B. Serial Covariance of Factor ReturnsJT examine whether the serial covariance of factor returns, the second term
in the decomposition given by Eq. (3), can explain momentum profits.
Under model (1), the serial covariance of an equally weighted portfolio of a
large number of stocks is:^5
(4)
If the serial covariance of factor returns were to contribute to momentum
profits, then the factor realizations should be positively serially correlated
(see Eq. [3]). Although the underlying factor is unobservable, Eq. (4) indi-
cates that the serial covariance of the equally weighted market index will
have the same sign as that of the common factor. JT examine this implica-
tion, and find that the serial covariance of six-month returns of the equally
weighted index is negative (−0.0028). Since the momentum strategy can
only benefit from positive serial covariance in factor returns, the finding
here indicates that the factor return serial covariance does not contribute to
momentum profits.
C. Lead-lag Effects and Momentum ProfitsIn addition to the three sources in Eq. (3), momentum profits can also po-
tentially arise if stock prices react to common factors with some delay. Intu-
itively, if stock prices react with a delay to common information, investors
will be able to anticipate future price movements based on current factor
realizations and devise profitable trading strategies. In some situations such
delayed reactions will result in profitable contrarian strategies and in some
other situations, it will result in profitable momentum strategies. To see
this, consider the following return generating process:
rit=μi+β0,ift+β1,ift− 1 +eit (5)where β0,iand β1,iare sensitivities to contemporaneous and lagged factor
realizations. Several papers, including Lo and MacKinlay (1990), JT,
Jegadeesh and Titman (1995), and Brennan, Jegadeesh, and Swaminathan
(1993) use this delayed-reaction model to characterize stock return dynam-
ics. If stock ipartly reacts to the factor with a lag then β1,i>0, and if it
overreacts to contemporaneous factor realizations and this overreaction is
corrected in the subsequent period then β1,i<0. Empirically, β1,i>0 when
the value-weighted market index is used as the common factor (see Jegadeesh
and Titman 1995), and therefore stocks seem to underreact to this factor.
cov( ,rrtt−− 1 )=bi^2 Cov( ,f ft t 1 ).366 JEGADEESH AND TITMAN
(^5) The contribution of the serial covariances of eitto the serial covariance of the equally
weighted index becomes arbitrarily small as the number of stocks in the index becomes arbi-
trarily large.