Schwert--Anomalies and Market Efficiency 9 portfolio is used.The independent variable,Weekend,equals one when the daily return spans a weekend (e.g.,Friday to Monday),and zero otherwise.Thus,the coefficient aw measures the difference between the average daily return over weekends and the other days of the week.If weekend returns are reliably lower than returns on other days of the week,aw should be reliably negative (and the sum of ao aw should be reliably negative to confirm French's (1980) results). The results for 1953-1977 replicate the results in French (1980).The estimate of the weekend effect for 1928-1952 is even more negative,as previously noted by Keim and Stambaugh(1984).The estimate of the weekend effect from 1885-1927 is smaller,about half the size for 1953-1977 and about one-third the size for 1928-1952,but still reliably negative. Interestingly,the estimate of the weekend effect since 1978 is not reliably different from the other days of the week.While the point estimate of aw is negative from 1978-2002,it is about one-quarter as large as the estimate for 1953-1977,and it is not reliably less than zero.The estimate of the average return over weekends is the sum ao aw,which is essentially zero for 1978-2002 Thus,like the size effect,the weekend effect seems to have disappeared,or at least substantially attenuated,since it was first documented in 1980. The Value Effect Around the same time as early size effect papers,Basu(1977,1983)noted that firms with high earnings-to-price(E/P)ratios earn positive abnormal returns relative to the CAPM.Many subsequent papers have noted that positive abnormal returns seem to accrue to portfolios of stocks with high dividend yields(D/P)or to stocks with high book-to-market(B/M)values
Schwert -- Anomalies and Market Efficiency 9 portfolio is used. The independent variable, Weekend, equals one when the daily return spans a weekend (e.g., Friday to Monday), and zero otherwise. Thus, the coefficient aW measures the difference between the average daily return over weekends and the other days of the week. If weekend returns are reliably lower than returns on other days of the week, aW should be reliably negative (and the sum of a0 + aW should be reliably negative to confirm French’s (1980) results). The results for 1953-1977 replicate the results in French (1980). The estimate of the weekend effect for 1928-1952 is even more negative, as previously noted by Keim and Stambaugh (1984). The estimate of the weekend effect from 1885-1927 is smaller, about half the size for 1953-1977 and about one-third the size for 1928-1952, but still reliably negative. Interestingly, the estimate of the weekend effect since 1978 is not reliably different from the other days of the week. While the point estimate of aW is negative from 1978-2002, it is about one-quarter as large as the estimate for 1953-1977, and it is not reliably less than zero. The estimate of the average return over weekends is the sum a0 + aW, which is essentially zero for 1978-2002. Thus, like the size effect, the weekend effect seems to have disappeared, or at least substantially attenuated, since it was first documented in 1980. The Value Effect Around the same time as early size effect papers, Basu (1977, 1983) noted that firms with high earnings-to-price (E/P) ratios earn positive abnormal returns relative to the CAPM. Many subsequent papers have noted that positive abnormal returns seem to accrue to portfolios of stocks with high dividend yields (D/P) or to stocks with high book-to-market (B/M) values
Schwert--Anomalies and Market Efficiency 10 Table 3 Day-of-the-Week Effects in the U.S.Stock Returns, February 1885-May 2002 Rt =ao+aw Weekendt +t Weekend 1 when the return spans Sunday (e.g.,Friday to Monday),and zero otherwise.The coefficient of Weekend measures the difference in average return over the weekend versus other days of the week.From 1885-1927,Dow Jones portfolios are used(see Schwert(1990)).From 1928-May 2002,the Standard Poor's composite portfolio is used.Heteroskedasticity- consistent standard errors are used to compute the t-statistics. Sample Period 00 t(00=0) aw t(aw=0) 1885-2002 0.0005 8.52 -0.0017 -10.13 1885-1927 0.0004 4.46 -0.0013 -4.96 1928-1952 0.0007 3.64 -0.0030 -6.45 1953-1977 0.0007 6.80 -0.0023 -8.86 1978-2002 0.0005 4.00 -0.0005 -1.37 Ball (1978)made the important observation that such evidence was likely to indicate a fault in the CAPM rather than market inefficiency,because the characteristics that would cause a trader following this strategy to add a firm to his or her portfolio would be stable over time and easy to observe.In other words,turnover and transactions costs would be low and information collection costs would be low.If such a strategy earned reliable"abnormal"returns,it would be available to a large number of potential arbitrageurs at a very low cost. More recently,Fama and French (1992,1993)have argued that size and value (as measured by the book-to-market value of common stock)represent two risk factors that are
