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Please cite this article in press as: Easterday, K. E., & Sen, P.K. Is the January effect rational? Insights from the accounting valuation
model. TheQuarterly Reviewof Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.05.001
ARTICLE IN PRESSG Model
QUAECO-852; No.of Pages18
The Quarterly Review of Economics and Finance xxx (2015) xxxxxx
Contents lists available at ScienceDirect
The Quarterly Review ofEconomics and Finance
journa l homepage: www.elsevier .com/ locate /qref
Is theJanuary effect rational? Insights from the accounting valuation
model
Kathryn E. Easterday a,, Pradyot K. Sen b
a Wright StateUniversity,UnitedStatesb University of Washington-Bothell, UnitedStates
a r t i c l e i n f o
Article history:
Received 30 May 2014Received in revised form 23 April 2015
Accepted 18 May 2015
Available online xxx
Keywords:
January effect
Permanent earnings
Tax-loss selling
a b s t r a c t
Employing a permanent earnings valuation model and a novel sample partition, we find evidence that the
January effect anomaly is consistent with rational economic market behavior. Investors in firms which
experienceJanuary effect return premiums appear to discount first quarter earnings performance but
reward permanent earnings and expectations offuture improvements. Our evidence also supports a tax-
loss selling explanation for theJanuary effect. We find that theJanuary effect is experienced by relatively
few firms in the sample overall, but a substantial percentage ofJanuary effect firms are identified as
potential tax-loss sellers. Our results complement prior research suggesting that the January effect is
neither a result of irrational noise traders nor consistent with systemic risk factor explanations. Our
study reconciles the assumption ofarbitrage inherent in trading studies with a fundamental accounting
valuation approach and offers some further insights into the nature ofthis market phenomenon.
2015 The Board ofTrustees ofthe University ofIllinois. Published by Elsevier B.V. All rights reserved.
1. Introduction
This paper finds that the January effect anomaly is associated
with accounting earnings and expectations about future earn-
ings, in a manner both economically rational and consistent with
accountingtheory. This workextends thatofHenkerand Debapriya
(2012), who argue against an irrational noise trader explana-
tion for the January effect. It complements that of Klein and
Rosenfeld (1991), who present evidence that the January effect can
be explained at least in part by new information in January about
upcoming earnings announcements. Finally, our accounting valua-
tion approach complements Mashruwala and Mashruwala (2011),
who argue that return seasonality is incompatible with systemic
risk explanations.Fama (1998) and Gerlach (2007, 2010) both argue that many
so-called market anomalies are tenuous in the sense that they are
sensitive to the methodologies used to detect or measure them.
Far from being tenuous, the January effect a capital markets
Corresponding author at: Wright State University, Raj Soin College of Business,
Department of Accountancy, 298 Rike Hall, 3640 Col. Glenn Highway, Dayton, OH
45435-0001, United States. Tel.: +1 937 775 3304.
E-mail addresses: [email protected](K.E. Easterday),
[email protected] (P.K. Sen).
phenomenon in which return premiums are on average higher
in January than in other months of the year1 persists in defi-
ance of economic theory which says it should be arbitraged away.
Although some studies suggest that the January effect is disappear-
ing (Gu, 2003; He & He, 2011; Hensel & Ziemba, 2000; Mehdian &
Perry, 2002), numerous others provide evidence that the January
effectcontinues toappear in modern US capital markets (Anderson,
Gerlach, & DiTraglia, 2007; Brown & Luo, 2006; Ciccone, 2011;
Dzhabarov & Ziemba, 2010; Easterday, Sen, & Stephan, 2009; Haug
& Hirschey, 2006; Mashruwala& Mashruwala, 2011; Ziemba, 2011)
although it does not occur every year (Easterday et al., 2009;
Hulbert, 2008).
Tax management is the most common rationalization for the
January effect: investors take advantage of capital losses at yearend for tax purposes, resulting in temporary downward mispric-
ings that create large January returns when prices rebound after
the turn of the year (Branch, 1977; Brown, Ferguson, & Sherry,
2010; Chen & Singal, 2004; Dalton, 1993; Givoly & Ovadia, 1983;
Griffiths & White, 1993; Grinblatt & Keloharju, 2004; Jones, Lee, &
Apenbrink, 1991; Koogler & Maberly, 1994; Ma, Rao, & Weinraub,
1988; Phua, Chan, Faff, & Hudson, 2010; Sikes, 2014; Starks, Yong,
1 Some researchers call it theturn of theyear effect. Both termsare widelyused
throughout the literature, often interchangeably.
http://dx.doi.org/10.1016/j.qref.2015.05.001
1062-9769/ 2015 The Board of Trustees of theUniversity of Illinois. Published by Elsevier B.V. All rightsreserved.
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Please cite this article in press as: Easterday, K. E., & Sen, P.K. Is the January effect rational? Insights from the accounting valuation
model. TheQuarterly Reviewof Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.05.001
ARTICLE IN PRESSG Model
QUAECO-852; No.of Pages18
2 K.E. Easterday, P.K. Sen / TheQuarterly Reviewof Economics andFinance xxx (2015) xxxxxx
& Zheng, 2006).2 However, there is evidence that tax minimizing
behavior by itself is not enough to drive the January effect (Brown,
Keim, Kleidon, & Marsh, 1983; Fountas & Segredakis, 2002; Jones &
Wilson, 1989; Pettingill, 1989; Reinganum, 1983; Ritter, 1988; Sias
& Starks, 1997; van den Bergh & Wessels, 1985).
Rather than attempting to explain the January effect,
Mashruwala and Mashruwala (2011) exploit this seasonal
increase in stock prices to examine whether accruals quality
measures proxy for information risk. Their findings suggest thatsuch measures proxy more for firm attributes associated with
tax-loss selling than for information risk. Studies by Brauer and
Chang (1990), Peterson (1990), and Reinganum and Gangopadhyay
(1991) also provide evidence that information risk is not related to
the January effect.
Extant research into the January effect itself appears primarily
in the finance literature where it is often explained as a temporary
mispricing anomaly resulting from various market inefficiencies
and risks resulting in arbitrage opportunities. However, some stud-
ies (Loughran, 1997; Mashruwala & Mashruwala, 2011; Roll, 1983;
Seyhun, 1993; Tinic & West, 1984) argue that systemic risk factor
explanations are not compatible with seasonal market behaviors.
A recent study by Henker and Debapriya (2012) provides evidence
that the January effect is not driven by irrational noise traders.
CAPMmodelsneither predict norexplain risk,especially (or only)in
January (Best, Hodges, & Yoder, 2006; Corhay, Hawawini, & Michel,
1987; Gultekin & Gultekin, 1987; Kryzanowski & Zhang, 1992;
Ritter & Chopra, 1989; Thaler, 1987).
Insights from the fundamental valuation theory of accounting
suggest that under a no arbitrage condition, returns in January
or any time period should be positively associated with
contemporaneous accounting earnings and information affecting
expectations about future accounting performance (Feltham &
Ohlson, 1995; Ohlson, 1995, 2001). With the exception ofKlein
and Rosenfeld (1991) there is little research considering how or
whether the January effect anomaly is associated with account-
ing earnings information in a market-efficient, rational economic
manner.3 Their evidence shows that low-PEstocks with lowannual
earnings forecasts in December outperform in January relativeto other low-PE stocks and they argue that the prices of these
stocks rise in January because it becomes apparent to investors
then that actual earnings for the just-completed year will be bet-
ter than was forecasted in December. Their analyses employ a
trailing-earnings-to-price ratio and focus on earnings forecasts and
investors expectations for the earnings announcement for the year
immediately past.
We extend Klein and Rosenfeld (1991) by employing a form
of the permanent earnings model developed in Easterday, Sen,
and Stephan (2011)4 to examine the association between January
returns and earnings in the first quarter. The ESS model expresses
returns as a function of contemporaneous earnings level, earn-
ings growth, and a term representing the sustainability of earnings
growth, and the model derives directly from Ohlsons (1995, 2001)valuation framework. Employing an accounting valuation model
rather than an ad hoc trading model enables us to forgo an assump-
tion of arbitrage and demonstrate that, consistent with economic
and accounting theory, earnings information plays an important
role in the economic intuition of the January effect phenomenon.
2 Additional studies focus on the January effect and its relation to tax rules for
individual and institutional investors (Lynch, Puckett, & Yan, 2014; Poterba and
Weisbenner, 2001; Slemrod, 1982).3 Lakonishok, Shleifer, and Vishny (1994) includecurrent P/Eratioas oneindica-
tor of possiblemispricing but their study does not examine fundamental valuation
implications of accountingearnings.4
Hereafter, ESS.
