provide evidence against Model 3, and in support of the factor model.
Strikingly, the mean return of this portfolio is positive, even though the
portfolio’s market beta is −0.54. Here we again find that the characteristic
matters and not the factor loading. In other words a stock earns the
“stock” premium even if its return pattern is similar to that of a bond (i.e.,
it has a low βMkt).
These results are similar to the results reported by Fama and French
(1992) and Jegadeesh (1992), who show that, after controlling for size,
there is a slightly negative relationship with beta.^26 We also see from the last
row of the table that the three-factor model is rejected for this portfolio
with a t-statistic of 2.2.
D. Factor Loadings, Characteristics, Turnover, and Past ReturnsThe fact that there are stocks with similar capitalizations and B/M ratios
but very different factor loadings deserves further analysis. We do not find
this surprising, given that firms in very different industries can be similar
along these two dimensions. However, we would like to know if these dif-
ferences in factor loadings are significantly related to either trading volume
or returns in the recent past, since there is evidence suggesting that momen-
tum (Jegadeesh and Titman 1993) and liquidity (Amihud and Mendelson
1986) can be important predictors of stock returns.
One possibility is that the low factor-loading stocks are the less liquid
stocks. (Perhaps, the factor loadings of the less liquid stocks are underesti-
mated because their returns lag the returns of the more liquid stocks in the
344 DANIEL AND TITMAN
Table 9.8 (cont.)Char Port Mean Returns: Char-Balanced Portfolio: t-Statistics
B/M SZ 1 2 3 4 5 αˆ βˆMkt βˆSMB βHML R^2
11 0.69 0.73 0.81 0.63 0.49 0.73 −4.86 −0.14 4.19 24.61
12 0.91 0.86 0.70 0.67 0.52 2.98 −6.56 −3.74 1.43 30.54
13 0.54 0.31 0.39 0.35 0.22 2.20 −5.36 −5.46 −0.16 27.78
21 0.80 1.04 1.16 0.98 1.07 1.11 −9.76 −7.41 0.87 51.41
22 0.88 0.86 0.84 0.87 0.98 0.91 −8.22 −5.24 1.63 41.88
23 0.59 0.46 0.59 0.71 0.58 0.56 −7.16 −3.60 0.47 30.88
31 1.33 1.13 1.23 1.20 1.03 2.87 −10.89 −5.53 −0.03 49.85
32 1.06 1.36 0.95 1.31 0.84 1.66 −6.40 −4.95 1.53 33.44
33 0.77 0.73 0.89 1.00 0.74 0.60 −5.72 −4.63 0.59 27.70
Avg/coef 0.84 0.83 0.84 0.86 0.72 0.474 −0.540 −0.540 0.150
(t-stat) (2.19) (−10.78) (−6.87) (1.78)
(^26) Bear in mind, though, that we are looking at the market coefficient in a multiple regres-
sion, whereas the two cited articles use a univariate regression.