Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Contents lists available at ScienceDirect
Journal of Accounting and Economics
journal homepage: www.elsevier.com/locate/jae
Earnings dispersion and aggregate stock returns$
Bjorn Jorgensen a,n, Jing Li b, Gil Sadka c
a
University of Colorado at Boulder, USA
Carnegie Mellon University, USA
c
Columbia University, USA
b
a r t i c l e i n f o
abstract
Article history:
Received 20 November 2008
Received in revised form
19 April 2011
Accepted 1 June 2011
This paper studies the relation between aggregate stock returns and contemporaneous
and future cross-sectional earnings dispersion. We hypothesize that increases in
expected earnings dispersion signal increases in uncertainty and increases in unemployment, thereby causing expected returns to rise, which in turn causes prices to
decline. We find a positive relation between aggregate stock returns and contemporaneous earnings dispersion because higher earnings dispersion is associated with higher
expected returns. Consequently, we also find a negative relation between aggregate
stock returns and future (one-year ahead) earnings dispersion, as investors anticipate
higher future earnings dispersion and higher expected returns.
& 2011 Elsevier B.V. All rights reserved.
JEL classification:
E32
G12
G14
M41
Keywords:
Accounting valuation
Earnings dispersion
Expected-return variation
Profitability
1. Introduction
The asset pricing literature derives and documents the determinants of time-varying risk premia. This literature concludes that
the risk premium depends on the current and expected states of the economy as well as uncertainty about these states. Work in
this area documents a robust relation between aggregate earnings changes and aggregate risk premia.1 While cross-sectional
earnings dispersion does not affect expected aggregate cash flows, various economic theories suggest that cross-sectional earnings
dispersion may impact stock prices. First, overall market uncertainty about future changes in fundamental values may manifest
itself in higher expected future earnings dispersion, and this development, in turn, should affect current aggregate stock prices.
Second, Lilien (1982) documents that performance dispersion and sectoral shifts, such as a shift from manufacturing to services,
result in unemployment shocks as employees migrate between employers and sectors.2 In addition, uncertainty per se may induce
$
We would like to thank an anonymous referee, Daniel Cohen, SP Kothari (editor), Bugra Ozel, Nick Polson, Steven Rock, Efraim Sadka, Ronnie Sadka,
Michael Staehr, Ane Tamayo (discussant), and Igor Vaysman as well as the workshop participants at Columbia University, London Business School
Accounting Symposium, 2010 Midwest Economic Association Meetings, University of Chicago, University of Colorado at Boulder, University of
Connecticut, and University of Pennsylvania (Wharton) for valuable comments and suggestions. Any errors are our own.
n
Corresponding author. þ 1 303 735 5027.
E-mail addresses: [email protected] (B. Jorgensen), [email protected] (J. Li), [email protected] (G. Sadka).
1
Asset pricing theories include Lucas (1978), Abel (1988), and Cox et al. (1985), French et al. (1987) while empirical studies using aggregate earnings
include Kothari et al. (2006), Anilowski et al. (2007), Ball et al. (2009), Hirshleifer et al. (2009), Sadka (2007), and Sadka and Sadka (2009), among others.
2
For more on the relation between unemployment and sectoral shifts, see Abraham and Katz (1986), Hamilton (1988), Loungani et al. (1990), and
Hosios (1994).
0165-4101/$ - see front matter & 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jacceco.2011.06.001
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
2
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
unemployment shocks: employers may be more hesitant to hire during periods of uncertainty. Expected future earnings dispersion
should also affect aggregate stock prices to the extent that it reflects either aggregate uncertainty, or unemployment, or both.
Consistent with these theories, we find that aggregate stock returns are (1) positively related with contemporaneous crosssectional earnings dispersion, and (2) negatively related with future cross-sectional earnings dispersion. This implies that prices
decline as investors demand higher expected returns when expected earnings dispersion increases. The robust role of earnings
dispersion, in addition to other macroeconomic factors, suggests that expected earnings dispersion is a determinant of the time
variation in aggregate expected returns and hence the equity risk premia. Since current existing theories suggest that discount
rates depend on the current state of the macroeconomy, our findings imply that future empirical analyses should incorporate
earnings dispersion when explaining the relation between the macroeconomy and equity prices.
We first test the association between earnings dispersion and uncertainty and unemployment shocks. We find that
earnings dispersion is positively associated with uncertainty in the prior period, as measured by market volatility (French
et al., 1987) and illiquidity (Amihud, 2002). This implies earnings dispersion is associated with higher unexpected
information uncertainty among investors about underlying fundamental values.3 We also find that earnings dispersion is
positively associated with contemporaneous unemployment shocks, as suggested by Lilien (1982).
We then test the relation between earnings dispersion and stock returns and document that one-year ahead earnings
dispersion is negatively related to current aggregate stock returns. This finding suggests that when investors anticipate
high earnings dispersion, they demand higher rates of return. If this implication is true, then earnings dispersion should be
positively correlated with contemporaneous stock returns. We document just such a correlation. Taken together, the
contemporaneous and forward relations suggest that investors react negatively to expected future earnings dispersion,
driving down aggregate stock prices, because investors demand higher (expected) rates of return. In unreported results, we
find no support for a relation between stock returns and lagged earnings dispersion.
We include variables that measure uncertainty and labor-income fluctuations in our analysis to further examine which
factors drive the documented relation between earnings dispersion and stock returns. After controlling for unemployment
and uncertainty measures, future earnings dispersion remains significantly negatively correlated with returns. However, it
becomes insignificant in the contemporaneous return regressions.
Finally, we include in our regressions additional macroeconomic indicators that previous studies have shown to be
correlated with stock returns. Because earnings dispersion can increase during recessions, we include measures of the
soundness of the economy such as real-GDP growth, inflation, and industrial production (e.g., Fama, 1990; Schwert, 1990),
as well as an indicator variable for recessions (using the NBER recession dates). We measure all these variables using the
unexpected shocks estimated by time-series models. The relation between earnings dispersion and stock returns remains
after controlling for these macroeconomic indicators.
In addition to including macroeconomic indicators, we conduct several robustness tests. First, we show that the relation
between earnings dispersion and aggregate stock returns is robust to using a more direct forward-looking measure of
uncertainty, implied market volatility. Second, since Jiang (2008) documents that aggregate stock returns are correlated
with the dispersion in book-to-market ratios and other fundamentals, we test whether our results are driven by similar
factors. Our results are robust to including cross-sectional dispersion in the book-to-market ratio. This suggests that our
findings are not driven by the scalar (market value). To further corroborate our approach, we use the dispersion in returnon-assets and find similar results. Finally, we control for the dispersion in stock returns, and the relation between stock
returns and future earnings dispersion holds.4
We also note that our measures of market uncertainty and unemployment cannot fully explain the relation between
earnings dispersion and stock returns. In particular, future earnings dispersion remains significantly negatively associated
with returns after controlling for the current uncertainty measures and contemporaneous unemployment. Our measures
of uncertainty and unemployment may not fully capture the level of unexpected market uncertainty and unemployment.
As such, we cannot exclude other possible explanations.
The remainder of the paper is organized as follows. Section 2 articulates why aggregate uncertainty results in earnings
dispersion ,which affects contemporaneous and lagged stock returns. Section 3 describes the data and its sources. Section 4
documents what macroeconomic factors explain earnings dispersion. Section 5 tests for the relation between earnings
dispersion and aggregate stock returns. Section 6 describes our robustness tests. Section 7 concludes.
2. Earnings dispersion and the macroeconomy
Our uncertainty argument is based on how investor uncertainty or ambiguity manifests itself in financial markets.
Consider, for example, the energy market, which is characterized by high uncertainty about future demand, regulation, and
the cost of alternative energy sources or technologies. As a result of technological uncertainty, firms invest in different
3
We do not include predictable components of market volatility or illiquidity in our tests as our dispersion measure is the unexpected dispersion
and, by definition, it should not be related to predictable components of market uncertainty. In unreported results, we include both components in the
tests, and find that only unpredictable volatility and illiquidity are significantly correlated with our earnings dispersion measure.
4
We cannot include the contemporaneous return dispersion due to its high correlation with average stock returns. Consider the case where the
spread in market betas is constant over time; the average market returns will determine the cross-sectional dispersion in returns. For the same reason,
we include both earnings dispersion and average earnings changes as independent variables.
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
3
production technologies, including coal, gas, nuclear, wind and solar. This causes estimation uncertainty among investors
regarding the future profitability of the sector. Consequently, we would expect dispersion in future performance as
technology evolves. Specifically, we would expect that, in anticipation of higher dispersion in future earnings (i.e., higher
estimation uncertainty concerning the next period), investors would require a higher expected return in the next period.
That, in turn, should push stock prices lower, resulting in lower current period stock return.
An extensive literature in finance investigates the effect of estimation uncertainty on equilibrium stock returns,
including Barry and Brown (1985), Clarkson et al. (1996), Coles and Loewenstein (1988), and Coles et al. (1995). In these
single-period horizon models, investors are a priori uncertain about parameters that determine the level or variance of
future cash flows. In these circumstances, they require compensation in the form of a higher risk premium. Thus, timevarying estimation uncertainty should result in time-varying risk premia.
