Differential Interpretation of Public Information:
A New Measure and Validity Tests
Xuguang (Simon) Sheng
American University
[email protected]
Maya Thevenot
Florida Atlantic University
[email protected]
Abstract:
Based on a standard Bayesian learning model, we propose a new measure of differential
interpretation of public information, which is applicable to a large sample of firms with
analyst following. We validate our measure in the context of earnings announcements
using four different applications and demonstrate its superiority over a number of
previously used proxies, such as the change in dispersion, Kandel and Pearson’s (1995)
metric, abnormal volume and bid-ask spread. Specifically, we find that the new measure
of differential interpretation is strongly positively related to the information content of
disclosure, the lack of readability in the earnings press releases, the trading volume
around the announcement and the cost of capital. This more precise measure of opinion
divergence will enable researchers to pursue studies that were previously difficult to
conduct.
JEL Classifications: M41, C01
Keywords: Differential Interpretation, Disagreement, Public Information, Disclosure
We thank Peter Easton, Jon Garfinkel, Peter Wysocki and workshop participants at
Florida Atlantic University, the George Washington University seminar on forecasting
and the University of Miami for many helpful suggestions. We also thank Zahn Bozanic
for sharing the readability data. David Caban and Phoebe Wong provided able research
assistance.
Differential Interpretation of Public Information:
A New Measure and Validity Tests
Based on a standard Bayesian learning model, we propose a new measure of differential
interpretation of public information, which is applicable to a large sample of firms with
analyst following. We validate our measure in the context of earnings announcements
using four different applications and demonstrate its superiority over a number of
previously used proxies, such as the change in dispersion, Kandel and Pearson’s (1995)
metric, abnormal volume and bid-ask spread. Specifically, we find that the new measure
of differential interpretation is strongly positively related to the information content of
disclosure, the lack of readability in the earnings press releases, the trading volume
around the announcement and the cost of capital. This more precise measure of opinion
divergence will enable researchers to pursue studies that were previously difficult to
conduct.
2
“After Apple Computer Inc. announced a decline in earnings for its second fiscal
quarter, analysts rushed to revise their estimates for the year. Some revised them
downward, as one might expect, but some raised their estimates and others even
issued new buy recommendations.”1
1. Introduction
For decades, researchers, practitioners and regulators have taken great interest in
the effect of disclosure on the behavior of market participants. Public disclosures, such as
earnings announcements, are particularly intriguing because they have a perceived role in
leveling out the information playing field (Levitt 1998), but often spur very different
responses from market participants. Researchers have provided a variety of potential
explanations for this phenomenon, one of which is differential interpretation of the public
disclosure. Unfortunately, obtaining an adequate measure of this unobservable construct
has been a challenge in the literature.2
To infer opinion divergence, researchers have used proxies such as dispersion,
abnormal volume or bid-ask spread. However, all of these measures capture more than
differential interpretation. For example, dispersion also reflects uncertainty, abnormal
volume may be driven by differences in prior beliefs, and bid-ask spread contains
inventory holding and order processing costs. Motivated by this issue, Garfinkel (2009)
conducts a systematic comparison of alternative proxies to a “true” measure of opinion
divergence, based on proprietary data of investors’ orders in NYSE stocks. We build
upon Garfinkel’s research by providing further comparative evidence on the adequacy of
different opinion divergence proxies. More importantly, we advance a new and improved
alternative, which is well aligned with theory and is obtainable for a large sample of
1
Fisher, L.M. “Market Place.” The New York Times (April 19, 1993). The article is available at:
http://www.nytimes.com/1993/04/19/business/market-place.html.
2
Differential interpretation and opinion divergence are used interchangeably throughout the paper.
3
firms. The more precise proxy for opinion divergence may prove crucial to future
research that examines the effect of disclosure on the cost of capital, market efficiency
and rationality of investor behavior.
The proposed measure of differential interpretation originates from the Bayesian
learning model developed by Kandel and Pearson (1995). In this context, we show that
the dispersion of analysts’ expectations following public disclosure comes from two
sources: differences in prior beliefs and differences in the interpretation of the public
signal. This decomposition allows us to abstract differential interpretation away from
differences in priors, providing an empirical estimate of opinion divergence based only
on analyst forecasts. The new empirical proxy is a function of pre- and post-disclosure
dispersion and the weight analysts place on their prior belief.
To assess our measure, we examine its ability to capture variation in opinion
divergence in four different settings. The results provide convincing evidence that our
new measure is as good or superior to previously used proxies, such as change in
dispersion, Kandel and Pearson’s (1995) measure, several estimates of abnormal volume
and bid-ask spread. Specifically, we find that it is positively related to the
informativeness of the earnings announcement and trading volume, similar to other
proxies examined in prior research. A more unique aspect is how only the new measure
provides statistically significant evidence that less readable earnings press releases, i.e.
less transparent disclosures, are associated with higher levels of differential
interpretation, which in turn translate into a higher cost of capital. These findings provide
one possible explanation for the recent evidence in Barth, Konchitchki and Landsman
(2013) that firms with more transparent earnings enjoy a lower cost of capital. Moreover,
4
our empirical estimates suggest that differential interpretation has a significant economic
effect on the cost of capital – having a level of opinion divergence above the sample
median is related to a 1.1 percent increase in firm cost of capital. Unlike other proxies,
our new measure illustrates this important relationship between differential interpretation
and the cost of capital. In sum, the analyses indicate that the proposed differential
interpretation measure captures the underlying construct and dominates the other proxies
in at least two important settings.
A potential disadvantage of the new metric is its dependence on heavy analyst
following to reliably estimate the weight analysts put on their prior belief. In our last set
of analyses, we relax the data requirements and perform the validity tests using three
alternative estimates of the new measure. For example, one approach requires only three
forecasts before and after an earnings announcement, which is a common data
requirement in studies that consider dispersion as a variable of interest. The results are
similar to those of the main analyses and suggest that our method can be applied to the
wider sample of firms, although some analyst following remains a requirement.
This paper contributes to the literature by suggesting a new and improved
measure of differential interpretation. The metric is preferable to previously used proxies
because of its strong alignment with the theoretical construct and its ease of
implementation using any statistical software with regression capabilities. Prior proxies
for differential interpretation provide measures that do not capture the construct fully
(Kandel and Pearson 1995) or rely on largely unavailable data (Garfinkel 2009). The
wide applicability of our new measure opens up the door to a myriad of new research
questions and untested hypotheses. Furthermore, in addition to validating the new
5
measure using empirical applications that exist in the literature, we also show that less
transparent earnings press releases and firm cost of capital are positively related to
differential interpretation.
The rest of the paper is organized as follows. Section 2 proposes our new measure
and summarizes alternative proxies for differential interpretation. Section 3 discusses the
validation tests and presents the results of our empirical analyses. Finally, Section 4
concludes.
2. Empirical Estimates of Differential Interpretation
2.1. A New Measure of Differential Interpretation
The proposed empirical measure of differential interpretation stems from a
Bayesian learning model, most closely related to the seminal work of Kandel and Pearson
(1995). A key feature of this model is that analysts may interpret the public information
differently. Similar learning models have recently been applied by a number of authors,
such as Kandel and Zilberfarb (1999), and Lahiri and Sheng (2008, 2010). The novelty of
the approach in this study is the isolation of differential forecast revisions attributable to
differential interpretation of public information. The key inferences of our model are
discussed next and the full details and theoretical results are presented in Appendix A.
In our Bayesian learning model, differential interpretations are modeled by
endowing analysts with different likelihood functions, which corresponds to analysts
using different models to interpret public signals. With respect to an earnings
announcement, this is akin to all analysts observing the same disclosure, but having
heterogeneous assessments of its implications for future earnings. Alternatively, investors
6
may use the public signal to develop new private information, which will also cause
differential interpretation following the earnings announcement. However, as Kim and
Verrecchia (1997, p.399) state, it is impossible to distinguish between differential
interpretations of an earnings announcement from event-period information or different
likelihood functions. Hence, the two types of models are analogous.
Under reasonable assumptions, the Bayesian learning model implies the following
relationship for disagreement before and after observing public signals:3
,
where
(
announcement,
(1)
) is the cross-analyst dispersion after (before) the earnings
is differential interpretation, and
is the weight analysts put on the
prior belief. In equation (1), forecast dispersion following disclosure,
to have two components: (i) differences in the prior beliefs,
interpretation of public signals,
, is postulated
and (ii) differential
. This decomposition of forecast dispersion is aligned
with a large body of theoretical and empirical research that explains how disagreement
arises from agents’ possessing private pre-disclosure information (e.g., Kim and
Verrecchia 1991, and Abarbanell, Lanen and Verrecchia 1995) or becoming differentially
informed following a commonly-observed signal (e.g., Holthausen and Verrecchia 1990
and Kim and Verrecchia 1994). Empirical results lend support for both sets of theories
(e.g., Bamber, Barron and Stober 1999 and Barron, Harris and Stanford 2005).
