts in Finance),and Easley and O'Hara(21-Market Microstructure and Asset Pricing).In fact,those chapeters draw on some of the same findings and papers that provide the basis for my conclusions. At a fundamental level,anomalies can only be defined relative to a model of"normal" This chapter is not meant to be a survey of all of the literature on market efficiency or anomalies.Failure to cite particular papers should not be taken as a reflection on those papers
Schwert -- Anomalies and Market Efficiency 1 1 Introduction Anomalies are empirical results that seem to be inconsistent with maintained theories of asset-pricing behavior. They indicate either market inefficiency (profit opportunities) or inadequacies in the underlying asset-pricing model. After they are documented and analyzed in the academic literature, anomalies often seem to disappear, reverse, or attenuate. This raises the question of whether profit opportunities existed in the past, but have since been arbitraged away, or whether the anomalies were simply statistical aberrations that attracted the attention of academics and practitioners. Surveys of the efficient markets literature date back at least to Fama (1970), and there are several recent updates, including Fama (1991) and Keim and Ziemba (2000), that stress particular areas of the finance literature. By their nature, surveys reflect the views and perspectives of their authors, and this one will be no exception. My goal is to highlight some interesting findings that have emerged from the research of many people and to raise questions about the implications of these findings for the way academics and practitioners use financial theory.1 There are obvious connections between this chapter and earlier chapters by Ritter (10 – Investment Banking and Securities Issuance) and Ferson (16 – Multifactor Pricing Models), as well as later chapters by Barberis and Thaler (18 – Behavioral Issues), Cochrane (20 – New Facts in Finance), and Easley and O’Hara (21 – Market Microstructure and Asset Pricing). In fact, those chapeters draw on some of the same findings and papers that provide the basis for my conclusions. At a fundamental level, anomalies can only be defined relative to a model of “normal” 1This chapter is not meant to be a survey of all of the literature on market efficiency or anomalies. Failure to cite particular papers should not be taken as a reflection on those papers
Schwert--Anomalies and Market Efficiency 2 return behavior.Fama(1970)noted this fact early on,pointing out that tests of market efficiency also jointly test a maintained hypothesis about equilibrium expected asset returns.Thus, whenever someone concludes that a finding seems to indicate market inefficiency,it may also be evidence that the underlying asset-pricing model is inadequate. It is also important to consider the economic relevance of a presumed anomaly.Jensen (1978)stressed the importance of trading profitability in assessing market efficiency.In particular,if anomalous return behavior is not definitive enough for an efficient trader to make money trading on it,then it is not economically significant.This definition of market efficiency directly reflects the practical relevance of academic research into return behavior.It also highlights the importance of transactions costs and other market microstructure issues for defining market efficiency. The growth in the amount of data and computing power available to researchers,along with the growth in the number of active empirical researchers in finance since Fama's(1970) survey article,has created an explosion of findings that raise questions about the first,simple models of efficient capital markets.Many people have noted that the normal tendency of researchers to focus on unusual findings(which could be a by-product of the publication process, if there is a bias toward the publication of findings that challenge existing theories)could lead to the over-discovery of"anomalies."For example,if a random process results in a particular sample that looks unusual,thereby attracting the attention of researchers,this"sample selection bias"could lead to the perception that the underlying model was not random.Of course,the key test is whether the anomaly persists in new,independent samples Some interesting questions arise when perceived market inefficiencies or anomalies seem to disappear after they are documented in the finance literature:Does their disappearance reflect
Schwert -- Anomalies and Market Efficiency 2 return behavior. Fama (1970) noted this fact early on, pointing out that tests of market efficiency also jointly test a maintained hypothesis about equilibrium expected asset returns. Thus, whenever someone concludes that a finding seems to indicate market inefficiency, it may also be evidence that the underlying asset-pricing model is inadequate. It is also important to consider the economic relevance of a presumed anomaly. Jensen (1978) stressed the importance of trading profitability in assessing market efficiency. In particular, if anomalous return behavior is not definitive enough for an efficient trader to make money trading on it, then it is not economically significant. This definition of market efficiency directly reflects the practical relevance of academic research into return