This estimation uncertainty likely has both a firm-specific component and an economy-wide component.5 While the
initial literature focused on the firm-specific component of estimation uncertainty, recent papers such as Barberis et al.
(1998) can be viewed as incorporating the economy-wide component as regime shifts that could explain investor
sentiment. In a similar vein, Easley and O’Hara (2010) use prospect theory to argue that some investors refrain from
participating in the stock market when they face too much ambiguity about the future payoffs. Overall, this literature
suggests estimation uncertainty might affect market-wide returns. Alternatively, dispersion in earnings may be related to
increased heterogeneity in investors’ beliefs, which in turn may affect stock prices (see Varian, 1985, among others).6 In a
recent paper, Barinov (2010) provides a risk-based explanation of the negative relation between analyst disagreement and
future returns, which is also related to our investigation of earnings dispersion from the time-varying risk premium
perspective.
The second link between earnings dispersion and aggregate stock prices stems from the labor market, specifically,
unemployment. Lilien (1982) uses labor market frictions to develop an economic prediction that unemployment rises with
dispersion as employees migrate from the poorly performing firms and sectors to more productive ones. But unemployment may also rise simply because employers are more reluctant to hire during periods of high uncertainty. In sum, the
relation between dispersion and unemployment may be due to the dispersion per se as employees migrate across
employers due to the associated uncertainty.
2.1. The role of predictability
Our empirical findings rely on the predictability of both earnings changes and dispersion. To see this, consider an efficient
market where earnings changes are unpredictable. In that case, prior period prices and lagged returns cannot reflect future
earnings changes and earnings dispersion. Consequently, we would only expect a contemporaneous relation between earnings
dispersion and returns. Now consider instead an efficient market where investors partially anticipate future earnings changes
and their dispersion. In this setting, prior period prices would reflect investors’ information about future earnings changes and
dispersion, and lagged returns would be associated with next period earnings changes and earnings dispersion.
Predictability also affects the interpretation of the contemporaneous relation between returns and predictable variables
such as earnings changes and dispersion. Period t stock returns have three components: expected returns, Et 1(rt) (the
discount rate demanded by investors), return news, Nr, and cash flow news, Ncf.7 Since earnings changes and dispersion are
predictable, their contemporaneous relation with returns is affected through the expected returns (Chen, 1991).8 For
example, if contemporaneous technological uncertainty leads to high expected dispersion (high future dispersion) in
productivity, stock returns should decline, resulting in a negative association between returns and future earnings
dispersion. In other words, cov[DISPt þ 1,rt] o0 because cov[DISPt þ 1,Nr]40. At the same time, investors respond in
anticipation of earnings dispersion and therefore demand higher (expected) rates of returns, resulting in a positive
contemporaneous relation between earnings dispersion and aggregate returns, that is cov[DISPt þ 1,Et(rt þ 1)] 40. Note that,
since the news component of returns is likely to be larger than the expected component, we expect a more robust relation
between returns and future earnings dispersion compared with contemporaneous dispersion.
3. Data
Our sample selection starts from all firms with December fiscal year-end from 1951 to 2005, with available return data
in the CRSP monthly file and accounting data in the Compustat annual database. The December fiscal year-end
5
In the limit, with infinitely large number of firms, we expect firm-level variations to be diversifiable. However, since the number of firms in the
market is finite and the earnings distribution has a fat tail (see Abarbanell and Lehavy, 2003), firm-level earnings variation may not be fully diversifiable.
6
Lambert et al. (2007) demonstrate that accounting quality can affect firms’ systematic risk premium when earnings are informative about the
covariance between the future cash flows of the firm and the overall market. To the extent that this covariance is correlated with cross-sectional earnings
dispersion, we expect dispersion to matter in the aggregate.
7
See Campbell (1991), Callen and Segal (2004), and Khan (2008).
8
Note that the positive contemporaneous relation between expected earnings dispersion and expected aggregate stock returns imply the
predictability of stock returns as well (see Fama and French, 1988, 1989; Campbell and Shiller, 1988a, 1988b; Campbell, 1991; Lettau and Ludvigson,
2001).
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
4
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
requirement avoids misspecifications due to different reporting periods. The annual return for each firm is measured by
cumulative return from April of year t through March of year t þ1. Our basic earnings change measure for each firm is the
change in income before extraordinary items, scaled by market value at the beginning of the fiscal period. For each year,
we exclude stocks with the beginning-of-period price per share below $1. We also exclude the top and bottom 5% of firms
based on earnings changes. Finally, we exclude firms with negative book values. The average number of stocks per year is
about 1320 in our sample, increasing from 220 in 1951 to 2865 in 2005.
For each year, we calculate the equal-weighted and value-weighted means of earnings changes for all firms in our
sample. We also calculate the equal-weighted and value-weighted returns of all individual stocks in our sample in each
year. The value weight is the market capitalization for each firm at the beginning of the period. We also use the CRSP
value-weighted index as a measure for buy-and-hold returns.
Table 1 reports summary statistics of the return and earnings variables in our sample. Both equal-weighted ðRew
t Þ and
value-weighted market returns ðRvw
Þ
are
approximately
15%
annually
in
our
sample.
These
figures
are
consistent
with
prior
t
studies such as Kothari et al. (2006) and Sadka (2007). The CRSP value-weighted return (CRSPt) in our sample period has an
average annual return of 12.6%, which suggests that our sample consists of relatively large firms. The statistics of equalweighted and value-weighted aggregate earnings changes are also similar to prior studies. For example, the means of equalweighed and value-weighted earnings changes are 0.006 and 0.004, with standard deviations of 0.012 and 0.010, respectively.
3.1. The time-series of earnings and returns
Fig. 1 presents the time-series of aggregate stock returns and earnings changes scaled by beginning period price. Fig. 1a
plots the equal-weighted and value-weighted market returns. Fig. 1b plots both the equal-weighted and value-weighted
earnings changes. These figures are consistent with those reported in Kothari et al. (2006). Note that neither earnings nor
returns exhibit a trend or any particular serial correlation.
Fig. 1 also reveals patterns regarding the relation between earnings changes and stock returns, previously documented in
Kothari et al. (2006) and Sadka and Sadka (2009). In particular, earnings changes appear to lag stock returns, i.e., stock returns
are positively correlated with the one-period-ahead earnings changes. This result is consistent with accounting conservatism
insofar as accounting income (earnings) lags economic income as reflected in stock returns. In addition, earnings changes
appear to be negatively correlated with contemporaneous stock returns. These apparent relations between earnings changes
and contemporaneous and lagged stock returns are consistent with the correlations reported in Table 2. For example, the
Table 1
Descriptive statistics.
This table reports the descriptive statistics for aggregate stock returns, earnings changes, and earnings dispersion from 1951 to 2005. Stock returns
ew
vw
is the cumulative market returns from April of year t until March of year tþ 1. Rt and Rt are equal-weighted and value-weighted returns of our
sample firms, respectively. CRSPt is the CRSP value-weighted returns accumulated from April of year t until March of year tþ 1. DXt/Pt 1_ew and
DXt/Pt 1_vw are the equal and value-weighted average change in income before extraordinary items in fiscal year t from fiscal year t 1, deflated by the
market value at the beginning of period t. The value-weighted measures use the market value at the beginning of fiscal year t as the weight. DISPt is the
de-trended dispersion (standard deviation) of earnings changes in year t. We exclude data for firms with non-December fiscal year-end for 1954–2005,
stock price below $1, and the top and bottom 5% of firms ranked by DXt/Pt 1 and the weight variables.
We also report the descriptive statistics for all macro variables in the table. ILIQt is the unexpected market illiquidity measure from Amihud (2002).
MVOLt is the unexpected market volatility measured following French et al. (1987). Ut is the de-trended shock in unemployment in year t. cayt is the
w
consumption to wealth ratio as in Lettau and Ludvigson (2001), available from 1954 to 2001. st is the labor income to consumption ratio as in Santos and
Veronesi (2006), available from 1954 to 2001. GDPt is the de-trended shock in GDP growth rate in year t. PRODt is the de-trended shock in the growth rate
of industrial production in year t. INFt is the de-trended shock in the inflation rate in year t.
Stock returns
Earnings changes
Average
Mean
Std. dev.
Median
Min.
Max.
Dispersion
ew
Rt
vw
Rt
CRSPt
DXt/Pt 1_ew
DXt/Pt 1_vw
DISPt
0.159
0.201
0.131
0.185
0.790
0.142
0.167
0.124
0.188
0.548
0.126
0.171
0.127
0.258
0.470
0.006
0.012
0.006
0.023
0.043
0.004
0.010
0.005
0.021
0.026
0.000
0.010
0.002
0.016
0.031
Macro variables
Mean
Std. dev.
Median
Min.