The decomposition of post-disclosure dispersion allows us to abstract differential
interpretation from differences in priors and obtain an empirical estimate of opinion
divergence across analysts as follows:
3
For simplicity, firm and forecast horizon subscripts are omitted.
7
̂
(2)
̂
In equation (2), ̂ is obtained from the following OLS regression:4
(3)
where
(
) is analyst i’s forecast and
(
) is the average forecast over
analysts after (before) the earnings announcement. The proposed measure of differential
interpretation,
, stems from theory and is easy to implement using any statistical
software that has regression capabilities. A higher estimate of
suggests that analysts
have more heterogeneous assessments of the implications of currently reported earnings
for future earnings.
2.2. Other Measures of Differential Interpretation
A commonly used measure of divergence of opinions is forecast dispersion or
change in dispersion around some disclosure event such as an earnings announcement
(Ajinkya, Atiase and Gift 1991, Garfinkel and Sokobin 2006, Rees and Thomas 2010).
The problem with this metric is that it captures differential interpretation with a
measurement error as shown by our model. Moreover, Sheng and Thevenot (2012) show
that dispersion captures other unobservable constructs and results may be biased in one
direction or another, based on the dominating factors. For example, Barron, Stanford and
Yu (2009) find that dispersion and changes in dispersion capture uncertainty and
information asymmetry to differing extents, which helps explain some conflicting
evidence in the literature concerning the association between dispersion and stock
returns.
4
See Appendix A for more details.
8
Another popular proxy for opinion divergence is the Kandel and Pearson’s (1995)
measure. Figure 1, adapted from Bamber et al. (1999, p.372), illustrates six possible types
of analysts’ revisions of annual earnings, following a quarterly earnings announcement.
Case 1 demonstrates the no revision situation, which occurs if the announcement has no
information content and analysts continue to rely on their priors. Case 2 shows
convergence of opinions, which occurs when analysts’ degree of consensus increases
following the announcement. Cases 3 through 6 illustrate instances where analysts revise
differentially. However, Kandel and Pearson’s (1995) divergence of opinions measure is
defined only as the percentage of analyst pairs that revise their expectations in opposite
directions as in Cases 5 and 6 in Figure 1. Revising in opposite directions happens only if
opinions about the signals diverge (even if pre-disclosure information also differs).
Kandel and Pearson’s approach underestimates differential interpretation because it
classifies Cases 3 and 4 where analysts revise in the same direction as homogenous. This
may occur due to differences in pre-disclosure information.5 However, it may also be the
case that the different degree of revision is due to differential interpretation. In the latter
case, Kandel and Pearson’s metric does not fully capture the underlying construct and
may not provide enough power in statistical tests. In addition, this measure is designed to
capture differential interpretation primarily in cases where the disclosure does not have
information content, which is only a small subset of all disclosures.6
The next set of proxies includes different measures of unexplained trading
volume. These measures derive justification from research that finds either abnormal
5
Bamber et al. (1999) provide an example for Case 3 as follows. If an analyst has more pre-disclosure
optimism and also more precise pre-disclosure information, then this analyst will weigh the news less
heavily and the revision will be smaller than the revision of the less informed analyst.
6
Bamber et al. (1999, p.379) discuss in detail the limitations and lack of power of Kandel and Pearson’s
measure.
9
amounts of volume that should not exist absent divergence of opinions (Kandel and
Pearson 1995) or a positive relation between volume and proxies for differential
interpretation (Bamber et al. 1999). Recent research by Garfinkel (2009) concludes that
such proxies are most consistently and strongly correlated with the author’s newly
constructed measure based on proprietary data of investors’ orders in NYSE stocks.
However, abnormal volume measures are not without shortcomings when used as proxies
for differential interpretation. Firm-specific volume may also be correlated with liquidity
(Petersen and Fialkowski 1994), market volume (Tkac 1999) and other information-based
variables (Atiase, Ajinkya, Dontoh and Gift 2011). Moreover, Banerjee and Kremer
(2010) show that volume around an earnings announcement consists of two components:
volume due to resolution of previous disagreement that leads to convergence and volume
due to differential interpretation. These dual trading incentives introduce measurement
error into volume-based measures of opinion divergence.
Finally, researchers have used bid-ask spread as a proxy for differential
interpretation (Handa, Schwarz and Tiwari 2003). However, bid-ask spreads have three
components: holding inventory cost, cost of processing orders and risk of trading with
more informed investors. To the extent that divergence of opinion makes some investors
become more informed than others, the information asymmetry component of the bid-ask
spread is correlated with differential interpretation. However, the presence of the other
two components adds noise to this measure. Furthermore, George, Kaul and Nimalendran
(1991) show that the order processing cost dominates the information asymmetry
component in bid-ask spread measures. Even if the information asymmetry aspect could
be isolated, Bloomfield and Fischer (2011) argue that information asymmetry and
10
differential interpretation are two distinct constructs and should not be substituted for one
another.
Overall, the accounting and finance literature provides various measures of
opinion divergence, but all have significant shortcomings. We address these problems
with our new measure of differential interpretation. Next, we examine the discussed
proxies and illustrate their performance in four validation tests.
3. Empirical Analysis
3.1. Precedents
It is usually difficult to convincingly demonstrate that a proxy for an unobservable
variable is adequate because a comparison to a true measure of the construct may not be
possible. Garfinkel (2009) is a notable exception because the author uses proprietary data
to obtain a presumably “true” measure of opinion divergence. This allows the author to
draw conclusions about which proxies are better than others, based on correlations with
the “true” measure. Since we are unable to perform such analysis, the validation of our
new measure is not as straightforward. However, we present results from four tests,
suggested by theory, prior research and intuition, and presume that a good measure
should perform well in all of those settings.
To illustrate the performance of the new and alternative differential interpretation
measures, we consider four empirical assessments. First, we examine the potential
determinants of differential interpretation and explore whether the measures are
positively related to the informativeness of the disclosure, as suggested by Holthausen
and Verrecchia (1990) and Kim and Verrecchia (1994). Second, we test whether opinion
11
divergence is also positively related to the lack of readability of the earnings press
releases. The intuition for this prediction is as follows. If the disclosure is more difficult
to understand and includes dubious language, i.e. is less readable, then analysts are more
likely to disagree about the implications of the disclosure for future earnings. Third, we
examine the theoretical implications of Kandel and Pearson (1995) and Kim and
Verrecchia (1994) and test whether firm volume increases with differential interpretation.
While this result has been documented by Bamber et al. (1999) and others, we use this
relationship to assess our new measure.
Finally, we explore the link between differential interpretation and the cost of
capital. Some theory suggests a positive relation (Varian 1985), but direct empirical
evidence on the link between opinion divergence and the cost of capital is
overwhelmingly scarce. In a recent review of the literature on trading volume around
earnings announcements, Bamber, Barron and Stevens (2011, p.433) state:
“There is a growing belief that the cost of capital increases in opinion divergence,
if this divergence results from some investors being at information disadvantage
that causes them to require a price lower that intrinsic value to enter the market”.
This implies an information asymmetry effect on the cost of capital, which has been well
documented (Easley and O’Hara 2004), but also an understudied differential
interpretation effect. It is important to note that these constructs are distinct. On one hand,
information asymmetry may arise due to differential interpretation as implied by Bamber
et al. (2011). However, Bloomfield and Fischer (2011) suggest that divergence of opinion
may occur without increased information asymmetry. Therefore, the link between
differential interpretation and the cost of capital should be studied directly. In addition,
prior research suggests that a higher cost of capital results when the amount of public
12
information is low or when the precision of private information is high (Botosan, Plumlee
and Xie 2004). All of these elements may be linked to investors having diverse opinions
about the firm, which translates into a positive relation with the cost of capital. Although
related, these constructs have significant theoretical differences and to date, the link
between differential interpretation and the cost of capital has not been carefully examined
in the literature.
In sum, we investigate the relations between differential interpretation and (i) the
information content of disclosure, (ii) the readability of the earnings press release, (iii)
firm trading volume around the announcement and (iv) firm cost of capital. Our ex ante
expectation is that our new measure is positively related to disclosure informativeness
and firm volume but those links are not necessarily the strongest, relative to the other
divergence of opinion proxies. Indeed, we expect that the volume-based measures will
have the strongest association to volume, simply by construction. However, we expect
that the new measure will outperform all other proxies in the readability and the cost of
capital tests because of the lack of a mechanical relation between the existing proxies and
these variables and the new measure’s close ties to theory.