Our model is consistent with the notions that (1) earnings change
not earnings level captures the permanent componentof earnings
(Ali & Zarowin, 1992; Ohlson & Shroff, 1992); and (2) information
about future earnings is essential to valuationbecause it adjusts for
transitorycomponents of current earnings. Valuation depends crit-
ically on permanent earnings (Pan,2007), as well as theexpectation
that permanent earnings will be sustained into the future. In addi-
tion,eschewing a CAPMapproachavoids the uncertainties inherent
in estimating required rates of return, a feature of valuation based
on asset pricing models.5
In order to examine the association of these anomalous returns
with accounting earnings information we introduce an innovative
sample partition, forming an ex postcategorization of firms that
experience the January effect (JE firms) versus those that do not
(NJEfirms).6 Thus,we specifically identifyfirms thatexhibitJanuary
effect return premiums rather than relying on some firm charac-
teristic(s) presumed to be associated with the January effect. NJE
firms act as a kind of comparison group; but under our model and
approach, evidence of rational economic behavior in one group
does not negate or preclude rational economic behavior in the
other.
We find that JE firms represent approximately nine percent of
all firms in our sample andrange across all market caps, suggesting
that theJanuaryeffectis drivenby relatively fewfirmsoverall andis
frequentlybut notexclusivelya smallfirm phenomenon. Our JE/NJE
partitiondelivers someintriguing results whenimplemented in our
valuation model.
For JE firms the coefficient on first quarter contemporaneous
earnings level is significantly negative, while the coefficients for
contemporaneous earnings growth and expectations for future
earnings growth remain significantly positive. Although a nega-
tive earnings level coefficient may seem at first irrational, it may
indeed be consistent with rational behavior. First and most impor-
tantly, our valuation model is more comprehensive in that it does
not rely only on current or past earnings information, but includes
all other information as captured by the construction of the ana-
lysts forecast variable. The inclusion of the term for information
about expected future earnings captures the reality that marketdecisions are based in large part on expectations for the future.
Second, it is well established that price leads earnings (Ball &
Brown, 1968; Beaver, Lambert, & Morse, 1980; Beaver, Lambert,
& Ryan, 1987; Collins, Kothari, Shanken, & Sloan, 1994; DeBondt
& Thaler, 1985, 1987; Kothari, 2001). We contend that poor year
end returns followed by superior January returns foreshadow poor
first quarter earnings followed by an earnings improvement. Our
examination of earnings for the quarters immediately preceding
and following the first quarter, as well as a correlation analysis of
sequential quarterly earnings, both support this contention. These
results are also compatible with those ofBeaver et al. (1980) and
DeBondt and Thaler (1987).7
Third, we arguethat permanentearningsand theirsustainability
should be quite relevant to higher return premiums in January,a proposal in keeping with the tax-loss trading explanation for
the January effect advanced in so many prior studies. Firms are
5 Penman (2004, p. 96) reminds us that a capital asset pricing model (CAPM)
generates a requiredrateof return,not asset value.Further,valuationmodelsrelying
on estimated rates of return canbe highly sensitive to theunderlying assumptions
used in theCAPM.6 If a firms January return premium is the highest of all 12 months of the year
then it is classified as a JE firm forthat year. Otherwise, thefirm is categorized as
NJE.7 Beaver et al. (1980) demonstrate that returns are positively associated with
earnings of the following period. DeBondt and Thaler (1987) present evidence that
earnings improve in subsequent periods for loser firms. They also observe that
January and December return premiums are negatively associated.
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Please cite this article in press as: Easterday, K. E., & Sen, P.K. Is the January effect rational? Insights from the accounting valuation
model. TheQuarterly Reviewof Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.05.001
ARTICLE IN PRESSG Model
QUAECO-852; No.of Pages18
K.E. Easterday, P.K. Sen / TheQuarterly Review of Economics andFinance xxx (2015) xxxxxx 3
tax-loss sellers when their prices have fallen, i.e., they are losers,
and investors sell them off at year end to capture capital losses for
income tax purposes. If a low December stock price drives the high
January return and also foreshadows poor first quarter earnings,
then it is natural that (increased) January return and first quarter
earnings, however transient, should be negatively correlated. The
evidence in our added correlation analysis also indicates that the
unannounced earnings in January related to the year t1 are pos-
itively correlated with the first quarter earnings for JE firms, but
not for others. Thus the bad news embedded in these two earnings
numbers seems to be captured in the lowered December return of
the previous year. The idea that JE firms possibly tax-loss sell-
ing losers in the prior year offer investors optimistic expectations
for future sustainability of permanent earnings is not unreason-
able if we admit the possibility that bargain hunting investors in
loser firms focus more on critical value generation capabilities in
the long run and less on currentearnings numbers that may reflect
transitory components. Given their weak (strong) near term (long
term) prospects these firms become candidates for tax-loss trans-
actions in December. Then their repurchase in January increases
their price hence, the high January returns. Evidence for such a
scenario can be found in Beyer, Garcia-Feijoo, and Jensen (2013),
who show that a trading strategy targeting small, outof favor firms
achieves superior return performance in January.
It is true that without the connections between tax-loss sell-
ing and repurchasing, and the notion that poor December returns
foreshadow short term earnings troubles, the negative correlation
between January returns and first quarter earnings may appear
at first glance to be irrational. However, our scenario proposed
above provides a reasonable explanation for why we see evidence
of tax-loss selling intertwined with the (apparently) counterintu-
itiveresult of negative correlation between high January return and
poor first quarter earnings performance.
Our valuation model, which anchors on both contemporane-
ous permanent earnings and expectations for their sustainability,
coupled with our sample partition that isolates JE firms from NJE
firms, offers the opportunity to examine whether an accounting
earnings valuation approach that does not admit arbitrage canprovide someinsight intoboth the observed return premiumschar-
acteristic of the January effect and the tax-loss selling hypothesis
for them.
An effective JE/NJE partition should result in a considerable
proportion of JE firms also being identifiable as probable tax-loss
sellers. And if January effect returns are rationally associated with
information about accounting earnings, then JE firms that are tax-
loss sellers could be expected to have more emphasis placed on
permanent earnings and expectations for the sustainability of per-
manent earnings in the future, and less emphasis on current (i.e.,
first quarter) earnings that are likely to be poor.
Following Dalton (1993) we identify firms in our sample whose
previous endof yearspriceperformancemakesthem likelytax loss
sellers, andthen implementour model usingpartitions for bothtax-loss selling candidacy and occurrence of the January effect. About
45% of our samples JE firms were tax-loss selling candidates at the
endof thepreviousyear,suggesting that although tax-loss selling is
an important market dynamic in understanding the January effect,
other factors likely play in as well.
Our partitions once more deliver interesting results. The sig-
nificantly negative coefficient on earnings level appears only for
JE tax-loss sellers; the permanent earnings coefficients are signifi-
cantly positive and approximately four times larger in magnitude
than the coefficient values for either NJE tax-loss sellers or any
non-tax-loss sellers. The explanatory value of our earnings model
increases by a factor of approximately 10 when we implement the
JE/NJE partition on our tax-loss selling firms. We interpret these
results as additional evidence that the January effect anomaly is
linked to economically rational market behavior: firms that are ex
postidentified as poor price performers at the end of the year (i.e.,
tax-loss selling candidates), but whose future earnings outlook is
expected to improve, are rewarded by investors.
Robustness testing for other quarters of the year provides sim-
ilar results, but they are much more pronounced for January than
for other first months of quarter (April, July, or October). Over-
all, we interpret this as support for the concepts that the January
effect anomaly appears to be a rational economic response to value
relevant accounting earnings information; that earnings levels do
not capture permanent earnings; and that the market focuses on
andrewards valuation implications of permanentearnings that are
expected to be sustainable into the future.
This study contributes to the literature in four ways. First, we
extend both Klein andRosenfeld (1991) and Henker and Debapriya
(2012)by using a valuationmodel ratherthana trading approach.In
doing so we findevidence that the January effectis linkedto funda-
mental valuation information represented in permanent earnings
and expectations for earnings growth. Second, we complement the
workofbothMashruwalaand Mashruwala(2011)and DeBondt and
Thaler (1987) by investigating tax-loss selling firms and demon-
strating that the January effectis related to information captured in
accrual accounting. Our results offer additional support for the tax
management story in a December year end tax environment such
as the US, yet are also consistent with the argument that there is
more to the January effect than just tax-loss selling (Bley & Saad,
2010; Brown et al., 1983; Corhay et al., 1987; Fountas & Segredakis,
2002; Heston & Sadka, 2010; Su, Dutta, Xu, & Ma, 2011). Third, we
extend Penman (1987) by testing the association between returns
and quarterly earnings performance without relying on an ex-post
categorization of earnings as good news or bad news.8 Finally,
partitioning our sample between firms that experience a January
effect and those that do not is an innovation that offers a more
precise inquiry into the nature of this market phenomenon.
