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Event-Specific Uncertainty and its Expected Resolution
Michael Iselin
Carlson School of Management
University of Minnesota
321 19th Ave S.
Minneapolis, MN 55455
[email protected]
Andrew Van Buskirk*
Fisher College of Business
The Ohio State University
2100 Neil Avenue
Columbus, OH 43210
[email protected]
First Draft: March 2015
*
Corresponding author
We gratefully acknowledge financial support from the Carlson School of Management and the Fisher College of
Business.
Abstract
Investor uncertainty, as measured by implied volatility, increases before anticipated
events. We characterize this increase as “event-specific uncertainty” and examine it in the
context of earnings announcements. We find that relative pre-earnings uncertainty is greatest
when the announcement is most likely to resolve significant uncertainty (e.g., larger firms, firms
with lower analyst coverage, firms with idiosyncratic earnings, and firms likely to issue a
forecast). We focus on the consequences of event-specific uncertainty and first find that
investors respond more strongly to an earnings surprise (i.e. larger ERC) when relative preearnings uncertainty is higher. We then show that event-specific uncertainty impacts the
temporal realization of returns. Specifically, we find that a larger proportion of annual returns
are realized during earnings announcement periods that are characterized by higher ex ante
event-specific uncertainty. Importantly, we also examine other measures of total uncertainty and
fail to find similar results. Overall, we show that the consequences of disclosure are a function
of the uncertainty about the disclosed information, rather than uncertainty about firm value
overall. We also show that the types of firms for which uncertainty is generally high are not the
types of firms for which uncertainty is primarily resolved at earnings announcements.
1. Introduction
Prior research documents that investor uncertainty, as represented by option-based
implied volatilities, increases prior to earnings announcements and other anticipated information
events (Patell and Wolfson 1979, 1981; Rogers et al. 2009). We examine this increase, which
we characterize as “event-specific uncertainty”, to understand its determinants and to test
predicted relations between event-specific uncertainty and event-period returns.
Specifically, we interpret the ratio of pre-announcement implied volatility to baseline
implied volatility as the extent to which investors believe the forthcoming earnings
announcement period will resolve uncertainty (generate greater price movement) relative to the
typical non-earnings period.1 We refer to this ratio as Relative Pre-Earnings Uncertainty and
view it as a specific case of event-specific uncertainty. We expect Relative Pre-Earnings
Uncertainty to be driven by the combined effect of: 1) pre-announcement investor uncertainty
related to the topics expected to be discussed and 2) the expected likelihood that the upcoming
disclosure will be effective in resolving that uncertainty, both of which are positively correlated
with the ratio.
We first show that Relative Pre-Earnings Uncertainty varies predictably with factors
likely to precede relatively consequential information announcements.2 Some of these factors
likely reflect an anticipation of more precise earnings announcement information: Larger firms,
firms with more stable (less noisy) earnings, and firms with a history of issuing earnings
forecasts have greater Relative Pre-Earnings Uncertainty. Other factors likely reflect inherent
uncertainty about the firm (or an inability to obtain information from other sources): firms with
1
In theory, investors could expect the earnings period to resolve less uncertainty than the typical non-earnings
period. However, prior research provides strong evidence that earnings announcement days experience more price
movement and are more informative than random non-announcement days (e.g., Ball and Shivakumar 2008).
2
Note that we are interested in the characteristics of earnings announcements, rather than characteristics of just the
firm’s earnings or the relevance of earnings in valuing the firm.
1
fewer analysts and firms whose earnings are less correlated with market-level or industry-level
earnings have greater Relative Pre-Earnings Uncertainty.
The focus of the paper then shifts to the relation between event-specific uncertainty and
realized event-period returns. We first ask whether the investor response to earnings surprises
increases with Relative Pre-Earnings Uncertainty, as models of Bayesian updating would predict
(e.g., Holthausen and Verrecchia 1988; Kim and Verrecchia 1991b). Empirically, this prediction
has received only mixed support, likely due to the difficulty of distinguishing uncertainty from
other factors that influence how investors respond to new information.
Our second question stems from a different prediction about the relation between
uncertainty and returns: the claim that the pattern of realized returns should reflect the pattern of
uncertainty resolution (Robichek and Myers 1966a; Epstein and Turnbull 1980). We build on
the empirical framework of Ball and Shivakumar (2008), who quantify the importance of
quarterly earnings announcements by estimating the proportion of annual returns associated with
the 4 quarterly earnings announcements. We predict that realized returns are more heavily
concentrated in earnings announcement periods when those earnings announcements have
greater Relative Pre-Earnings Uncertainty.3
We find support for both of our predictions. First, we show that earnings-period returns
are more sensitive to a unit of unexpected earnings (i.e., have larger ERCs) when Relative PreEarnings Uncertainty is greater. This finding is consistent with Bayesian investors responding
more strongly to new information when they were more uncertain about that information before
it was announced.4 Second, we show a positive correlation between Relative Pre-Earnings
3
This differs from predicting that earnings announcements earn larger risk premia when uncertainty is greater,
because we are holding total annual return constant.
4
We acknowledge that this could indicate either greater pre-announcement uncertainty or a more precise earnings
signal; both would lead to a higher ERC. In our empirical tests, though, we control for factors likely to capture the
2
Uncertainty and the Ball and Shivakumar (2008) measure of earnings informativeness. This
result supports the claim that realized returns are concentrated in periods of greater (expected)
uncertainty resolution. The magnitude of this relation is substantial: Ball and Shivakumar
(2008) document an average abnormal adjusted R2 (their measure of informativeness) of about
5.8% for the 1990-2006 period. In our sample, the lowest quintile of Relative Pre-Earnings
Uncertainty has an abnormal adjusted R2 of 5.6% while the highest quintile has an abnormal
adjusted R2 of 14.4%.5
Moreover, the magnitude of the abnormal adjusted R2 increases
monotonically moving from the lowest quintile of Relative Pre-Earnings Uncertainty to the
highest quintile.