3.2. Data and Descriptive Statistics
The initial sample used to calculate the new measure of differential interpretation
proposed in this study is taken from I/B/E/S Detail tape, which includes U.S. firms with
available annual forecasts and actual earnings data during the 1984 to 2012 time period.
We require that quarterly earnings announcement dates are within 90 days of the fiscal
quarter end and are available on I/B/E/S. In order to estimate our new measure of
differential interpretation, we require that at least ten analysts provide a forecast prior to
13
announcement of quarterly earnings and these analysts revise their forecasts following
the announcement. To be included in the sample, an analyst must make a forecast no
more than 90 days before the earnings announcement and revise no later than 45 days
following the announcement. If an analyst makes multiple forecasts in either of these
windows, we keep the forecasts closest to the earnings announcement.7 We include data
from three horizons; differential interpretation is measured around the first three quarters’
earnings announcements using analyst forecasts for the current year’s earnings.
As previously discussed, we consider several alternative measures of differential
interpretation in addition to our new measure, DI, which is obtained as shown in
equations (2) and (3). First, our model shows that differential interpretation is a function
of dispersion pre and post-disclosure. Therefore, we consider the change in dispersion
(ChangeD) as one candidate metric. Second, we take Kandel and Pearson’s (1995)
measure (KP), defined as the percentage of pairs of analysts who revise their forecasts as
in Cases 5 and 6 of Figure 1. For consistency, we obtain the change in dispersion around
the earnings announcement and Kandel and Pearson’s (1995) measure using the same
I/B/E/S forecast data we use to estimate our new measure of differential interpretation.
Since DI and ChangeD produce large outlying observations, we winsorize these variables
at the top and bottom one percent.8 The volume-based measures are taken from Garfinkel
(2009). We calculate three measures of unexplained volume using daily CRSP over a
three-day window, centered on the day of the earnings announcement: MATO (market7
While the 90-day threshold for forecasts prior to the earnings announcement may cause some stale
forecasts to be included in the sample and the length of the after-EA window of 45 days may include
forecast revisions unrelated to the earnings announcement, we choose these windows to avoid the loss of
too many observations. However, we also employ a second sample that requires forecasts made 45 days
pre- and 30 days following the earnings announcement. Since the results from both samples are
qualitatively similar and the inferences are identical, we present the results of the long window sample
only.
8
All of our results remain the same if we do not winsorize these variables.
14
adjusted turnover), DTO (MATO adjusted for liquidity trading) and SUV (the
standardized prediction error from a regression of trading volume on the absolute value
of returns). Our last measure is the average percentage bid-ask spread over the three-day
window, centered on the day of the earnings announcement, BAspread.9 For the purpose
of comparing the alternative measures of differential interpretation, we keep only
observations with valid values for all proxies. The definition of all variables is
summarized in Appendix B.
Table 1 shows descriptive statistics for the differential interpretation proxies and
the variables used in our regression analyses. The distributions of the measures based on
analyst forecasts are skewed with large standard deviations. Hence, we take the logarithm
transformation of DI and KP to mitigate skewness in the distributions (denoted by “L” in
front of the variable’s name). For the dispersion measure, we take the difference in the
logarithm transformations of dispersion after and before the earnings announcement
(ChangeLD) as in Barron et al. (2009).10 This metric can be interpreted as the logarithm
transformation of the ratio of dispersion after to dispersion before the earnings
announcement, which is why we also include this ratio, RatioD, in Table 1. While this
specification does not capture the change in dispersion per se, it behaves similarly to the
change in dispersion and mitigates distributional problems.11
Table 1 shows that the mean (median) market value of equity (Mktvalue) is
approximately $16,038 ($4,975) million and indicates that our sample consists of
9
We also use five-day versions of the volume and bid-ask spread measures, centered on the day of the
earnings announcement. Since the results for the alternative windows are very similar, we present the
results for the three-day window only.
10
We also use raw change in dispersion and the ranked change in dispersion as in Rees and Thomas (2010).
The results for these alternative specifications are insignificant or less significant than the ones reported.
11
The Spearman correlation coefficient between our specification of the variable and the change in
dispersion is 0.722 and highly statistically significant.
15
primarily large firms, which is not surprising given our data requirement for heavy
analyst following. Mean (median) book-to-market ratio is 0.494 (0.409), implying that
our sample firms trade at a large premium above book value. We follow prior research by
taking the natural logarithm transformations of Mktvalue and BM in our subsequent
analyses. Mean (median) market beta (Beta) for the full sample, 1.312 (1.166), suggests
that the average sample firm is riskier than the market. The mean (median) cost of capital
estimate based on Easton’s (2004) PEG ratio is 12.6 (10.3) percent. The average number
of years of education, required to comprehend our sample firms’ earnings press releases
is about 17 years. The sample of firms with available readability score, Fog, is
substantially smaller because it is restricted to firm/quarters after year 2004 – the initial
year earnings press releases were required to be furnished to the SEC.
Table 2 presents Pearson and Spearman correlation coefficients among variables
of interest. The new measure is strongly positively correlated with most other differential
interpretation measures, except for LSUV with which it is negatively correlated, while the
Spearman correlation coefficients with DTO and BAspread are statistically insignificant.
LBAspread is insignificantly or negatively correlated with all proxies, except for the
Pearson’s correlation with LDI and ChangeLD. This result is not surprising based on
evidence in the finance literature that heavily traded stocks experience narrower spreads
(e.g., Petersen and Fialkowski 1994). However, this incompatibility raises the concern
that either bid-ask spread or abnormal volume is an inappropriate measure of differential
interpretation or that they capture other constructs in addition to opinion divergence.
Interestingly, LKP is negatively correlated with all measures but LDI and ChangeLD. The
three volume-based measures are positively correlated to each other. Our new measure is
16
positively related to firm and market volume, analyst following, book-to-market ratio,
growth and cost of capital, but negatively related to market beta. However, its relation to
AbCAR is ambiguous, which is why we need to examine these relations in a multivariate
setting.
3.3. Assessment of Opinion Divergence Measures
Our initial analysis examines whether the degree of differential interpretation
increases with the information content of the public announcement, measured by the
absolute abnormal return around the announcement, AbCAR. We expand this analysis by
exploring whether the differential interpretation metrics are related to certain firm
characteristics, such as size, book-to-market ratio and analyst following. In this continued
analysis, we regress each of the alternative divergence of opinion measures on AbCAR,
LMktvalue, LBM and LFollow and year and firm fixed effects. The results are presented
in Table 3, Panel A.
Our new measure is strongly positively related to the absolute value of the
abnormal earnings announcement return; the coefficient is 1.008 and is highly
statistically significant with a t-value of 4.034. In addition, the evidence suggests that
larger firms, firms with higher book-to-market ratios and higher analyst following have a
higher degree of opinion divergence, following an earnings announcement. All other
measures are also strongly positively related to the information content of the
announcement, except LKP, which is negative and significant. This difference casts doubt
on the ability of LKP to capture investors’ differential interpretation of information. The
three volume-based measures are especially strongly positively related to AbCAR, which
is not surprising given the well-documented and robust relation between earnings
17
announcement information content and volume (see, e.g., Kim and Verrecchia 1991 and
Bamber et al. 1999). As a whole, all but one measure of differential interpretation show a
positive relation to the informativeness of the earnings announcement, providing
evidence that they capture differential interpretation.12
Panel B of Table 3 presents the results of the readability analysis. We expect that
investors will differ in their interpretation of the earnings release more when the
disclosure is less readable. Since higher Fog implies a less readable document, we predict
a positive coefficient on Fog. The results show that our new measure is significantly
positively related to Fog, with a t-value of 3.066. The only other differential
interpretation proxy that is positively related to readability is LKP, but it is only
marginally significant at the ten percent level. None of the other metrics exhibit a
significant relation to Fog. While this is not a conclusive evidence of the superiority of
the new measure over others, it provides initial support for the new method.
Next, we examine two factors – trading volume and the cost of capital – that may
be affected by the degree of opinion divergence. Both theoretical (e.g., Kim and
Verrecchia 1994) and empirical (e.g., Bamber et al. 1999) research establish that
divergence of opinions increases trading volume. Therefore, we expect a positive and
statistically significant coefficient on LDI in regressions of volume on differential
interpretation and other factors that affect volume, such as the informativeness of the
earnings announcement, market value of equity and market volume. We use total firm
12
In addition, we examine whether higher levels of differential interpretation are related to lower returns
around the earnings announcement, as documented by Berkman et al. (2009). We find that all opinion
divergence proxies are negatively related to the three-day abnormal return centered on the earnings
announcement, although the results are statistically insignificant for MATO and DTO, statistically
significant at the five percent level for LKP and ChangeLD, and statistically significant at the one percent
level for LDI, SUV and BAspread.