Max.
w
ILIQt
MVOLt
Ut
cayt
st
GDPt
PRODt
INFt
0.006
0.236
0.045
0.515
0.670
0.009
0.049
0.016
0.148
0.120
0.030
0.824
0.183
1.920
2.557
0.001
0.014
0.003
0.051
0.028
0.819
0.034
0.829
0.755
0.858
0.000
0.022
0.002
0.054
0.041
0.001
0.050
0.002
0.115
0.092
0.000
0.018
0.000
0.046
0.053
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
5
0.8
ew
Rt
vw
Rt
0.6
0.4
0.2
-0.2
19
51
19
55
19
59
19
63
19
67
19
71
19
75
19
79
19
83
19
87
19
91
19
95
19
99
20
03
0
-0.4
0.05
ΔXt /Pt-1_ew
0.04
ΔXt /Pt-1_vw
0.03
0.02
0.01
63
19
67
19
71
19
75
19
79
19
83
19
87
19
91
19
95
19
99
20
03
59
19
55
19
19
19
-0.01
51
0
-0.02
-0.03
Fig. 1. (a) Aggregated Annual Returns, 1951–2005. (b) Aggregated annual earnings change, 1951–2005. This figure plots the time-series average return
and earnings changes for all firms from 1951 to 2005. Rt_ew and Rt_vw are equal-weighted and value-weighted returns, calculated as cumulative market
return from April of year t until March of year t þ 1. DXt/Pt 1_ew and DXt/Pt 1_vw are the equal-weighted and value-weighted average deflated change in
earnings, which is defined as the ratio of change in earnings before extraordinary items from fiscal year t 1 to fiscal year t, deflated by the market value
at the beginning of fiscal year t.
correlation coefficient between contemporaneous earnings changes and equal-weighted stock returns is 0.170, and the
correlation coefficient between equal-weighted earnings changes and lagged equal-weighted stock returns is 0.295.
3.2. Our dispersion measure
Our earnings dispersion measure, DISPt, is based on the cross-sectional standard deviation of firm-level changes in
earnings scaled by beginning period market values. We use earnings changes consistent with previous studies such as
Collins et al. (1987), Collins and Kothari (1989), and Kothari and Sloan (1992). Specifically, we define earnings changes as
earnings at period t minus earnings at period t 1, scaled by the market value at t 1. Using this measure for earnings
changes, we define our annual measure of earnings dispersion as the cross-sectional variation in earnings changes for each
year (s[DXj,t/Pj,t 1]).9 While earnings changes and returns do not appear to have a trend, the cross-sectional firm-level
dispersion in earnings changes is increasing over time (Fig. 2a). The time trend in cross-sectional dispersion is apparent
from casual inspection. This trend in dispersion is probably not due to the increase over time in the number of firms in our
sample. If the earnings distribution remains unchanged, sampling more observations should not change its standard
deviation. A larger sample should increase the accuracy of our measures for both average earnings change and dispersion,
but a larger sample should not generate a trend.10
The trend in earnings dispersion is more likely due to changes in the distribution of earnings. In particular, Basu (1997)
and Givoly and Hayn (2000) suggest that accounting conservatism has increased over time, which should increase the
dispersion in earnings changes. Note that the time trend, apparent in Fig. 2a, resembles the trend in the earnings response
to bad news reported in Basu (1997). Fig. 3 presents the evolution of the Basu (1997) measure of conservatism as bad news
coefficient, (b1 þ b2), from the following cross-sectional regression equation:
Xj,t
¼ a0 þ a1 DRj,t þ b1 Rj,t þ b2 DRj,t Rj,t þ Zj,t
Pj,t1
ð1Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
PJt
PJt
2
Formally, we define dispersion for a cross-sectional variation in fxj,t gJjt¼ 1 as: st ¼
j ¼ 1 ðxj,t xt Þ =Jt where xt ¼
j ¼ 1 xj,t =Jt and Jt is the number of
observations in year t.
10
Since the opening of the NASDAQ exchange significantly increases our sample, we excluded the NASDAQ firms and found the same trend in
earnings dispersion. In addition, our findings are not sensitive to the exclusion of NASDAQ firms. These results are not tabulated.
9
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
6
Panel A: Correlation between contemporaneous returns and earnings measures
ew
Rt
ew
Rt
vw
Rt
CRSPt
DXt/Pt 1_ew
DXt/Pt 1_vw
DISPt
1
0.970
(0.000)
0.851
(0.000)
0.170
( 0.215)
0.191
( 0.161)
0.345
(0.012)
vw
Rt
CRSPt
DXt/Pt 1_ew
DXt/Pt 1_vw
DISPt
1
0.931
(0.000)
0.210
( 0.124)
0.218
( 0.110)
0.291
(0.036)
1
0.238
( 0.089)
0.227
( 0.105)
0.184
(0.192)
1
0.957
(0.000)
0.295
( 0.034)
0.380
( 0.005)
1
CRSPt
DXt þ 1/Pt_ew
DXt þ 1/Pt_vw
DISPt þ 1
0.295
(0.031)
0.223
(0.104)
0.229
(0.102)
0.261
(0.057)
0.188
(0.172)
0.231
(0.099)
1
Panel B: Correlation between returns and one-year ahead earnings measures
ew
Rt
ew
Rt
1
vw
Rt
vw
Rt
0.970
(0.000)
1
CRSPt
0.851
(0.000)
0.931
(0.000)
1
0.535
( 0.000)
0.513
( 0.000)
0.554
( 0.000)
Panel C: Correlation between returns and lagged earnings measures
ew
Rt
ew
Rt
vw
Rt
CRSPt
1
vw
Rt
0.970
(0.000)
1
CRSPt
0.851
(0.000)
0.931
(0.000)
1
DXt 1/Pt 2_ew
0.183
(0.184)
0.176
(0.204)
0.122
DXt 1/Pt 2_vw
0.193
(0.161)
0.203
(0.140)
0.186
DISPt 1
0.190
( 0.182)
0.172
( 0.227)
0.260
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Table 2
Correlation matrix.
ew
vw
This table reports the correlations among time-series of returns, earnings dispersion and macro variables. Return is the cumulative market return from April of year t until March of year t þ1. Rt and Rt are
equal-weighted and value-weighted returns, respectively. CRSPt is the CRSP value-weighted return accumulated from April of year t until March of year t þ 1. DXt/Pt 1_ew and DXt/Pt 1_vw are the equal and
value weighted average change in income before extraordinary items in fiscal year t from fiscal year t 1, deflated by the market value at the beginning of period t. The value-weighted measures use the market
value at the beginning of fiscal year t as the weight. DISPt is the de-trended dispersion of earnings change in year t, respectively. The data covers 1954 2005. We exclude firm-years with non-December fiscal
year-end, stock price below $1, and the top and bottom 5% of firms ranked for each year by DXt/Pt 1 and the weight variables. p-value of Pearson correlation is reported in parenthesis.
ew
Rt
ew
Rt
ew
Rt 1
DISPt
ILIQt 1
MVOLt 1
Ut 1
cayt 1
w
st 1
D_rect 1
GDPt 1
PRODt 1
INFt 1
1
0.396
(0.003)
0.345
(0.011)
0.117
(0.406)
0.087
(0.530)
0.047
(0.736)
0.336
(0.016)
0.020
(0.891)
0.005
(0.973)
0.023
(0.869)
0.261
(0.059)
0.033
(0.812)
ew
Rt 1
DISPt
ILIQt 1
MVOLt 1
Ut 1
cayt 1
w
st 1
D_rect 1
GDPt 1
PRODt 1
1
0.535
(0.000)
0.383
(0.005)
0.368
(0.006)
0.363
(0.007)
0.027
(0.852)
0.039
(0.787)
0.103
(0.457)
0.296
(0.031)
0.013
(0.929)
0.041
(0.769)
1
0.458
(0.001)
0.415
(0.002)
0.087
(0.542)
0.115
(0.430)
0.094
(0.519)
0.183
(0.195)
0.023
(0.873)
0.365
(0.008)
0.145
(0.307)
1
0.388
(0.004)
0.142
(0.311)
0.180
(0.212)
0.049
(0.734)
0.245
(0.077)
0.033
(0.817)
0.249
(0.072)
0.207
(0.137)
1
0.004
(0.976)
0.155
(0.278)
0.131
(0.361)
0.182
(0.188)
0.029
(0.837)
0.186
(0.182)
0.340
(0.013)
1
0.261
(0.026)
0.230
(0.105)
0.699
(0.000)
0.885
(0.000)
0.583
(0.000)
0.340
(0.013)
1
0.013
(0.928)
0.197
(0.167)
0.239
(0.095)
0.206
(0.152)
0.000
(0.997)
1
0.055
(0.701)
0.113
(0.435)
0.273
(0.055)
0.266
(0.062)
1
0.636
(0.000)
0.548
(0.000)
0.327
(0.017)
1
0.504
(0.000)
0.249
(0.073)
1
0.481
(0.000)
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Panel D: Correlation between returns, earnings measures and macro variables
7
8
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
0.12
0.1
0.08
0.06
0.04
0.02
19
51
19
55
19
59
19
63
19
67
19
71
19
75
19
79
19
83
19
87
19
91
19
95
19
99
20
03
0
0.035
0.025
0.015
58
19
62
19
66
19
70
19
74
19
78
19
82
19
86
19
90
19
94
19
98
20
02
19
19
-0.005
54
0.005
-0.015
-0.025
-0.035
Fig. 2. (a) The time-series plot of raw dispersion of earnings change and (b) presents its de-trended time-series. The raw dispersion, st, is the crosssectional dispersion of earnings changes scaled by beginning period market values, that is, (DXt/Pt 1) for all sample firms in year t. DISPt is the estimated
residual, et, from the regression: st ¼ a0 þ a1t þ a2D1973 þ g1st 1 þ g2st 2 þ g3st 3 þ et, where D1973 is a dummy variable equal to 1 for years after 1973, and
0 otherwise.