The study proceeds as follows. Section 2 explains the develop-
ment of our empirical model. Analysis and results are in Section 3.
Section 4 discusses robustness testing. Section 5 concludes.
2. Theoreticalmodel andempirical application
A rigorous theoretical discussion of the link between price and
accounting earnings is provided in Feltham and Ohlson (1995) and
Ohlson (1995), beginning with the following assumptions:
I. The value of the firm is equal to the present value of future
expected dividends (PVED).
Pt=
=1
REtdt+
(1)
Pt= price atdate t;dt= netdividends paid at date t;R= 1 + r= the dis-
count rate plus one;Et[.] = the expected valueoperator, conditionedon information at date t.
IICleansurplus accounting. That is,change in book value is equal
to earnings less dividends:
bt= bt1 +xt dt. (2)
Using (2) to substitute recursively for the dividend term in
(1) yields the abnormal earnings model which expresses PVED as
current book value plus capitalized abnormal earnings, defining
8 Penman(1987) appearsto acknowledge a potentiallydistorting effect of January
returns in first quarter data and focuses his analysis on the other three quarters of
the year.
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Please cite this article in press as: Easterday, K. E., & Sen, P.K. Is the January effect rational? Insights from the accounting valuation
model. TheQuarterly Reviewof Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.05.001
ARTICLE IN PRESSG Model
QUAECO-852; No.of Pages18
4 K.E. Easterday, P.K. Sen / TheQuarterly Reviewof Economics andFinance xxx (2015) xxxxxx
abnormal earnings as accounting earnings less a charge for use of
capital.
Pt= bt+
=1
REt
xat+, provided that Et
bt+
/R 0
as (3)
bt= book value at date t;xt= accounting earnings during the period
t;xat xt (R 1)bt1 = abnormal earnings.III. Appeal to a first order autoregressive process for abnormal
earnings and information other than current abnormal earnings.
(Ohlson, 1995 refers to this as assumption [A3].)
xat+1 = xat+ t+ 1,t+1
t+1 = t+ 2,t+1
t= other value relevant information; , = parameters known bythe market but unknown to researchers.
Combining (3) and [A3] yields an expression defining firm value
as a function of book value, abnormal earnings, and other informa-
tion notyet captured in earnings butrelevant forforecasting future
earnings:
Pt= bt+ 1xat+ 2t (4a)
which can be expressed equivalently as
Pt= (1 k)bt+ k (xt dt)+2t (4b)
1 = /(R) 0
2 = R/(R)(R ) > 0
k = r/(R) 0
= R/r
Eq. (4b) presents a challenge to empirical researchers because
other value relevant information, t, is not observable. A commonempirical approach is to assume that t is equal to zero (Easton &
Harris, 1991; Easton, Harris, & Ohlson, 1992;Penman & Sougiannis,
1998 are three well known examples). Ohlson (2001) warns that
although this assumption is analytically convenient it may be
overly simplistic. ESS exploit Ohlsons assumption that earnings
expectations are observable in analysts forecasts to show that in
returns form, t can be captured as the difference between thechange in forecasted future earnings and contemporaneous change
in earnings:
RETt=
1
Pt1
1xt+
2+
3r
xt+
3r
xt+1t xt
+ 3dt+ 2dt1
(5)
RETt= Pt Pt1 + dt
Pt1
xt=xtxt1
xt+1t =xf(t+1)t x
f(t)t1 = the forecast in period t for earnings per
share of period t+ 1, minus the forecast in period t1 for earn-ings per share of period t; Pt1 =price per share at beginning of
period t.
1 = R(1)(1 )/(R)(R )
2 = r/(R)(R )
3= Rr/(R)(R )
1 +2 +3 = 1
The problematic term tis thus transformed into terms that areall readily observable and measurable. Both the second and third
terms on the right hand side are divided by the cost of capital, con-
sistent with evidence in Ali and Zarowin (1992) and Ohlson and
Shroff (1992) that earnings changes capture permanent earnings.
Note that the term xt+1t =xf(t+1)t x
f(t)t1
does not represent a fore-
cast revision, but rather the difference between future earningsforecasts for two consecutive periods.9 Because analysts forecast
total earnings including any transitory components of earnings
the third term provides a correction for the portion of current
earnings change that may notbe permanent. Returns increase with
larger earnings changes from the prior period [second expression
in Eq. (5)]. When these changes are accompanied by an expecta-
tion that future earnings growth will be of even greater magnitude
[third expression in Eq. (5)], an additional premium is placed on
the realized earnings change. If the quantityxt+1t xt
is neg-
ative, i.e., earnings growth is not judged sustainable or a decline
is expected to accelerate, then current period realized earnings
change is discounted.
ESS show for both annual and quarterly time frames that this
expressionof the otherinformationvariablesubstantiallyimprovestheexplanatorypowerof thereturns model relative to theassump-
tion that t is equal to zero. They also provide evidence that the
dividend terms can be ignored without sacrificing explanatory
power. In addition, they show that contemporaneous measure-
ment of returns and earnings is both theoretically and empirically
appropriate and that proper specification of the other information
variable in the returns model removes the need for ad hoc control
variables. Based on their derivations and results the basic form of
our empirical model is as follows:
Rt= 0 + 1xtPt1
+ 2xt xt1
Pt1+ 3
xf(t+1)t x
f(t)t1
(xt xt1)
Pt1(6)
t= t ime period of interest; Rt= return in period t, computed
using CRSP monthly holding returns; Pt1 = price per share
at beginning of period t; xt= earnings per share for quar-
ter t; 0 = intercept; 1 = 1; 2 = 2+ 3
r ; 3 = 3
r ; xf(t+1)t =
the latest earnings forecast for period t+ 1 made during period
t;xf(t)t1= the latest earnings forecast for period t made during
period t 1.
Because ourfocus is onthe January effect, ourtests ideally would
be carried out by mapping monthly returns into earnings of the
same period. Of course this is not possible because firms report
earnings information on quarterly and annual bases, not monthly.
Thenextbestcandidateistomap monthly returns to corresponding
quarterly earnings. This modification fits well with the idea that
prices lead earnings, and to the extent that earnings of February
and March (May and June, August and September, November and
December) are also included in earnings of the first (second, third,
9 ESSdiscussthispointin detailand it is presentedpictoriallyin their Fig.1 (page
1131).
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Please cite this article in press as: Easterday, K. E., & Sen, P.K. Is the January effect rational? Insights from the accounting valuation
model. TheQuarterly Reviewof Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.05.001
ARTICLE IN PRESSG Model
QUAECO-852; No.of Pages18
K.E. Easterday, P.K. Sen / TheQuarterly Review of Economics andFinance xxx (2015) xxxxxx 5
Fig. 1. Timeline of eventsand measurementpoints forquarterly returns, earningsand forecastsas modeled in Eq. (7). Rqn is holding return duringthe quarter.m1 (m2, m3)
is thefirst (second, third)monthof quarter n andxqnis earningsper share in quartern.xf(n+1)qn is thelatest analyst forecast forquartern+ 1 earningsper sharethat comes out
in quarter n (denoted by theshort solid vertical marker), and is after theannouncement of quarter n1 earnings (denoted by the short dashed vertical marker).xf(n)q(n1)
is the
latest analyst forecast for quartern earningsper sharethat comes outin quarter n1 after theannouncement of quarter n2 earnings.
fourth) quarter there is a bias against finding an effect for returns
of the first month only.
There is strong evidence that firm size is negatively correlated
with the magnitude of the January effect (Blume & Stambaugh,
1983; Easterday et al., 2009; Haug & Hirschey, 2006; Hensel &
Ziemba, 2000; Keim,1983; Lamoureux& Sanger, 1989; Reinganum,
1983), and we add firm size as a control variable.10 The general
empiricalform of ourquarterly data focused, expanded model thus
becomes
Rqn = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+3
x
f(n+1)
qn x
f(t)
q(n1)xqn xq(n1)
Pq(n1)
+ 4Size (7)
qn= quarter, n= 1, 2, 3, 4; Rqn = r eturn in quarter n, com-
puted using CRSP monthly holding returns; Pq(n1) =price
per share at the end of quarter (n1); xqn =earnings per
share in quarter n; 0 = intercept; 1 = 1; 2 = 2+ 3
r ;
3 = 3
r ; xf(n+1)qn = the latest earnings forecast for quarter n+
1 made during quarter n;xf(n)q(n1)
= the latest earnings forecast
for quarter n made during quarter n 1; Size= l ogarithm of firm assets at the close of quarter n.
Although we focus on monthly rather than quarterly returns
and our addition of the firm size control variable also deviates
slightly from the ESS model, we strictly follow their efforts to
avoid uncertainty related to availability of value relevant informa-
tion. We adopt the identical data measurement timeline plan as
ESS, as shown in Fig. 1 for our analyses of quarterly returns and
earnings.
