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Modeling earnings momentum using a representative agent
framework.
William Forbes & Aloysius Igboekwu.
Loughborough Business School,
Loughborough,
LE11 3TU.
Abstract
This paper examines the predictive performance of two representative agent
models of earnings momentum using the US S & P 500 sample frame in the
years 1991-2006. For successive sequences of quarterly earnings outcomes, two,
three, increases, etc. we ask whether the model can capture the likelihood of
reversion and secondly the stock market response to observed earnings change
sequences for our chosen sample.
This paper applies two of the simplest representative agent earnings momen-
tum models ([8], [1])to predict stock market responses to earning announcements
on S & P 500 constituents in the years 1995-2007 . The models used is very
parsimonious and tractable. A good theory explains little by much and our
paper inquires whether there is more to earnings momentum than these very
simple models explain. We examine some of the contrasting predictions of the
two models on offer to discern which model fits the historical data best. As
large and still growing literature documents the failure of stock markets to ad-
equately process earnings information (see [3],[5]). To be deemed ”anomalous”
the stock market’s response to earnings must deviate from that of a reasonable,
or rational, investor. A reasonable investor in the standard Finance literature
is one who forms his expectation of earnings in accordance with Bayes’ rule.
So earnings ”surprises” are movements in earnings that do not accord with
Bayesian projections. One commonly studied earnings anomaly is long-term
over-reaction to earnings, based on over-extrapolation of recent earnings trends
[4]. Our paper studies the matching short-run anomaly of stock-market under-
reaction based on a failure to fully impound recent information about earnings
into stock prices. It does so by examining the evidence of monthly earnings
responses to sequences of quarterly earnings announcements on the S & P 500
in the years 1991-2006.
1 Models of earnings momentum
The representative agent framework envisages a prototypical, ”everyman”, in-
vestor facing different states of the world, say famine and feast, or momentum
and reversion regimes. The investor conditions his response to earnings accord-
ing to the state of the world believed to currently hold. To understand S & P
500 companies responses to earnings quarterly earnings changes sequences we
examine the predictive power of two such representative agent models one by
Matthew Rabin and another Nick Barberis and co-authors ([8],[1]).
1.1 Rabin’s law of small numbers
Rabin (2002) considers the responses to information of an investor who is a stan-
dard Bayesian apart from believing that the Urn, or population, from which he
draws the observed sample of (say earnings) outcomes is sampled without re-
placement This induces a form of the “gambler’s fallacy” that it is time one’s
“luck turned” after observing a streak of successive (usually bad) outcomes.
Rabin terms such an aberrant projection of outcomes a belief in the ”law of
large numbers”. This is, of course, simply a spoof of the true rule of inference
entitled the law of large numbers. We follow Rabin homely feel in calling be-
lievers in the small numbers Freddie. The focus now becomes how a Bayesian
and Freddie differ in their projection of (earnings) outcomes given a recently
observed sequence.
1
1.1.1 Bayesian inference about earnings outcomes
Consider a bayesian investor faced with a recent sequence of quarterly earnings
changes, say two consecutive increases in quarterly earnings–per–share (hence-
forth eps), or an increase followed by a fall. What weight does such an investor
put on a further increase in quarterly earnings (prrise)? The answer is of course
given by the bayesian posterior inferred from multiplying the likelihood of a
rise in earnings this quarter (∆Et(+)) by its prior probability, given past quar-
terly earnings outcomes ∆Et−1. So Bayes’ rule implies that the probability of
a sequence of quarterly earning increases by mapping past quarterly earnings
outcomes
prise =pr[∆Et(+)| × ∆Et−1(+)]
pr[(∆Et(+)| × ∆Et−1(+)]) + (pr[∆Et(+)| × ∆Et−1(−)]) + pr(∆Et(+)| × ∆Et−1(0))]
(1)
so the prior probability of a rise is simply the probability of a rise in earnings
as a proportion of all possible outcomes, be they past rises, falls (∆Et−1(+),
∆Et−1(−)) or no of change (∆Et−1(0)).