Schwert -- Anomalies and Market Efficiency 10 Table 3 Day-of-the-Week Effects in the U.S. Stock Returns, February 1885 – May 2002 Rt = a0 + aW Weekendt + et Weekend = 1 when the return spans Sunday (e.g., Friday to Monday), and zero otherwise. The coefficient of Weekend measures the difference in average return over the weekend versus other days of the week. From 1885-1927, Dow Jones portfolios are used (see Schwert (1990)). From 1928-May 2002, the Standard & Poor’s composite portfolio is used. Heteroskedasticityconsistent standard errors are used to compute the t-statistics. Sample Period a0 t(a0 = 0) aW t(aW = 0) 1885-2002 0.0005 8.52 -0.0017 -10.13 1885-1927 0.0004 4.46 -0.0013 -4.96 1928-1952 0.0007 3.64 -0.0030 -6.45 1953-1977 0.0007 6.80 -0.0023 -8.86 1978-2002 0.0005 4.00 -0.0005 -1.37 Ball (1978) made the important observation that such evidence was likely to indicate a fault in the CAPM rather than market inefficiency, because the characteristics that would cause a trader following this strategy to add a firm to his or her portfolio would be stable over time and easy to observe. In other words, turnover and transactions costs would be low and information collection costs would be low. If such a strategy earned reliable “abnormal” returns, it would be available to a large number of potential arbitrageurs at a very low cost. More recently, Fama and French (1992, 1993) have argued that size and value (as measured by the book-to-market value of common stock) represent two risk factors that are
Schwert--Anomalies and Market Efficiency 11 missing from the CAPM.In particular,they suggest using regressions of the form: (Rit-Ra)=ai+Bi(Rmt-RA)+si SMBt+hi HMLt +Sit (2) to measure abnormal performance,ai.In(2),SMB represents the difference between the returns to portfolios of small-and large-capitalization firms,holding constant the B/M ratios for these stocks,and HML represents the difference between the returns to portfolios of high and low B/M ratio firms,holding constant the capitalization for these stocks.Thus,the regression coefficients si and hi represent exposures to size and value risk in much the same way that Bi measures the exposure to market risk. Fama and French(1993)used their three-factor model to explore several of the anomalies that have been identified in earlier literature,where the test of abnormal returns is based on whether ai=0 in(2).They found that abnormal returns from the three-factor model in (2)are not reliably different from zero for portfolios of stocks sorted by:equity capitalization,B/M ratios,dividend yield,or earnings-to-price ratios.The largest deviations from their three-factor model occur in the portfolio of low B/M(i.e.,growth)stocks,where small-capitalization stocks have returns that are too low and large-capitalization stocks have returns that are too high (ai> 0). Fama and French (1996)extended the use of their three-factor model to explain the anomalies studied by Lakonishok,Shleifer,and Vishny (1994).They found no estimates of abnormal performance in (2)that are reliably different from zero based on variables such as B/M,E/P,cash flow over price(C/P),and the rank of past sales growth rates. In 1993,Dimensional Fund Advisors (DFA)began a mutual fund that focuses on small firms with high B/M ratios (the DFA US 6-10 Value Portfolio).Based on the results in Fama and French(1993),this portfolio would have earned significantly positive"abnormal"returns of
Schwert -- Anomalies and Market Efficiency 11 missing from the CAPM. In particular, they suggest using regressions of the form: (Rit – Rft) = ai + bi (Rmt – Rft) + si SMBt + hi HMLt + eit (2) to measure abnormal performance, ai . In (2), SMB represents the difference between the returns to portfolios of small- and large-capitalization firms, holding constant the B/M ratios for these stocks, and HML represents the difference between the returns to portfolios of high and low B/M ratio firms, holding constant the capitalization for these stocks. Thus, the regression coefficients si and hi represent exposures to size and value risk in much the same way that bi measures the exposure to market risk. Fama and