behavior. It also highlights the importance of transactions costs and other market microstructure issues for defining market efficiency. The growth in the amount of data and computing power available to researchers, along with the growth in the number of active empirical researchers in finance since Fama’s (1970) survey article, has created an explosion of findings that raise questions about the first, simple models of efficient capital markets. Many people have noted that the normal tendency of researchers to focus on unusual findings (which could be a by-product of the publication process, if there is a bias toward the publication of findings that challenge existing theories) could lead to the over-discovery of “anomalies.” For example, if a random process results in a particular sample that looks unusual, thereby attracting the attention of researchers, this “sample selection bias” could lead to the perception that the underlying model was not random. Of course, the key test is whether the anomaly persists in new, independent samples. Some interesting questions arise when perceived market inefficiencies or anomalies seem to disappear after they are documented in the finance literature: Does their disappearance reflect
Schwert--Anomalies and Market Efficiency 3 sample selection bias,so that there was never an anomaly in the first place?Or does it reflect the actions of practitioners who learn about the anomaly and trade so that profitable transactions vanish? The remainder of this chapter is organized as follows.Section 2 discusses cross-sectional and times-series regularities in asset returns,including the size,book-to-market,momentum,and dividend yield effects.Section 3 discusses differences in returns realized by different types of investors,including individual investors (through closed-end funds and brokerage account trading data)and institutional investors (through mutual fund performance and hedge fund performance).Section 4 evaluates the role of measurement issues in many of the papers that study anomalies,including the difficult issues associated with long-horizon return performance. Section 5 discusses the implications of the anomalies literature for asset-pricing theories,and Section 6 discusses the implications of the anomalies literature for corporate finance.Section 7 contains brief concluding remarks. 2 Selected Empirical Regularities 2.1 Predictable Differences in Returns Across Assets Data Snooping Many analysts have been concerned that the process of examining data and models affects the likelihood of finding anomalies.Authors in search of an interesting research paper are likely to focus attention on "surprising"results.To the extent that subsequent authors reiterate or refine the surprising results by examining the same or at least positively correlated data,there is really no additional evidence in favor of the anomaly.Lo and MacKinlay (1990) illustrate the data-snooping phenomenon and show how the inferences drawn from such exercises are misleading
Schwert -- Anomalies and Market Efficiency 3 sample selection bias, so that there was never an anomaly in the first place? Or does it reflect the actions of practitioners who learn about the anomaly and trade so that profitable transactions vanish? The remainder of this chapter is organized as follows. Section 2 discusses cross-sectional and times-series regularities in asset returns, including the size, book-to-market, momentum, and dividend yield effects. Section 3 discusses differences in returns realized by different types of investors, including individual investors (through closed-end funds and brokerage account trading data) and institutional investors (through mutual fund performance and hedge fund performance). Section 4 evaluates the role of measurement issues in many of the papers that study anomalies, including the difficult issues associated with long-horizon return performance. Section 5 discusses the implications of the anomalies literature for asset-pricing theories, and Section 6 discusses the implications of the anomalies literature for corporate finance. Section 7 contains brief concluding remarks. 2 Selected Empirical Regularities 2.1 Predictable Differences in Returns Across Assets Data Snooping Many analysts have been concerned that the process of examining data and models affects the likelihood of finding anomalies. Authors in search of an interesting research paper are likely to focus attention on “surprising” results. To the extent that subsequent authors reiterate or refine the surprising results by examining the same or at least positively correlated data, there is really no additional evidence in favor of the anomaly. Lo and MacKinlay (1990) illustrate the data-snooping phenomenon and show how the inferences drawn from such exercises are misleading