To illustrate this we adopt a simple example from [8] to illustrate the process
of Bayesian updating of expectations. Consider an investor who believes any
of three earnings outcomes (rise, fall or no change) are currently equally likely.
So the investor’s prior is a third for each state, but that investor also believes
that the probability of observing a rise is conditioned on past earnings quar-
terly earnings changes. So the likelihood of observing an increase in earnings
this quarter varies with the previous quarter’s reported quarterly change. So
a company whose earnings fell last time only has a 25% of probability of its
earnings rising this time, a company whose earnings remained unchanged last
quarter has half a chance of rising this quarter and finally, a company whose
earnings rose last year has a 75% chance of rising again this in the current
quarter. Applying our Bayesian revision rule to this case we obtain.
prrise =1/4
1/4+1/2+3/4=1/4
1= 1/4 (2)
so the conditional probability of observing a sequence of two consecutive quar-
terly earnings rises is 1
4
2=1/16. Similar reasoning implies a probability of 1
4or
1
2
2of a increase in earnings for a company recording no change in earnings last
quarter and, finally, of 9
12 , or 3
4
2, of observing a sequence of two consecutive
quarterly earnings increases.
1.1.2 Inference under the law of small numbers
Recall Freddie, a believer in the law of small numbers, who is simply a bayesian
who believes he samples from a Urn, or population, that is sampled without re-
placement in each consecutive period only to be replenished between the second
and third draw. This is simply a formal modeling device employed to mimic the
“overinference” of Freddie who infers likely patterns where there are none.
2
In the particular numerical example used in the example of bayesian revision
above, there are 2 states (quarterly earnings falls and rises) and 4 balls. So
an Freddie believes, because there is no replacement of sampled balls, a second
earnings increase cannot be sampled if one occurred last time (i.e. his luck must
turn). So if a rise in earnings has already been drawn it has been used up and
cannot be drawn again next time because the sample, or Urn, is not replenished
next period. Hence, in our numerical example employed before, the probability
of observing a quarterly earnings fall next time declines from 1
4to zero (1−1
4−1
1
4
(or 0
3×1
4= 0), or of a company whose earnings did not change last quarter is
2−1
4−1×1
2or 1
3×1
2=1
6for Freddie and, finally, to 3−1
4−1×or 2
3×3
4=6
12 =1
2to
infer the probability of two successive quarterly earnings increases.
The overall impact of then of belief in the law of small numbers is to shift
the distribution of earnings from 1
4for prior earnings falls, 1
2for a company
recording no earnings change last quarter. and finally, 9
12 for companies who
already reported one quarterly increase towards a analogous distribution for
Freddie of, zero , a sixth and a half. That is Freddie’s distribution of quarterly
earnings changes expectations are skewed to the right of a bayesian who puts
more weight on reversals of recent earnings trends (zero versus 1
16 ), less weight
on continued quarterly earnings stability (a quarter versus a sixth) and, finally,
roughly the same weight on momentum in earnings when one quarterly earnings
increase following another ( 9
16 for a bayesian investor versus half for Freddie).
At the corners of the distribution (the earnings extreme momentum cases) the
shift in earnings expectations is predicted to be fairly slight (one sixteenth).
It is in the prediction of stability of earnings expectations that Freddie and a
bayesian will primarily differ.
So this model predicts the least investor earnings surprises for those extreme
momentum cases. In our our empirical tests we focus of this implication of
the Rabin (2002) explanation of earnings momentum. Does the Rabin model
illuminate the phenomena of how investor’s earnings expectations shape price
formation in more than simply theoretical interest? Is the impact of earnings
momentum primarily felt once a sequence is initiated (a reversal averted) or
primarily as earnings momentum intensifies.