0.12
0.45
t
1+2
0.4
0.1
0.35
0.08
0.3
0.25
0.06
0.2
0.04
0.15
0.1
0.02
0.05
0
1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003
0
Fig. 3. plots the time-series equal-weighted raw dispersion and the slope coefficient of earnings on negative returns in Basu (1997). The raw dispersion,
st, is the standard deviation of scaled earnings changes (DXt/Pt 1) for all sample firms in year t. We estimate b1 þ b2 from the following cross-sectional
regressions: Xj,t/Pj,t 1 ¼ a0 þ a1DRj,t þ b1Rj,t þ b2DRj,t Rj,t þ Zj,t, where Xj,t/Pj,t 1 is earnings deflated by the price at the beginning of period t, Rj,t is the returns
for firm j in year t, and DRj,t is a dummy variable for negative returns firm-year observations. The scale of the left vertical axis is for st, and the scale of the
right vertical axis is for the Basu coefficient, b1 þ b2.
where Xj, t and Rj, t denote net income before extraordinary items and stock returns for firm j in period t. Pj,t 1 denotes
market value for firm j at the beginning of period t. DRj, t is an indicator variable that equals 1 if Rj, t o0 and zero otherwise.
Fig. 3 presents the sensitivity of earnings to negative returns (bad news), b1 þ b2, along with raw dispersion, st. The figure
is consistent with the hypothesis that earnings dispersion has increased due to an increase in conservatism. For example,
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
9
both dispersion and asymmetric timeliness increase significantly after 1973, the year of the Financial Accounting Standard
Board’s (FASB) formation.
In addition to the trend, the cross-sectional dispersion in earnings changes is serially correlated. Therefore, to estimate
shocks in the cross-sectional dispersion, we use the following regression models to obtain shocks to the cross-sectional
raw dispersion in earnings changes:
st ¼ a0 þ a1 t þ a2 D1973 þ
3
X
gn stn þ et
ð2Þ
n¼1
where t is a time variable, D1973 is an indicator variable, which equals one if the year is after 1973 and 0 otherwise. We
added this time indicator to control for the spike in conservatism reported in Basu (1997). Fig. 2b presents the shocks to
dispersion defined as the residual of these regression models. That is, the time-series of shocks to earnings dispersion,
DISPt, is the time-series estimate of the regression residuals, et, which we refer to as dispersion.
Because we employ the full sample period to estimate Eq. (2), we may introduce a forward-looking bias. However, this
forward bias would matter only if we found that dispersion predicts returns, which we do not. In fact, our results, reported
below, suggest that earnings dispersion is anticipated and does not predict future aggregate stock returns.
Our results might be highly sensitive to the definition of shocks. We therefore use several different models to capture
the relation between the cross-sectional dispersion of earnings changes and aggregate stock returns. Our results
hold when excluding the time and indicator variables, and they are also robust to excluding the third lag crosssectional standard deviation, st 3. In addition, one can add a squared time trend, t2, to the regression model in Eq. (2),
without qualitative changes to our results. In sum, we believe our results to be robust to different estimates of shocks in
dispersion.
Table 1 reports summary statistics for our time-series shocks to earnings dispersion (henceforth, earnings dispersion).
By construction, the mean shock is zero. In addition, the median shock to dispersion, 0.002, is very low in absolute value.
3.3. Earnings dispersion and aggregate earnings
The value-weighted average (DXt/Pt 1_vw) and equal-weighted average (DXt/Pt 1_ew) are as expected highly
correlated, 0.957. The results reported in Table 2 suggest that the cross-sectional dispersion in firm-level earnings
changes is higher during period of low aggregate earnings changes, i.e., dispersion is higher during recessions. The
contemporaneous correlation between earnings dispersion, DISPt, and the average earnings change varies from 0.295 to
0.380. These correlations are statistically significant and may be partly attributable to accounting conservatism. Recall
that the conservatism principle does not allow the full recognition of economic gains until they are realized but requires
the full recognition of an economic loss when anticipated.11 This makes accounting earnings more sensitive to bad news
than to good news, and the cross-sectional dispersion in earnings therefore is likely to be higher during periods of lower
aggregate profits.
4. What explains earnings dispersion?
Here, we test potential explanations of time-varying earnings dispersion: one is related to information uncertainty and
asymmetry, and the other is related to the real effect from the labor market. We also test the effects of several macro
variables.
We use primarily two measures for uncertainty: unexpected market illiquidity and unexpected market volatility.
We follow Amihud (2002) to construct a market illiquidity measure, which is a coarse measure of the price impact in the
Kyle (1985) model. To obtain this measure, we first calculate the daily ratio of absolute stock return to its dollar volume
averaged over each year. We then decompose the illiquidity measure into expected and unexpected components using
the AR(1) process. Following Amihud (2002), we also use the logarithmic transformation of the liquidity measure in the
autoregression model. The unexpected component of market illiquidity is denoted as ILIQt for each year. Our measure of
unexpected (unpredictable) market volatility is the measure used by French et al. (1987). We first estimate the variance of
annual return to market portfolio as follows:
s2t ¼
Jt
X
j¼1
R2j,t þ 2
Jt 1
X
Rj,t Rj,t þ 1
ð3Þ
j¼1
where there are Jt daily value-weighted market returns, Rj,t, in year t. Then we follow French et al.’s (1987) approach to
decompose the market volatility into predictable and unpredictable components using a third order ARIMA model for the
logarithm of the standard deviation of market returns. The unpredictable component of realized market volatility in year t
is denoted by MVOLt.
11
See for example, Basu (1997) and Ball et al. (2000).
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
10
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
We then examine whether earnings dispersion is related to the real effect from the shocks in the labor market
(Lilien, 1982). We first construct the unemployment shock variable from the unemployment data available from the
Federal Reserve Economic Data (FRED). To obtain the annual measure, we use the average of unemployment rates in
12 months beginning April of year t until March of year t þ1. We then use an AR(2) model to estimate shocks to
unemployment, denoted as Ut. As unemployment shocks also directly affect household incomes, wealth, and intertemporal
rates of substitution, we also more directly examine the relation between earnings dispersion and other direct measures of
consumption and wealth. Specifically we use two variables previously documented in the asset pricing literature to be
related to stock returns: consumption-to-wealth ratio (cayt), as in Lettau and Ludvigson (2001), and labor income-to12
consumption ratio ðsw
t Þ, as in Santos and Veronesi (2006).
We also test whether earnings dispersion is likely to reflect economic transitions and business cycles caused by
technology and production shocks, etc. We follow Fama and French (1989) to proxy the business condition over years by
an indicator variable, D_rect, which equals one in the recession periods using the business cycle dates provided by NBER
and zero otherwise.13 We also test several other macro variables, such as GDP growth, industrial production growth, and
the inflation rate. For these variables, we use an AR(3) time-series model to estimate shocks in each year. We extract the
data on unemployment, real GDP, inflation, and industrial production from the FRED.
Descriptive statistics of these macro variables appear in Panel C of Table 1. Since most of our explanatory variables are
unpredictable or shock components, their means and medians are close to zero. When we move on to examine what
factors can explain earnings dispersion, one thing we need to consider is the lead-lag relations between earnings
dispersion and these market and macro variables. The market uncertainty and macro variables are most likely unexpected
by the market as we construct the de-trended shocks to measure these variables. We expect higher uncertainty and shocks
to the labor market and macroeconomy will manifest themselves in higher future earnings dispersion. Therefore the
current earnings dispersion is more likely related to lagged macro variables. Although our measures for earnings
dispersion and macro variables are both based on the de-trended shocks, this lead-lag relation may still be possible given
that earnings typically lack timeliness. In Table 2, we show the correlations among returns, earnings dispersion and the
lagged macro variables. However, when we test the explanation for earnings dispersion through regressions, we include
both contemporaneous and lagged macro variables in Table 3 in Panel A and Panel B, respectively.
As shown in the first two columns of Panel A of Table 3, both the unexpected market illiquidity (ILIQt 1) and
unexpected market volatility (MVOLt 1) are positively related to future earnings dispersion (DISPt). The t-statistics after
adjusting for the Newey–West standard errors are 4.01 and 3.86, respectively. This result is consistent with our conjecture
that uncertainty in the market is related to earnings dispersion across firms. We do not include the predictable market
volatility and illiquidity components in our model, because our dispersion measure is the unexpected shock to raw
dispersion in earnings changes and should not be correlated with predictable uncertainty in the market. Unreported
results that include the predictable components are consistent with our conjecture. The contemporaneous uncertainty
measures are not significantly related to earnings dispersion.
