Schwert--Anomalies and Market Efficiency 14 Table 4 Momentum Effects,1927-2001 UMD:=a+B(Rmt-Ra)+s SMB:+h HML+ UMD,is the return to a portfolio that is long stocks with high returns and short stocks with low returns in recent months(months-13 through-2).The market risk premium is measured as the difference in return between the CRSP value-weighted portfolio of NYSE,Amex and Nasdag stocks(Rm)and the one-month Treasury bill yield(R).SMB,is the difference between the returns to portfolios of small-and large- capitalization firms,holding constant the B/M ratios for these stocks,and HML is the difference between the returns to portfolios of high and low B/M ratio firms,holding constant the capitalization for these stocks.Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Sample Period Size,T t(a=0) B t(B=0) t(s=0) h th=0) Single-Factor CAPM Benchmark 1926- 2001 900 0.0095 6.98 -0.280 -3.48 1926- 1964 456 0.0100 5.33 -0.415 -4.06 1965- 1989 300 0.0082 4.00 0.016 0.22 1926- 1989 756 0.0091 6.37 -0.303 -3.50 1990- 2001 144 0.0107 2.71 -0.063 -0.56 Three-Factor Fama-French Benchmark 1926- 2001 900 0.01108.25 -0.193 -3.75 -0.102 -1.14 -0.484 -4.65 1926- 1964 456 0.0103 5.72 -0.204 -3.45 -0.137 -0.95 -0.525 -3.67 1965- 1989 300 0.0100 4.61 -0.010 -0.13 -0.132 -1.17 -0.276 -2.08 1926- 1989 756 0.0107 7.77 -0.170 -3.27 -0.128 -1.25 -0.519 -4.50 1990- 2001 144 0.0123 2.95 -0.201 -1.83 0.093 0.54 -0.245 -1.35
Schwert -- Anomalies and Market Efficiency 14 Table 4 Momentum Effects, 1927 – 2001 UMDt = a + b (Rmt – Rft) + s SMBt + h HMLt + et UMDt is the return to a portfolio that is long stocks with high returns and short stocks with low returns in recent months (months -13 through -2). The market risk premium is measured as the difference in return between the CRSP value-weighted portfolio of NYSE, Amex and Nasdaq stocks (Rm) and the one-month Treasury bill yield (Rf). SMBt is the difference between the returns to portfolios of small- and largecapitalization firms, holding constant the B/M ratios for these stocks, and HMLt is the difference between the returns to portfolios of high and low B/M ratio firms, holding constant the capitalization for these stocks. Heteroskedasticity-consistent standard errors are used to compute the t-statistics. Sample Period Sample Size, T a t(a=0) b t(b=0) s t(s=0) h t(h=0) Single-Factor CAPM Benchmark 1926- 2001 900 0.0095 6.98 -0.280 -3.48 1926- 1964 456 0.0100 5.33 -0.415 -4.06 1965- 1989 300 0.0082 4.00 0.016 0.22 1926- 1989 756 0.0091 6.37 -0.303 -3.50 1990- 2001 144 0.0107 2.71 -0.063 -0.56 Three-Factor Fama-French Benchmark 1926- 2001 900 0.0110 8.25 -0.193 -3.75 -0.102 -1.14 -0.484 -4.65 1926- 1964 456 0.0103 5.72 -0.204 -3.45 -0.137 -0.95 -0.525 -3.67 1965- 1989 300 0.0100 4.61 -0.010 -0.13 -0.132 -1.17 -0.276 -2.08 1926- 1989 756 0.0107 7.77 -0.170 -3.27 -0.128 -1.25 -0.519 -4.50 1990- 2001 144 0.0123 2.95 -0.201 -1.83 0.093 0.54 -0.245 -1.35
Schwert--Anomalies and Market Efficiency 15 Fama and French (1996)noted that their three-factor model does not explain the momentum effect,since the intercepts in the bottom panel of Table 4 are all reliably positive.In fact,the intercepts from the three-factor models are larger than from the single-factor CAPM model in the upper panel. Lewellen(2002)has presented evidence that portfolios of stocks sorted on size and B/M characteristics have similar momentum effects as those seen by Jegadeesh and Titman (1993, 2001)and Fama and French (1996).He argues that the existence of momentum in large diversified portfolios makes it unlikely that behavioral biases in information processing are likely to explain the evidence on momentum. Brennan,Chordia,and Subrahmanyam (1998)found that size and B/M characteristics do not explain differences in average returns,given the Fama and French three-factor model.Like Fama and French (1996),they found that the Fama-French model does not explain the momentum effect.Finally,they found a negative relation between average returns and recent past dollar trading volume.They argue that this reflects a relation between expected returns and liquidity as suggested by Amihud and Mendelson (1986)and Brennan and Subrahmanyam (1996). Thus,while many of the systematic differences in average returns across stocks can be explained by the three-factor characterization of Fama and French(1993),momentum cannot. Interestingly,the average returns to index funds that were created to mimic the size and value strategies discussed above have not matched up to the historical estimates,as shown in Table 1. The evidence on the momentum effect seems to persist,but may reflect predictable variation in risk premiums that are not yet understood