French (1993) used their three-factor model to explore several of the anomalies that have been identified in earlier literature, where the test of abnormal returns is based on whether ai = 0 in (2). They found that abnormal returns from the three-factor model in (2) are not reliably different from zero for portfolios of stocks sorted by: equity capitalization, B/M ratios, dividend yield, or earnings-to-price ratios. The largest deviations from their three-factor model occur in the portfolio of low B/M (i.e., growth) stocks, where small-capitalization stocks have returns that are too low and large-capitalization stocks have returns that are too high (ai > 0). Fama and French (1996) extended the use of their three-factor model to explain the anomalies studied by Lakonishok, Shleifer, and Vishny (1994). They found no estimates of abnormal performance in (2) that are reliably different from zero based on variables such as B/M, E/P, cash flow over price (C/P), and the rank of past sales growth rates. In 1993, Dimensional Fund Advisors (DFA) began a mutual fund that focuses on small firms with high B/M ratios (the DFA US 6-10 Value Portfolio). Based on the results in Fama and French (1993), this portfolio would have earned significantly positive “abnormal” returns of
Schwert--Anomalies and Market Efficiency 12 about 0.5%per month over the period 1963-1991 relative to the CAPM.The estimate of the abnormal return to the DFA Value portfolio from 1994-2002 in the last row of Table 1 is -0.2% per month,with a t-statistic of-0.59.Thus,as with the DFA US 9-10 Small Company Portfolio, the apparent anomaly that motivated the fund's creation seems to have disappeared,or at least attenuated. Davis,Fama,and French (2000)collected and analyzed B/M data from 1929 through 1963 to study a sample that does not overlap the data studied in Fama and French(1993).They found that the apparent premium associated with value stocks is similar in the pre-1963 data to the post-1963 evidence.They also found that the size effect is subsumed by the value effect in the earlier sample period.Fama and French(1998)have shown that the value effect exists in a sample covering 13 countries (including the U.S.)over the period 1975-1995.Thus,in samples that pre-date the publication of the original Fama and French(1993)paper,the evidence supports the existence of a value effect. Daniel and Titman(1997)have argued that size and M/B characteristics dominate the Fama-French size and B/M risk factors in explaining the cross-sectional pattern of average returns.They conclude that size and M/B are not risk factors in an equilibrium pricing model. However,Davis,Fama,and French(2000)found that Daniel and Titman's results do not hold up outside their sample period. The Momentum Effect Fama and French (1996)have also tested two versions of momentum strategies. DeBondt and Thaler (1985)found an anomaly whereby past losers (stocks with low returns in the past three to five years)have higher average returns than past winners (stocks with high returns in the past three to five years),which is a "contrarian"effect.On the other hand
Schwert -- Anomalies and Market Efficiency 12 about 0.5% per month over the period 1963-1991 relative to the CAPM. The estimate of the abnormal return to the DFA Value portfolio from 1994-2002 in the last row of Table 1 is -0.2% per month, with a t-statistic of -0.59. Thus, as with the DFA US 9-10 Small Company Portfolio, the apparent anomaly that motivated the fund’s creation seems to have disappeared, or at least attenuated. Davis, Fama, and French (2000) collected and analyzed B/M data from 1929 through 1963 to study a sample that does not overlap the data studied in Fama and French (1993). They found that the apparent premium associated with value stocks is similar in the pre-1963 data to the post-1963 evidence. They also found that the size effect is subsumed by the value effect in the earlier sample period. Fama and French (1998) have shown that the value effect exists in a sample covering 13 countries (including the U.S.) over the period 1975-1995. Thus, in samples that pre-date the publication of the original Fama and French (1993) paper, the evidence supports the existence of a value effect. Daniel and Titman (1997) have argued that size and M/B characteristics dominate the Fama-French size and B/M risk factors in explaining the cross-sectional pattern of average returns. They conclude that size and M/B are not risk factors in an equilibrium pricing model. However, Davis, Fama, and French (2000) found that Daniel and Titman’s results do not hold up outside their sample period. The Momentum Effect Fama and French (1996) have also tested two versions of momentum strategies. DeBondt and Thaler (1985) found an anomaly whereby past losers (stocks with low returns in the past three to five years) have higher average returns than past winners (stocks with high returns in the past three to five years), which is a “contrarian” effect. On the other hand
