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