1.2 Transitions between momentum and reversion regimes
While for Rabin the representative investor, Freddie, is an imperfect bayesian
in the projection of earnings for Barberis and co-authors [1] the investor is
“always wrong but never in doubt”. In their model the investor believe they are
observing an earnings process that constantly cycles between eras of momentum
and reversion despite the fact in reality earnings always follows a random walk.
So while earnings follows a process Et=Et−1+ytwhere ytis an earnings
shock/innovation, that while in reality always zero in expectation, is believed
to contain a trend in momentum states or to mean-revert in reversion states.
Hence while quarterly changes in earnings always follow a random walk and
innovation in earnings are always zero in expectation the investor wrongly beliefs
themselves to be in one of two states, either reversion or momentum (so s=R
3
or M). So the Barberis et al model makes more dramatic claims about investor
rationality than Rabin’s (2002) model requires. Investors simply never learn the
true nature of the earnings process (assumed to be a random–walk) and only
vary in the nature of their self delusion sometimes feigning a belief in momentum
and at other times in earnings reversion.
Clearly the difference between momentum and reversion regimes is the degree
of confidence attached to observing a continuation or reversion in past earning
innovations, yt. In the reversion regime the chances of a reversal in the sign of
last quarter’s earnings shock, πt, is believed to be low (between zero and a half,
so 0 > πL<0.5) and in the momentum regime the opposite expectation is held
by the investor (so 0.5> πH<1). So the contrasting regimes take the form
Reversion yt+1 =y yt+1 =−y
yt=y πL1−πL
yt=−y1−πLπL
Table 1: The reversion regime
Reversion yt+1 =y yt+1 =−y
yt=y πH1−πH
yt=−y1−πHπH
Table 2: The momentum regime
As stated previously investor’s in the Barberis et al believe they are either
in the momentum or reversion regime in each quarter despite the fact quarterly
earnings always follow a random-walk. Consistent with this delusion investors
infer probabilities of leaving the state they are in. So let λRthe probability of
leaving the reversion regime and hence that of entering the momentum regime
anew and λMis the probability of leaving the momentum regime and entering
the reversion regime this quarter. Barberis et al focus on the case when both
Prevailing regime In reversion regime next quarter In momentum regime next quarter
Reversion 1 −λRλR
Momentum λM1−λM
Table 3: The transition from reversion to momentum and back
λRand λMare low and hence the quarterly earnings regime rarely changes
although this is not a structural requirement of model.
One very clear property of Barberis et al model is the the constancy of
earnings reversion expectations within the momentum and reversion regimes.So
once the investor believes he is in the momentum regime his belief regarding
the chances of leaving it are fixed regardless of how long he has been in that
state. The credibility of this assumption is one way of distinguishing between
the empirical value of the two alternative representative agent models of how
warnings momentum emerges in the stock market.
The central dilemma for the representative investor in this sort of world
4
is to form a best guess of which earnings regime currently prevails (denoted qt
henceforth). In reality earnings always follow a random–walk making this a false
choice. Yet to make this decision over a false choice the investor must optimally
infer the probability of being in the reversion regime and so see earnings change
direction next quarter. The investor’s best guess of being in the reversion regime
is given by application of Bayes’ rule as
qt=(1 −λR×qt−1+λ2×(1 −qt−1)) ×πL
((1 −λR)×qt+λM×(1 −qt−1)) ×πL+ (λR×qt−1+ (1 −λM)×(1 −qt−1)) ×(1 −πH)
(3)
for a sequence of two quarterly earnings rises when qt−1< qtbecause the ob-
served sequence confirms the investor’s (false) belief they are in a reversion
regime and
qt=((1 −λR)×qt−1+λM×(1 −qt−1)×(1 −πL)
((1 −λR)×qt−1+λM×(1 −qt−1)×(1 −πL)+(λR×qt−1+ (1 −λM)×(1 −qt−1)×(1 −πH)
(4)
when quarterly earnings have recently changed direction and so the investor
attaches a lower probability his belief he is in the reversion regime, qt−1> qt.