We then rerun our two main tests using other proxies for uncertainty, including the
median level of implied volatility (based on options without earnings announcements in their
horizons), the pre-earnings level of implied volatility, and analyst dispersion. We find that ERCs
are negatively associated with each of these measures. We interpret the combined results as
evidence that investors do not necessarily respond more strongly to a signal when total
uncertainty is high; instead, investors respond more strongly to a signal when uncertainty about
that signal is high. In terms of our second test, we find no consistent relation between the
proportion of returns attributable to earnings periods and either measure based on the level of
implied volatility. We also find a strong negative relation between analyst dispersion and the
proportion of returns attributable to earnings periods. This latter result is consistent with prior
precision of the earnings signal (e.g., analyst dispersion and the volatility of the firm’s earnings series) and find that
the relation between our uncertainty measure and ERCs is virtually unchanged. As a consequence, we interpret our
results as stemming from investor pre-announcement uncertainty rather than variation in the precision of the signal.
5
The abnormal adjusted R2 reported in Ball and Shivakumar (2008) is increasing across time in their sample period.
The average results for our sample are similar in magnitude to their results during the years in which the two
samples overlap.
3
research (Imhoff and Lobo 1992) that concludes that analyst dispersion is a better measure of
earnings noise than ex ante earnings uncertainty.
Our paper provides new evidence on how investor uncertainty influences the way
investors respond to new information, and how the expected resolution of uncertainty relates to
the temporal realization of returns. Our results indicate that the choice of uncertainty measure
matters a great deal in assessing these relations; the types of firms where uncertainty is generally
high are not the types of firms for which uncertainty is primarily resolved at earnings
announcements.
2. Prior research and hypothesis development
Our paper examines the concept of event-specific uncertainty. We start by discussing
prior research on investor anticipation of public disclosures. In Section 2.2, we present a simple
disclosure-based model that provides the intuition for our measure of event-specific uncertainty.
Sections 2.3 and 2.4 present hypotheses related to our measure. Because our paper touches upon
several broad areas of accounting research, we necessarily reference only a small fraction of the
existing research in each area.
2.1. Anticipation of public information releases
Anticipated information events drive significant activity in capital markets, and
researchers have examined several aspects of this activity. Analytical papers, including Gonedes
(1980), Kim and Verrecchia (1991a), and McNichols and Trueman (1994), explore how the
anticipation of public disclosure encourages the production and acquisition of private
information.
Empirical work provides corroborating evidence that sophisticated investors
4
acquire non-public information before anticipated events. Seppi (1992) shows that pre-earnings
block trades reveal private information about impending earnings. El-Gazzar (1998) finds that
firms with more institutional ownership have more of their earnings information preempted
before the announcement. There is an entire branch of research that finds evidence of informed
trading in the options market prior to information events (e.g., Amin and Lee 1997; Xing et al.
2010; Jin et al. 2012; Johnson and So 2012). Finally, Lee et al. (1993) and Yohn (1998)
document one expected consequence of this private information acquisition: bid-ask spreads
increase prior to an earnings announcement, and decline after the announcement as the perceived
information advantage dissipates.
Another consequence of anticipated disclosure is the expectation of temporarily elevated
stock price volatility around the announcement. Even in the absence of private information,
investors expect that earnings announcements will generate larger-than-normal price changes.
This expectation of greater event-period price movement leads to an increase in call option prices
as the announcement approaches, and can be measured with the implied volatility extracted from
those call option prices.
Empirically, research has shown a pattern of increasing implied
volatility around both earnings announcements (Patell and Wolfson 1979, 1981; Isakov and
Perignon 2001) and, to a lesser extent, management earnings forecasts (Rogers et al. 2009).
Prior papers have decomposed the level of pre-announcement option volatility into two
components: a baseline level of volatility and the increase in volatility as a result of the pending
earnings announcement. Barth and So (2014) use options with different horizons to estimate
these two components and then focus on the level of pre-announcement implied volatility and the
associated volatility premium.6 Billings et al. (2014) examine short window changes in volatility
6
Specifically, they model expected earnings announcement volatility as
+ /252, where
is expected
is baseline volatility. They use 30- and 60-day standardized
(excess) earnings announcement volatility and
5
ahead of earnings announcements and find that firms with larger changes are more likely to issue
an earnings forecast concurrent with the earnings announcement. They also include the level of
pre-announcement volatility in their tests and find that greater average uncertainty leads to a
lower likelihood of issuing a forecast. They conclude that managers respond to increases in
uncertainty by issuing volatility-decreasing information.
Patell and Wolfson (1981) also characterize the level of volatility ahead of earnings
announcements as a combination of baseline volatility and an increase in volatility ahead of
earnings announcements. More similar to our study, they focus on the increase in volatility and
conclude that firms with larger implied volatility increases demonstrate greater event-period
volatility.7
We build on the work of Patell & Wolfson (1981) by investigating both the
determinants of the pre-event increase in implied volatility and how that event-specific
uncertainty manifests in the temporal realization of returns. In the next section, we present a
simple disclosure-based model that characterizes the pre-event increase in implied volatility as
event-specific uncertainty.
2.2. A simple model of event-specific uncertainty
We start with a simple disclosure model presented in Verrecchia (2001). In this model,
the firm has uncertain value, , with mean m and variance 1 ℎ. Investors receive a noisy signal,
, equal to
+
(where
has mean 0 and variance 1 ), and upon receiving the signal
investors revise their beliefs about the value of the firm. The disclosure-related price change is a
function of the surprise in the signal (the difference between the realization and the expectation)
options (which have a different proportion of event and non-event days in their horizon) to infer the values of
and . Their focus is on the relation between non-diversifiable volatility risk and risk premia.
7
Patell and Wolfson (1981) examine a series of option prices prior to earnings announcements to capture the
implied event period volatility in options (as opposed to a baseline level of volatility in non-earnings periods).
