postformation factor loadings. In table 9.5, we report the results of regress-
ing the postformationexcess returns for each of the forty-five portfolios on
an intercept and on the returns of the zero-investment Mkt, HML, and
SMB portfolios.
We see in table 9.5 that the HML coefficients are clearly different for the
different B/M groups, as they should be: we know that, unconditionally,
B/M ratios and HML loadings should be highly correlated. But the important
thing for us is that within a book-to-market/size grouping, the sort on the
preformationHML factor loadings produces a monotonic ordering of the
postformationfactor loadings. Moreover, there appears to be a highly sig-
nificant difference between the loadings of the low and high factor-loading
portfolios, something we shall verify shortly.^22
We are especially interested in the estimated intercepts. Models 1 and 2
predict that the regression intercepts (αs) should be zero, while Model 3
suggests that the mean returns of the portfolios should depend only on
characteristics (size and B/M), and should be independent of variation in
the factor loadings. Hence, Model 3 also predicts that the αs of the low
factor-loading portfolios should be positive and that those of the high
factor-loading portfolios should be negative. The αs reported in table 9.5
indicate that this is generally the case. Only one of the nine high loading
portfolios (see column 5) has a positive αand only two of the low loading
portfolios (see column 1) has a negative α. Furthermore, the average αfor
factor loading portfolio 1 is 0.02 percent per month, and for factor loading
338 DANIEL AND TITMAN
Table 9.5(cont.)Char Port Factor Loading Portfolio Factor Loading Portfolio
B/M SZ 1 2 3 4 51 2 345
βˆMkt t(βˆMkt)11 1.12 1.03 1.07 1.04 1.15 33.32 32.30 38.04 36.38 29.66
12 1.14 1.03 1.03 1.07 1.08 28.90 38.38 38.90 39.26 39.07
13 0.99 0.98 0.95 1.04 1.04 30.72 36.77 33.61 38.47 36.39
21 0.99 0.93 0.95 0.95 1.08 35.45 45.11 48.49 41.54 34.84
22 1.06 0.96 0.94 1.01 1.06 33.42 35.91 37.40 41.19 39.56
23 0.97 1.02 0.96 1.04 1.07 25.56 28.22 29.97 31.22 30.42
31 1.01 0.92 0.94 1.05 1.17 39.10 39.96 45.23 46.16 34.94
32 1.05 0.99 0.98 1.02 1.20 32.59 32.78 32.32 32.82 27.74
33 1.02 1.03 0.99 1.03 1.15 25.81 31.25 26.97 27.20 24.96
Average 1.04 0.99 0.98 1.03 1.11 31.65 35.63 36.77 37.14 33.06
(^22) We note that the dispersion in preformationfactor-loadings is considerably greater. This
is because the preformationfactor loading dispersion is due to both measurement error effects
and the actual variation in factor-loadings. The postformationdispersion results almost exclu-
sively from true variation in the loadings.