Schwert--Anomalies and Market Efficiency 4 One obvious solution to this problem is to test the anomaly on an independent sample. Sometimes researchers use data from other countries,and sometimes they use data from prior time periods.If sufficient time elapses after the discovery of an anomaly,the analysis of subsequent data also provides a test of the anomaly.I supply some evidence below on the post- publication performance of several anomalies. The Size Effect Banz (1981)and Reinganum (1981)showed that small-capitalization firms on the New York Stock Exchange (NYSE)earned higher average returns than is predicted by the Sharpe (1964)-Lintner (1965)capital asset-pricing model (CAPM)from 1936-75.This "small-firm effect"spawned many subsequent papers that extended and clarified the early papers.For example,a special issue of the Journal of Financial Economics contained several papers that extended the size effect literature.2 Interestingly,at least some members of the financial community picked up on the small- firm effect,since the firm Dimensional Fund Advisors(DFA)began in 1981 with Eugene Fama as its Director of Research.'Table 1 shows the abnormal performance of the DFA US 9-10 Small Company Portfolio,which closely mimics the strategy described by Banz(1981). The measure of abnormal return ai in Table 1 is called Jensen's (1968)alpha,from the following familiar model: (Rit-Ra)=ai+Bi(Rmt-RA)+&it. (1) where Rit is the return on the DFA fund in month t,Ra is the yield on a one-month Treasury bill, 2Schwert(1983)discusses all of these papers in more detail 3Information about DFA comes from their web page:http://www.dfafunds.com and from the Center for Research in Security Prices(CRSP)Mutual Fund database.Ken French maintains current data for the Fama-French factors on his web site:http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
Schwert -- Anomalies and Market Efficiency 4 One obvious solution to this problem is to test the anomaly on an independent sample. Sometimes researchers use data from other countries, and sometimes they use data from prior time periods. If sufficient time elapses after the discovery of an anomaly, the analysis of subsequent data also provides a test of the anomaly. I supply some evidence below on the postpublication performance of several anomalies. The Size Effect Banz (1981) and Reinganum (1981) showed that small-capitalization firms on the New York Stock Exchange (NYSE) earned higher average returns than is predicted by the Sharpe (1964) – Lintner (1965) capital asset-pricing model (CAPM) from 1936-75. This “small-firm effect” spawned many subsequent papers that extended and clarified the early papers. For example, a special issue of the Journal of Financial Economics contained several papers that extended the size effect literature.2 Interestingly, at least some members of the financial community picked up on the smallfirm effect, since the firm Dimensional Fund Advisors (DFA) began in 1981 with Eugene Fama as its Director of Research.3 Table 1 shows the abnormal performance of the DFA US 9-10 Small Company Portfolio, which closely mimics the strategy described by Banz (1981). The measure of abnormal return ai in Table 1 is called Jensen’s (1968) alpha, from the following familiar model: (Rit – Rft) = ai + bi (Rmt – Rft) + eit, (1) where Rit is the return on the DFA fund in month t, Rft is the yield on a one-month Treasury bill, 2 Schwert (1983) discusses all of these papers in more detail. 3 Information about DFA comes from their web page: http://www.dfafunds.com and from the Center for Research in Security Prices (CRSP) Mutual Fund database. Ken French maintains current data for the Fama-French factors on his web site: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
Schwert--Anomalies and Market Efficiency 5 and Rmt is the return on the CRSP value-weighted market portfolio of NYSE,Amex,and Nasdaq stocks.The intercept ai in (1)measures the average difference between the monthly return to the DFA fund and the return predicted by the CAPM.The market risk of the DFA fund,measured by Bi,is insignificantly different from 1.0 in the period January 1982-May 2002,as well as in each of the three subperiods,1982-1987,1988-1993,and 1994-2002.The estimates of abnormal monthly returns are between -0.2%and 0.4%per month,although none are reliably below zero. Thus,it seems that the small-firm anomaly has disappeared since the initial publication of the papers that discovered it.Alternatively,the differential risk premium for small-capitalization stocks has been much smaller since 1982 than it was during the period 1926-1982. The Turn-of-the-Year Effect Keim (1983)and Reinganum(1983)showed that much of the abnormal return to small firms (measured relative to the CAPM)occurs during the first two weeks in January.This anomaly became known as the "turn-of-the-year effect."Roll (1983)hypothesized that the higher volatility of small-capitalization stocks caused more of them to experience substantial short-term capital losses that investors might want to realize for income tax purposes before the end of the year.This selling pressure might reduce prices of small-cap stocks in December, leading to a rebound in early January as investors repurchase these stocks to reestablish their investment positions.4 There are many mechanisms that could mitigate the size of such an effect,including the choice of a tax year different from a calendar year,the incentive to establish short-term losses before December,and the opportunities for other investors to earn higher returns by providing liquidity in December