However, for our analyses of monthly returns we require that
our current period latest forecast of future earnings occurs during
10 Seasonal earnings change also has been shown to capture cyclical behavior in
accounting earnings (Bathke, Lorek, & Willinger, 1989; Bernard & Thomas, 1990;
Brown & Rozeff, 1979; Foster, 1977; Warfield & Wild, 1992). ESS provide evidence
thataddingseasonalchange asa controlvariableto themodeladds littleexplanatory
value to the model, and we obtained the same results when we ran our analyses
including seasonal change in our modified version of the ESS model. As they were
notsignificant,thoseresults arenot presentedfor the sake of brevity.
the first month of the current quarter, no earlier than the day of the
previous quarters earnings announcement, as follows:
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+3
x
f(n+1)qn,m1
xf(n)q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size (8)
Rqn,m1 = holding return for the first month in quarter n;xf(n+1)qn,m1 =
the latest analyst forecast for quarter n+ 1 earnings per share that
comes out during the first month of quarter n and is no earlier than
the same day as the earnings announcement for quarter n1.
All other variable are as previously defined. Fig. 2 illustrates the
timing of earnings, earnings announcements, and earnings fore-
casts, and measurement points in this study.
3. Analysis and results
3.1. Data sample and primary analysis
Our data sample consists of domestic firms trading ordinary
common shares on NYSE, AMEX or NASDAQ from 1991 through
2011. We imposea December year endrequirementin orderto sim-
plify the alignment of calendar and fiscal quarter dates. Selection
parameters are:
1. Monthly holding return, price and outstanding share data avail-
able in CRSP.
2. Share price $1, to avoid very small price deflators creating
extreme values in regression variables.
3. In order for a firm to be included in any year t, CRSP data must
be available for all 12 months in year t, and also for December of
year t1.
4. Earnings per share excluding extraordinary items (EPSXQ),
report date of quarterly earnings, cash dividends per share,
quarterly revenues, and end of quarter assets available in the
Compustat quarterly database.
5. Inorderfor a firmto beincludedin anyfirm-quarter,earnings per
share and report date of quarterly earnings for the immediately
previous quarter must also be available.
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Fig. 2. Timeline of events and measurement points for monthly returns,quarterly earningsand forecasts as modeled in Eq. (8). Rqn,m1 is holding returnduring thefirstmonth
ofquartern. m1 (m2, m3) is thefirst(second,third) month of quartern andxqn is earningsper share in quarter n.xf(n+1)qn is the latest analyst forecastfor quartern +1 earnings
per share that comes out in month 1 (denoted by the short solid vertical marker), and is after the announcement of quarter n1 earnings (denoted by the short dashed
vertical marker).xf(n)
q(n1)is the latest analyst forecast for quarter n earningsper sharethat comes outin quarter n1 after theannouncement of quarter n2 earnings.
6. At least two consecutive one-quarter-ahead earnings forecasts
available in I/B/E/S: the forecast for quarter n earnings per
share that was announced during quarter n1, and the fore-
cast announced in quarter n for earnings per share of quarter
n+ 1. Individual firm-quarter observations are eliminated if the
quarter n1 earnings report date in Compustat is later than the
announcement date from I/B/E/S of the n+ 1 earnings forecast.
Stock prices and EPS are adjusted for stock splits and dividends
using the cumulative adjustment factors in CRSP andCompustat. In
order to alleviatethe distorting effects of outlierswe removethetop
1% of returns and prices and the top and bottom 1% of earnings and
earnings forecasts. Firms having all the necessary pricing, earnings
and forecast data for at least one quarter in any year tare included
in the sample.
Matching of data obtained from all three datasets results in74,871 firm-quarter observations (23,716 firm-years) representing
3950 unique firms. The number of firms in each year ranges from
447 firms (1991) to 1590 (2010). Summary statistics forthe sample
are presented in Table 1, Panels A and B.
Our data constraints, especially the requirement for I/B/E/S
earnings forecast data, tend to instill in our sample a tendency
toward larger, more established firms. Evidence from numerous
prior studies suggests that the magnitude of the January effect
return premium is negatively associated with firm size (Blume &
Stambaugh, 1983; Easterday et al., 2009; Haug & Hirschey, 2006;
Hensel & Ziemba, 2000; Keim, 1983; Lamoureux & Sanger, 1989;
Reinganum, 1983). In order to establish that the small firm January
effect is present in our sample, we divide all firm-years in the
sample into deciles based on beginning of year market value ofequity, then compute mean value weighted return premiums for
each month and firm size decile. Fig. 3 shows that the January
effect is present as described in prior research. Mean return pre-
miums for January decrease monotonically and range from 7.8%
for the smallest firms to negative 0.5% for the largest firms in the
sample.11,12
11 Later in this study we examine returns for the first month, rather than for the
entire quarter, and our regression sample size shrinks due to more restrictive data
requirements for earningsforecast data. TheJanuary effect is present in the reduced
samplealso, rangingfrom a highof 7.6%for thesmallest firmsto0.5%for thelargest
firms.12 It is importantto note that weuse returnpremiumas a categorizationtool only,
in order to partition oursample between JE and NJE firms.Using returnpremiumas
Table 1a
Sample descriptive information. Panel A: Number of firms and firm-quarter obser-vations by year and in total.
Year Firms Firm-quarter observations
1991 447 1,230
1992 483 1,316
1993 570 1,494
1994 735 1,913
1995 798 2,208
1996 881 2,485
1997 1,025 2,839
1998 1,144 3,302
1999 1,118 3,243
2000 1,014 2,491
2001 1,135 3,397
2002 1,179 3,805
2003 1,242 4,050
2004 1,312 4,4122005 1,418 4,709
2006 1,504 5,052
2007 1,500 5,132
2008 1,516 5,270
2009 1,530 5,401
2010 1,590 5,567
2011 1,575 5,555
Total 23,716 74,871
The dataset consists of firm-quarter observations having 12 months of CRSP data
for each year tas well as for December of year t1, and share price $1. EPS and
report dateof quarterly earningsare available in Compustat forthe currentand prior
quarter.One-quarter-aheadearnings forecastand forecastannouncement dates are
availablein I/B/E/S for thecurrent andprior quarter.
Some studies assert that most market anomalies do not sur-vive after being made known to investors and that the January
effect has disappeared altogether (Gu, 2003, 2004; Gu & Simon,
2007). In a second examination, we followed a methodological
example included in Gu and Simons (2007) investigation into the
September phenomenon.13 Correspondingly,we hypothesized that
a dependent variable in our regression model would be inappropriate because the
model reliesupon raw returns, as demonstratedin ourEq. (5) and in Appendix B of
ESS.13 Gu and Simon (2007,page292) argue thefollowing: Ifall monthshad anequal
likelihood of being theworst performing month of theyearoverour sampleperiod,
Septemberwould be the worst about one-twelfth of the time, or 8.3% of the time.
Theyproceedto showthatin theirsample,Septemberwas theworstmonthbetween
10.7% and17.1% of thetime.
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Table 1b
Sample descriptive information.Panel B: Descriptivestatistics for quarterly earningslevels andchanges,and firmsize in theentire sample.
N Mean Std. dev. Median
Quarter 1 EPS 16,046 0.226 0.406 0.180
Quarter 2 EPS 19,672 0.247 0.463 0.200
Quarter 3 EPS 20,622 0.241 0.491 0.200
Quarter 4 EPS 18,531 0.181 0.643 0.190
Quarter 1 change in EPS 16,046 0.036 0.496 0.000
Quarter 2 change in EPS 19,672 0.037 0.384 0.027
Quarter 3 change in EPS 20,622 0.000 0.405 0.010Quarter 4 change in EPS 18,531 0.073 0.587 0.000
Total assets 23,716 5,927.7 32,927.8 645.9
Total revenues 23,716 3,202.0 12,028.1 591.8
Market value of equity 23,716 3,943.3 16,348.2 688.3
Quarter n EPSis earnings per share excluding extraordinary items(EPSXQ in the Compustat quarterlydataset), adjusted for effects of stock splits and dividends. Marketvalue
ofequity is measured at the beginning of the year. Total assets, Total revenues and Market value of equity are in $millions. Descriptive statistics are cross-sectional averages
over the years 19912011.
-0.020
-0.010
0.000
0.010
0.020
0.0300.040
0.050
0.060
0.070
0.080
0.090
sm-1 2 3 4 5 6 7 8 9 lg-10
meanvalue-weightedreturnpremium
decile of firm size
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Fig.3. Mean monthlyreturnpremiumsfor thesample,19912011.Regressionsam-
ple firm-years are divided into deciles based on beginning-of-yearmarket value of
equity. Return premium= CRSP monthly holding return value-weighted market
return. There are 23,716 firm-years representing 3,950 unique firms.
if all months have an equal likelihood of being a firms best per-
forming month, then JE firms should make up approximately one
twelfth (8.3%) of our sample.
