traders can condition on the fact that there was a public news announcement
at some given date t, they can refine their strategies. In particular, they can
make their strategies time-dependent, so that they only trend-chase aggres-
sively in the periods right after public news, and lay low at other times. If they
do this, there need be no overreaction to public news in equilibrium; rather,
the impulse response function may be increasing everywhere.
Of course, it is conceivable that momentum traders are not so sophisti-
cated, and continue to use strategies that do not depend on how recently
public news was released. If so, the impulse response to public news is also
hump-shaped. But the important point is that the logic of our model admits
(even strongly suggests) the possibility that the response to public news
looks different than that to private information. This is clearly a testable
proposition.
D. Trading Horizons and the Pattern of Return AutocorrelationsOne novel feature of our model is that it explicitly links momentum traders’
horizons to the time pattern of return autocorrelations. This link is loosely
suggested by Proposition 2, and it emerges clearly in the comparative statics
results of figure 14.1: the longer the momentum traders’ horizon j, the
longer it takes for the autocorrelations to switch from positive to negative.
The first thing to note in this regard is that our model seems to get the av-
erage magnitudes about right. For example, Jegadeesh and Titman (1993)
find that autocorrelations for stock portfolios are positive for roughly
twelve months, and then turn systematically negative. According to our cal-
culations (see the appendix), this is what one should expect if jis on the
order of twelve to eighteen months, which sounds like a plausible value for
the horizon of a trading strategy.^22
A second observation is that we can make cross-sectional predictions, to the
extent that we can identify exogenous factors that influence the trading hori-
zon j. One natural candidate for such a factor is trading cost. It seems plausi-
ble to conjecture that as trading costs increase, momentum traders choose to
hold their positions for longer. If so, we would expect stocks with relatively
high bid-ask spreads to have autocorrelations that stay positive for longer pe-
riods of time before turning negative. Or going across assets classes, we would
expect the same thing for assets such as houses, and collectibles, where trad-
ing costs are no doubt significantly higher.^23 Some evidence on this latter
point is provided by Cutler, Poterba, and Summers (1991). They find that, in
A UNIFIED THEORY OF UNDERREACTION 527(^22) As a benchmark, turnover on the NYSE has been in the range of 50 to 60 percent in re-
cent years, implying an average holding period of twenty to twenty-four months. Of course,
momentum traders may have shorter horizons than the average investor.
(^23) Some care should be taken in testing this prediction, since assets with higher trading costs
are likely to have more stale prices, which can induce spuriously positive autocorrelations in
measured returns.