18
share turnover in the three-day window centered on the earnings announcement, LVol, as
the dependent variable and control for total market turnover in the same time period,
LMktvol. First, LVol is regressed only on LDI and firm and year fixed effects and the
results are presented in the first column of Table 4. The coefficient on LDI is 0.009 with a
t-value of 3.427. When control variables are included, LDI continues to be positive and
statistically significant, although the coefficient is now 0.006 with a t-value of 2.490. All
control variables are highly statistically significant in the expected direction. This
analysis provides additional convincing evidence that our new measure captures
differential interpretation.
Next, we perform this analysis using all other measures of opinion divergence.
ChangeLD is statistically insignificant, while LKP and BAspread are negatively related to
LVol. The negative coefficient on LKP is surprising and contrary to prior research. More
specifically, Bamber et al. (1999) find an insignificant relation to volume in their full
sample but a positive relation in a sub-sample of firms where the information content of
the earnings announcement is very low. The negative relation between BAspread and
LVol is consistent with prior research (e.g., Petersen and Fialkowski 1994) but suggests
that BAspread captures other constructs that may be unrelated to opinion divergence. All
volume-based measures are strongly positively associated with volume, which is not
surprising; this analysis should not be used to evaluate the adequacy of these measures
because a strong relation follows by construction.
Finally, we test for a positive relation between differential interpretation and the
cost of capital. We use two different analyses to examine this relation to avoid making
19
erroneous inferences caused by inaccurate cost of capital measures. Our first analysis
relies on firm-specific cost of capital estimates based on Easton (2004) as follows:
COCit = √(epsi(t+2) - epsi(t+1))/pit
,
(4)
where COC is the cost of capital estimate obtained in the month following the earnings
announcement, epsi(t+1) (epsi(t+2)) is the firm’s one-year ahead (two-year ahead) mean
forecast of earnings and pit is the current price from I/B/E/S summary files.
We choose this method because it provides some of the most reliable and wellbehaved estimates of the cost of capital (Botosan and Plumlee 2005).13 Following prior
research on the cost of capital, we include control variables for risk, size and growth in all
of our empirical analyses. We examine the relation between divergence of opinions and
the cost of capital with the expectation that good proxies of differential interpretation will
be strongly positively related to the cost of capital, after controlling for market beta, size,
growth and year and firm fixed effects. The result of this analysis is presented in Table 5,
Panel A. Direct empirical evidence on the relation between opinion divergence and the
cost of capital is overwhelmingly scarce and this paper explores this connection.14
The coefficient on LDI is 0.007 and highly statistically significant with a t-value
of 21.904, suggesting that differential interpretation of the earnings announcement
13
We acknowledge that estimating the cost of capital using the PEG ratio has disadvantages. First, it limits
the sample as it requires analyst coverage and the two-year ahead forecast must be higher than the one-year
ahead earnings forecast. Indeed, Table 1 shows that we lose almost 10 percent of our sample based on the
second requirement. Second, prior research raises the concern that bias in analysts’ forecasts could lead to
measurement error in the cost of capital estimates (Easton and Sommers 2007). Even if a systematic
optimistic bias exists in analysts’ forecasts and implied cost of capital estimates are inflated, this does not
necessarily imply that it induces spurious results, unless the bias in the estimates is systematic and is
correlated with other variables of interest. Nevertheless, we examine the robustness of our results to the
potential optimistic bias in analysts’ forecasts later in the paper.
14
One exception is Rees and Thomas (2010) whose primary research question deals with the relation
between change in dispersion and contemporaneous stock returns. As a sensitivity check, the authors
examine the relation between change in dispersion and change in cost of capital around earnings
announcements. However, the authors do not investigate the effect of opinion divergence on the cost of
capital, per se.
20
increases firm cost of capital. This is important because one purpose of public disclosures
is to level out the information playing field. However, if the common signal is
differentially interpreted, then public disclosure has a detrimental effect on the firm,
indicated by a higher cost of equity capital. This evidence is consistent with predictions
in Varian (1985) and findings in Garfinkel and Sokobin (2006).
Most other measures do not yield convincing evidence of a positive link to the
cost of capital. The measure capturing the change in dispersion, ChangeLD has a
coefficient of 0.001 and is only marginally significant, which is consistent with it
measuring differential interpretation with noise. The Kandel and Pearson’s measure is not
statistically significant casting doubt once again on its ability to capture variation in
differential interpretation. The volume-based measures provide mixed results. MATO has
a positive and statistically significant coefficient, DTO is insignificant and SUV is
negative and statistically, but not economically, significant.
Another metric that exhibits a strong relation to the cost of capital is LBAspread.
However, there are reasons besides differential interpretation for the strong association
between BAspread and the cost of capital. For example, bid-ask spread is a popular proxy
for information asymmetry (see, e.g. Armstrong et al. 2011). The positive relation
between information asymmetry and the cost of capital is well accepted in the literature
and the significant coefficient on BAspread may be driven by information asymmetry,
not differential interpretation. Additionally, bid-ask spread incorporates inventory
holding and order processing costs, which may also positively affect the cost of capital.
There is a stream of research that suggests investors pay less for stocks with high
transaction costs, which renders a higher cost of capital. For example, Amihud and
21
Mendelson (1986) argue that investors in firms with larger bid-ask spreads require a
higher expected return to compensate for higher transaction costs. As Table 2 shows,
BAspread correlates negatively with most alternative differential interpretation measures
and positively with COC, suggesting that it is positively related to the cost of capital due
to a construct other than differential interpretation.15
Our cost of capital analysis so far tests the joint hypothesis that there is a positive
relation between divergence of opinions and cost of capital and that Easton’s (2004)
method provides an appropriate measure of the cost of capital. However, there is a great
debate in the literature about the most appropriate measure of the cost of capital and the
second assumption may not hold. Therefore, we check the robustness of our results by
performing the portfolio-based analysis that does not require firm-specific estimates of
the cost of capital, suggested by Easton et al. (2002) and described in Easton (2009). The
method regresses median one-year-ahead earnings forecast, scaled by book value, which
we define as Y, on price, scaled by book value, defined as X. The intercept captures the
estimated average growth rate and the sum of the intercept and the regression coefficient
on X captures the estimated average cost of capital. The effect of a variable of interest,
such as differential interpretation, on the cost of capital is then examined using a dummyvariable approach. We define a variable DDiffInt, equal to 1 if the value of the given
15
We perform several additional analyses to examine the robustness of the positive relation between our
new measure and the cost of capital. First, we run a regression of cost of capital on all differential
interpretation metrics together, control variables and firm and year fixed effects and find that the new
measure is positive and highly statistically significant, suggesting that it includes variation not fully
captured by the other metrics. Second, we include controls for other information environment variables,
such as uncertainty and information asymmetry, and find that LDI continues to be positive and highly
statistically significant, implying that the new measure does not capture previously documented uncertainty
and asymmetry effects. Third, we include AbCAR as an additional control to alleviate the concern that the
differential interpretation variable captures the magnitude of news, which may affect the cost of capital.
The inclusion of the additional control does not affect the magnitude or statistical significance of LDI.
Finally, since prior research suggests that analysts issue optimistic forecasts of annual earnings (see, e.g.,
Francis and Philbrick 1993), we obtain “debiased” forecasts by subtracting a measure of the average
optimism from the original forecasts and repeat the analysis. Our results and inferences do not change.
22
differential interpretation measure is above the median, and zero otherwise. We then
include DDiffInt and an interaction term between DDiffInt and X in the regression model
discussed above. The coefficient on DDiffInt captures the effect of differential
interpretation on growth and the sum of the coefficients on DDiffInt and the interaction
term captures the effect of opinion divergence on the cost of capital. In addition, we
include control variables for beta, size, and book-to-market ratio, as suggested by Easton
(2009), where these variables are mean-centered and interactions between X and the
mean-centered control variables are also included. The result of this analysis is presented
in Panel B of Table 5.
The first column provides the result of the benchmark regression, where Y is
regressed on X and control variables. The estimated growth rate is 5.8 percent and the
estimated cost of capital is 8.8 percent for a firm with average beta, size and book-tomarket ratio. This estimate to the cost of capital is lower than the one presented in Table
1, which is consistent with the tendency of the PEG ratio to provide an inflated estimate
of the cost of capital (Easton and Sommers 2007). The subsequent columns provide
results for the effect of differential interpretation on the cost of capital, using the
alternative proxies. Based on the new measure, higher levels of differential interpretation
are associated with higher levels of growth and cost of capital and both effects are
statistically and economically significant. For example, having a level of opinion
divergence above the sample median is associated with 1.4 percent higher growth and 1.1
percent higher cost of capital for a firm with average beta, size and book-to-market ratio.