We conductedchi-square tests to evaluate whether the number
of JE firms in our sample is within the expected range. Inability to
reject the null hypothesis would indicate that JE firms are no more
frequent than other month effect firms, and suggest that there is
nothing special about January.14 We examined our entire sample.
Then we separated the firms by size using market value of equity,
categorizing them as small, medium, or large, and assessed each
size category. The results of our chi-square analysis are as follows:
1. For the entire sample, we reject the null hypothesis that JE firms
are no more frequent than other month effect firms, with a
probability of
-
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Table 2
Results of regressions of quarterlyreturnson price-deflatedearnings level, earningschange,and other value relevantinformation.The ESS model, as wellas a morerestricted
form of it that uses only contemporaneousearnings level and earningschange, are also included for comparison purposes.
Rqn = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 3
xf(n+1)qn x
f(t)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(7)
N 0 1 2 3 4 Adj. R2
Pooled 74,871 0.034
*
0.255 0.166 0.0050.037* 0.215 2.532*** 2.470*** 0.023
0.057* 0.224 2.257*** 2.468*** 0.003 0.023
Quarter 1 16,046 0.008 0.563** 0.050 0.008
0.020 0.537*** 2.642*** 2.676*** 0.030
0.055 0.585*** 2.652*** 2.685*** 0.005 0.032
Quarter 2 19,672 0.064 0.305 0.419*** 0.007
0.060 0.241 2.498*** 2.155*** 0.021
0.082 0.226 2.492*** 2.153*** 0.003 0.021
Quarter 3 20,622 0.007 0.518 0.062 0.008
0.006 0.429 2.316*** 2.402*** 0.024
0.002 0.433 2.311*** 2.399*** 0.001 0.024
Quarter 4 18,531 0.073* 0.061 0.047 0.016
0.076* 0.198 3.067* 2.907* 0.038
0.105 0.209 3.076* 2.923* 0.004 0.038
Significant at < 0.10.* Significant at < 0.05.
**
Significant at < 0.001.*** Significant at < 0.0001.
Rqn is holding period return for quarter n, Pq(n1) is beginning of period price, xqn is earnings per share in quarter n, xf(n)
q(n1) is the latest analyst forecast that comes out in
quarter n1 forquartern earnings per share. Earnings and prices are adjusted for stock splits and dividends. Regressions utilize two-way cluster robust standard errors.
Table 3
Results of regressions of returns forthe first month of each quarter on price-deflated earningslevel, earnings change, other value relevant information,and firmsize.
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 3
xf(n+1)
qn,m1 xf(n)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(8)
N 0 1 2 3 4 Adj. R2
Pooled 39,601 0.017 0.141* 1.802*** 1.719*** 0.000 0.021
Quarter 1 4,744 0.067* 0.194 1.915* 1.998** 0.008* 0.027
Quarter 2 11,598 0.032 0.088 1.425*** 1.272** 0.001 0.011
Quarter 3 12,657 0.032 0.081 1.608** 1.635** 0.004 0.020Quarter 4 10,602 0.036 0.222 2.297* 2.217* 0.002 0.037
* Significant at < 0.05.** Significant at < 0.001.
*** Significant at < 0.0001.
Rqn,m1 is holding period return for the first month in quarter n, Pq(n1)is beginning of period price, xqn is earnings per share in quarter n, xf(n)
q(n1) is the latest analyst forecast
that comes outin quarter n1 forquartern earningsper share,xf(n+1)qn,m1
is thelatest analyst forecastthat comes out in thefirstmonth of quarter n for quartern+1 earnings per
share. Size is measured as the logarithm of total assets. Earnings and prices are adjusted for stock splits and dividends. Regressions utilize two-way cluster robust standard
errors.
contemporaneous returns, even when limited to the first month of
the quarter.
3.2. JE firms versus NJE firms
In order to more closely examine whether the January effect is
associated with accounting earnings information, it is important
to identify firms whose returns are representative of this market
anomaly. Rather than apply an ad hoc return premium variable to
our regression that is unsupported by the economic intuition of
the ESS model, we partition the sample into firms that experience
the January effect (JE firms) and those that do not (NJE firms); the
NJE firms act as a comparison sample. Our partition method pro-
ceeds as follows: foreach firmobservation in year t, we compute its
monthly return premiums by subtracting the value weighted mar-
ket return from the CRSP monthly holding return. If the January
return premium is the highest of all 12 months in year t then
the firm is categorized as a JE firm for that year; otherwise it is
categorized as NJE.16 Table 4, Panel A shows the distribution of JE
and NJE firms in the sample by year and overall. Over the entire
time period of study 9.1% of our sample firms are classified as JE
firms; the proportion of JE firms varies from 4.4% in 2000 to 22.2%
in 1992.17 This is consistent with previously cited evidence that the
January effect is more pronounced in some years than in others.
Table 4 Panels B and C show summary statistics for the parti-
tioned sample. Unsurprisingly, firms that experience January effect
returns are on average smaller in terms of assets, annual revenues,
and market value of equity but there is little discernible differ-
ence in price-deflated earnings or change in earnings between JE
and NJE. The mean January return premium for JE firms is 22.6%,
versus negative 1.6% for the much larger population of NJE firms.
16 If January is tied with any other month(s) for highest premium, the firm is
classified as JE for that year.17 We conducted a similar analysis, not presented here for the sake of brevity, of
the 93,112 firms that met our CRSP selection criteria prior to being matched with
Compustat or I/B/E/S data. JE firms made up 10.8% of that CRSP dataset.
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Table 4a
Descriptiveinformation for thepartitioned sample. Panel A: Distribution of JE and NJE firms by year andoverall.
Year Firms JE firms NJE firms % JE firms % NJE firms
1991 447 81 366 18.1% 81.9%
1992 483 107 376 22.2% 77.8%
1993 570 67 503 11.8% 88.2%
1994 735 73 662 9.9% 90.1%
1995 798 60 738 7.5% 92.5%
1996 881 64 817 7.3% 92.7%
1997 1,025 78 947 7.6% 92.4%1998 1,144 64 1,080 5.6% 94.4%
1999 1,118 75 1,043 6.7% 93.3%
2000 1,014 45 969 4.4% 95.6%
2001 1,135 191 944 16.8% 83.2%
2002 1,179 83 1,096 7.0% 93.0%
2003 1,242 89 1,153 7.2% 92.8%
2004 1,312 155 1,157 11.8% 88.2%
2005 1,418 90 1,328 6.3% 93.7%
2006 1,504 265 1,239 17.6% 82.4%
2007 1,500 123 1,377 8.2% 91.8%
2008 1,516 71 1,445 4.7% 95.3%
2009 1,530 164 1,366 10.7% 89.3%
2010 1,590 119 1,471 7.5% 92.5%
2011 1,575 106 1,469 6.7% 93.3%
Total 23,716 2,170 21,546 9.1% 90.9%
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan thereturn premium for January in thecalendar year. Return premium= CRSP monthly holding return value weightedmarket return.
Table 4b
Descriptive information for the partitioned sample. Panel B: Descriptive statistics for earnings levels, earnings changes, and firm size (JE firms).
N Mean Std. dev. Median
January return premium 1,423 0.226 0.179 0.180
Quarter 1 EPS 1,423 0.225 0.449 0.173
Quarter 2 EPS 1,777 0.232 0.541 0.178
Quarter 3 EPS 1,886 0.209 0.535 0.160
Quarter 4 EPS 1,676 0.186 0.630 0.160
Quarter 1 change in EPS 1,423 0.015 0.463 0.000
Quarter 2 change in EPS 1,777 0.023 0.371 0.025
Quarter 3 change in EPS 1,886 0.013 0.375 0.000
Quarter 4 change in EPS 1,676 0.042 0.502 0.000Total assets 2,170 4,834.6 24,537.6 505.2
Total revenues 2,170 3,156.4 13,254.1 506.1
Market value of equity 2,170 3,317.2 13,715.7 549.3
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan thereturn premium for January in thecalendar year. Return premium= CRSP monthly holding return value weighted
market return. Quarter n EPSis earnings per share excluding extraordinary items (EPSXQ in the Compustat quarterly dataset) deflated by beginning of quarter share price
obtained from CRSP, and adjusted for effects of stock splits and dividends. Market value of equity is measured at the beginning of the year. Total assets, Total revenues and
Marketvalue of equityare in $millions. Descriptive statistics are cross-sectional averages over the years 19912011.