6
and a disclosure response coefficient. The disclosure response coefficient indicates how strongly
investors react to that surprise, and depends on the relative precision of the market’s prior
information and the precision of the new information. As stated in Verrecchia (2001), the price
change is:
∆
−
=
)
Equation (1) yields relatively straightforward and testable predictions.8
(1)
First, price
changes should be increasing in the earnings surprise. Second, price changes (per unit of
surprise) should be increasing in the precision of the disclosure, n. Third, price changes (per unit
of surprise) should be increasing in investors’ pre-announcement uncertainty (1 ℎ).
Empirically, the first two predictions have been well documented. A substantial literature
investigates the determinants of earnings response coefficients (ERCs), and demonstrates that
price changes are an increasing function of earnings surprises (for a summary, see Kothari 2001).
The second prediction is borne out by studies that show stronger investor response to forecast
revisions issued by more accurate analysts (Clement and Tse 2003) as well as to management
earnings forecasts when those forecasts are more precise (Baginski et al. 1993) or are
accompanied by supplemental information that lends the forecast greater credibility (Hutton et
al. 2003).
The third prediction, that investors will respond more strongly to disclosure when
uncertainty is greater, has been more difficult to establish. On one hand, Lang (1991) and
Christensen (2002) examine small samples and identify a positive relation between uncertainty
8
In practice, the response to information releases is substantially more complicated than this model suggests, in part
because the quality of one period’s disclosures influences investor precision prior to the next disclosure. Holthausen
and Verrecchia (1988) develop a more robust model that incorporates both sequential information releases and
multiple, potentially correlated, assets. We use this more simple model as an illustration, though, because it yields
the straightforward empirical predictions that earlier empirical work has relied upon (Imhoff and Lobo 1992;
Christensen et al. 2005; Bailey et al. 2006)
7
and investor response.9 On the other hand, Imhoff and Lobo (1992) use analyst dispersion as a
proxy for investors’ ex ante uncertainty. They find that investor response is weaker when
uncertainty is higher and conclude that analyst dispersion better captures the noise in earnings
than investor uncertainty. (In terms of equation 1, analyst dispersion captures low n rather than
low h.) Barron and Stuerke (1998) and Christensen et al. (2005) show a similar result with
analyst dispersion.
The conflicting results in prior research raise the question: what is the appropriate
uncertainty measure in this context? In a world where investors periodically receive an estimate
of fair value, it seems appropriate to use the level of pre-announcement uncertainty about fair
value. In practice, though, investors receive a stream of information about different factors that
influence estimated fair value to various degrees. Some of this information comes in periodic,
scheduled releases like earnings announcements, while other information may come irregularly
and unexpectedly. In this environment, total pre-announcement investor uncertainty reflects the
likelihood of the anticipated disclosure being consequential, as well as the likelihood of other
consequential information coming to light. As a result, firms with high levels of uncertainty may
nonetheless exhibit weak investor response to their earnings announcements if that uncertainty
relates to factors not discussed in the earnings announcement.
As an extreme example, consider an early-stage pharmaceutical company with a single
(potentially valuable) drug under FDA review. Investors have no information about when the
FDA will release the results of their review, and the firm has no private information about the
progress of the review. In this example, investor uncertainty will be high, because the value of
the firm is likely to change dramatically upon the conclusion of the FDA review. If the firm
9
Lang (1991) examines a sample of 200 IPO firms and shows decreasing ERCs over time, arguing that investors’
uncertainty about the firm decreases over time. Christensen (2002) studies 92 Property & Casualty firms from 1989
to 1992 and shows that ERCs increase with firms’ exposure to catastrophe losses (the proxy for uncertainty).
8
announces earnings prior to the FDA’s announcement, investors will respond very little to
unexpected earnings because current period unexpected earnings have little effect on the
distribution of possible firm values. In this case, there would be a high level of pre-earnings
uncertainty, but a weak investor response to unexpected earnings. Such an outcome would seem
contrary to the model’s prediction that high investor uncertainty leads to stronger investor
reaction.10
We expand the earlier model to incorporate the fact that investors typically do not receive
periodic estimates of firm value, but instead receive periodic estimates of parameters they use as
inputs to value the firm, some of which arrive on an unknown and unscheduled timetable. (This
framework is consistent with Verrecchia (2001), who discusses the possibility of variables
other than
that are related to both firm value and the change in price.)
In the spirit of multi-factor pricing models (e.g., Ross 1976), we assume that, over time,
investors receive information about P parameters used as inputs to estimate firm value. Investors
respond to these announcements as a function not only of the precision, surprise, and preannouncement uncertainty about each parameter, but also as a function of how relevant to the
firm’s value that parameter is (i.e., how sensitive firm value is to changes in the parameter
value). We use ωij to represent the relative importance of parameter i in valuing firm j and show
price changes as a function of these variables:
=
ℎ +
−
) +
−
ℎ +
10
) + ⋯+
ℎ +
−
One could argue that the earnings signal conveys little information about firm value, and is therefore very
imprecise, so that the weak investor response is consistent with the model represented in equation 1. This relatively
broad notion of disclosure precision would be consistent with Kim and Verrecchia (1991a), who use the terms
impact, quality, and precision as synonyms in their informal discussion.
9
(2)
where
is the reported value of parameter i which, prior to the release of
has a mean of
and
variance 1 ℎ . ωij can be thought of as a pricing function for each parameter .11
In this framework, stock prices of different firms (or different securities of the same firm)
can adjust differentially to common disclosures, holding the characteristics of those disclosures
constant. For example, if firm j discloses current period earnings
signal for firm j’s value) would be relatively large compared to
,
(the relevance of that
, the relevance of that signal
for firm k’s value (as we would observe if there is information transfer across firms j and k). As
a consequence, firm j’s stock price would respond more strongly than firm k’s stock to the
disclosure, even with common values of ℎ ,
,
, and
.12
What makes this framework useful in our context is that it allows for news about
different parameters to be revealed in different temporal patterns.