Schwert -- Anomalies and Market Efficiency 5 and Rmt is the return on the CRSP value-weighted market portfolio of NYSE, Amex, and Nasdaq stocks. The intercept ai in (1) measures the average difference between the monthly return to the DFA fund and the return predicted by the CAPM. The market risk of the DFA fund, measured by bi , is insignificantly different from 1.0 in the period January 1982 – May 2002, as well as in each of the three subperiods, 1982-1987, 1988-1993, and 1994-2002. The estimates of abnormal monthly returns are between -0.2% and 0.4% per month, although none are reliably below zero. Thus, it seems that the small-firm anomaly has disappeared since the initial publication of the papers that discovered it. Alternatively, the differential risk premium for small-capitalization stocks has been much smaller since 1982 than it was during the period 1926-1982. The Turn-of-the-Year Effect Keim (1983) and Reinganum (1983) showed that much of the abnormal return to small firms (measured relative to the CAPM) occurs during the first two weeks in January. This anomaly became known as the “turn-of-the-year effect.” Roll (1983) hypothesized that the higher volatility of small-capitalization stocks caused more of them to experience substantial short-term capital losses that investors might want to realize for income tax purposes before the end of the year. This selling pressure might reduce prices of small-cap stocks in December, leading to a rebound in early January as investors repurchase these stocks to reestablish their investment positions.4 4 There are many mechanisms that could mitigate the size of such an effect, including the choice of a tax year different from a calendar year, the incentive to establish short-term losses before December, and the opportunities for other investors to earn higher returns by providing liquidity in December
Schwert--Anomalies and Market Efficiency 6 Table 1 Size and Value Effects,January 1982-May 2002 Performance of DFA US 9-10 Small Company Portfolio relative to the CRSP value-weighted portfolio of NYSE,Amex,and Nasdaq stocks(Rm)and the one-month Treasury bill yield(R), January 1982-May 2002.The intercept in this regression,a,is known as "Jensen's alpha" (1968)and it measures the average difference between the monthly return to the DFA fund and the return predicted by the CAPM. (Rit-Ra)=ai+Bi(Rmt-RA)+Sit The last row shows the performance of the DFA US 6-10 Value Portfolio from January 1994- May 2002.Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Period 04 t(0:=0) B tβ：=1) DFA 9-10 Small Company Portfolio 1982-2002 0.0020 0.67 1.033 0.68 1982-1987 -0.0019 -0.44 1.000 0.00 1988-1993 0.0038 0.80 1.104 1.21 1994-2002 0.0035 0.66 1.013 0.15 DFA US 6-10 Value Portfolio 1994-2002 -0.0022 -0.59 0.816 -2.14
Schwert -- Anomalies and Market Efficiency 6 Table 1 Size and Value Effects, January 1982 – May 2002 Performance of DFA US 9-10 Small Company Portfolio relative to the CRSP value-weighted portfolio of NYSE, Amex, and Nasdaq stocks (Rm) and the one-month Treasury bill yield (Rf), January 1982 – May 2002. The intercept in this regression, ai , is known as “Jensen’s alpha” (1968) and it measures the average difference between the monthly return to the DFA fund and the return predicted by the CAPM. (Rit – Rft) = ai + bi (Rmt – Rft) + eit The last row shows the performance of the DFA US 6-10 Value Portfolio from January 1994 – May 2002. Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Period ai t(ai = 0) bi t(bi = 1) DFA 9-10 Small Company Portfolio 1982-2002 0.0020 0.67 1.033 0.68 1982-1987 -0.0019 -0.44 1.000 0.00 1988-1993 0.0038 0.80 1.104 1.21 1994-2002 0.0035 0.66 1.013 0.15 DFA US 6-10 Value Portfolio 1994-2002 -0.0022 -0.59 0.816 -2.14
Schwert--Anomalies and Market Efficiency > Table 2 shows estimates of the turn-of-the-year effect for the period 1962-2001,as well as for the 1962-1979 period analyzed by Reinganum(1983),and the subsequent 1980-1989 and 1990-2001 sample periods.The dependent variable is the difference in the daily return to the CRSP NYSE small-firm portfolio (decile 1)and the return to the CRSP NYSE large-firm portfolio(decile 10),(RIt-Riot).The independent variable,January,equals one when the daily return occurs during the first 15 calendar days of January,and zero otherwise.Thus,the coefficient aj measures the difference between the average daily return during the first 15 calendar days of January and the rest of the year.If small firms earn higher average returns than large firms during the first half of January,a should be reliably positive. Unlike the results in Table 1,it does not seem that the turn-of-the-year anomaly has completely disappeared since it was originally documented.The estimates of the turn-of-the- year coefficient au are around 0.4%per day over the periods 1980-1989 and 1990-2001,which is about half the size of the estimate over the 1962-1979 period of 0.8%.Thus,while the effect is smaller than observed by Keim(1983)and Reinganum(1983),it is still reliably positive. Interestingly,Booth and Keim (2000)have shown that the turn-of-the-year anomaly is not reliably different from zero in the returns to the DFA 9-10 portfolio over the period 1982- 1995.They conclude that the restrictions placed on the DFA fund(no stocks trading at less than $2 per share or with less than $10 million in equity capitalization,and no stocks whose IPO was less than one year ago)explain the difference between the behavior of the CRSP small-firm portfolio and the DFA portfolio.Thus,it is the lowest-priced and least-liquid stocks that apparently explain the turn-of-the-year anomaly.This raises the possibility that market microstructure effects,especially the costs of illiquidity,play an important role in explaining some anomalies(see Chapters 12(Stoll)and 21 (Easley and O'Hara))