Table 4c
Descriptive information for the partitioned sample. Panel C: Descriptive statistics for earnings levels, earnings changes, and firm size (NJE firms).
N Mean Std. dev. Median
January return premium 14,623 0.016 0.108 0.016Quarter 1 EPS 14,623 0.226 0.402 0.180
Quarter 2 EPS 17,895 0.249 0.454 0.204
Quarter 3 EPS 18,736 0.244 0.486 0.205
Quarter 4 EPS 16,855 0.180 0.644 0.195
Quarter 1 change in EPS 14,623 0.038 0.499 0.000
Quarter 2 change in EPS 17,895 0.038 0.386 0.027
Quarter 3 change in EPS 18,736 0.001 0.408 0.010
Quarter 4 change in EPS 16,855 0.077 0.594 0.000
Total assets 21,546 6,038.0 33,656.5 658.484
Total revenues 21,546 3,206.6 11,897.7 602.341
Market value of equity 21,546 4,014.2 16,250.4 709.853
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan thereturn premium for January in thecalendar year. Return premium= CRSP monthly holding return value weighted
market return. Quarter n EPSis earnings per share excluding extraordinary items (EPSXQ in the Compustat quarterly dataset) deflated by beginning of quarter share price
obtained from CRSP, and adjusted for effects of stock splits and dividends. Market value of equity is measured at the beginning of the year. Total assets, Total revenues and
Marketvalue of equityare in $millions. Descriptive statistics are cross-sectional averages over the years 19912011.
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Table 5a
Regressions on the partitioned sample. Panel A: Results of regressing January returns on price deflated first quarter earnings level, earnings change, other value relevant
information, and firm size.
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)
Pq(n1)+ 3
xf(n+1)
qn,m1 xf(n)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(8)
N 0 1 2 3 4 Adj. R2
All firms 4,744 0.067
*
0.194 1.915
*
1.998
**
0.008
*
0.027JE firms 538 0.530*** 2.434** 3.683* 2.836 0.039*** 0.293
NJE firms 4,206 0.000 0.421* 1.339*** 1.409*** 0.003 0.026
Significant at < 0.10.* Significant at < 0.05.
** Significant at < 0.001.*** Significant at < 0.0001.
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least one other month is higher than the return premium for January in the calendar year. Return premium =CRSP monthly holding returnvalue weighted
market return. Rqn,m1 is holding period return for the first month in quarter n, Pq(n-1) is beginning of period price,xqn is earnings per share in quarter n, xf(n)
q(n1)is the latest
analyst forecast that comes out in quarter n-1 for quarter n earnings per share,xf(n+1)
qn,m1 is the latestanalyst forecast that comes out in thefirst month of quarter n for quarter
n+1 earnings per share.Size is measured as thelogarithm of total assets. Earningsand pricesare adjusted forstocksplits anddividends. Regressionsutilize two-way cluster
robust standard errors.
Table 5b
Regressionson the partitioned sample. Panel B: Results of regressing firstquarterreturnson price-deflatedearnings level, earningschange,other value relevantinformation,
and firm size after partitioning the sample into JE and NJE firms. Results from the unpartitioned sample of first quarter observations shown in Table 2 are presented in the
third row for comparison.
Rqn = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 3
xf(n+1)qn x
f(t)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(7)
N 0 1 2 3 4 Adj. R2
All firms 15,819 0.055 0.585*** 2.652*** 2.685*** 0.005 0.032
JE firms 1,377 0.347*** 0.299 2.529* 2.288* 0.024** 0.053
NJE firms 14,442 0.012 0.672*** 2.669*** 2.707*** 0.002 0.038
* Significant at < 0.05.** Significant at < 0.001.
*** Significant at < 0.0001.
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least one other month is higher than the return premium for January in the calendar year. Return premium =CRSP monthly holding returnvalue weighted
market return. Rqn,m1 is holding period return for the first month in quartern, Pq(n1) is beginning of period price,xqn is earnings per share in quarter n, x
f(n)
q(n1)is the latestanalyst forecast that comes out in quarter n-1 for quarter n earnings per share,xf(n
+1)
qn.m1 is the latestanalyst forecast that comes out in thefirst month of quarter n for quarter
n+1 earnings per share.Size is measured as thelogarithm of total assets. Earningsand pricesare adjusted forstocksplits anddividends. Regressionsutilize two-way cluster
robust standard errors.
Table 6a
Potential tax-lossselling and non-tax-lossselling firms. Panel A: Distributionof PTLS andNTLS in thefull sample and forJE firms.
Year PTLS NTLS % PTLS % NTLS %PTLS and JE %NTLS and JE
1991 52 208 20.0% 80.0% 19.2% 15.9%
1992 43 292 12.8% 87.2% 30.2% 21.9%
1993 120 187 39.1% 60.9% 12.5% 9.6%
1994 122 274 30.8% 69.2% 13.1% 8.4%
1995 177 296 37.4% 62.6% 9.0% 6.1%
1996 245 317 43.6% 56.4% 9.4% 5.7%
1997 305 332 47.9% 52.1% 9.5% 6.3%
1998 377 387 49.3% 50.7% 6.9% 3.4%
1999 303 479 38.7% 61.3% 8.6% 5.4%2000 213 374 36.3% 63.7% 3.3% 4.5%
2001 242 523 31.6% 68.4% 29.8% 9.0%
2002 226 676 25.1% 74.9% 8.4% 7.0%
2003 620 319 66.0% 34.0% 7.4% 6.0%
2004 319 642 33.2% 66.8% 15.7% 9.8%
2005 249 641 28.0% 72.0% 6.4% 6.2%
2006 437 452 49.2% 50.8% 21.1% 17.3%
2007 378 448 45.8% 54.2% 11.6% 6.0%
2008 489 420 53.8% 46.2% 7.0% 4.5%
2009 305 588 34.2% 65.8% 12.1% 11.1%
2010 136 710 16.1% 83.9% 8.8% 8.0%
2011 111 682 14.0% 86.0% 7.2% 6.5%
Total 5,469 9,247 37.2% 62.8% 11.2% 8.2%
Firms represented are those for which 12 months of CRSP holding returns are available for year t1. Firms with negative holding returns for December of year t1 are
categorized as potential tax-loss-sellers (PTLS). All other firms are classified as non-tax-loss sellers (NTLS). JE firms are those for which the January return premium is
higherthan thereturn premium of any other month in thecalendaryear.Return premium =CRSP monthly holding return valueweightedmarket return.
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Table 6b
Potential tax-lossselling and non-tax-lossselling firms. Panel B: Distribution of PTLS and NTLS forboth JE and NJE firms, by year and overall.
Year JE firms % PTLS % NTLS NJE firms % PTLS % NTLS
1991 43 23.3% 76.7% 217 19.4% 80.6%
1992 77 16.9% 83.1% 258 11.6% 88.4%
1993 33 45.5% 54.5% 274 38.3% 61.7%
1994 39 41.0% 59.0% 357 29.7% 70.3%
1995 34 47.1% 52.9% 439 36.7% 63.3%
1996 41 56.1% 43.9% 521 42.6% 57.4%
1997 50 58.0% 42.0% 587 47.0% 53.0%1998 39 66.7% 33.3% 725 48.4% 51.6%
1999 52 50.0% 50.0% 730 37.9% 62.1%
2000 24 29.2% 70.8% 563 36.6% 63.4%
2001 119 60.5% 39.5% 646 26.3% 73.7%
2002 66 28.8% 71.2% 836 24.8% 75.2%
2003 65 70.8% 29.2% 874 65.7% 34.3%
2004 113 44.2% 55.8% 848 31.7% 68.3%
2005 56 28.6% 71.4% 834 27.9% 72.1%
2006 170 54.1% 45.9% 719 48.0% 52.0%
2007 71 62.0% 38.0% 755 44.2% 55.8%
2008 53 64.2% 35.8% 856 53.2% 46.8%
2009 102 36.3% 63.7% 791 33.9% 66.1%
2010 69 17.4% 82.6% 777 16.0% 84.0%
2011 52 15.4% 84.6% 741 13.9% 86.1%
Total 1,368 44.7% 55.3% 13,348 36.4% 63.6%
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan the returnpremium for January in thecalendar year. Return premium= CRSP monthly holding return value weightedmarket return. Firms represented are those for which 12 months of CRSP holding returns are available for year t1. Firms are categorized as potential tax-loss sellers
(PTLS) if they have negative holding returns for Decemberof year t1. Allother firms areclassified as not tax-losssellers(NTLS).
t. PTLS firms are also on average smaller and have lower revenues
than NTLS firms.
We perform the regression analysis in Eq. (8) on firms hav-
ing sufficient available data, examining the association between
January returns and first quarter earnings information for all cat-
egories of tax-loss seller status and JE/NJE experience. Results are
shown in Table 7.