Investors may expect
information about some parameters to be revealed uniformly or unpredictably over time (e.g.,
natural disasters or the actions of foreign governments), while they expect information about
other parameters to be disclosed only at periodic information events (e.g., quarterly earnings).13
This difference in expected information flow leads to differences in how uncertainty is captured
in option prices and implied volatilities.
11
A simple example would be the case of a private equity fund whose value depends upon the uncertain (and
uncorrelated) values of its holdings. Investors would respond to the disclosure of holding 1’s value based on its
− ), the relative precision of the disclosure,
, and its weight in the fund’s portfolio,
. In
surprise
general, though, price change will not be a linear function of the surprise in each parameter, particularly when some
parameters (like growth rates or discount rates) influence price in a nonlinear manner. We simply view this equation
as useful in presenting the intuition that the response to new information about a parameter depends upon the
precision of that news and uncertainty about the parameter, rather than uncertainty about the firm overall.
12
The Holthausen and Verrecchia (1988) model includes multiple risky assets and allows for news about one asset
to inform investors about the value of a second (or more) asset.
13
For simplicity, we ignore parameters that investors learn about from scheduled events that are not earnings
announcements. For example, the earnings announcements of related firms or the release of FOMC monetary policy
decisions.
10
In this setting, options’ implied volatilities will always reflect the expectation of news
about the parameters that investors expect to learn about with equal likelihood each period. The
magnitude of that expectation will be driven by investors’ uncertainty about each of those signals
as well as the expected precision, possible surprise, and impact of those parameters on firm value
(ω). For options with an anticipated information event in their horizon, though, there is an
additional component of implied volatility that reflects anticipation of news about the parameters
whose news release is specific to that information event, again driven by investor uncertainty
about the signal and the other factors specific to that parameter.
As a consequence, the
difference in implied volatilities between options that have anticipated information events in
their horizon compared to options that do not reflects the uncertainty about parameters whose
disclosure is specific to that event.
In the case of the earnings announcements that we study in this paper, we refer to the
difference in implied volatility from these two types of options as Relative Pre-Earnings
Uncertainty.14 We expect greater values of this measure to reflect circumstances where investors
are particularly uncertain about earnings information (or non-earnings information expected to
be released at the earnings announcement), where that information is consequential for firm
value, and where the earnings announcement is likely to be effective in resolving the uncertainty.
We employ this measure in our empirical tests, and discuss the use of alternative measures of
uncertainty later in the paper.
2.3. The relation between event-specific uncertainty and investor response to new
information
14
In our empirical tests, we use the natural logarithm of the ratio of pre-earnings implied volatility to baseline
implied volatility.
11
Our first hypothesis relates to the link between investors’ pre-announcement uncertainty
and their response to earnings announcements, and comes directly from the model in the prior
section: We predict that investors will respond more strongly to an earnings surprise when their
earnings-related uncertainty is greater. We formally state our first hypothesis as follows:
H1:
Investors will react more strongly to a unit of unexpected earnings when
Relative Pre-Earnings Uncertainty is greater.
There are two challenges in testing this hypothesis.
First, firms issue a variety of
information along with their quarterly earnings figure. Taken literally, our model suggests a
different investor response to the news about each parameter (
−
) discussed at the earnings
announcement, depending on the pre-event uncertainty about that parameter.
Empirically,
though, we observe neither the uncertainty specific to each parameter, nor the unexpected
component of each parameter disclosed. For this reason we focus the analysis on earnings
surprises and act as if the current period’s earnings realization is the only type of information
disclosed at the earnings announcement. To the extent that Relative Pre-Earnings Uncertainty
relates to non-earnings information expected to be disclosed at the earnings announcement, it
will be more difficult to find support for our hypothesis.
Second, our measure of Relative Pre-Earnings Uncertainty captures not just the
uncertainty construct that we care about (pre-announcement investor uncertainty about earnings,
or 1/h in the model), but rather the total expected price change, which is a function of the
expected precision of earnings, the possible range of earnings surprise, and the relevance of
earnings to firm value. We argue, though, that large earnings surprises are likely to be perceived
as less precise (Subramanyam 1996), so that the expectation of a large absolute surprise would
be offset by the expectation of a less precise signal. Empirically, Truong et al. (2012) show no
statistical association between pre-earnings changes in implied volatility and the magnitude of
12
the earnings surprise. Therefore, it seems unlikely that our measure is affected to a large extent
by the expectation of a potentially large earnings surprise. In our empirical tests, we also control
for variables that we expect to capture the precision of the earnings signal (e.g., earnings
volatility and analyst dispersion), which we believe leaves us able to draw inferences about ex
ante uncertainty related to earnings information, weighted by the importance of earnings to the
firm.
2.4. Relation between the timing of uncertainty resolution and realized returns
Our second hypothesis relates to what Robichek and Myers (1966b) refer to as “The
Manner in which Uncertainty is Expected to be Resolved over Time”. They emphasize that the
rewards to bearing risk are not necessarily earned uniformly over time, but rather according to
the way in which uncertainty is expected to be resolved over time. In a separate paper, Robichek
and Myers (1966a) offer the example of a ship owner sending a vessel on a voyage that will
return cargo of uncertain value. If the value of the cargo is unknown until the vessel’s return to
port, then investors would earn a risk premium only when the uncertainty is resolved at the
vessel’s arrival. Until that point, investors would earn only the risk-free rate. Adopting this
argument, we hypothesize the following:
H2:
When Relative Pre-Earnings Uncertainty is higher, more of a firm’s annual stock
return will be concentrated in its quarterly earnings announcement periods.
Many papers have used the uncertainty resolution argument as motivation to test for the
existence of an earnings announcement premium15, but we are aware of few papers that focus on
the concentration of returns around information events, while holding total returns constant. The
15
Examples include Ball and Kothari (1991), Cohen et al. (2007), and Barber et al. (2013). Our research question
differs from these papers in that they focus on the presence of short-window positive abnormal returns around
earnings announcements. In contrast, our interest is in measuring the concentration of returns around earnings
announcements while holding total annual return constant.