Schwert -- Anomalies and Market Efficiency 15 Fama and French (1996) noted that their three-factor model does not explain the momentum effect, since the intercepts in the bottom panel of Table 4 are all reliably positive. In fact, the intercepts from the three-factor models are larger than from the single-factor CAPM model in the upper panel. Lewellen (2002) has presented evidence that portfolios of stocks sorted on size and B/M characteristics have similar momentum effects as those seen by Jegadeesh and Titman (1993, 2001) and Fama and French (1996). He argues that the existence of momentum in large diversified portfolios makes it unlikely that behavioral biases in information processing are likely to explain the evidence on momentum. Brennan, Chordia, and Subrahmanyam (1998) found that size and B/M characteristics do not explain differences in average returns, given the Fama and French three-factor model. Like Fama and French (1996), they found that the Fama-French model does not explain the momentum effect. Finally, they found a negative relation between average returns and recent past dollar trading volume. They argue that this reflects a relation between expected returns and liquidity as suggested by Amihud and Mendelson (1986) and Brennan and Subrahmanyam (1996). Thus, while many of the systematic differences in average returns across stocks can be explained by the three-factor characterization of Fama and French (1993), momentum cannot. Interestingly, the average returns to index funds that were created to mimic the size and value strategies discussed above have not matched up to the historical estimates, as shown in Table 1. The evidence on the momentum effect seems to persist, but may reflect predictable variation in risk premiums that are not yet understood
Schwert--Anomalies and Market Efficiency 16 2.2 Predictable Differences in Returns Through Time In the early years of the efficient markets literature,the random walk model,in which returns should not be autocorrelated,was often confused with the hypothesis of market efficiency (see,for example,Black (1971)).Fama(1970,1976)made clear that the assumption of constant equilibrium expected returns over time is not a part of the efficient markets hypothesis,although that assumption worked well as a rough approximation in many of the early efficient markets tests. Since then,many papers have documented a small degree of predictability in stock returns based on prior information.Examples include Fama and Schwert (1977)[short-term interest rates],Keim and Stambaugh(1986)[spreads between high-risk corporate bond yields and short-term interest rates],Campbell(1987)[spreads between long-and short-term interest rates],French,Schwert,and Stambaugh (1987)[stock volatility],Fama and French (1988) [dividend yields on aggregate stock portfolios],and Kothari and Shanken (1997)[book-to- market ratios on aggregate stock portfolios].Recently,Baker and Wurgler(2000)have shown that the proportion of new securities issues that are equity issues is a negative predictor of future equity returns over the period 1928-1997. An obvious question given evidence of the time-series predictability of returns is whether this is evidence of market inefficiency,or simply evidence of time-varying equilibrium expected returns.Fama and Schwert(1977)found weak evidence that excess returns to the CRSP value- weighted portfolio of NYSE stocks (in excess of the one-month Treasury bill yield)are predictably negative.Many subsequent papers have used similar metrics to judge whether the evidence of time variation in expected returns seems to imply profitable trading strategies.I am not aware of a paper that claims to find strong evidence that excess stock returns have been
Schwert -- Anomalies and Market Efficiency 16 2.2 Predictable Differences in Returns Through Time In the early years of the efficient markets literature, the random walk model, in which returns should not be autocorrelated, was often confused with the hypothesis of market efficiency (see, for example, Black (1971)). Fama (1970, 1976) made clear that the assumption of constant equilibrium expected returns over time is not a part of the efficient markets hypothesis, although that assumption worked well as a rough approximation in many of the early efficient markets tests. Since then, many papers have documented a small degree of predictability in stock returns based on prior information. Examples include Fama and Schwert (1977) [short-term interest rates], Keim and Stambaugh (1986) [spreads between high-risk corporate bond yields and short-term interest rates], Campbell (1987) [spreads between long- and short-term interest rates], French, Schwert, and Stambaugh (1987) [stock volatility], Fama and French (1988) [dividend yields on aggregate stock portfolios], and Kothari and Shanken (1997) [book-tomarket ratios on aggregate stock portfolios]. Recently, Baker and Wurgler (2000) have shown that the proportion of new securities issues that are equity issues is a negative predictor of future equity returns over the period 1928-1997. An obvious question given evidence of the time-series predictability of returns is whether this is evidence of market inefficiency, or simply evidence of time-varying equilibrium expected returns. Fama and Schwert (1977) found weak evidence that excess returns to the CRSP valueweighted portfolio of NYSE stocks (in excess of the one-month Treasury bill yield) are predictably negative. Many subsequent papers have used similar metrics to judge whether the evidence of time variation in expected returns seems to imply profitable trading strategies. I am not aware of a paper that claims to find strong evidence that excess stock returns have been