None of the other variables provide significant growth or cost of capital effects.
23
Therefore, our earlier results are not driven by a potentially noisy or biased estimate of
the cost of capital based on PEG ratios.
Overall, the new measure of opinion divergence gives results that are consistent
with theory and prior research, and has high explanatory power in all four applications.
No other proxy seems to capture differential interpretation as consistently and predictably
as the proposed measure. We believe that the superiority of the new measure is due to its
close alignment and direct relation to the theoretical construct. Furthermore, our proposed
metric is easy to estimate using only analyst forecast data and its wide applicability will
enable researchers to examine new questions and hypotheses, which may not have been
possible with existing proxies. However, a disadvantage of the specification of the new
measure so far is that it requires ten or more analysts around an earnings announcement.
Next, we relax this requirement and examine whether our new measure can be reliably
obtained with fewer analysts.
3.4. Alternative estimates of DI
To relax the data requirement in estimating our new measure, we compute three
alternative estimates of DI requiring: i) five analysts revising around a given quarterly
earnings announcement (rather than ten as in previous analyses), defined as DI5hor; ii)
three analysts revising around a given earnings announcement, defined as DI3hor and iii)
ten analysts revising around any quarterly earnings announcement in a given year,
defined as DI10yr. Then we repeat all previous analyses and present the evidence in
Table 6.
24
In the most general case, a minimum of only three analysts are needed around a
given earnings announcement, which provides the largest number of usable observations.
This improves the applicability of the new method dramatically, provided that the
generalization does not come at the cost of reliability. Empirical results from our analyses
are extremely promising. All three alternative estimates provide highly statistically
significant results in the correct direction for all analyses. Although some analyst
following remains a requirement, our new method can measure opinion divergence for a
large number of firms.
4. Conclusion
Using a standard Bayesian learning model, we quantify opinion divergence by
decomposing dispersion following information disclosure into two separate components:
heterogeneous prior beliefs and differential interpretation of new disclosure. We validate
our differential interpretation measure by showing a positive relation to: (1) the
information content of the earnings announcement, (2) the lack of readability in the
earnings press release, (3) the trading volume around the announcement and (4) the cost
of capital. Moreover, our measure outperforms other previously used proxies, such as the
change in dispersion, Kandel and Pearson’s (1995) metric, several measures of abnormal
volume and bid-ask spread, on at least two of these dimensions. As such, we extend
Garfinkel (2009) by providing comparative evidence on the adequacy of different opinion
divergence proxies but also by introducing a potentially superior alternative.
Furthermore, our new empirical evidence of a direct positive relation between differential
25
interpretation of public information and firm cost of capital has significant economic and
policy implications to managers, regulators and academics.
Admittedly, our new measure of opinion divergence has some limitations. First,
following the literature on financial analysts, we presume that divergence in analysts’
opinions reflects differences of opinions among investors. To the extent that this
assumption does not hold, our measure captures analysts’ differing beliefs and not
necessarily those of investors. Second, our approach requires sufficient analyst following
before and after an earnings announcement and hence, is not applicable to all firms.
However, we demonstrate the performance of our new measure using relaxed data
requirements and the results are promising.
This study provides a better and widely applicable tool for further understanding
of the effect of public disclosure on investor behavior. One perceived benefit of providing
information to everyone simultaneously is leveling out the information playing field and
decreasing information asymmetry in the market. However, our research shows that less
transparent public disclosures may have a detrimental effect on firms via an increase in
their cost of capital if the public information is interpreted differently. Our measure
provides the means to consider future research questions, such as whether more
transparent disclosures are related to less divergence in opinions or whether firms change
their disclosure policies to manage the disagreement among market participants. We
believe that such research will provide new insights into additional unintended
consequences of public disclosures or perhaps, some benefits of opinion divergence.
26
Appendix A: Theoretical justification of the new differential interpretation measure
Following Kandel and Pearson (1995) and Lahiri and Sheng (2008, 2010), we
present a simple model of analysts making earnings forecasts. Before observing any
public signals, analysts hold prior beliefs about firm j’s earnings. We assume that the
initial prior belief of firm j’s earnings for the year t, held by the analyst i,
represented by ̃
for
,
, where
and
̃ , is
are the
mean and precision of analyst i’s initial prior belief, respectively. For simplicity, the firm
and horizon subscripts are omitted. Thus, in our model specification, analysts are
endowed with divergent prior beliefs.
With the arrival of new public information, analysts modify their initial beliefs.
We assume that analysts receive a common signal,
, about future earnings but may not
interpret it identically. In particular, analyst i’s estimate,
, of earnings, conditional only
on the new public signal that is observed at time t, can be written as
. This implies that analysts form an expectation about earnings, based on the
public signal plus a random error, but they may disagree about the mean of the error,
which is captured by
. With respect to an earnings announcement, this is akin to all
analysts observing the same disclosure, but having heterogeneous assessment of its
implications for future earnings. For the tractability of our model, we follow Banerjee
and Kremer (2010) by assuming that analysts agree on the precision of the public signal,
, although it is allowed to vary over time.
Under the normality assumption, Bayes rule implies that analyst i’s posterior
mean,
, is the weighted average of his prior mean and his estimate of earnings,
conditional on the new public signal:
27
,
where
(A.1)
is the ratio of the precision of the prior to the precision of
posterior forecast. Assuming that the prior mean,
and the interpretation bias,
are
mutually independent, we can easily derive the following relationship for disagreement
before and after observing public signals:
,
(A.2)
where
is the dispersion after the earnings announcement (cross-analyst variance of
),
is dispersion before the earnings announcement (cross-analyst variance of
), and
is differential interpretation (cross-analyst variance of
) for each
firm/year. In equation (A.2), forecast disagreement is postulated to have two components
due to cross-analyst differences in (i) the prior beliefs,
public signals,
and (ii) the interpretation of
.16
We assume that the reported forecasts represent the true means of the analysts’
beliefs at that time, subject to a random reporting error,
identically distributed
, with
independently and
for all i and t. Consequently we can rewrite equation
(A.1) as follows:
,
where
and
(A.3)
. Two issues arise in the estimation of
equation (A.3). First, the error terms are possibly correlated across analysts, since their
16
In the general case where analysts assign different weights to new information relative to their prior
beliefs, forecast disagreement comes from a third source – the cross-analyst differences in the weights
attached to public information. However, in this case we cannot separately estimate the cross-analyst
differences in (i) interpreting the public information and (ii) the weights attached to the new information for
each horizon and each time period. By pooling the observations over time, Lahiri and Sheng (2008) find
that the cross-analyst differences in the weights, that is, the third channel, barely have any effect on forecast
disagreement on average, implying that professional forecasters place very similar weights on their updated
prior beliefs.
28
forecasts are affected by the same public information. To control for the potential
correlation, we perform the cross-analyst demeaned estimation in the following
regression:
,
where
(
(A.4)
) is the average forecast over analysts after (before) the earnings
announcement and
is the averaged error terms over analysts. Second, the error terms
exhibit heteroskedasticity of unknown form. However, an OLS estimation still yields
. Once ̂ is obtained from the OLS estimation of (A.4), we
consistent estimates of
substitute it into equation (A.2) and get:17
̂
̂
Our new measure,
.
(A.5)
, isolates differential forecast revisions attributable to differential
interpretation of public information.
17
We include an intercept in the empirical estimation of equation (A.4).
29
Appendix B: Variable measurement
̂
(
DI
=
ChangeD
=
RatioD
=
KP
=
MATO
=
DTO
=
SUV
=
BAspread
=
AbCAR
=
Vol
=
Mktvol
=
Follow
=
Mktvalue
=
BM
=
Growth
=
̂)
, where ̂ is the coefficient estimate obtained from regressing
each analyst’s deviation from the mean forecast after an earnings
announcement on each analyst’s deviation from the mean forecast prior
to the earnings announcement, and AD (BD) is dispersion after (before)
an earnings announcement. LDI is the logarithm transformation of DI.
change in dispersion, AD-BD. ChangeLD indicates the change in
logarithm transformations of AD and BD.
ratio of AD to BD.
percentage of pairs of analysts whose forecasts flip or diverge around an
earnings announcement as in cases 5 and 6 in Figure 1. LKP indicates the
logarithm transformation of KP.
percentage of outstanding shares traded in the three-day window centered
on the earnings announcement less the percentage of all shares traded in
the same window of all NYSE/AMEX stocks. LMATO indicates the
logarithm transformation of MATO.
