McGraw-Hill

62 selecting Securities
pendent of other effects. We refer to the multivariate return
attributions as “pure” returns and to the univariate attributions as
“nake” returns. The univariate regressions nakely measure only
one anomaly at a time, with no effort to control for other related effects.
A single anomaly will often be a proxy for several related effects;
a multivariate anomaly framework properly attributes retur
to its underlying sources.
Table 2-1 presents summary statistics for the monthly crosssectional
regressions over the period January 1978 to December
1986. The average monthly retum and associated t-statistic for each
anomaly are shown in both nake and pure forms?* A paired t-test
on the difference between naYve and pure returns is also dis
played.% In several instances (notably residual reversals), the diffe
ence in returns is significant. These differences are due to the substantial
proxying that muddies the waters in simple univariate
regressions because of omitted-variable bias [see Kmenta (1971) pp.
392-395). A regression of retum on just casMow/price, for example,
may unintentionally pick up part of the low-P/E effect, as the
average correlation between a stock’s casMow/price and eamings/price
ratios is 0.65 for our sample.
The use of multivariate regression to disentangle highly corre
lated effects may, however, raise the specter of multicollinearity. Does
our use of so many closely related regressors somehow cause ineffiaency,
or are potential problems obviated by our large sample size?
One simple diagnostic test is a comparison of the timeseries standard
deviation of payoffs to each ndive versus pure anomaly. Because
”both strategies have the same standardized exposure.. . a reduction
in time-series variability can occur only if the risk reduction from immunizing
the effects of other common factors has exceeded the risk in
crease due to higher specific variance” [Rosenberg, Reid, htein and
(1985), p. 141” In fact, the time-series risk all of 25 anomalies is lower
in the multivariate regression, often by over 50 percent. Thus
multicollinearity is not a serious problem.
P/E and Size Effects
The results displayed in Table 2-1 reveal significant return regularities
during the period studied. First, P/E low paid off handsomely,
on average, from 1978 to 1986. The nake return attribution aver-