13
most relevant paper for our purposes is Ball and Shivakumar (2008), who examine the relative
importance of earnings announcements as an information source.
They quantify earnings
announcement informativeness by regressing firms’ calendar-year stock returns on their four
quarterly earnings announcement period returns. The R2 values from these regressions indicate
the proportion of total annual information attributable to firms’ earnings announcements.
Using this approach, Ball and Shivakumar conclude that earnings announcements
contribute only a modest amount of information to annual returns. Although they do perform
some sub-sample analyses,16 their primary focus is on estimating the amount of information in
quarterly earnings announcements for the average firm.
In contrast, our focus is on
understanding how the Ball and Shivakumar (2008) measure of informativeness varies across
firms and, more importantly, the linkage between Relative Pre-Announcement Uncertainty and
the pattern of realized annual returns.
We note that, unlike for the first hypothesis, the disclosure of non-earnings information at
the earnings announcement does not pose a problem for testing this hypothesis. Our hypothesis
is simply that when investors are uncertain about the impending announcement (regardless of
which parameter they care about) more of the firm’s annual returns will be concentrated in that
announcement period (regardless of which parameter news caused the returns).
3. Sample, uncertainty measurement, and descriptive statistics
We start with a sample of quarterly earnings announcements disclosed from 1996 through
2014, and retain all observations with required financial statement, stock price, analyst estimates,
and option information. Table 1 presents the distribution of the 130,002 observations across
16
Ball and Shivakumar (2008) perform subsample analyses on portfolios based on size, market-to-book, and
leverage, but do not find a monotonic relation between earnings announcement informativeness and any of those
variables.
14
years. The number of observations per year is generally increasing throughout the sample period
as options become traded on more firms each year.
We present three measures of investor uncertainty. The first, Pre-Earnings Uncertainty,
is the implied volatility from a 30-day at-the-money option as of two trading days prior to
reported earnings. The second, Average Uncertainty, is the median value of daily implied
volatility from 30-day constant-maturity, at-the-money option prices over the window starting
two days after the prior quarter’s earnings announcement and with maturities at least two days
before the current quarter’s earnings announcement.
The third measure of uncertainty, Relative Pre-Earnings Uncertainty, is the focus of our
study. This measure starts with a calculation of excess firm volatility on each trading day, equal
to implied volatility from a 30-day at-the-money option for the firm minus the 30-day VIX
(index option implied volatility level). We calculate Relative Pre-Earnings Uncertainty as the
ratio of the pre-earnings excess volatility to the median of daily excess volatility between
earnings announcements.17 We characterize this measure as reflecting how important investors
expect the earnings announcement to be in terms of resolving uncertainty about firm value,
relative to the average non-earnings day.
We present the descriptive statistics for these uncertainty measures as well as all other
variables that we include in our tests in Table 2. Consistent with expectations and prior research,
Pre-Earnings Uncertainty is, on average, greater than Average Uncertainty (0.49 vs. 0.45 at the
mean, 0.44 vs. 0.41 at the median).
The mean (median) value of Relative Pre-Earnings
Uncertainty is 1.36 (1.16), which again is consistent with the well-documented pattern of
17
This allows for time-varying changes in market-wide volatility, which may include increased volatility in
anticipation of clustered earnings announcements by other firms or economy-wide shocks to uncertainty. Our
inferences are unchanged if we simply take the ratio of unadjusted pre-earnings implied volatility to median
unadjusted implied volatility.
15
increasing uncertainty ahead of anticipated events (Patell and Wolfson 1979, 1981; Isakov and
Perignon 2001). This table also shows that the firms/earnings announcements in our sample are
fairly large, with a median market value greater than $1.5 billion, and well-followed, with a
median analyst following of 4.
Table 3 shows the correlation among the three measures of uncertainty, as well as the
correlations between each of these measures and the other firm characteristics included in
subsequent analyses. Although there is a significant increase in implied volatility prior to
earnings announcements, there continues to be a substantial correlation (0.81) between the
average level of implied volatility between earnings announcements and the level of implied
volatility immediately prior to earnings announcements. Relative Pre-Earnings Uncertainty is
positively associated with the pre-earnings level and negatively associated with the average (nonearnings) level of uncertainty.
Importantly, Relative Pre-Earnings Uncertainty is slightly
negatively correlated with the absolute value of the earnings surprise in the current period (0.08). This supports our claim that our measure of event-period uncertainty is not simply
picking up expectations of the magnitude of the pending earnings surprise.
4. Empirical Results
4.1. Characteristics of firms with high EA uncertainty
Before discussing the results of our hypothesis tests, we examine the characteristics of
firms/earnings announcements that are associated with high levels of Relative Pre-Earnings
Uncertainty. We regress the log of our measure, log(Relative Pre-Earnings Uncertainty), on
variables that we expect to influence the relative importance of earnings announcements for
investors. We subjectively classify these determinants into 4 groups:
16
•
General firm characteristics (Size, Book-to-Market, Stock Return Volatility)
•
Analyst characteristics (Analyst Following, Analyst Dispersion)
•
The firm’s earnings characteristics (Prior Loss, Earnings Volatility, Earnings
Non-Commonality)
•
Prior announcement characteristics (Magnitude of 3-day Return, magnitude of the
earnings surprise, whether the firm issued a forecast)
Table 4 presents the results of this regression.18 In terms of general firm characteristics,
we find that earnings announcements are perceived to be relatively more important for large
firms and for firms with less return volatility. One interpretation of the negative coefficient on
Stock Return Volatility is that greater volatility between earnings announcements may result from
more information about the firm being released in this interim period. That being said, each of
these measures have been used to proxy for a variety of underlying constructs, so we are
reluctant to draw many inferences based on these estimated coefficients.
