Our results are disturbing in that, like Fama and French (1992), they sug-
gest that traditional measures of risk do not determine expected returns. In
equilibrium asset pricing models the covariance structure of returns deter-
mine expected returns. Yet we find that variables that reliably predict the
future covariance structure do not predict future returns. Our results indi-
cate that high B/M stocks and stocks with low capitalizations have high av-
erage returns whether or not they have the return patterns (i.e., covariances)
of other high B/M and small stocks. Similarly, after controlling for size and
B/M ratios, a common share that “acts like” a bond (i.e., has a low market
beta) has the same expected return as other common shares with high mar-
ket betas.
The article is organized as follows: In section 1 we reexamine the return
characteristics of portfolios of stocks sorted on size and B/M, paying partic-
ular attention to seasonalities in these returns, something that is important
in our later analysis. In section 2 we present a simple, purely descriptive,
return-generating model that provides some structure to our discussion of
the empirical evidence presented in sections 3 and 4. The model also pro-
vides some insights about why the Fama and French (1993) tests might fail
to reject the factor pricing model when the model is incorrect, and why a
factor analysis test, like the tests presented in Roll (1994), might falsely re-
ject a factor pricing model. In section 3 we present evidence on one feature
of this model, that there is no additional factor risk associated with high
B/M firms. Then in section 4 we perform a set of empirical tests on another
implication of our descriptive model, showing that, after controlling for
firm characteristics, estimated factor loadings do not explain returns. Sec-
tion 5 concludes the article.
1.A Summary of the Return Patterns of Size and
Book-to-Market Sorted PortfoliosIn this section we reexamine the return patterns of size and B/M sorted
portfolios. What we show is that there are important interactions between
the size and B/M effects and that the return patterns are different in Janu-
ary and non-January months. As we later discuss, both of these observa-
tions play important roles in our research design.
Panel A of table 9.1 presents the mean excess returns for the twenty-five
size/book-to-market sorted portfolios from Fama and French (1993), over
the period 63:07 to 93:12.^6 These portfolios are based on unconditional sorts
using New York Stock Exchange (NYSE) breakpoints. Therefore, for exam-
ple, the small/low B/M portfolio is that set of firms included on NYSE/Amex
or Nasdaq that have B/M ratios in the range of the lowest quintile of NYSE
320 DANIEL AND TITMAN
(^6) We wish to thank Eugene Fama and Kenneth French for supplying the portfolio returns.
The construction of these portfolios is described in detail in Fama and French (1993).