quintiles and the low B/M quintiles of the same size were more than 50
basis points (bp) per month over this period (except for the very largest
firms, where the difference is only 34 bp per month).^8 Across size quintiles,
the premia for the smallest quintile of firms over the largest is 30–50 bp per
month, except for the low B/M quintile where they are equal.
An analysis of these returns suggests that after controlling for B/M there
is more of a large firm rather than a small firm anomaly. Although the re-
turns are almost monotonic in size, there are no significant differences in
the returns of the small and medium size firms within any of the B/M
groupings. However, the largest quintile of firms do have significantly lower
returns than the rest, with this being especially true for the high B/M
stocks.^9 One implication of this is that a simple linear or log-linear regres-
sion of returns on capitalization and B/M ratios will not adequately charac-
terize observed stock returns. There are important interaction effects that
would be ignored in such a specification. For this reason, we will continue
our strategy of examining the return patterns of various characteristic-
sorted portfolios.
It is also possible that a factor structure could be artificially induced be-
cause of a common January seasonal. For this reason, we separately analyze
the returns of the size and B/M sorted portfolios in January and non-January
months. Panels B and C of table 9.1 give the mean returns of the same
twenty-five Fama and French portfolios, only now separated into January
and non-January months. This table shows that the size effect is almost
exclusively a January phenomenon and that the B/M phenomenon occurs
mainly in January for the larger firms, while the medium size and smaller
high B/M firms exhibit about a 3 percent return premium in January and
another 3 percent premium over the other eleven months. For the largest
quintile of firms, high B/M stocks exhibit the same 3 percent January pre-
mium over the returns of low B/M stocks; however, for these stocks, the
difference between the high and low B/M portfolio returns has been nega-
tive in the other eleven months.^10
2.A Model of the Return Generating ProcessIn this section we present three models that clarify the motivation for our
empirical tests. These should be viewed as purely descriptive models that
322 DANIEL AND TITMAN
(^8) Interestingly, we also find that the market-betas for both small and large high B/M stocks
are lower than for the corresponding low B/M stocks.
(^9) The contrast between this and what has typically been found in other studies is due to our
use of value-weighted portfolios. The very smallest firms do have larger returns, but these
firms are not heavily weighted in these portfolios.
(^10) Davis (1994) finds similar results. We note also that this is consistent with DeBondt and
Thaler (1985), although they look at past returns rather than B/M ratios.