Of the two analyst characteristics, only Analyst Following is significantly associated with
the perceived importance of earnings announcements; earnings are perceived to be less important
when the firm has more analyst coverage. This outcome is consistent with the idea that analysts
generate and release information about the firm throughout the period, and can effectively act as
a substitute source of information for investors. There is no detectable relation between Analyst
Dispersion and Relative Pre-Earnings Uncertainty.
All three earnings characteristics are associated with the pre-earnings increase in
uncertainty in intuitive ways. When the firm has reported a loss in the prior period (Loss in
Prior Quarter), earnings announcements are perceived to be less important (or alternatively, less
18
The number of observations in this regression is significantly lower than in the overall sample primarily because
of the Forecast at Last EA variable, which is available only from 2003 through the end of our sample. If we exclude
the forecast variable, the number of observations used in the regression increases by about 50%. In this regression,
Book-to-Market and Analyst Dispersion are significantly greater than 0, and all remaining variables have the same
inference and statistical significance.
17
precise). This finding is consistent with the idea that losses are not expected to persist, and are
thus less informative about the firm’s future cash flows (Hayn 1995).19 Along the same lines,
when a firm’s earnings are volatile (Earnings Volatility), a single earnings report provides
relatively less information about firm value. Finally, when earnings do not co-move with
market-level or industry-level earnings (Earnings Non-Commonality), a firm’s earnings
announcement is relatively more important because investors are less able to infer the firm’s
performance from other sources (e.g., other firms’ earnings announcements).
The final group of variables relates to characteristics of the firm’s prior earnings
announcement, and again the associations are somewhat intuitive.
If the prior earnings
announcement generated a significant market reaction (|Prior EA 3-day Return|), investors are
likely to infer that the current earnings announcement will do the same. This could be due to a
variety of reasons, such as the firm tending to issue very detailed earnings releases, analysts
generating significant complementary information, or the firm issuing information only during
quarterly earnings announcements.
We find a negative relation between the magnitude of
earnings surprises in the prior quarter, which is consistent with Subramanyam’s (1996) model, in
which large unexpected earnings are perceived as less precise signals.
Finally, the likelihood that a firm will issue an earnings forecast along with its results
increases the perceived importance of an upcoming earnings announcement. We proxy for this
likelihood with a simple indicator variable (Forecast at Prior EA) equal to 1 if the firm issued a
forecast with their prior earnings announcement. (The autocorrelation in forecasting is about
19
We similarly find a negative relation between Relative Pre-Earnings Uncertainty and the disclosure of a loss for
the current period. However, our focus is on the determinants of pre-disclosure anticipation, so we use only proxies
that are observable prior to the current earnings announcement.
18
0.80.) This positive association is consistent with the notion that management forecasts provide
a substantial amount of information to investors (Beyer et al. 2010).20
Overall, the results in Table 4 support our claim that Relative Pre-Earnings Uncertainty
captures investors’ expectation of how important/influential the upcoming earnings
announcement will be.
4.2. Relation between announcement-specific uncertainty and investor response to
unexpected earnings
We next test hypothesis H1, which predicts investors will respond more strongly to a unit
of unexpected earnings when Relative Pre-Earnings Uncertainty is greater. Table 5, Panel A
shows the results of 4 regressions that model (signed) 3-day stock returns centered on quarterly
earnings announcement dates. In each case, we estimate realized returns as a function of the
analyst-based earnings surprise and allow that relation (i.e., the ERC) to vary depending on
whether the earnings surprise is positive or negative. We also include calendar-quarter fixed
effects to account for variation in market-wide discount rates and risk likely to affect ERCs
(Kothari 2001):
3-day Return = α0 + α1Earnings Surprise + α2Negative Earnings Surprise
+ Quarter Fixed Effects + εi .
(3)
In the first column, we add to these variables just our variable of interest – Relative PreEarnings Uncertainty – as an interaction with the earnings surprise. Our test of H1 is whether
20
This result offers an alternative interpretation of the results shown in Billings et al. (2014). They show that
managers are more likely to issue earnings forecasts when there has been a recent increase in implied volatility, and
they interpret their results as evidence that managers respond to increased pre-earnings uncertainty by providing
more information. An alternative interpretation consistent with our results is that investors anticipate the likelihood
that an earnings forecast (or other consequential disclosure) will be made at the upcoming earnings announcement,
and that anticipation manifests in greater announcement-specific uncertainty. When we include variables for both
the lagged forecast decision and the current forecast decision, both are positively and significantly associated with
Relative Pre-Earnings Uncertainty, with coefficients that are not statistically different from one another at the 10%
level.
19
this interaction term is positively associated with signed returns or, said another way, whether
ERCs are positively related to our measure of announcement-specific uncertainty. The results in
Column 1 support our prediction – investors respond more strongly per unit of earnings surprise
when their announcement-specific uncertainty is greater. In the next several columns, we add
additional variables to assess the robustness of this relation.
Column 2 adds the level of
announcement-specific uncertainty, while Columns 3 and 4 add a variety of firm/earnings
characteristics identified by earlier research as important determinants of earnings response
coefficients (Kothari 2001). In each case, the interaction between announcement-specific
uncertainty and 3-day returns is positive and significant at the p<0.01 level. Importantly, when
we include Earnings Volatility and Analyst Dispersion (proxies for noise in earnings) with the
other control variables, the coefficient of interest changes very little (0.594 in column 1
compared to 0.572 in column 3, and 0.581 in column 2 compared to 0.556 in column 4). The
fact that including or excluding these measures of earnings precision has very little effect on our
results gives us comfort that our measure is primarily capturing variation in ex ante investor
uncertainty about earnings.