Schwert--Anomalies and Market Efficiency 13 Jegadeesh and Titman (1993)found that recent past winners(portfolios formed on the last year of past returns)out-perform recent past losers,which is a "continuation"or "momentum"effect. Using their three-factor model in (2),Fama and French found no estimates of abnormal performance that are reliably different from zero based on the long-term reversal strategy of DeBondt and Thaler (1985),which they attribute to the similarity of past losers and small distressed firms.On the other hand,Fama and French are not able to explain the short-term momentum effects found by Jegadeesh and Titman(1993)using their three-factor model.The estimates of abnormal returns are strongly positive for short-term winners. Table 4 shows estimates of the momentum effect using both the CAPM benchmark in(1) and the Fama-French three-factor benchmark in (2).The measure of momentum is the difference between the returns to portfolios of high and low prior return firms,UMD,where prior returns are measured over months-2 to-13 relative to the month in question.'The sample periods shown are the 1965-1989 period used by Jegadeesh and Titman (1993),the 1927-1964 period that preceded their sample,the 1990-2001 period that occurred after their paper was published,and the overall 1927-2001 period.Compared with the CAPM benchmark in the top panel of Table 4,the momentum effect seems quite large and reliable.The intercept a is about 1%per month,with t-statistics between 2.7 and 7.0.In fact,the smallest estimate of abnormal returns occurs in the 1965-1989 period used by Jegadeesh and Titman (1993)and the largest estimate occurs in the 1990-2001 sample after their paper was published.6 SThis Fama-French momentum factor for the period 1927-2001 is available from Ken French's web site, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F Momentum Factor.zip. Jegadeesh and Titman(2001)also show that the momentum effect remains large in the post 1989 period.They tentatively conclude that momentum effects may be related to behavioral biases of investors
Schwert -- Anomalies and Market Efficiency 13 Jegadeesh and Titman (1993) found that recent past winners (portfolios formed on the last year of past returns) out-perform recent past losers, which is a “continuation” or “momentum” effect. Using their three-factor model in (2), Fama and French found no estimates of abnormal performance that are reliably different from zero based on the long-term reversal strategy of DeBondt and Thaler (1985), which they attribute to the similarity of past losers and small distressed firms. On the other hand, Fama and French are not able to explain the short-term momentum effects found by Jegadeesh and Titman (1993) using their three-factor model. The estimates of abnormal returns are strongly positive for short-term winners. Table 4 shows estimates of the momentum effect using both the CAPM benchmark in (1) and the Fama-French three-factor benchmark in (2). The measure of momentum is the difference between the returns to portfolios of high and low prior return firms, UMD, where prior returns are measured over months -2 to -13 relative to the month in question.5 The sample periods shown are the 1965-1989 period used by Jegadeesh and Titman (1993), the 1927-1964 period that preceded their sample, the 1990-2001 period that occurred after their paper was published, and the overall 1927-2001 period. Compared with the CAPM benchmark in the top panel of Table 4, the momentum effect seems quite large and reliable. The intercept a is about 1% per month, with t-statistics between 2.7 and 7.0. In fact, the smallest estimate of abnormal returns occurs in the 1965-1989 period used by Jegadeesh and Titman (1993) and the largest estimate occurs in the 1990-2001 sample after their paper was published.6 5This Fama-French momentum factor for the period 1927-2001 is available from Ken French’s web site, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Momentum_Factor.zip. 6 Jegadeesh and Titman (2001) also show that the momentum effect remains large in the post 1989 period. They tentatively conclude that momentum effects may be related to behavioral biases of investors