4.1.1.6.1. Assumptions and variable definitions.
present a simple model of
the relation between earnings growth rates and stock returns, which captures
the prices-lead-earnings phenomenon.I use growth rates because it simplifies
the analysis.How ever, the intuition from the analysis is equally applicable to
return–earnings analysis that uses earnings or earnings change deflated by price
as the earnings variable in the regressions.The particulars of the econometrics
naturally change with different specifications of the variables, but the
qualitative results continue to hold.
Xt ¼ xt þ yt1; ð1Þ
where xt is the portion of earnings growth that is news to the market, whereas
yt1 is the portion of earnings growth that the market had anticipated at the
beginning of period t: Stated differently, yt1 is past earnings news that shows
up in period t’s earnings, i.e., prices lead earnings. Further assume that xt and
yt1 are uncorrelated and i.i.d. with s2ðxÞ ¼ s2ðyÞ ¼ s2U These assumptions
imply earnings follow a random walk and that each component of earnings
growth contributes to a new permanent level of earnings.Usin g earnings
growth rates empirically poses practical difficulties because earnings can be
negative.I assume this issue away here in the interest of a simple analysis that
communicates the intuition.
Stock prices respond only to information about earnings growth, i.e.,
discount rates are assumed constant inter-temporally and cross-sectionally.
Given the assumptions about earnings growth rates, return in period t; Rt; is
Rt ¼ xt þ yt: ð2Þ
Current stock return reflects the news in current earnings and news about
earnings growth that will be captured in the next period’s earnings.In this
model, the market is assumed to have information about one-period-ahead
earnings growth rate.This is a conservative assumption in that previous
research suggests prices reflect information about two-to-three-year-ahead
earnings growth (e.g., Kothari and Sloan, 1992).
Since all the earnings information is expressed in terms of growth rates
and because all earnings growth is assumed to be permanent, annual
stock returns are simply the sum of the earnings growth rates that are news
to the market.That is, there is a one-to-one correspondence between stock
returns and news in earnings growth rates, and the price response to
unexpected earnings growth, i.e., the earnings response coefficient, is one. If,
instead of using earnings growth rates, unexpected earnings deflated by the
beginning of the period price are used, then the earnings response coefficient is
ð1 þ 1=rÞ: