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90 selecting securities
35. For example, Arbel (1985) suggested that P/E might be a proxy for
neglect; Reinganum (1981~) and Banz and Breen (1986) found the
size effect to subsume P/E. Our results are more consistent with
those of Cook and Rozeff (1984) and Dowen and Bauman (1986),
who identify an independent P/E effect.
36. In fact, an arbitrary split of the sample period into two subperiods of
equal length reveals significantly different (at 1 the percent level)
pure return variances across time 8 for of our 25 anomaly measures,
and signihcantly different pure average monthly returns for of three
our measures. These frequencies of rejecting equality are, of course,
much greater than expected from chance alone at the 1 percent level
if the series were truly stationary. h F-test was used to check for
equality of variances across subperiods for each attribute. A
difference-of-means test was then performed using the stricter
Cochran criteria in those cases where equality of variances was
rejected. These tests were two-sided. For a discussion of these tests,
see Snedecor and Cochran (1967).
37. This contradicts Basu (1983), who found the P/E effect to subsume
the size effect. Consistent with our findings, however, all three
previously cited multifactor models indicate a significant size effect.
38. Brown, Kleidon, and Marsh (1983) document major time periods
when small size was deleterious to returns.
39. See Chan, Chen, and Hsieh.(1985) for an analysis of linkages
between the size effect and macroeconomic measures. Keimand See
Stambaugh (1986) for linkages to several ex ante risk premiw. For
analyses of various univariate retum effects and their
macroeconomic correlates, see Amott and Copeland (1985); for an
analysis with multivariate factors, see Marathe (1979). ‘
40. See BARRA Research Seminar, Berkeley, California, June 1986.
41. Lakonishok and Shapiro (1984) find that the size effect subsumes
returns to both beta and sigma. Tinic and West (1986) report that th
interaction of returns to beta, sigma, and size depends on whether or
not the month is January. We will examine January separately later.
Shape’s (1982) multifactor beta did accumulate significantly over
time; Reid’s (1982) multifactor beta also had a positive total payoff,
but a tstatistic test that was not quite sigruficant. In addition, Reid’s
model included co-skewness and sigma factors. His co-skewness
factor had a significantly positive accumulation; sigma had a
marginally significant negative payoff.
42. Nonstationarity of returns to systematic risk has been demonstrated
by Tini.c and West (1986).