Table 4 presents a numerical illustration of the revision process based on Table
5 of the original Barberis et al paper. As the number of repeated sequences of
improvements occur (so y > 0) the probability attached to being in the reversion
state in the reversion state declines for a Bayesian investor. Similarly, repeated
alternations of the sign of quarterly earnings changes confirms the representative
investor’s belief that he is in the reversion regime. As the number of repeated
sequences of improvements occur (so y > 0) the probability attached to being
in the reversion state declines for a Bayesian investor. Similarly, repeated alter-
nations of the sign of quarterly earnings changes confirms the investors belief
that he is in the reversion regime.
A particular example considered by Barberis et al the probability of getting
out of the reversion (i.e. entering the momentum) regime is low compared
to that of leaving in the momentum regime (staying in the reversion) regime.
Indeed in the particular example considered in Table 4 not leaving the reversion
regime is both unlikely (λ1=10%) and three times as low as leaving the reversion
regime (λ2=30%). But this assumption is open to exploration via comparative
static exercises based on inducing variations in exit state probabilities to induce
predicted behaviour conformable with the observed data. This variation in the
rate of transition can itself be optimally updated and constitutes a degree of
freedom available to characterise observed market behaviour not available in
Rabin’s (2002) model. Hence the temporal stability of reversion probabilities
becomes a way of differentiating the Barberis et al and Rabin models of how
earnings momentum persists and impacts upon equity returns.
5
1.3 Which model best captures the key characteristics of
observed earnings momentum Barberis et al or Rabin?
We have outlined two very different representative–agent based models of earn-
ings momentum which of them best fits the stylised facts of earnings momentum?
In the following work we present evidence on two of the most basic stylised facts
that may help us decide which of the two models on offer best characterises ob-
served momentum, at least as it is manifested within the US S & P 500 in the
last two decades. These are
1. is the distribution of earnings sequences symmetric,so that all that mat-
ters is the distinction between momentum and reversion regimes as the
Barberis et al paper seems to imply? Or does both the duration and sign
of earnings sequences markedly differ in their frequency?
2. regardless of the frequency, or intensity, of consecutive earnings changes
how surprised are investors by them and, consequently, what is there price
impact? So does it matter for price momentum what the distribution of
consistency and intensity of earnings changes is?
2 Data and research method
Our sample frame is companies within the S & P 500 in the years 1991 to
2006, some 525 companies, yielding 23,139 company-quarters of earning-per-
share changes in all in our final sample. Some 837 S & P 500 constituent
companies have quarterly earnings change data in our sample and our final
sample companies derive from including only companies for which we can calcu-
late share-price performance. Earnings per-share data were collected from the
I/B/E/S database to reconcile earnings outcomes with investor expectations of
them (see [7]). Since our focus is largely upon the distribution and impact of
earnings sequences we work here with simple earnings-per-share changes scaled
by current price. We used an annually smoothed quarterly earnings metric of
the form Qt+Qt−1+Qt−2+Qt−3
Qt−5+Qt−6+Qt−7+Qt−8
(5)
recalling each quarter’s earnings is scaled by current price.
While we excluded a few extremely large changes in earnings per-share which
seemed suggestive of errors in the IBES database we do not systematically
windsorise,or otherwise adjust,the data. Table 6 presents some basic summary
statistics for our sample data. This table exposes the fact while the average
earning-per-share change for S & P 5000 firms in the sample is fairly small and
positive there is very wise variation around that mean value.
The stock market response to quarterly earning-per-share changes are cap-
tured by returns, calculated from Datastream prices subject to a Fama-French
3-factor asset pricing model (see [6]) using weights from rolling annual regres-
sions for each sample company over five years of monthly data and the factors
given for the US market on Professor Ken French’s data library website.