Table 3 also reports the results for testing the relation between earnings dispersion and the labor market conditions. Of
all three variables we employ in the test, only the contemporaneous unemployment shock (Ut) is significantly and
positively related to earnings dispersion, with a coefficient of 0.005 and t-statistics of 2.31. The other two variables are also
positively related to dispersion, though they are not significant. The contemporaneous relation suggests the dispersion in
performance among firms occurs at the same time of the unemployment fluctuation. If, however, we include both the
uncertainty variables and the unemployment shock in the regression, as shown in the column next to the last, the
unemployment shock becomes statistically insignificant, while the uncertainty measures remain significantly positive.
This suggests that earnings dispersion is more likely related to uncertainty than to the labor market effect.
We also test the effects of other macro variables on earnings dispersion. Our results in Table 3 show that most of these
variables are insignificantly related to earnings dispersion, except the contemporaneous GDP growth shock (GDPt) and the
lagged shock in industrial production (PRODt 1). We do not have a good explanation for such a difference in timing for
these two variables. But in unreported results for the remaining tests in the paper, we perform the regressions with both
contemporaneous and lagged variables to ensure that our main results about earnings dispersion are unaffected. The last
column in each panel shows the result of regressing earnings dispersion on all these explanatory variables, indicating that
lagged uncertainty variables (ILIQt 1 and MVOLt 1) remain significantly positively related to dispersion, while other
factors have no explanatory power beyond these two variables. However, since some of the macro variables that we
include are highly correlated with each other, such as unemployment shock and GDP growth shock, we also test the
regression by excluding one of the highly correlated variables. The results remain similar in that uncertainty variables
remain most significant in explaining the dispersion. The results in Table 3 are overall consistent with the correlations
reported in Table 2 Panel D.
12
The data for cayt from 1948 to 2001 is extracted from the author’s website http://faculty.haas.berkeley.edu/lettau/datacay.html. For the variable
sw
t , we follow Santos and Veronesi (2006) to measure consumption as nondurables plus services and to measure labor income as wages and salaries, plus
transfer payments plus other labor income (minus personal contributions for social insurance minus taxes). These data are obtained from Bureau of
Economic Analysis.
13
http://www.nber.org/cycles.html.
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
11
Table 3
Earnings dispersion.
This table reports time-series regression results of earnings dispersion on explanatory variables. DISPt is the de-trended dispersion of earnings changes.
ILIQt is the unexpected market illiquidity measure from Amihud (2002). MVOLt is the unexpected market volatility measured following French et al.
(1987). Ut is the de-trended shock in the unemployment in year t. D_rect is the dummy variable which equals 1 if year t is in the recession period based on
the NBER definition. cayt is the consumption to wealth ratio as in Lettau and Ludvigson (2001), available from 1954 to 2001. sw
t is the labor income to
consumption ratio as in Santos and Veronesi (2006), available from 1954 to 2001. GDPt is the de-trended shock in GDP growth rate in year t. PRODt is the
de-trended shock in the growth rate of industrial production in year t. INFt is the de-trended shock in the inflation rate in year t. The t-statistic with
Newey–West standard errors is reported in parenthesis. #Obs is the number of observations used in each regression.
Panel A: Earnings dispersion and lagged macro variables
Dependent variable: DISPt
Intercept
DXt/Pt 1_ew
ILIQt 1
0.001
(0.66)
0.149
( 1.49)
0.019
(4.01)
0.001
(0.72)
1.155
( 1.55)
0.001
(0.73)
0.221
( 2.13)
0.002
(0.92)
0.264
( 2.71)
0.033
( 1.14)
0.271
( 2.90)
0.000
(0.01)
0.194
( 2.00)
0.001
(0.72)
0.211
( 2.09)
0.001
(0.43)
0.119
( 1.31)
0.001
(0.67)
0.188
( 2.05)
0.089
(3.86)
MVOLt 1
0.002
(1.02)
Ut 1
0.096
(0.99)
cayt 1
sw
t1
0.042
(1.15)
0.004
(1.42)
D_rect 1
0.032
( 0.54)
GDPt 1
0.067
( 2.58)
PRODt 1
0.084
49
0.099
49
0.023
52
0.116
52
0.067
(0.54)
0.032
52
0.002
(0.90)
0.268
( 2.66)
0.039
( 1.14)
0.288
( 2.92)
0.000
(0.02)
0.008
( 0.09)
0.001
(0.68)
0.192
( 1.71)
0.001
(0.70)
0.199
( 2.16)
INFt 1
2
Adj. R
#Obs
0.027
( 1.02)
0.227
( 2.39)
0.013
(2.64)
0.053
(2.20)
0.000
(0.21)
0.075
(0.80)
0.035
(1.07)
0.210
52
0.188
52
0.037
52
0.083
52
0.283
49
0.021
( 0.61)
0.134
( 1.00)
0.011
(2.23)
0.052
(1.89)
0.001
( 0.41)
0.058
(0.62)
0.027
(0.64)
0.001
(0.32)
0.023
(0.20)
0.053
( 1.19)
0.050
( 0.50)
0.246
49
Panel B: Earnings dispersion and contemporaneous macro variables
Dependent variable: DISPt
Intercept
DXt/Pt 1_ew
ILIQt
0.001
(0.74)
0.218
( 2.36)
0.008
( 1.15)
0.001
(0.60)
0.219
( 2.18)
0.000
( 0.06)
0.013
( 0.12)
0.002
( 0.89)
0.062
( 0.56)
0.035
( 1.58)
MVOLt
0.005
(2.31)
Ut
0.059
(0.91)
cayt
sw
t
0.049
(1.15)
0.007
(1.67)
D_rect
0.186
( 2.69)
GDPt
0.006
( 0.18)
PRODt
0.027
(0.51)
INFt
0.5
Adj. R2
#Obs
0.0259
( 0.70)
0.171
( 1.27)
0.001
( 0.12)
0.032
( 1.43)
0.003
(1.40)
0.012
( 0.16)
0.032
(0.69)
0.080
( 1.87)
0.270
( 1.68)
0.005
(0.84)
0.054
( 1.75)
0.002
( 0.45)
0.005
(0.09)
0.095
(1.84)
0.008
(1.29)
0.099
( 0.78)
0.086
(2.10)
0.071
(0.95)
0.052
0.048
0.141
0.078
0.099
0.134
0.149
0.073
0.075
0.333
0.325
52
52
52
52
48
48
52
52
52
48
48
5. Earnings dispersion and aggregate stock returns
This section tests the relation between the cross-sectional firm-level dispersion in earnings changes and aggregate
stock returns. We test the contemporaneous relation between returns and earnings dispersion and the lead-lag relation
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
12
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
between returns and one-year-ahead earnings dispersion. Since our dispersion measure is correlated with the average
earnings changes, it is important to control for the latter. This section utilizes the following regression model:
Rw
t ¼ d0 þ d1 ðDXt þ t =Pt þ t1 _wÞ þ d2 DISPt þ t þ xt
ð4Þ
where t ¼{ 1,0,1} and w¼{ew, vw, CRSP}.
The time-series of shocks to the cross-sectional dispersion in earnings changes appears to have some significant spikes.
Note that the results in this section hold when we exclude these observations. Specifically, our results are robust to
excluding years 1975, 1991, 2001, and 2003.
In Table 2, we report the correlation between cross-sectional dispersion (DISPt) and all three measures of market
returns. The results indicate a positive association between the cross-sectional earnings dispersion and contemporaneous
aggregate stock returns. The correlation varies from 0.184 to 0.345 and is statistically significant. Next we test the relation
between earnings dispersion and stock returns through multivariate regressions.
5.1. The relation between stock returns and contemporaneous earnings dispersion
Table 4 reports OLS results for estimating the regression presented in Eq. (4) using different measures of aggregate
returns. All t-statistics employ Newey–West adjusted standard errors. The results in the first column of each Panel in
Table 4 are consistent with the correlations reported in Table 2: aggregate stock returns are positively related to
contemporaneous earnings dispersion DISPt. The regression coefficient on dispersion varies from 1.968 to 6.677. The most
significant result with a t-statistic of 2.590 is in the equal-weighted return regression ðRew
t Þ. Consistent with Kothari et al.
(2006), Sadka (2007), and Sadka and Sadka (2009), Table 4 reaffirms a negative association between earnings changes and
contemporaneous aggregate returns. The coefficient varies from 1.199 to 3.185 with a t-statistic varying from 0.43
to 1.12.
To test whether the relation between aggregate returns and contemporaneous earnings dispersion is driven by factors
other than earnings dispersion, we also perform the regression by including each factor as shown in Table 4. We control for
the lagged measures of these variables given our previous discussion in Section 4.14 Two lagged uncertainty measures,
ILIQt 1 and MVOLt 1, are negatively correlated with aggregate returns in all three panels, but they are statistically
insignificant.15 This is not surprising as the lagged uncertainty has very little information to predict future returns and is
manifested in earnings dispersion. The relation between returns and contemporaneous earnings dispersion cannot be
explained by uncertainty in the previous period. We then add the variables related to labor market in the regression.