For both tax-loss sellers and non-tax-loss sellers overall the
model performs as expected: the coefficient on earnings level is
insignificantly different from zero, coefficients related to perma-
nent earnings performance are significantly positive, explanatory
value does not exceed 4.3%. However, the JE/NJE partition once
more delivers interesting results. The large and significantly neg-
ative coefficient on earnings level again appears, but only for JE
tax-loss sellers. For allother categories it is insignificantly different
fromzero or slightly positive.Permanentearningscoefficients for JE
PTLS are significantly positive and approximately four times larger
in magnitude than the coefficient values for either NJE PTLS or any
Table 6cPotential tax-loss selling and non-tax-loss selling firms. Panel C: Descriptive statistics for PTLS and NTLS.
N Mean Std. dev. Median
PTLS
Quarter 1 EPS 1,781 0.253 0.440 0.180
Quarter 2 EPS 4,043 0.257 0.460 0.220
Quarter 3 EPS 4,356 0.233 0.533 0.207
Quarter 4 EPS 3,616 0.182 0.692 0.200
Quarter 1 change in EPS 1,781 0.003 0.460 0.010
Quarter 2 change in EPS 4,043 0.035 0.364 0.030
Quarter 3 change in EPS 4,356 0.020 0.436 0.010
Quarter 4 change in EPS 3,616 0.069 0.623 0.005
Total assets 5,469 6765.2 35,367.4 765.2
Total revenues 5,469 3890.1 14,434.3 749.7
Market value of equity 5,469 5001.0 20,252.7 827.1
NTLS
Quarter 1 EPS 2,963 0.321 0.433 0.250
Quarter 2 EPS 6,796 0.326 0.455 0.270
Quarter 3 EPS 7,400 0.321 0.466 0.270
Quarter 4 EPS 6,195 0.269 0.591 0.250
Quarter 1 change in EPS 2,963 0.023 0.417 0.000
Quarter 2 change in EPS 6,796 0.043 0.345 0.030
Quarter 3 change in EPS 7,400 0.006 0.346 0.010
Quarter 4 change in EPS 6,195 0.064 0.535 0.000
Total assets 9,247 7,414.0 37,506.6 1,020.1
Total revenues 9,247 4,233.9 14,055.1 983.6
Market value of equity 9,247 5,278.0 18,610.2 1,117.0
Firms arecategorized as potential tax-loss sellers (PTLS) if they have negative holding returns for themonth of Decemberin year t-1. All other firms areclassified as not
tax-loss sellers (NTLS).Quarter n EPSis earningsper share excluding extraordinary items(EPSXQ in the Compustat quarterly dataset)deflated by beginningof quarter share
price obtained from CRSP, and adjusted for effects of stock splits and dividends. Market value of equity is measured at the beginning of the year. Total assets, Total revenues
and Market value of equityare in $millions. Descriptive statistics are cross-sectional averages over the years 19912011.
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Table 7
Results of regressing January returns on price-deflated first-quarter earnings level, earnings change, other value relevant information, and firm size, after partitioning the
sample as to tax loss-sellingstatus and JE/NJE firms, 19912011.
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 3
xf(n+1)
qn,m1 xf(n)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(8)
N 0 1 2 3 4 Adj. R2
All PTLS 1,781 0.113
*
0.157 2.609
*
2.786
*
0.013
*
0.043JE PTLS 233 0.547*** 4.131*** 5.753*** 3.915* 0.038*** 0.395
NJE PTLS 1,548 0.020 0.432* 1.379* 1.538* 0.005 0.028
All NTLS 2,963 0.035 0.422 1.442* 1.433* 0.005 0.020
JE NTLS 305 0.456*** 0.913 1.005 0.799 0.033*** 0.203
NJE NTLS 2,658 0.014 0.492* 1.344** 1.326* 0.002 0.024
* Significant at < 0.05.** Significant at < 0.001.
*** Significant at < 0.0001.
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan thereturn premium for January in thecalendar year. Return premium= CRSP monthly holding return value weighted
market return. Firms are categorized as potential tax-loss sellers (PTLS) if they have negative holding returns for the month of December in year t1. All other firms are
classified as not tax-loss sellers (NTLS). Rqn,m1 is holding period return for the first month in quarter n, in this case January returns.Pq(n1)is beginning of period price,xqn
is earningsper share in quarter n,xf(n)
q(n1)is thelatest analyst forecast that comes outin quarter n1 for quarter n earnings per share,x
f(n+1)qn,m1
is thelatest analyst forecast that
comes out in thefirstmonthof quartern for quartern+ 1 earningsper share.Size is measured as thelogarithmof total assets. Earningsand prices areadjusted forstock splits
and dividends. Regressions utilize two-way cluster robust standard errors.
NTLS. The explanatory value of our earnings model increases by a
factorof about tenfor theJE firms in both thePTLSand NTLS groups;
the JE PTLS explanatory value is nearly twice that of JE NTLS. Fur-
ther, none of the earnings variables are significantly different from
zero for the JE NTLS. Together with its adjusted R2 value, this sug-
gests thatin the case of JE NTLS firms the model does a good job of
explaining the variability in January effect returns but we cannot
sort out which, if any, variable(s) matter(s), apart from firm size.
In summary, consistent with previous studies suggesting that
tax-loss selling is at least a partial explanation for January return
premiums, we find a sizable, though not complete, correspondence
between JE firms andthose we categorize as potentialtax-loss sell-
ers. This suggests that our categorization scheme is reasonable.
Further, complementing the evidence of Henker and Debapriya
(2012), our partitioning methodology teases out evidence that
January effect investors behavior is economically rational: excep-
tionally high January returns on PTLS loser firms may occur as
investors discount comparatively poor current earnings perfor-
mance and give extra weight to permanent earnings and their
sustainability in the future. Finally, the existence of JE firms that
are not tax-loss sellers and our inability to determine significant
explanatory variables for them suggest that there are still some
aspects of this market puzzle that are not well understood, and
that invite future investigation.
4. Robustness testing
4.1. Expectations and EPS performance of JE firms
As a reasonableness check on our findings, we investigate
how expectations and actual performance change over the time
period from the fourth quarter of year (t1) through the first
and second quarters of year (t). Table 8 presents mean quarterly
earnings and expectations for permanent earnings sustainabilityx
f(n+1)qn x
f(n)q(n1)
xqn xq(n1)
21 for the fourth through
second quarters for JE firms. The outlook for permanent earnings
is very negative in the fourth quarter for JE firms and then highly
21 This is the other information term described previously. It is the difference
between the change in forecasted future earnings and contemporaneous change in
earnings, and it captures expectations for the sustainability of earnings growth.
Table 8
Mean quarterly earnings per share and expectations for permanent earnings sus-
tainability (JE firms).
N=1,781
Quarter 4 EPS(year t1) 0.391***
Quarter 1 EPS 0.340***
Quarter 2 EPS 0.398***
Quarter 4 expectation for permanent earnings sustainability 0.062**
Quarter 1 expectation for permanent earningssustainability 0.089***
** Significant at
-
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Table 9a
Correlations of quarterly earnings. Panel A: JE versus NJE firms, 19912011.
NJE firms JE firms
Quarter 4 (t1) Quarter 1 (t) Quarter 2 (t) Quarter 3 (t)
Quarter 4 (t1) 1.000 0.0457*
Quarter 1 (t) 0.0057 1.000 0.0389*
Quarter 2 (t) 0.0344*** 1.000 0.0366***
Quarter 3 (t) 0.0508*** 1.000
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which thereturn premium of at least one other month is higher than the return premium for January in the calendar year. Return premium= CRSP monthly holding return value
weightedmarket return. Theyear in whichthe comparison quarter fallsis designated as t. N= 3,909for JEfirms.N= 35,645 for NJEfirms. Correlationspresented areSpearman
correlations, which do not depend upon assumptions of the datas normal distribution or heteroskedasticity.* Significant at < 0.05.
*** Significant at < 0.0001.
Table 9b
Correlations of quarterly earnings. Panel B: JE versus NJE firms, 19912011 (PTLS).
NJE firms JE firms
Quarter 4 (t1) Quarter 1 (t) Quarter 2 (t) Quarter 3 (t)
Quarter 4 (t1) 1.000 0.0650*
Quarter 1 (t) 0.0229* 1.000 0.1127***
Quarter 2 (t) 0.0326** 1.000 0.0474
Quarter 3 (t) 0.0548*** 1.000
* Significant at < 0.05.** Significant at < 0.001.