MATO less median market-adjusted turnover averaged over 180-day
period prior to the measurement of MATO. LDTO indicates the
logarithm transformation of DTO.
standardized prediction error from a regression of trading volume on the
absolute value of returns as in Garfinkel (2009). LSUV indicates the
logarithm transformation of SUV.
average percentage bid-ask spread over the three-day window centered
on the earnings announcement. LBAspread indicates the logarithm
transformation of BAspread.
absolute value of the three-day abnormal return centered on the earnings
announcement (using standard market-model methodology).
percentage of outstanding shares traded in the three-day window centered
on the earnings announcement. LVol indicates the logarithm
transformation of Vol.
percentage of all shares traded in the market in the three-day window
centered on the earnings announcement. LMktvol indicates the logarithm
transformation of Mktvol.
number of analysts revising their forecasts around an earnings
announcement. LFollow indicates the logarithm transformation of
Follow.
market value of equity at the end of the prior quarter. If unavailable,
Mktvalue is calculated at the fiscal year-end immediately prior.
LMktvalue indicates the logarithm transformation of Mktvalue.
book to market ratio at the end of the prior quarter. If unavailable, BM is
calculated at the fiscal year-end immediately prior. LBM indicates the
logarithm transformation of BM.
short-term earnings growth, calculated as (epsi(t+2) – epsi(t+1))/|epsi(t+1)|,
where epsi(t+1) (epsi(t+2)) is the firm’s one-year ahead (two-year ahead)
30
Beta
COC
Fog
mean forecast of earnings.
market beta estimated using the market model with a minimum of 30 out
=
of 60 monthly returns prior to the month in which COC is estimated.
√(epsi(t+2) – epsi(t+1))/pit , where epsi(t+1) (epsi(t+2)) is the firm’s one-year
ahead (two-year ahead) mean forecast of earnings and pit is the current
=
price from IBES summary files. COC is estimated in the month
following the current earnings announcement.
is the number of years of education required to comprehend the earnings
= press release, computed as .4[(words/sentences)+100(three or more
syllable words/words)].
31
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34
Figure 1. Alternative Possible Reactions to Public News (adapted from Bamber, Barron and Stober 1999, p. 372)
Case 1
No Reaction
Case 2
Convergence
Case 3
Flipping: Both
analysts interpret
news as positive
Case 4
Divergence: Both
analysts interpret
news as negative
Case 5
Inconsistent
Flipping: News
interpreted as
positive and
negative
Case 6
Inconsistent
Divergence: News
interpreted as
positive and
negative
Announcement
Announcement
Announcement
Announcement
Announcement
Announcement
Notes
Figure 1 illustrates six possible types of analysts’ revisions of annual earnings following a quarterly earnings announcement. Case 1 provides the no revision
situation, which occurs if the announcement has no information content and analysts continue to rely on their priors. Case 2 shows convergence of opinions,
which occurs when analysts’ degree of consensus increases following the announcement. Cases 3 and 4 illustrate instances where analysts revise differentially
due to either difference in their pre-disclosure information or to differential interpretation or both, but differential interpretation need not exist. Cases 5 and 6 may
occur only if opinions about the signals diverge (even if pre-disclosure information differs).
Table 1. Descriptive statistics
N
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,837
16,610
16,609
16,810
16,180
15,350
6,521
DI
ChangeD
RatioD
KP
MATO
DTO
SUV
BAspread
AbCAR
Vol
Mktvol
Follow
Mktvalue
BM
Growth
Beta
COC
Fog
Mean
0.629
-0.027
0.858
11.041
0.023
0.017
3.144
0.007
0.055
0.066
0.027
14.473
16,037.640
0.494
0.683
1.312
0.126
17.001
Std Dev
3.690
0.147
2.482
12.293
0.037
0.024
4.595
0.013
0.061
0.077
0.013
4.570
35,290.580
0.445
3.476
0.778
0.085
2.485
Q1
0.001
-0.009
0.339
0.000
-0.003
0.002
0.133
0.001
0.017
0.020
0.017
11.000
1,913.050
0.250
0.106
0.797
0.084
15.383
Median
0.008
-0.001
0.600
7.500
0.010
0.010
2.244
0.001
0.038
0.043
0.024
13.000
4,974.900
0.409
0.183
1.166
0.103
16.822
Q3
0.058
0.000
0.968
19.853
0.038
0.027
5.070
0.008
0.073
0.085
0.036
17.000
14,055.740
0.640
0.380
1.639
0.140
18.491
Notes
The table is based on available firm/quarter observation from 1984 – 2011. We require that at least ten analysts make a forecast of
annual earnings in the 90 days before the earnings announcement of first, second and third quarter’s earnings and then these same
analysts revise their forecasts in the 45 days following the quarterly earnings announcement.
̂
DI is equal to
, where ̂ is the coefficient estimates obtained from regressing each analyst’s deviation from the mean forecast
(
̂)
after an earnings announcement on each analyst’s deviation from the mean forecast prior to the earnings announcement, and AD (BD)
is dispersion after (before) the quarterly earnings announcement. If the obtained estimate of ̂ is less than zero, it is set to zero and if it
is more or equal to one, it is set to missing. ChangeD is the change in dispersion, AD-BD. RatioD is the ratio of AD to BD, AD/BD. KP
is the percentage of pairs of analysts whose forecasts flip or diverge around an earnings announcement as in cases 5 and 6 in Figure 1.
MATO is the percentage of outstanding shares traded in the three-day window centered on the earnings announcement less the
percentage of all shares traded in the same window of all NYSE/AMEX stocks. DTO is MATO less median market-adjusted turnover
averaged over 180-day period prior to the measurement of MATO. SUV is the standardized prediction error from a regression of trading
volume on the absolute value of returns as in Garfinkel (2009). BAspread is the average percentage bid-ask spread over the three-day
window centered on the earnings announcement. AbCAR is the absolute value of the three-day abnormal return centered on the
earnings announcement. Follow is the number of analysts following the firm. Vol is the percentage of outstanding shares traded in the
three-day window centered on the earnings announcement. MktVol is the percentage of all shares traded in the three-day window
centered on the earnings announcement of all NYSE/AMEX stocks. Mktvalue is the market value of equity as of the most recent
quarter prior to the earnings announcement, stated in millions of dollars; if unavailable market value of equity at the previous fiscal
year end is used. BM is common equity divided by market value of equity as of the most recent quarter prior to the earnings
announcement; if unavailable book-to-market ratio at the previous fiscal year end is used. Growth is the two-year ahead analyst
consensus forecast of earnings less the one-year ahead consensus forecast, scaled by the absolute value of the one-year ahead consensus
forecast. Beta is the market beta estimated using the market model with a minimum of 30 out of 60 monthly returns ending in the
month of the earnings announcement using the value-weighted market index return. COC is the implied cost of capital based on the
PEG ratio method (Easton 2004) estimated in the month after the current earnings announcement. Fog is the number of years of
education required to comprehend the earnings press release, computed as .4[(words/sentences)+100(three or more syllable
words/words)].
ChangeD and DI are winzorized at the one and 99 percent level.
36
Table 2. Spearman (below the diagonal) and Pearson (above the diagonal) correlation coefficients
LDI (1)
ChangeLD (2)
LKP (3)
MATO (4)
DTO (5)
SUV (6)
BAspread (7)
LVol (8)
LMktvol (9)
AbCAR (10)
LFollow (11)
LMktvalue (12)
LBM (13)
Growth (14)
Beta (15)
COC (16)
(1)
1
0.466
0.209
0.035
0.002
-0.061
-0.015
0.019
0.152
-0.023
0.063
0.012
0.305
0.024
-0.044
0.291
(2)
0.288
1
0.051
-0.021
0.016
0.024
0.015
-0.033
-0.010
0.006
0.031
0.043
-0.021
-0.046
-0.069
-0.035
(3)
0.148
-0.001
1
-0.057
-0.107
-0.135
-0.024
-0.045
0.081
-0.095
0.022
0.047
0.096
0.013
-0.043
0.095
(4)
0.077
-0.011
-0.035
1
0.711
0.451
-0.184
0.868
0.174
0.399
0.150
-0.252
-0.075
0.175
0.400
0.140
(5)
0.030
0.010
-0.090
0.761
1
0.587
-0.288
0.720
0.315
0.418
0.088
-0.147
-0.091
0.078
0.242
0.003
(6)
-0.042
0.030
-0.115
0.359
0.506
1
-0.221
0.462
0.205
0.258
0.078
0.052
-0.132
-0.001
0.102
-0.089
(7)
0.032
0.022
-0.034
-0.155
-0.184
-0.096
1
-0.404
-0.617
-0.008
-0.162
-0.264
0.164
0.127
-0.001
0.241
(8)
0.029
-0.027
-0.040
0.788
0.655
0.397
-0.330
1
0.508
0.441
0.134
-0.261
-0.141
0.144
0.397
0.067
(9)
0.108
-0.005
0.068
0.229
0.289
0.171
-0.497
0.528
1
0.157
0.059
0.026
0.013
-0.089
0.020
-0.066
(10)
0.000
-0.002
-0.101
0.405
0.416
0.257
0.006
0.431
0.154
1
0.019
-0.188
-0.056
0.116
0.222
0.060
(11)
0.064
0.038
0.073
0.128
0.075
0.055
-0.088
0.144
0.073
-0.002
1
0.320
-0.073
-0.018
0.067
-0.029
(12)
0.009
0.040
0.064
-0.219
-0.150
0.056
-0.141
-0.243
0.043
-0.196
0.326
1
-0.241
-0.254
-0.231
-0.329
(13)
0.250
0.002
0.087
-0.052
-0.060
-0.102
0.130
-0.140
-0.012
-0.028
-0.067
-0.253
1
-0.005
-0.018
0.366
(14)
0.067
-0.013
0.016
0.066
0.034
-0.014
0.017
0.043
-0.003
0.030
-0.019
-0.084
0.070
1
0.256
0.762
(15)
-0.043
-0.060
-0.018
0.382
0.247
0.061
-0.051
0.399
0.040
0.227
0.055
-0.237
-0.026
0.056
1
0.198
Notes
All variables are defined in Table 1, except the following. LDI is the logarithm transformation of DI. ChangeLD is the change in the logarithm transformations of AD and BD. LKP is the
logarithm transformation of the percentage of pairs of analysts whose forecasts flip or diverge around an earnings announcement as in cases 5 and 6 in Figure 1. LVol is the logarithm
transformation of Vol. LMktvol is the logarithm transformation of Mktvol. LFollow is the logarithm transformation of Follow. LMktvalue is the logarithm transformation of Mktvalue. LBM is the
logarithm transformation of BM.
