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Disentangling Equity Return Regularities 57
systematic risk have been contrary to theory [see Tinic and
West (1986)]. We included a historical beta measure our in
model, not merely for risk adjustment, also but to explore the
payoff to beta when controlling for multiple anomalies. We
calculated beta for each security from the rolling 60-month
regression described previously. We then applied Vasicek‘s
(1973) Bayesian adjustment, in light of the well-known
tendency of historical betas to regress over time toward the
mean [see Klemkosky and Martin (1975)l.
CO-skewness. Investors may prefer positive skewness in their
portfolios. Because the market has positive skewness, investor
might pay more for securities having positive coskewness with
the market Waus and Litzenberger (1976)’ Friend and
Westerfield (1980)’ and Barone-Adesi (1985)].”We calculated
coskewness on a rolling 60-month basis
follows:
c
(Ri -Ri)(Rm -Rm)’
C (Rm
where R, is stock excess return, R,,, is the S&P 500 excess
return, and R,and R,are rolling 60-month arithmetic
averages.
Earnings controversy. Some maintain that stocks with more
uncertainty about future prospects produce superior returns,
perhaps as compensation for information deficiency or even
as a proxy for systematic risk [Cragg and Malkiel(1982),
Arnott (1983)’ and Carvell and Strebel (1984)]. We usedthe
standard deviation of next year’s analysts’ earnings estimates
normalized by stock price.
Trends in analysts’ earnings estimates. There is substantial
empirical support for the proposition that stocks whose
earnings estimates have been recently upgraded by analysts
tend to produce abnormal returns [Hawkins, Chamberlin,
and Daniel (1984), Kerrigan (1984), Arnott (1985), and Benesh
and Peterson (1986)l. Some possible explanations are
imperfect information dissemination and the psychology of
Wall Street analysts (notably, their “herd instinct” and
aversion to substantial earnings-estimate revisions). We