6
We calculate investor returns on the standard cumulative abnormal return
metric popularised by many event-day studies in corporate finance as well as a
buy and hold metric. Since many institutional investors are required to hold
S & P 500 companies, or some subset thereof, in their portfolios we emphasize
the buy-hold investor returns metric in our results reported below.
3 Results
3.1 The distribution of consistent earnings rises and falls
and the stock market response to them.
We begin our analysis of the two questions we wish to focus upon in Figure 1
which provides a histogram of the percentage frequency distribution of earnings
sequences in our sample. The asymmetric and uneven distribution of quarterly
earnings-per-share changes in our sample data is very striking. About 22% of
our sample data derives from companies reporting quarterly earnings increases
of at least three years, or twelve quarters, or more. This of course affirms a
long line of market-based accounting research on meeting and beating earnings
targets and the required earnings management to do so (see [2]).
Figure 2 plots mean quarterly earnings changes over 3 years of consistent
earnings rises and falls. The cumulatively larger nature of repeated falls in
quarterly earnings is very clear in our data while the scale of repeated quarterly
earnings growth stabilises to smallish values after a year. Consistent quarterly
declines seem to cumulate fairly alarmingly, while consistent quarterly earnings
growth appears to be a fairly stable, possibly even manageable, form of corpo-
rate reporting in our sample data. Figure 3 simply reconstructs Figure 2 using
median quarterly earnings changes. The basic pattern of Figure 2, cumulative
quarterly earnings falls becoming more dramatic in scale while cumulative quar-
terly earnings growth stabilise to small values, is confirmed by Figure 3. This
suggests that the pattern does not result from a few rogue, outlier, observations
which imply no broader trend in the data. We conclude that it is most probably
not wise to pool consistent quarterly earnings rises and falls into the same state
as the Barberis et al model does. This is because the cumulative impact of
quarterly earnings falls is far more dramatic than smaller consecutive quarterly
earnings rises. Further, consistent quarterly earnings rises are so common, con-
stituting almost a quarter of our sample data, as to make it unlikely they will
have a dramatic stock market impact.
In Figure 4 we now continue to explain how more extreme sequences of
quarterly earnings-per-share changes are received by investors. Figure 4 plots
investor buy and hold returns in the three months following the reported quar-
terly earnings change for increasing durations of quarterly earnings rises and
falls for a three year period. Once again the average stock market response to
successive earnings changes is highly uneven across consistent quarterly earn-
ings rises and falls. For consistent quarterly earnings rises the response is always
small and positive with little increase in the intensity of stock market response
7
as the run of positive earnings changes lengthens. The stock market response
amongst investors to consistent quarterly earnings falls is far more uneven, with
no real discernable trend being present. This may make some sense since quar-
terly earnings falls, especially large cumulative ones, are by their very nature
transitory because the company either right the trend or faces liquidation once
earnings falls become earnings losses. Companies with declining quarterly earn-
ings over a long period must offer a higher rate of return to compensate investors
for the risk of holding them if they are to survive. Payment of such compensa-
tion is fairly clear for the most extreme consistent group of earnings fallers, but
fairly ephemeral, if present at all, for companies reporting only , two, or less
years of earnings falls.
Figure 5 confirms the asymmetric stock market responses to quarterly earn-
ings rises and falls using the median buy and hold Fama-French adjusted return
over a three month period following the quarterly earnings announcement. In
this alternative test the payment of premium returns in order to compensate for
the risk of repeated losses is more clear but again companies reporting repeated
earnings falls for a period less than two years display no discernable pattern.
3.2 Regression based tests.
In a final section we undertake some tentative regression based tests to establish
whether then duration of past quarterly earnings rises falls impact upon the
amount of earnings generated stock market price momentum. Once again we
employ buy and hold returns, corrected by the Fama-French 3-factors, covering
a three month period following the announcement of the most recent quarterly
earnings change as our dependent variable in all reported regressions.