In Panel B, we conduct the same tests using three alternative measures of uncertainty:
the level of implied volatility immediately prior to the earnings announcement (Pre-Earnings
Uncertainty), the average level of implied volatility between earnings announcements (Average
Uncertainty), and the standard deviation of analyst earnings forecasts (Analyst Dispersion). In
each case, we continue to focus on the interaction between the uncertainty proxy and the
earnings surprise.21 If these alternative proxies capture investor uncertainty in the spirit of
21
We control for the full set of independent variables used in Column 4 of Panel A, but do not report the estimated
coefficients on those variables for the sake of brevity. In untabulated tests, we also confirm that our results from
Panel A are robust to including these additional uncertainty variables and their interaction with the earnings surprise.
20
Verrecchia (2001) and other disclosure models, we expect the interactions to be positive and
significant.
For each of the three proxies, we fail to find the predicted positive association between
uncertainty and the intensity of investor response.
For two of the three proxies (Average
Uncertainty and Analyst Dispersion), we find a significantly negative relation between the
uncertainty proxy and the strength of investor response. Although inconsistent with theorybased predictions, these associations are consistent with two ideas. First, as discussed in Imhoff
and Lobo (1992), analyst dispersion is likely to be a better proxy for noisy earnings than for
fundamental uncertainty. Second, what matters for understanding how investors respond to
information is not their total pre-announcement uncertainty, but rather the uncertainty that is
specific to the factors that are expected to be discussed in that announcement.
4.3. Relation between announcement-specific uncertainty and the relative informativeness of
earnings announcements
Our second hypothesis deals with the temporal realization of returns, and how the pattern
of returns around earnings announcements relates to the relative uncertainty about those
announcements prior to their release. We predict that a greater proportion of firms’ annual
returns will result from earnings announcement periods when investors perceive more ex ante
uncertainty about those earnings announcements.
We test this hypothesis using the approach developed by Ball and Shivakumar (2008).
They regress a firm’s annual returns on the firm’s four quarterly earnings announcement period
returns during the same year, as follows:
Ri(annual) = α0 + α1Ri(window1) + α2Ri(window2)
In all cases, the Relative Pre-Earnings Uncertainty interaction continues to have a positive and significant
association with earnings period stock returns.
21
+ α3Ri(window3) + α4Ri(window4) + εi
(4)
Using annual cross-sectional regressions run each year, they interpret the R2 values from
those regressions as “a measure of the proportion of the total information incorporated in share
prices over a year that is associated with its four quarterly earnings announcements” (p. 976).22
They find that earnings announcements provide only a modest amount of information compared
to what would be expected from a randomly-selected period from that year.
While the primary interest of Ball and Shivakumar (2008) is in quantifying the importance
of earnings announcements at the aggregate level, we are interested in whether cross-sectional
variation in Relative Pre-Earnings Uncertainty leads to variation in their R2 measure. We
predict that when investors expect more uncertainty resolution during earnings announcements
(relative to an average non-earnings period), a greater proportion of annual returns will be
concentrated in the earnings period.
Similar to Ball and Shivakumar (2008) the window over which we calculate earnings
announcement returns is the day before to the day after the announcement. Returns around each
firm’s announcement that occurs in the first calendar quarter is denoted Ri(window1). Similarly,
announcements from the second, third and fourth calendar quarter are denoted Ri(window2),
Ri(window3) and Ri(window4), respectively. We use arithmetic buy-and-hold returns for both
the annual return and the 4 announcement period returns.
Our test proceeds as follows: we first measure Relative Pre-Earnings Uncertainty for
each firm-quarter, then we sort firm-years into quintiles based on the average value of Relative
Pre-Earnings Uncertainty for the four quarters of that year. We then run the regression in
equation (2) by year and quintile resulting in a total of 90 values of adjusted R2, one for each of
22
Ball and Shivakumar (2008) point out that this approach does not rely upon market efficiency. Investor reaction
that spills into other periods (e.g., a post-earnings announcement drift) will be captured by α coefficients that differ
from 1.
22
the 5 quintiles and each year from 1996 – 2013. To calculate abnormal adjusted R2 for each
regression we again follow Ball and Shivakumar (2008) and subtract from the adjusted R2 value
the proportion that we would expect from a random day if returns were distributed i.i.d.23
We average coefficient estimates and abnormal adjusted R2 estimates for each Relative
Pre-Earnings Uncertainty quintile across years and present the results in Table 6, Panel A. The
right-most column of the table shows the average abnormal adjusted R2 values for each quintile.
We observe a monotonic relation between Relative Pre-Earnings Uncertainty and the
concentration of realized stock returns around quarterly earnings announcements – the lowest
quintiles have abnormal adjusted R2 values of 5.6 and 8.9, while the highest two quintiles have
abnormal adjusted R2 values of 13.5 and 14.4. These results validate the Robichek and Myers
(1966a) claim that “the rate at which income is expected to be realized over time depends on the
rate at which uncertainty is expected to be resolved over time” (p. 730).
We next present a more formal test of whether the differences in abnormal adjusted R2
across quintiles are statistically significant. We regress the estimated abnormal adjusted R2 from
each of the 90 regressions on the quintile ranking as follows:
.
=
+
)+ (5)
Table 6 Panel B presents results of this regression and confirms the significance of the relation
shown in Panel A. Specifically, abnormal adjusted R2 from the Ball and Shivakumar (2008)
regression is significantly associated with the degree of pre-announcement uncertainty.
A
movement from one quintile to the next increases abnormal R2 by an estimated 2.219%
(significant at the p<0.01 level).
23
Assuming i.i.d. daily returns, each day contributes 1/252 of the explanatory power for annual returns where 252 is
the number of trading days in the year. We include 12 days in our earnings announcement return windows so the
normal adjusted R2 is 12/total number of trading days in that year.
23
In Table 7, we examine whether different measures of uncertainty exhibit the same
property. In Panel A, we assign firm-years to quintiles 1-5 based on the total level of implied
volatility prior to the earnings announcement. We find no obvious relation between the quintile
of pre-earnings uncertainty and abnormal R2. Instead, the two extreme quintiles show the lowest
abnormal R2 (6.4 and 7.3), while the remaining three quintiles share approximately the same
level of abnormal R2 (ranging from 10.5 to 11.3). A similar pattern holds in Panel B, where we
sort firm-year observations based on Average Uncertainty, the median implied volatility for 30day options without earnings announcements in their horizons. The extreme quintiles have the
lowest abnormal R2 values (8.2 and 6.5), while the three middle quintiles have comparable
values (11.0 to 11.5).