Among our three measures, only the lagged consumption-to-wealth ratio cayt 1 exhibits a significantly positive
relationship with aggregate returns. This is consistent with prior research (Lettau and Ludvigson, 2001) that cay can
predict future returns. Given that our results in Table 3 suggest that earnings dispersion is not significantly related to
either contemporaneous or lagged cay, this result mainly suggests that the predictive power of cay dominates in explaining
contemporary returns.
We perform additional tests by including other macro variables as specified in Table 3. These variables do not show any
significant relation to aggregate returns, and our earnings dispersion measure remains significant in all three regressions.16
When we include all variables in one regression, as in the last column of each panel, the earnings dispersion measure
becomes insignificant. The insignificance may be due to small numbers of observations or the multicollinearity among
macro variables. In sum, the contemporaneous relation between stock returns and earnings dispersion is generally
positive, but the statistical significance of the relation varies significantly with respect to our control variables. We
acknowledge there is potential problem of bias in our results when we use lagged macro variables and contemporaneous
dispersion in the contemporaneous return regression. This could bias our results towards dispersion, but as noted
previously, the relation between return and earnings dispersion is more pronounced for the future earnings dispersion
than contemporaneous dispersion.
5.2. The relation between stock returns and future earnings dispersion
The accounting literature documents that earnings are not timely (e.g., Ball and Brown, 1968; Basu, 1997). Therefore,
earnings lag stock returns and are predictable. In fact, Sadka and Sadka (2009) find that contemporaneous aggregate
earnings changes provide little or no new information and that cash flow news is reflected mostly in future earnings.
Therefore, earnings dispersion may be predictable as well. To investigate this, we test the relation between stock returns
and future earnings dispersion (DISPt þ 1).
Table 5 reports OLS results for estimating Eq. (4) using three specifications of returns: equal-weighted, value-weighted,
and CRSP value-weighted returns. The results with earnings dispersion and earnings change variables are shown in the
14
We also perform the regression controlling the contemporaneous measures of these variables, and the results do not change significantly.
We also run the regressions including the predictable components of illiquidity and market volatility, respectively, and both variables are
insignificant in the regression.
16
Consistent with prior studies, in unreported results, labor income-to-consumption ratio and wealth-to-consumption ratio are significantly
associated with one-period ahead stock returns.
15
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Panel A: Equal-weighted return and contemporaneous earnings dispersion regressions
ew
Dependent variable: Rt
Intercept
DXt/Pt 1_ew
DISPt
0.168
(5.16)
1.199
( 0.43)
6.677
(2.59)
ILIQt 1
0.168
(5.09)
1.232
( 0.44)
7.186
(2.54)
0.049
( 0.61)
MVOLt 1
0.166
(4.96)
1.230
( 0.45)
7.321
(2.44)
0.168
(5.20)
1.290
( 0.44)
6.609
(2.43)
0.177
(6.16)
4.079
( 1.69)
2.949
(1.36)
0.272
(0.46)
3.293
( 1.20)
4.087
(1.82)
0.178
(4.64)
1.205
( 0.42)
6.922
(2.51)
0.169
(5.27)
1.294
( 0.45)
6.637
(2.53)
0.164
(5.24)
0.628
( 0.25)
5.759
(2.00)
0.329
( 0.74)
Ut 1
0.006
(0.26)
cayt 1
4.559
(2.21)
sw
t1
0.130
( 0.18)
D_rect 1
0.035
( 0.47)
GDPt 1
0.275
( 0.33)
PRODt 1
0.615
( 1.32)
INFt 1
Adj. R
#Obs
0.169
(5.23)
1.259
( 0.46)
6.756
(2.44)
2
0.074
52
0.077
52
0.072
52
0.179
52
0.057
49
0.076
49
0.076
52
0.073
52
0.091
52
0.392
(0.22)
0.073
52
0.164
(7.19)
4.403
( 2.50)
0.902
(0.51)
0.153
(0.29)
3.663
( 1.72)
2.006
(0.98)
0.162
(4.77)
2.093
( 0.97)
3.896
(2.04)
0.157
(5.99)
2.244
( 1.08)
3.677
(1.99)
0.152
(5.83)
1.575
( 0.79)
2.915
(1.47)
0.157
(5.740)
2.134
( 1.02)
3.800
(1.96)
0.771
(1.17)
2.668
( 0.81)
2.467
(1.04)
0.075
( 0.77)
0.244
( 0.50)
0.044
(0.74)
4.732
(2.18)
0.710
( 0.87)
0.063
( 0.79)
2.215
(1.00)
0.858
( 1.14)
0.310
(0.14)
0.049
49
Panel B: Value-weighted return and contemporaneous earnings dispersion regressions
vw
Dependent variable: Rt
Intercept
DXt/Pt 1_vw
DISPt
ILIQt 1
MVOLt 1
Ut 1
cayt 1
0.156
(5.67)
2.100
( 0.99)
3.906
(1.88)
0.016
( 0.23)
0.154
(5.60)
2.118
( 1.02)
4.326
(2.00)
0.156
(5.89)
2.237
( 1.04)
3.629
(1.90)
0.298
( 0.80)
0.010
(0.43)
4.718
(3.04)
0.001
0.494
(0.80)
3.608
( 1.40)
0.389
(0.18)
0.027
( 0.27)
0.188
(0.46)
0.078
(0.44)
4.831
(2.74)
0.387
13
sw
t1
0.154
(5.76)
2.395
( 0.82)
3.520
(1.70)
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Table 4
Contemporaneous earnings dispersion and returns.
This table reports time-series regression results for contemporaneous stock returns. The earnings and return measures are defined as in Table 1. ILIQt is the unexpected market illiquidity measure from
Amihud (2002). MVOLt is the unexpected market volatility measured following French et al. (1987). Ut is the de-trended shock in the unemployment in year t. D_rect is the dummy variable which equals 1 if
w
year t is in the recession period based on the NBER definition. cayt is the consumption to wealth ratio as in Lettau and Ludvigson (2001), available from 1954 to 2001. st is the labor income to consumption ratio
as in Santos and Veronesi (2006), available from 1954 to 2001. GDPt is the de-trended shock in GDP growth rate in year t. PRODt is the de-trended shock in the growth rate of industrial production in year
t. INFt is the de-trended shock in the inflation rate in year t. The t-statistic with Newey–West standard errors is reported in parenthesis. #Obs is the number of observations used in each regression.