*** Significant at < 0.0001.
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan the returnpremium for January in thecalendar year. Return premium= CRSP monthly holding return value weighted
market return. Firms are categorized as potential tax-loss sellers (PTLS) if they have negative holding returns for the month of December in year t1. All other firms
are classified as not tax-loss sellers (NTLS). The year in which the comparison quarter falls is designated as t. N=1,607 for JE firms. N= 12,171 for NJE firms. Correlations
presented are Spearman correlations, which do not depend upon assumptions of the datas normal distribution or heteroskedasticity.
In Panels B andC, we partitionthe samplealongthe dual dimen-
sions of tax-loss selling status and JE versus NJE firms. For JE PTLS
firmsthe earnings correlation coefficientsare of the predictedsigns,
and stronger. On the other hand, Panel C shows that the first quar-
ter (t)-fourth quarter (t1), as well as the second quarter (t)-firstquarter (t) correlation coefficients are both insignificantly different
from zero for JE NTLS firms. NJE firms in Panels B and Panel C are
positively significant for the first-second quarter earnings correla-
tions, but the correlation between the first and fourth quarters for
PTLS (NTLS) firms is significantly negative (insignificantly different
from zero). Earnings correlations between quarters two and three
are positively significant in all cases except NJE PTLS, where the
correlation is insignificantly different from zero.
Taken together, we interpret these results as evidence suppor-
ting our argument that in the case of JE firms, investors seem to
rationally discount relativelypoor earnings performance in the first
quarter and focus on increased expectations for future improved
earnings in awarding large return premiums.
4.2. The role of dividends
Hand and Landsman (2005) argue that dividends could proxy
for other value relevant information because they are included
in the linear information dynamics supporting the Ohlson valua-tion framework. Their argument is consistent with evidence that
investors may look for information about expected future perfor-
mance in firmsdividendpolicies (Brucato & Smith,1997; Jin, 2000).
ESS test the role of dividends in their returns specification and find
no evidence that current or past period dividends add explanatory
power, nor that dividends proxy for other value relevant informa-
tion in the absence of their term representing information about
expected growth in permanentearnings,
xf(t+1)t x
f(t)t1
(xtxt1)
Pt1. We
re-examine dividends as a potential proxy for value relevant infor-
mation here for two reasons. First, measuring
xf(t+1)t x
f(t)t1
(xtxt1)
Pt1requires analysts forecasts, the availability of which introduces a
Table 9c
Correlations of quarterly earnings. Panel C: JE versus NJE firms, 19912011 (NTLS).
NJE firms JE firms
Quarter 4 (t1) Quarter 1 (t) Quarter 2 (t) Quarter 3 (t)
Quarter 4 (t1) 1.000 0.0234
Quarter 1 (t) 0.0011 1.000 0.0114
Quarter 2 (t) 0.0354*** 1.000 0.0813***
Quarter 3 (t) 0.0408*** 1.000
*** Significant at < 0.0001.
JE firms are those for which the January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which the return
premium of at least oneother month is higherthan the returnpremium for January in thecalendar year. Return premium= CRSP monthly holding return value weighted
market return. Firms are categorized as potential tax-loss sellers, PTLS if they have negative holding returns for the month of December in year t1. All other firms are
classifiedas nottax-loss sellers,NTLS.The yearin whichthe comparison quarterfalls is designated as t. N= 1,991forJE firms.N= 21,336 for NJEfirms. Correlationspresented
are Spearman correlations, which do not depend upon assumptions of the datas normal distribution or heteroskedasticity.
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Table 10
Results of regressing January returns on price-deflated first quarter earnings level, earnings change, dividends, and firm size on the unpartitioned and partitioned sample.
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 4Size+ 5dqn
Pq(n1)+ 6
dq(n1)Pq(n1)
(9)
N 0 1 2 4 5 6 Adj. R2
All firms 3,707 0.059 0.304 0.079 0.007* 1.062 0.145 0.010
JE firms 418 0.509*** 3.139* 1.155* 0.033*** 0.759 1.923 0.275
NJE firms 3,289 0.008 0.431* 0.038 0.002 0.742 0.027 0.008
* Significant at < 0.05.*** Significant at < 0.0001.
JE firms are those for which the return in January return premium is higher than the return premium of any other month in the calendar year. NJE firms are those for which
the returnpremium of at least oneothermonthis higher than thereturn premium forJanuary in thecalendaryear. Return premium =CRSP monthly holding return value
weighted market return. Rqn,m1 is holding period return for the first month in quarter n, in this case January returns. Pq(n1)is beginning of period price, xqn is earnings per
share in quartern, dqnis cash dividend per share in quartern. Size is measured as thelogarithm of total assets. Earningsand pricesare adjustedfor stock splitsand dividends.
Regressions utilize two-way cluster robust standard errors.
selection bias toward larger, more established firms. Second, the
main difference in specification between our empirical model in
thisstudyandthatproposedbyESSisourfocusonthefirstmonthof
the quarter, when investors may be struggling to determine expec-
tations for future earnings performance. In such a setting there
may be an informational function for dividends. We investigate therole of dividends in explaining January returns using the following
empirical form of the model, which follows from Eq. (5) and in
which current (first quarter) and the previous years fourth quarter
price deflated dividends replace
xf(t+1)t x
f(t)t1
(xtxt1)
Pt1, as follows:
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 4Size+ 5dqn
Pq(n1)
+6dq(n1)Pq(n1)
(9)
dqn = cash dividends paid in quarter n, in this case quarter 1 and all
other variables are as previously defined.
Results are shown in Table 10. As we are limited to using firms
for which we have two-consecutive-quarter dividend data avail-
able our sample size decreases slightly from 538 (4,206) JE (NJE)
observations in quarter 1 with analysts forecasts to 418 (3,707).
The analysis indicatesthat substituting firstand fourth quarter divi-
dends for the other information term results in a model with little
explanatory power for either NJE firms or firms overall, as their
respective adjusted R2 values are only 0.008 and 0.010. Consistent
with the idea that dividends represent a decrease in future value-generating power, the coefficients on 5 and 6, are negative inall cases but nowhere significant. In the case of JE firms adjusted
R2 using dividends is higher than for NJE firms or for the pooled
sample. Adjusted R2 values for JE firms are slightly lower for the
dividend model than for the ESS model (0.275versus 0.293). Taken
together,we findlittle support for dividends as an explanatory vari-
able that is preferable to the other information term specified by
ESS.
4.3. April (July, October) effects
As a final check, we perform similar partitions for firms that
experience an April (July, October) effect; that is, April (July,
October) return premiums are higher than return premiums of
all other months in the year. Consistent with the methodology
Table 11
Results of regressing April (July, October) returns on price-deflated second (third, fourth) quarter earnings level, earnings change, other value relevantinformation, and firm
size, afterpartitioning thesample into AE (JULE,OE) and NAE (NJULE, NOE) firms. Results forJE and NJE firms from Table5, Panel A are shown in the top line ofeachsection
for comparison purposes.
Rqn,m1 = 0 + 1xqn
Pq(n1)+ 2
xqn xq(n1)Pq(n1)
+ 3
xf(n
+1)
qn,m1 xf(n)
q(n1)
xqn xq(n1)
Pq(n1)
+ 4Size
(8)
N 0 1 2 3 4 Adj. R2
JE firms 538 0.530*** 2.434** 3.683* 2.836 0.039*** 0.293
AE firms 1,427 0.488***
0.677
1.356***
0.672 0.029*
0.074JULE firms 1,154 0.414*** 0.541*** 3.248* 2.918* 0.029*** 0.208
OE firms 1,202 0.560*** 0.800* 2.451* 2.095* 0.040** 0.192
NJE firms 4,206 0.000 0.421* 1.339*** 1.409*** 0.003 0.026
NAE firms 10,171 0.019 0.092 1.125** 0.853* 0.004* 0.014
NJULE firms 11,503 0.066* 0.445* 1.385*** 1.513*** 0.006* 0.037
NOE firms 9,400 0.026 0.296 1.572* 1.525* 0.002 0.034
Significant at < 0.10.* Significant at < 0.05.
** Significant at < 0.001.*** Significant at < 0.0001.
JE (AE, JULE, OE) firms are those for which the return premium in January (April, July, October) is higher than the return premium of any other month in the calendar year.
NJE (NAE, NJULE, NOE) firms are those for which the return premium of at least one other month is higher than the return premium for January (April, July, October) in
the calendar year. Rqn,m1 is holding period return for first month in quartern, Pq(n1) is beginning of period price, xqn is earnings per share in quarter n, xf(n)
q(n1)is the latest
analyst forecast that comes out in quarter n1 forquartern earnings per share,xf(n+1)
qn,m1 is thelatest analyst forecast that comes outin thefirst month of quartern for quarter
n+1 earningsper share. Size is measured as thelogarithm of total marketvalueof equity. Earnings and prices areadjusted forstocksplits anddividends. Regressions utilize
two-way cluster robust standard errors.
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7/25/2019 market janurary
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