Table 8 presents the results of a basic regression of quarterly earnings changes
on their matched three month ahead Fama-French risk-adjusted buy and hold
returns. Furthermore, within the S & P 500 any observed short-term earnings-
based momentum will very likely be arbitraged out in such a large and liquid
market. More marked is the way the stock market response to quarterly earnings
rises or falls as a sequence of earnings rises/falls lengthens. We already know
from the graphical analysis of the previous subsection that while stock market
responses to lengthy sequences of quarterly earnings rises are pretty stable the
stock market response to lengthy declines in quarterly earnings is more erratic.
Specifically, it appears companies reporting a long stream of quarterly earnings
falls are forced to pay a premium for risk to their remaining long-suffering
investors. This requirement is especially marked at the longest earnings fall
sequences, say after two years or eight quarters of earnings declines.
The differing stock market responses to lengthy quarterly earnings-per-share
rises and falls motivates our preferred regression equation which we present in
Table 9. In this regression we allow regression intercepts to shift, depending on
the nature of the quarterly earnings sequence. So we include a dummy variable
in the regression for the quarterly earnings sequence being either positive or
negative and two further dummy variables to capture quarterly earnings rises
and falls of over two year’s duration. Further, we include the year of the quar-
8
terly earnings change as a control variable. While the stock market response to
quarterly earnings changes are strongly effected by the year in which they occur,
with stock price responses being more muted as the years go on, there seems
little difference in the average stock market response to quarterly earnings rises
and falls. But while lengthening earnings rises and fall sequences differ little
in their average response a separation is clearly present at the extreme of the
earnings sequence distribution.
When we include two separate dummy variables to capture quarterly earn-
ings rises and falls beyond two years, or eight quarters, in length a clear dif-
ference in how the stock market processes these prolonged quarterly earnings
sequences emerges. Companies with prolonged quarterly earnings falls pay a
premium to investors who remain with them, presumably as a compensation for
the risk of the company failing while companies reporting consistent quarterly
earnings growth enjoy a small discount on their cost of capital.
4 Conclusion
This paper presents some initial tentative evidence on the suitability for em-
pirical application of two representative agent style models of the stock market
impact of momentum in reported earnings. The early evidence we have leads us
to favour Rabin’s (2002) model based on the ”law of small numbers” as against
to Barberis et al (1998) model. We express this preference for two reasons.
Firstly, because of the essential incredibility of a model that assumes investors
never infer the true nature of the quarterly earnings process they face. Secondly,
because of the centrality of the distinction of between earnings momentum and
reversion regimes in the Barberis et al model. Our empirical work suggests that
it is the duration of quarterly earnings momentum and its sign which primar-
ily determines their impact on stock prices rather than earnings momentum as
such. Prolonged sequences of quarterly earnings falls seem particularly marked
in a exerting risk premium from US S & P 500 constituent firms in our chosen
sample period.
References
[1] Nicholas Barberis, Andrei Shleifer, and Robert Vishny. A model of investor
sentiment. Journal of Financial Economics, forthcoming, 49(3), September
1998.
[2] Eli. Bartov, Dan. Givoly, and Carla. Hayn. The rewards to meeting or
beating earnings expectations. Journal of Accounting & Economics, 33(2),
June 2002.
[3] Werner F. M. DeBondt. Betting on trends: Intuitive forecasts of financial
risk and return. International Journal of Forecasting, 9(2):355–371, Winter
1993.
9
[4] Werner F. M. DeBondt and Richard H. Thaler. Does the stock market
overreact? Journal of Finance, 40(3):793–808, 1985.
[5] John. Doukas and Phil. McKnight. European momentum strategies: Infor-
mation diffusion and investor conservatism. European Journal of Financial
Management, 11(3):313, June 2005.
[6] Eugene F. Fama and Kenneth R. French. Common risk factors in the returns
on stocks and bonds. Journal of Financial Economics, 33:3–56, 1993.
[7] Michael P. Keane and David E. Runkle. Testing the rationality of price fore-
casts: New evidence from panel data. American Economic Review, 80:714–
735, 1990.