14
Panel B: Value-weighted return and contemporaneous earnings dispersion regressions
vw
Dependent variable: Rt
(0.00)
D_rect 1
0.018
( 0.35)
GDPt 1
0.446
( 0.49)
PRODt 1
0.554
( 1.30)
INFt 1
Adj. R
#Obs
2
0.052
52
0.088
52
0.181
52
0.076
49
0.060
49
0.062
52
0.046
52
0.031
52
0.291
( 0.19)
0.028
52
0.159
(7.33)
5.159
( 3.67)
0.958
( 0.53)
0.243
(0.46)
4.074
( 1.97)
0.627
(0.27)
0.149
(4.10)
2.885
( 1.41)
2.369
(1.25)
0.145
(4.85)
2.986
( 1.47)
2.190
(1.12)
0.141
(4.71)
2.509
( 1.28)
1.634
(0.82)
0.145
(4.74)
2.962
( 1.46)
2.338
(1.19)
0.135
52
( 0.51)
0.051
( 0.77)
1.231
(0.52)
0.553
( 0.79)
0.136
(0.07)
0.346
49
Panel C: CRSP value-weighted return and contemporaneous earnings dispersion regressions
Dependent variable: CRSPt
Intercept
DXt/Pt 1_vw
DISPt
0.116
(4.65)
3.185
( 1.12)
1.968
(0.92)
ILIQt 1
0.144
(4.73)
2.881
( 1.41)
2.224
(1.03)
0.001
( 0.01)
MVOLt 1
0.143
(4.64)
2.905
( 1.48)
2.696
(1.22)
0.145
(4.85)
3.034
( 1.51)
2.116
(1.08)
0.236
( 0.68)
Ut 1
0.011
(0.44)
cayt 1
6.491
(5.15)
sw
t1
0.121
( 0.18)
D_rect 1
0.016
( 0.31)
GDPt 1
0.300
( 0.33)
PRODt 1
0.402
( 0.96)
INFt 1
Adj. R
#Obs
2
0.026
52
0.065
52
0.181
52
0.135
52
0.076
49
0.060
49
0.062
52
0.046
52
0.031
52
0.601
( 0.33)
0.028
52
0.614
(1.00)
4.565
( 2.04)
1.384
( 0.56)
0.065
( 0.64)
0.505
( 1.27)
0.044
(0.72)
7.025
(5.20)
0.529
( 0.70)
0.064
( 1.14)
1.702
(0.72)
0.389
( 0.61)
0.198
( 0.11)
0.339
49
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Table 4 (continued )
Panel A: Equal-weighted return and future earnings dispersion regressions
ew
Dependent variable: Rt
Intercept
DXt þ 1/Pt_ew
DISPt þ 1
0.139
(6.82)
2.917
(1.86)
9.988
( 4.19)
ILIQt
0.139
(7.53)
2.821
(1.77)
8.503
( 3.45)
0.142
( 1.56)
MVOLt
0.138
(6.60)
2.832
(1.74)
8.728
( 3.14)
0.144
(6.32)
1.502
(0.89)
11.082
( 5.02)
0.110
(4.09)
2.934
(1.66)
10.742
( 4.92)
0.136
(7.73)
3.072
(1.76)
8.428
( 3.52)
0.325
(0.63)
3.220
(1.82)
8.272
( 3.34)
0.146
(6.64)
1.984
(1.17)
10.385
( 4.31)
0.132
(5.74)
3.923
(2.10)
11.603
( 4.44)
0.136
(6.19)
3.156
(1.91)
10.300
( 4.34)
0.651
( 1.57)
Ut
0.099
(5.50)
cayt
0.127
(0.06)
sw
t
0.232
( 0.37)
D_rect
0.090
(2.13)
GDPt
2.707
( 2.95)
PRODt
1.082
( 2.15)
INFt
2
Adj.R
#Obs
0.290
52
0.298
52
0.283
52
0.436
52
0.319
48
0.243
48
0.245
52
0.360
52
0.334
52
1.563
( 1.40)
0.293
52
0.189
(0.39)
0.855
(0.35)
7.265
( 3.55)
0.141
(7.23)
0.209
(0.10)
8.831
( 4.37)
0.133
(6.86)
1.581
(0.67)
9.517
( 4.54)
0.136
(6.77)
0.798
(0.35)
8.728
( 4.51)
0.934
(1.83)
1.397
(0.72)
5.923
( 2.38)
0.188
( 2.75)
0.416
( 0.89)
0.241
(5.37)
1.390
( 0.73)
0.963
( 1.57)
0.054
( 0.75)
4.167
(3.36)
0.269
(0.41)
0.456
(0.42)
0.480
48
Panel B: Value weighted return and future earnings dispersion regressions
vw
Dependent variable: Rt
Intercept
DXt þ 1/Pt_vw
DISPt þ 1
ILIQt
MVOLt
Ut
cayt
sw
t
D_rect
0.138
(7.72)
0.558
(0.27)
8.194
( 4.01)
0.039
( 0.53)
0.136
(7.93)
0.702
(0.35)
7.355
( 3.16)
0.137
(6.88)
0.001
(0.00)
9.398
( 5.04)
0.112
(4.38)
0.885
(0.38)
9.145
( 5.10)
0.139
(7.88)
0.681
(0.30)
7.513
( 3.95)
0.611
( 1.64)
0.085
(5.60)
0.898
(0.72)
0.064
( 0.11)
0.077
(2.17)
2.131
0.649
(1.36)
0.696
( 0.29)
5.524
( 2.92)
0.093
( 1.71)
0.296
( 1.09)
0.234
(5.26)
0.539
( 0.41)
0.620
( 1.07)
0.047
( 0.71)
4.240
15
GDPt
0.138
(7.62)
0.567
(0.27)
8.606
( 4.49)
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Table 5
One-year ahead earnings dispersion and returns.
This table reports time-series regression results for stock returns and one-year ahead earnings dispersion. The earnings and return measures are defined as in Table 1. ILIQt is the unexpected market illiquidity
measure from Amihud (2002). MVOLt is the unexpected market volatility measured following French et al. (1987). Ut is the de-trended shock in the unemployment in year t. D_rect is the dummy variable which
w
equals 1 if year t is in the recession period based on the NBER definition. cayt is the consumption to wealth ratio as in Lettau and Ludvigson (2001), available from 1954 to 2001. st is the labor income to
consumption ratio as in Santos and Veronesi (2006), available from 1954 to 2001. GDPt is the de-trended shock in GDP growth rate in year t. PRODt is the de-trended shock in the growth rate of industrial
production in year t. INFt is the de-trended shock in the inflation rate in year t. The t-statistic with Newey–West standard errors is reported in parenthesis. #Obs is the number of observations used in each
regression.
16
Panel B: Value weighted return and future earnings dispersion regressions
vw
Dependent variable: Rt
( 2.85)
PRODt
0.715
( 1.71)
INFt
Adj. R2
#Obs
0.261
52
0.240
52
0.245
52
0.420
52
0.284
48
0.178
48
0.170
52
0.317
52
0.274
52
0.825
(0.71)
0.245
52
0.351
(0.70)
1.517
(0.58)
7.754
( 3.05)
0.124
(5.96)
0.390
( 0.18)
9.167
( 3.66)
0.119
(5.70)
1.246
(0.52)
9.470
( 3.71)
0.122
(5.63)
0.772
(0.32)
9.016
( 3.63)
(3.48)
0.553
(1.05)
0.242
( 0.21)
0.431
48
Panel C: CRSP value-weighted return and future earnings regressions
Dependent variable: CRSPt
Intercept
DXt þ 1/Pt_vw
DISPt þ 1
0.122
(6.21)
0.695
(0.31)
8.975
( 3.69)
ILIQt
0.122
(6.19)
0.695
(0.31)
8.962
( 3.18)
0.001
( 0.02)
MVOLt
0.120
(6.99)
0.853
(0.42)
7.517
( 2.75)
0.121
(5.71)
0.183
(0.09)
9.692
( 4.08)
0.100
(3.76)
0.958
(0.40)
9.421
( 4.03)
0.125
(6.51)
1.199
(0.49)
8.141
( 3.57)
0.712
( 1.80)
Ut
0.077
(5.02)
cayt
0.064
(1.73)
sw
t
0.961
(0.79)
D_rect
0.278
( 0.45)
GDPt
1.813
( 2.52)
PRODt
0.389
( 0.96)
INFt
2
Adj.R
#Obs
0.281
52
0.266
52
0.273
52
0.415
52
0.297
48
0.215
48
0.212
52
0.323
52
0.276
52
0.275
(0.24)
0.266
52
0.767
(1.44)
0.427
( 0.17)
5.910
( 2.28)
0.058
( 0.88)
0.338
( 1.00)
0.224
(5.14)
0.067
( 0.91)
0.409
( 0.36)
0.768
( 1.19)
3.662
(2.69)
0.671
(1.28)
0.586
( 0.58)
0.431
48
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
Table 5 (continued )
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
17
first column of each panel. The results are consistent with prior studies, suggesting that earnings lack timeliness and are
predictable. Higher future earnings dispersion is preceded by lower aggregate stock returns. The coefficient on dispersion
varies from 8.606 to 9.988. The t-statistic varies from 3.69 to 4.69, i.e., the relation is statistically significant in all
models. This result is consistent with the correlations reported in Panel B of Table 2, where the correlations between
DISPt þ 1 and Rw
t (for w¼{ew, vw, CRSP}) vary from 0.513 to 0.554 and are statistically significant as well. The results in
Table 5 suggest that expected future earnings dispersion explains a significant portion of the time-series variation in
aggregate stock returns. When earnings dispersion is added as an independent variable in Eq. (4), the explanatory power
more than quadruples that from the regression with earnings change alone.
To explore whether other factors explain the lead-lag relation between future earnings dispersion and stock returns, we
perform the regressions including other factors similar to the last section. We use contemporaneous values of these
variables as we do not expect these factors have a delayed effect like accounting earnings. We first include each variable
into the return-dispersion regression one by one, and then we also run the regression including all variables. These results
show that the negative relation between one-year-ahead earnings dispersion and aggregate returns is not due to other
factors such as uncertainty, labor market, or other macroeconomic conditions. Earnings dispersion remains statistically
significant in all regressions. The uncertainty measures ILIQt and MVOLt are in general insignificant. Unemployment shock
(Ut) is positively related to returns and statistically significant (the t-statistic varies from 5.02 to 5.60). Overall, our control
variables do not impede the relation between one-year-ahead future earnings dispersion and returns.
Since we are regressing stock returns on future realization of dispersion, look-ahead bias may be a concern. Recall that we
estimate the relation between aggregate stock returns and expected future earnings dispersion using the actual future earnings
dispersion, which is a noisy measure of expectations. Specifically, actual future earnings dispersion is a proxy for expected
future dispersion, measured with error.17 This error creates an errors-in-variables problem, which may bias our coefficients. If
this error has non-zero correlation with our other independent variables, our coefficients estimates may be biased towards
finding our results. If, instead, this error is uncorrelated with our other independent variables, then the bias is towards zero, i.e.,
a bias against our findings. Since all other independent variables in our tests (except for aggregate earnings changes) are lagged
measures, these variables cannot be correlated with the future error, which is the unexpected component. As a sensitivity test,
we ran our regressions omitting the aggregate earnings changes and found qualitatively similar results.