Schwert -- Anomalies and Market Efficiency 7 Table 2 shows estimates of the turn-of-the-year effect for the period 1962-2001, as well as for the 1962-1979 period analyzed by Reinganum (1983), and the subsequent 1980-1989 and 1990-2001 sample periods. The dependent variable is the difference in the daily return to the CRSP NYSE small-firm portfolio (decile 1) and the return to the CRSP NYSE large-firm portfolio (decile 10), (R1t - R10t). The independent variable, January, equals one when the daily return occurs during the first 15 calendar days of January, and zero otherwise. Thus, the coefficient aJ measures the difference between the average daily return during the first 15 calendar days of January and the rest of the year. If small firms earn higher average returns than large firms during the first half of January, aJ should be reliably positive. Unlike the results in Table 1, it does not seem that the turn-of-the-year anomaly has completely disappeared since it was originally documented. The estimates of the turn-of-theyear coefficient aJ are around 0.4% per day over the periods 1980-1989 and 1990-2001, which is about half the size of the estimate over the 1962-1979 period of 0.8%. Thus, while the effect is smaller than observed by Keim (1983) and Reinganum (1983), it is still reliably positive. Interestingly, Booth and Keim (2000) have shown that the turn-of-the-year anomaly is not reliably different from zero in the returns to the DFA 9-10 portfolio over the period 1982- 1995. They conclude that the restrictions placed on the DFA fund (no stocks trading at less than $2 per share or with less than $10 million in equity capitalization, and no stocks whose IPO was less than one year ago) explain the difference between the behavior of the CRSP small-firm portfolio and the DFA portfolio. Thus, it is the lowest-priced and least-liquid stocks that apparently explain the turn-of-the-year anomaly. This raises the possibility that market microstructure effects, especially the costs of illiquidity, play an important role in explaining some anomalies (see Chapters 12 (Stoll) and 21 (Easley and O’Hara))
Schwert--Anomalies and Market Efficiency 8 Table 2 Small Firm/Turn-of-the-Year Effect,Daily Returns,1962-2001 (Rit -Riot)=ao a Januaryt+ Rit is the return to the CRSP NYSE small-firm portfolio (decile 1)and Riot is the return to the CRSP NYSE large-firm portfolio (decile 10).January 1 when the daily return occurs during the first 15 calendar days of January,and zero otherwise.The coefficient of January measures the difference in average return between small-and large-firm portfolios during the first two weeks of the year versus other days in the year.Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Period 00 t(00=0) 0 t(0=0) 1962-2001 -0.00007 -0.92 0.00641 9.87 1962-1979 0.00009 0.97 0.00815 7.14 1980-1989 -0.00014 -0.73 0.00433 4.55 1990-2001 -0.00026 -1.72 0.00565 5.37 The Weekend Effect French (1980)observed another calendar anomaly.He noted that the average return to the Standard Poor's(S&P)composite portfolio was reliably negative over weekends in the period 1953-1977.Table 3 shows estimates of the weekend effect from February 1885 to May 2002,as well as for the 1953-1977 period analyzed by French(1980)and the 1885-1927,1928- 1952,and 1978-2002 sample periods not included in French's study.The dependent variable is the daily return to a broad portfolio of U.S.stocks.For the 1885-1927 period,the Schwert (1990)portfolio based on Dow Jones indexes is used.For 1928-2002,the S&P composite
Schwert -- Anomalies and Market Efficiency 8 Table 2 Small Firm/Turn-of-the-Year Effect, Daily Returns, 1962-2001 (R1t - R10t) = a0 + aJ Januaryt + et R1t is the return to the CRSP NYSE small-firm portfolio (decile 1) and R10t is the return to the CRSP NYSE large-firm portfolio (decile 10). January = 1 when the daily return occurs during the first 15 calendar days of January, and zero otherwise. The coefficient of January measures the difference in average return between small- and large-firm portfolios during the first two weeks of the year versus other days in the year. Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Period a0 t(a0 = 0) aJ t(aJ = 0) 1962-2001 -0.00007 -0.92 0.00641 9.87 1962-1979 0.00009 0.97 0.00815 7.14 1980-1989 -0.00014 -0.73 0.00433 4.55 1990-2001 -0.00026 -1.72 0.00565 5.37 The Weekend Effect French (1980) observed another calendar anomaly. He noted that the average return to the Standard & Poor's (S&P) composite portfolio was reliably negative over weekends in the period 1953-1977. Table 3 shows estimates of the weekend effect from February 1885 to May 2002, as well as for the 1953-1977 period analyzed by French (1980) and the 1885-1927, 1928- 1952, and 1978-2002 sample periods not included in French’s study. The dependent variable is the daily return to a broad portfolio of U.S. stocks. For the 1885-1927 period, the Schwert (1990) portfolio based on Dow Jones indexes is used. For 1928-2002, the S&P composite