[8] Matthew Rabin. Inference by believers in the law of small numbers. Quar-
terly Journal of Economics, 117:775–816, 2002.
Table 4: Earnings expectations in the
Barberis et al model.
Date q(t) Length of Run
0 0.5 0
1 0.8 0
2 0.86 0
3 0.88 0
4 0.88 0
5 0.84 1
6 0.87 0
7 0.83 1
8 0.87 0
9 0.88 0
10 0.88 0
11 0.84 1
12 0.81 2
13 0.80 3
14 0.79 4
NBThis table is based on a illustrative sim-
ulation of their model presented by Barberis
et al in which πL=1
3,πH=3
4and
10
Table 5: How a believer in the law of of small
numbers (Freddie) varies in his beliefs from
a Bayesian investorb
Sequence Permutations Bayes 4 Freddy
aa aa 1 0.06 0.03
bb bb 1 0.06 0.03
aa ab 4 0.25 0.11
bb ab 4 0.25 0.11
ab ab 4 0.25 0.44
aa bb 2 0.13 0.06
aBased on Table 2 of Rabin (2002) pp. 795
bBased on Table 2 of Rabin (2002) pp. 795
Table 6: Summary statistics for sample variables
Variable N Mean σMin Max
∆ EPS 23138 0.02 7.19 -372.00 196.00
ABRET(T) 23145 0.00 0.11 -0.73 1.33
ABRET(T+1) 23144 0.01 0.12 -0.86 5.49
ABRET(T+2) 23144 0.01 0.11 -0.68 2.65
ABRET(T+3) 23143 0.00 0.11 -0.73 1.33
CAR 23149 0.03 0.22 -1.59 4.58
Buy & Hold 23149 0.00 0.05 -0.51 0.51
Table 7: Spearman rank correlations for key sample variables
∆EPS Consistency CAR Buy & Hold
∆EPS 1
Consistency 0.62 1
CAR 0.08 0.05 1
Buy & Hold 0.08 0.06 0.99 1
Table 8: Regression of Buy & Hold returns on earnings variables
Constant ∆EPS Consistency Consistency×∆EPS N R2
0.015 0.003 22698 0.001
(3.79) (8.70)
-0.0004 0.011 0.0005 0.007 22698 0.01
(-0.89) (2.74) (9.55) (8.05)
0.002 0.0001 0.0004 23138 0.003
(4.90) (1.35) (8.17)
NB
∆EPS is the absolute change in quarterly earning-per-share, Consistency is
the length of the earnings sequence, 1,2...,12 denoting earnings sequences
lasting 1 quarter, 2 quarters, 12 quarters, etc.
11
Table 9: Regression tests of preferred specification
OLS estimates of price impact of consistent earnings patterns (N=23138)
Constant ∆EPS Consistency More2year >0 More2year<0 year Rise R2
0.015 0.0001 0.0009 -0.0053 0.011 -0.007 -0.0013 0.007
(5.79) (1.40) (4.55) (-3.01) (4.30) (-6.67) (-0.72)
Panel estimates of price impact of consistent earnings patterns (N=23138)
Constant ∆EPS Consistency More2year >0 More2year<0 year Rise R2
1.53 0.0001 0.0006 -0.0049 0.0100 -0.0007 -0.0003 0.0190
(8.22) (1.94) (3.01) (-2.63) (4.03) (-8.20) (-0.21)
NB year is simply the year in our sample period 1991-2007 in which the
quaterly earnings sequence is recorded, Morethan2year >0 is a dummy that
equals 1 for quaterly earnings rise sequences beyond eight quarters in length
and zero otherwise, Morethan2year <0 is a dummy that equals 1 for quarterly
earnings fall quarterly earnings sequences beyond eight quarters in length and
zero otherwise, positive is a dummy set equal to one for quarterly earnings
rises and zero for falls.
12