Correlation coefficients presented in bald are significant at the five percent level or better.
37
(16)
0.330
0.002
0.060
0.158
0.047
-0.079
0.135
0.097
0.004
0.111
-0.031
-0.289
0.330
0.220
0.142
1
Table 3. Determinants of differential interpretation
Panel A. The information content of the earnings announcement and firm characteristics
Intercept
AbCAR
LMktvalue
LBM
LFollow
N
R-squared
LDI
-9.335***
(-25.213)
1.008***
(4.034)
0.300***
(9.894)
0.293***
(8.725)
0.774***
(12.113)
ChangeLD
-2.053***
(-6.086)
0.612***
(2.687)
0.057**
(2.077)
-0.042
(-1.386)
0.284***
(4.879)
LKP
0.672
(0.659)
-6.691***
(-9.727)
0.232***
(2.784)
0.784***
(8.471)
-0.878***
(-4.992)
MATO
0.036***
(6.717)
0.170***
(47.287)
-0.006***
(-13.023)
-0.007***
(-15.402)
0.011***
(11.588)
DTO
0.009**
(2.190)
0.131***
(46.087)
-0.002***
(-5.362)
-0.003***
(-8.704)
0.004***
(5.596)
SUV
-4.282***
(-4.394)
20.527***
(31.214)
0.559***
(7.015)
-0.324***
(-3.658)
0.199
(1.186)
BAspread
0.030***
(15.082)
0.014***
(9.951)
-0.001***
(-3.686)
0.001***
(6.873)
-0.000
(-0.712)
16,362
0.57
16,362
0.12
16,362
0.24
16,362
0.66
16,362
0.50
16,362
0.25
16,362
0.62
38
Panel B. Disclosure readability and firms characteristics
Intercept
Fog
LMktvalue
LBM
LFollow
Observations
R-squared
LDI
-6.236***
(-5.738)
0.056***
(3.066)
-0.122
(-1.289)
0.149*
(1.652)
0.787***
(5.218)
ChangeLD
-1.476**
(-2.249)
0.014
(1.292)
-0.031
(-0.537)
-0.092*
(-1.684)
0.172*
(1.886)
LKP
-0.566
(-0.244)
0.076*
(1.929)
0.031
(0.152)
0.632***
(3.280)
-0.501
(-1.551)
MATO
0.173***
(11.648)
-0.000
(-0.889)
-0.017***
(-13.027)
-0.007***
(-5.767)
0.015***
(7.451)
DTO
0.085***
(6.974)
-0.000
(-1.398)
-0.008***
(-7.277)
-0.003***
(-3.021)
0.007***
(4.074)
SUV
-1.335
(-0.580)
-0.003
(-0.073)
0.705***
(3.517)
-0.107
(-0.561)
0.208
(0.651)
BAspread
0.008***
(9.501)
0.000
(0.302)
-0.001***
(-10.740)
0.000
(0.369)
0.000
(0.584)
6,427
0.53
6,427
0.17
6,427
0.30
6,427
0.65
6,427
0.44
6,427
0.30
6,427
0.38
Notes
Panel A presents results of regressions of alternative proxies for differential interpretation, indicated on top of the columns, on the absolute value of the three-day
abnormal return centered on the earnings announcement and firm characteristics. Panel B presents results of regressions of alternative proxies for differential
interpretation, indicated on top of the columns, on the readability of the earnings press release and firm characteristics. Each column represents a separate
regression. All regressions include year and firm fixed effects. All variables are defined in Table 1 and Table 2. T-statistics are presented in parentheses below
the coefficient estimates.
*, **, *** indicates significance of the coefficient at the 10%, 5% and 1% levels, respectively, two tailed test.
39
Table 4. The relation between differential interpretation measures and trading volume
Full sample
Intercept
DiffInt
LDI
-4.291***
(-47.817)
0.009***
(3.427)
LDI
-1.748***
(-10.481)
0.006**
(2.490)
3.776***
(50.417)
-0.053***
(-6.903)
0.448***
(17.044)
ChangeLD
-1.782***
(-10.728)
0.003
(1.120)
3.780***
(50.487)
-0.052***
(-6.772)
0.449***
(17.065)
16,837
0.771
16,610
0.811
16,610
0.811
AbCAR
LMktvalue
LMktvol
N
R-squared
Dependent Variable = LVol
LKP
MATO
-1.763***
-1.850***
(-10.618)
(-17.125)
-0.004***
15.610***
(-4.760)
(141.724)
3.751***
1.081***
(49.961)
(20.682)
-0.052***
-0.020***
(-6.839)
(-4.064)
0.452***
0.535***
(17.200)
(31.272)
16,610
0.811
16,610
0.920
DTO
-1.427***
(-9.952)
13.187***
(71.141)
2.011***
(29.056)
-0.047***
(-7.229)
0.537***
(23.646)
SUV
-2.071***
(-13.881)
0.050***
(59.421)
2.767***
(39.895)
-0.088***
(-12.843)
0.341***
(14.403)
BAspread
-1.715***
(-10.101)
-0.947**
(-2.052)
3.793***
(50.555)
-0.052***
(-6.859)
0.457***
(17.177)
16,610
0.859
16,610
0.848
16,610
0.811
Notes
This table presents results of regressions of firm trading volume on alternative proxies for differential interpretation, indicated on top of the columns, and control
variables. Each column represents a separate regression. All regressions include year and firm fixed effects. All variables are defined in Table 1 and Table 2. Tstatistics are presented in parentheses below the coefficient estimates.
*, **, *** indicates significance of the coefficient at the 10%, 5% and 1% levels, respectively, two tailed test.