5.3. Using volatility index as a measure of uncertainty
Our measure of uncertainty using unexpected market volatility (MVOLt), estimated from realized returns, seems not to
work very well in most of the regressions we performed. To better test the results, we employ a more direct forward-looking
measure of uncertainty, the implied market volatility known as VIX. Monthly VIX data is available from Chicago Board
Options Exchange (CBOE) Volatility Index. The current methodology by which VIX is measured starts with data only from
1990 forward. Due to this limited period, we perform the tests relying on the annualized quarterly data basis. The total
sample period covers the first quarter of 1990 to the third quarter of 2008. We only include firms with the fiscal year-end at
March, June, September, and December. For each quarter q in our sample period, we first calculate the annual earnings
aggregated from the previous four quarters, denoted by Xq. We then calculate the equal-weighted average annualized
earnings change for each quarter, DXq/Pq 4_ew, based on the change from the earnings four quarters before deflated by the
price at the beginning of quarter q 4, i.e., (Xq–Xq 4)/Pq 4. Accordingly our measure of earnings dispersion (DISPq) is the detrended dispersion (standard deviation) of earnings changes in that quarter. We also calculate the equal-weighted returns
using the same methodology. Rew
q is the equal-weighted annualized return for quarter q, which is accumulated in the last 12
months starting from 10 months before the fiscal quarter-end. By this construction, we have a total sample of 75 periods, and
the data contains overlapping observations. Therefore, we report the t-statistic with Newey–West standard errors. In Table 6
we only report the results using equal-weighted returns, but value-weighted and CRSP value-weighted results are similar.
The results using VIX are reported in Table 6. First, VIXq is positively related to our earnings dispersion measure with a
coefficient of 0.0003 and statistically significant with a t-statistic of 2.48. In the contemporaneous return regression,
earnings dispersion is positively related to aggregate stock returns with a coefficient of 14.287 and t-statistic of 2.50.
The uncertainty measured by VIXq is negatively related to contemporaneous returns, with a coefficient of 0.007 and
t-statistic of 1.98. These are all consistent with our prior results using unexpected market illiquidity measure (ILIQ).
In the lead-lag regression, the future earnings dispersion is negatively related to aggregate returns with a coefficient of
18.564 and t-statistic of 3.14. VIXq is insignificant with a t-statistic of 0.18 in the lead-lag regression.
We also control for other macro variables that are found to be significant in prior results. Similarly, for each quarter,
we construct the unemployment shock (Uq) based on the annualized unemployment rate, the GDP growth shock (GDPq)
based on the annualized GDP growth, and the industrial production shock (PRODq) based on the annualized production.
The results are presented in Table 6. They resemble what we find in Tables 4 and 5. After controlling for these macro
variables, VIXq is still positively related to earnings dispersion and statistically significant. Earnings dispersion remains
statistically significant and positive in the contemporaneous regression and significantly negative in the lead-lag
17
This point is well-understood in the literature, see Miller and Scholes (1972), Levi (1973), Chan and Chen (1988), and Handa, Kothari, and Wasley
(1989), among others.
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
18
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
Table 6
Earnings dispersion and implied market volatility.
This table reports the relationship between earnings dispersion and the implied market volatility and the contemporaneous and lagged return results
controlling the implied market volatility. VIX is CBOE Volatility Index under new methodology starting from 1990. In this table all variables are measured
on the annualized quarterly data basis due to the limited time period of the VIX data. The total sample period covers the first quarter of 1990 to the third
quarter of 2008. We only include firms with fiscal year end at March, June, September and December. For each quarter q in our sample period, we first
calculate the annual earnings aggregated from last four quarters, denoted as Xq. DXq/Pq 4_ew is the equal-weighted average earnings change, calculated
as (Xq Xq 4)/Pq 4 , where Pq 4 is the price at the beginning of quarter q-4. Accordingly our measure of earnings dispersion (DISPq) is the de-trended
ew
dispersion (standard deviation) of earnings changes in that quarter. Rq is the equal-weighted annualized return for quarter q, which is accumulated in
the last 12 months starting from ten months before the fiscal quarter end. Other macro variables are also constructed based on the rolling-window
method each quarter. Uq is the de-trended shock in unemployment for quarter q. GDPq is the de-trended shock in GDP growth for quarter q. PRODq is the
de-trended shock in production for quarter q. The t-statistic with Newey–West standard errors is reported in parenthesis.
ew
Intercept
0.006
( 2.15)
0.653
(1.62)
DXq þ t/Pq þ t 1_ew
0.006
( 2.36)
0.737
(1.31)
DISPq þ t
VIXq þ t
0.0003
(2.48)
Uq þ t
GDPq þ t
PRODq þ t
Adj. R2
#Obs
0.156
75
ew
Rq (t ¼0)
DISPq
0.0003
(2.87)
0.015
(3.61)
0.122
( 0.50)
0.157
(1.42)
0.211
67
0.235
(3.20)
14.578
(0.88)
14.287
(2.50)
0.007
( 1.98)
0.174
75
Rq (t ¼4)
0.220
(3.56)
0.197
(0.02)
9.360
(3.34)
0.005
( 1.67)
0.156
(1.13)
18.511
(3.03)
0.131
( 0.04)
0.242
67
0.094
(1.24)
19.324
(2.33)
18.564
( 3.14)
0.001
(0.18)
0.208
71
0.097
(1.72)
7.214
( 0.74)
12.135
( 4.19)
0.001
(0.48)
0.292
(2.01)
19.191
(2.90)
2.313
(0.64)
0.315
67
regression, while VIXq becomes weak in the contemporaneous return result and insignificant in the lead-lag return result.
All these results are consistent with our prior findings using other measures of uncertainty.
6. Robustness tests
The denominator in dispersion – market values – might drive our results. To address this concern, we first control for
the dispersion in the book-to-market ratio in the contemporaneous and lead-lag return regressions in Tables 4 and 5. We
next use different dispersion measures, such as earnings changes deflated by total assets. We then test whether our results
hold for returns in excess of the risk-free rate. Our results are robust to all these tests.
6.1. Controlling for book-to-market
Our first robustness test covers the period from 1963 to 2005, as the book value data is available after 1962. We delete
the top and bottom 5% of firms ranked by book-to-market ratio each year. Similar to earnings dispersion, we first obtain
the time-series shocks to cross-sectional dispersion in book-to-market ratio, DISPtbtm , as the estimated residual from the
following regression model:
sbtm
¼ a0 þ
t
3
X
btm
bn sbtm
tn þ et
ð5Þ
n¼1
If our previous results were driven by the beginning-of-period price volatility, we would expect that the book-tomarket dispersion at the beginning of period would capture this effect and make the earnings dispersion insignificant.
Untabulated results indicate that the coefficients on cross-sectional earnings dispersion are consistent with previous tests.
Controlling for book-to-market dispersion does not qualitatively affect our results.
6.2. Scaling by total assets
We also perform tests using an alternative earnings dispersion measure: earnings change deflated by total assets at the
beginning of the year. We delete the bottom 10% and top 5% of the asset-deflated earnings change since accounting numbers
are more negatively skewed due to conservatism. We calculate both the equal-weighted and asset value-weighted means
and standard deviations for asset-deflated earnings changes.18 The shocks to asset-deflated earnings dispersion are again
18
We use total asset value as weights to calculate the weighted average and standard deviation of asset-deflated earnings changes in a similar
fashion to the aggregate measure (dE/B-agg) in Kothari et al. (2006).
Please cite this article as: Jorgensen, B., et al., Earnings dispersion and aggregate stock returns. Journal of Accounting
and Economics (2011), doi:10.1016/j.jacceco.2011.06.001
B. Jorgensen et al. / Journal of Accounting and Economics ] (]]]]) ]]]–]]]
19
obtained from the AR(3) time-series model with an indicator variable for years after 2000.19 Untabulated results using the
asset-deflated earnings change measures are consistent with our prior tests results.
6.3. Excess returns
Our results above use the raw aggregate market returns. We next test whether the relation between earnings
dispersion and stock returns holds for returns in excess of the risk-free rate (extracted from the Fama and French database
on WRDS). Untabulated results show that the relation between earnings dispersion and stock returns holds for returns in
excess of the risk-free rate as well, suggesting that earnings dispersion is not driven by variation in the risk-free rate but is
in fact related to the risk premium. Excess returns are high, for example, during periods of high dispersion because
investors demand a high risk premium.
7. Conclusion
An extensive literature documents time-varying risk preferences and time-varying risk premiums. We hypothesize that
earnings dispersion is associated with variation in risk premiums over time through two mechanisms. First, aggregate
uncertainty may manifest itself in higher earnings dispersion. Second, dispersion in performance may result in higher
unemployment shocks. Our empirical findings support these hypothesized links between earnings dispersion and both
unemployment and aggregate uncertainty. Consistent with this, we provide evidence that aggregate stock returns are
negatively related to the future cross-sectional dispersion in earnings changes. The association between contemporaneous
aggregate stock returns and cross-sectional dispersion in earnings is weak but positive. Our findings are robust to
including different macroeconomic indicators that prior studies show to be related to aggregate stock returns.
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