the risk-free rate except for the zero investment P1–P10 portfolio) on the
monthly returns of both the value-weighted index less the risk-free rate
(CAPM alpha) and the three Fama-French factors (Fama-French alpha).
The CAPM alpha for the winner minus loser portfolio is about the same as
the raw return difference since both winners and losers have about the
same betas. The Fama-French alpha is 1.36 percent, which is larger than
the corresponding raw return of 1.23 percent that Jegadeesh and Titman
(2001) report. This difference arises because the losers are more sensitive to
the Fama-French factors.
The results here indicate that the cross-sectional differences in expected
returns under the CAPM or the Fama-French three-factor model cannot ac-
count for the momentum profits. Of course, it is possible that these models
omit some priced factors and hence provide inadequate adjustments for dif-
ferences in risk. To circumvent the need for specifying an equilibrium asset
pricing model to determine the benchmarks, Conrad and Kaul (1998) as-
sume that unconditional returns are constant, and use the sample mean of
realized returns of each stock (including the ranking period returns) as their
measure of the stock’s expected return. Then, they use the decomposition in
Eq. (3) to examine the contribution of cross-sectional differences in ex-
pected returns (the first term on the right-hand side) to momentum profits.
They find that the cross-sectional variance of sample mean returns is close
to the momentum profits for the WRSS. This finding leads them to con-
clude erroneously that the observed momentum profits can be entirely ex-
plained by cross-sectional differences in expected returns rather than any
“time-series patterns in stock returns.”
Jegadeesh and Titman (2002), however, point out that while sample
mean is an unbiased estimate of unconditional expected return, the cross-
sectional variance of sample mean is not an unbiased estimate of the vari-
ance of true expected returns. Since sample means contain both expected
and unexpected components of returns, variance of sample mean is the sum
of the variances of these components. Consequently, the variance of sample
mean overstates the dispersion in true expected returns, and therefore, the
Conrad and Kaul approach overestimates the contribution the first term on
the right-hand side in (3).
Jegadeesh and Titman (2002) address this bias in detail and suggest a few
alternatives to avoid the bias. In one of their tests, they use the sample aver-
age returns outside the ranking and holding periods to obtain unbiased esti-
mates of unconditional expected returns during the holding period. They
find that with this estimate, cross-sectional differences in expected holding-
period returns explain virtually none of the momentum profits.^4 Their addi-
tional tests also confirm this conclusion.
MOMENTUM 365(^4) Also see Grundy and Martin (2001).