40
Table 5. The relation between differential interpretation measures and the cost of capital
Panel A. The PEG ratio as a measure of the cost of capital
Intercept
DiffInter
Beta
LMktvalue
LBM
Growth
N
R-squared
LDI
0.413***
(29.364)
0.007***
(21.904)
0.005***
(4.639)
-0.026***
(-22.366)
0.011***
(8.425)
0.003***
(17.954)
ChangeLD
0.358***
(25.436)
0.001*
(1.714)
0.005***
(3.912)
-0.024***
(-19.927)
0.014***
(10.224)
0.003***
(18.366)
14,333
0.561
14,333
0.544
Dependent Variable = COC
LKP
MATO
DTO
0.358***
0.350***
0.358***
(25.427)
(24.824)
(25.359)
0.000
0.152***
0.021
(1.641)
(6.962)
(0.749)
0.005***
0.003***
0.005***
(3.841)
(2.714)
(3.826)
-0.024***
-0.023***
-0.024***
(-19.961)
(-19.181)
(-19.869)
0.014***
0.015***
0.014***
(10.082)
(10.861)
(10.224)
0.003***
0.003***
0.003***
(18.350)
(17.991)
(18.312)
14,333
0.544
14,333
0.546
14,333
0.544
SUV
0.357***
(25.360)
-0.000**
(-2.084)
0.005***
(3.894)
-0.024***
(-19.825)
0.014***
(10.158)
0.003***
(18.357)
BAspread
0.345***
(24.349)
0.390***
(6.703)
0.005***
(3.966)
-0.024***
(-19.692)
0.013***
(9.828)
0.003***
(18.412)
14,333
0.544
14,333
0.545
41
Panel B. Portfolio-based approach to estimation of the relation between differential interpretation measures and the cost of capital
Intercept
X
0.058***
(7.711)
0.030***
(8.205)
DDiffInt
X*DDiffInt
AdjBeta
X*AdjBeta
AdjMktvalue
X*AdjMktvalue
AdjBM
X*AdjBM
-0.002
(-0.548)
-0.007***
(-6.383)
0.010***
(4.862)
0.000
(0.487)
-0.034***
(-9.384)
0.008***
(3.864)
Observations
14,849
R-squared
0.477
Estimated Growth rate
0.058
Estimated COC
0.088
Effect of DiffInt on Growth
Effect of DiffInt on COC
P-value
LDI
0.053***
(7.626)
0.032***
(9.744)
0.014***
(3.158)
-0.003*
(-1.835)
-0.001
(-0.425)
-0.007***
(-6.463)
0.010***
(4.871)
0.000
(0.520)
-0.037***
(-9.717)
0.009***
(4.443)
14,849
0.478
0.053
0.085
0.014***
0.011***
0.000
Dependent Variable = Y
ChangeLD
LKP
0.057***
0.058***
(7.324)
(7.269)
0.032***
0.030***
(8.117)
(7.486)
0.001
-0.001
(0.236)
(-0.494)
-0.003**
0.001
(-2.322)
(0.685)
-0.002
-0.002
(-0.644)
(-0.555)
-0.007***
-0.007***
(-6.380)
(-6.383)
0.010***
0.010***
(4.930)
(4.864)
0.000
0.000
(0.475)
(0.485)
-0.034***
-0.034***
(-9.410)
(-9.421)
0.008***
0.008***
(3.867)
(3.909)
14,849
0.478
0.057
0.089
0.001
-0.002
0.236
14,849
0.477
0.058
0.088
-0.001
0.000
0.752
MATO
0.058***
(7.626)
0.030***
(8.065)
0.000
(0.072)
0.001
(0.570)
-0.002
(-0.497)
-0.007***
(-5.884)
0.010***
(4.852)
0.000
(0.548)
-0.034***
(-9.215)
0.008***
(3.853)
DTO
0.057***
(7.785)
0.030***
(8.504)
0.001
(0.395)
-0.000
(-0.091)
-0.002
(-0.585)
-0.007***
(-6.040)
0.010***
(4.827)
0.000
(0.470)
-0.034***
(-9.276)
0.008***
(3.826)
SUV
0.058***
(7.921)
0.030***
(8.506)
-0.000
(-0.054)
0.001
(0.524)
-0.002
(-0.546)
-0.007***
(-6.339)
0.010***
(4.896)
0.000
(0.471)
-0.034***
(-9.342)
0.008***
(3.827)
BAspread
0.056***
(6.105)
0.030***
(7.763)
0.002
(0.342)
0.001
(0.601)
-0.002
(-0.597)
-0.007***
(-6.302)
0.010***
(4.938)
0.000
(0.535)
-0.035***
(-9.498)
0.008***
(3.811)
14,849
0.477
0.058
0.088
0.000
0.001
0.663
14,849
0.477
0.057
0.087
0.001
0.001
0.586
14,849
0.477
0.058
0.088
-0.000
0.001
0.791
14,849
0.477
0.056
0.086
0.002
0.003
0.519
42
Notes
Panel A presents results of regressions of cost of capital on alternative proxies for differential interpretation indicated on top of the columns, and control
variables. All regressions include year and firm fixed effects. All variables are defined in Table 1 and Table 2. Panel B presents results of the portfolio-based
approach to estimation of the effect of differential interpretation on the cost of capital, described in Easton (2009), based on Easton et al. (2002). The variables
used in this analysis are as follows. Y is the median consensus forecast of one-year-ahead earnings, scaled by book value per share. X is price per share, scaled by
book value per share. Following Easton et al. (2002), observations in the top and bottom 2 percent for Y and X are trimmed. DDiffInt is a dummy variable, equal
to one if the value of the given differential interpretation measure is above the median, zero otherwise. AdjBeta is Beta less the mean of Beta. AdjMktvalue is
Mktvalue less the mean of Mktvalue. AdjBM is BM less the mean of BM. Each column represents a separate regression. T-statistics are calculated using standard
errors clustered by firm and are presented in parentheses below the coefficient estimates.
The “Effect of DiffInt on COC” represents the effect of differential interpretation, measured by the given proxy, on the cost of capital for the average-beta, size
and book-to-market firm. The “P-value” presents the p-values of F-tests of whether the given effect on the cost of capital is equal to zero, i.e. a test of DDiffInt +
X*DDiffInt = 0.
*, **, *** indicates significance of the coefficient at the 10%, 5% and 1% levels, respectively, two tailed test.
43
Table 6. Alternative estimation of DI
Panel A. Information content analysis
Intercept
AbCAR
LMktvalue
LBM
LFollow
N
R-squared
LDI5hor
-11.454***
(-5.489)
1.444***
(8.071)
0.466***
(21.342)
0.487***
(20.478)
0.983***
(30.091)
LDI3hor
-14.382***
(-4.440)
1.384***
(8.893)
0.421***
(22.422)
0.432***
(21.029)
1.329***
(57.429)
LDI10yr
-11.807***
(-12.566)
0.948***
(8.119)
0.512***
(35.930)
0.611***
(39.104)
0.465***
(27.754)
48,567
0.56
74,278
0.53
67,130
0.68
LDI5hor
-10.459***
(-16.297)
0.044***
(3.992)
-0.153***
(-3.190)
0.167***
(3.798)
0.991***
(16.463)
LDI3hor
-7.144***
(-7.017)
0.042***
(4.238)
-0.206***
(-4.981)
0.157***
(4.084)
1.337***
(31.221)
LDI10yr
-8.274***
(-18.775)
0.027***
(3.800)
-0.004
(-0.127)
0.269***
(9.458)
0.378***
(12.706)
19,167
0.57
27,846
0.55
25,161
0.71
Panel B. Readability analysis
Intercept
Fog
LMktvalue
LBM
LFollow
N
R-squared
44
Panel C. Volume analysis
Intercept
DiffInt
AbCAR
LMktvalue
LMktvol
N
R-squared
Dependent Varible = LVol
LDI5hor
LDI3hor
LDI10yr
-0.742
-1.243
-3.000***
(-1.296)
(-1.408)
(-8.688)
0.005***
0.009***
0.003**
(3.642)
(9.204)
(2.363)
4.343***
4.537***
4.383***
(91.179)
(109.322)
(106.618)
0.059***
0.137***
0.086***
(12.033)
(32.829)
(20.228)
0.396***
0.396***
0.389***
(22.680)
(25.610)
(25.938)
49,522
0.76
75,841
0.74
68,521
0.75
Panel D. Cost of capital analysis
Intercept
DiffInter
Beta
LMktvalue
LBM
Growth
N
R-squared
Dependent Variable = COC
LDI5hor
LDI3hor
LDI10yr
0.356***
0.340***
0.387***
(5.096)
(4.212)
(9.643)
0.006***
0.005***
0.010***
(37.280)
(43.687)
(55.023)
0.007***
0.008***
0.008***
(9.395)
(13.490)
(12.954)
-0.039***
-0.041***
-0.042***
(-52.161)
(-69.230)
(-66.251)
0.010***
0.012***
0.007***
(11.495)
(17.658)
(9.274)
0.002***
0.002***
0.002***
(20.544)
(24.375)
(22.542)
45,766
0.50
72,131
0.50
62,642
0.51
Notes
This table presents results with alternative estimates of DI. LDI5hor requires that at least five analysts make a forecast in
the 90 days prior to a given earnings announcement and then the same analysts revise in the 45 days following the
earnings announcement. LDI3hor requires that at least three analysts make a forecast in the 90 days prior to a given
45
earnings announcement and then the same analysts revise in the 45 days following the earnings announcement. LDI10yr
requires that at least ten analysts make a forecast in the 90 days prior to the announcement of either first, second or third
quarter’s earnings in a given year and then the same analysts revise in the 45 days following the earnings announcement.
Then LDI5hor, LDI3hor and LDI10yr are estimated similarly to DI using the specified above analyst forecasts. Each
column represents a separate regression. All regressions include year and firm fixed effects. All other variables are
defined in Table 1 and Table 2. T-statistics are presented in parentheses below the coefficient estimates.
*, **, *** indicates significance of the coefficient at the 10%, 5% and 1% levels, respectively, two tailed test.
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