Panel C shows the results when we sort by analyst dispersion. Unlike the prior two
panels, there is a monotonic relation – firms with the lowest level of analyst dispersion
experience the greatest proportion of their annual return during quarterly earnings windows.
This result is the opposite of what we would expect if analyst dispersion captures fundamental
investor uncertainty, and is further evidence that it better captures the noise in reported earnings.
We interpret the monotonic relation in Panel C as evidence that returns are concentrated in
earnings announcements when firms issue earnings with less noise.
Finally Panel D presents our formal test of the differences in the abnormal adjusted R2
across quintiles for the different quintile rankings in Panels A, B and C. This test confirms that
there is not a linear relation between abnormal adjusted R2 and quintile ranking when quintiles
are formed on the basis of Pre-Earnings Uncertainty or Average Uncertainty. However, the
negative relation when quintiles are formed on the basis of Analyst Dispersion is statistically
significant. Our interpretation of this finding is consistent with evidence in Tables 3 and 4 that
24
Relative Pre-Earnings Uncertainty is greater when analyst dispersion is lower; investors
anticipate more uncertainty resolution when earnings have less noise.
5. Conclusion
This paper examines event-specific uncertainty in the context of earnings
announcements.
We use the well-known increase in pre-earnings implied option volatility
(Patell and Wolfson 1979, 1981) to measure that event-specific uncertainty in order to better
understand its determinants and, more importantly, its consequences for realized event-period
returns. We find that larger firms, firms with more stable earnings, and firms that tend to issue
forecasts with their earnings announcement are more likely to experience increased levels of
event-specific uncertainty. Firms that are covered by fewer analysts and have earnings that are
less correlated with market and industry earnings also tend to have larger event-specific
uncertainty.
In other words, event-specific uncertainty is greatest when investors have less
ability to infer earnings from alternative sources, and when the impending announcement is
likely to be effective in resolving earnings-related uncertainty.
We then look to the consequences of increased event-specific uncertainty. First, we show
that when a firm has greater event-specific uncertainty, investors respond more strongly per unit
of earnings surprise. This result does not hold for other measures of uncertainty, including
analyst dispersion, the pre-earnings level of implied volatility, or the median non-earnings level
of implied volatility. Our results indicate that investor response to new information is a function
of investor uncertainty about the factors likely to be discussed in the upcoming announcement,
rather than their total uncertainty about firm value.
25
Second, we show that when investors have greater earnings-specific uncertainty (relative
to their uncertainty during non-earnings periods), their annual returns are more concentrated in
their quarterly earnings announcement periods. This finding substantiates the Robichek and
Myers (1966a) argument that returns for holding uncertain positions should only be earned when
that uncertainty is resolved. Again, these results do not hold when we use alternative measures
of uncertainty, which indicates that the types of firms that investors are most uncertain about are
not the types of firms for which uncertainty is primarily resolved at earnings announcements.
26
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29
Table 1 – Earnings announcement sample, by year
Earnings
Announcements
4,613
5,948
6,521
7,165
6,466
5,875
5,623
5,490
6,370
7,021
7,523
7,827
7,477
7,173
7,753
7,923
7,989
8,630
6,615
130,002
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Total
Table 1 Notes:
This table shows the distribution of quarterly earnings announcements from 1996-2014.
Observations are retained for all earnings announcements with available pre-earnings market
value, financial statement information, and implied option volatility.
30
N
130,002
130,002
130,002
129,992
106,793
110,466
130,002
130,002
130,002
120,476
120,476
130,002
130,002
130,002
130,002
Mean
5,798.9
0.56
5.7
19.4%
0.018
0.043
0.49
0.45
1.36
-0.17%
0.57%
0.03%
0.34%
0.33%
6.10%
Median
1,535.9
0.42
4.0
0
0.010
0.019
0.44
0.41
1.16
0.00%
0.23%
0.04%
0.12%
0.21%
4.22%
Std. Dev.
13,161.2
0.70
4.8
0.3956954
0.024
0.075
0.23
0.21
0.84
1.03%
1.02%
0.62%
0.65%
8.29%
6.02%
25th Pctile
611.7
0.24
2.0
0
0.005
0.008
0.33
0.30
0.94
-0.31%
0.08%
-0.04%
0.04%
-3.88%
1.85%
75th Pctile
4,419.1
0.68
8.0
0
0.021
0.044
0.60
0.55
1.49
0.17%
0.59%
0.18%
0.33%
4.58%
8.30%
31
This table shows descriptive statistics for the firms/earnings announcements in our sample from 1996-2014. Market Value is the
firm’s market value of equity two trading days prior to the reported earnings announcement date (in millions). Book-to-Market is the
prior quarter’s shareholders’ equity divided by the market value of equity two trading days prior to the earnings announcement.
Analyst Following is the number of analysts issuing earnings forecasts for the current quarterly period. Loss in Prior Quarter is an
indicator variable equal to 1 if the firm’s income before extraordinary items was less than 0 in the prior quarter, and 0 otherwise.
Earnings Volatility is the standard deviation of the firm’s prior 12 quarters of income before extraordinary items (deflated by average
total assets). Analyst Dispersion is the standard deviation of analyst forecasts for the current quarter. Pre-Earnings Uncertainty is the
implied volatility from a 30-day option measured two trading days prior to the earnings announcement. Average Uncertainty is the
median value of the implied volatility from 30-day options based on closing prices between the last quarter’s earnings announcement
and this quarter’s earnings announcement. Relative Pre-Earnings Uncertainty is the ratio of Pre-Earnings Uncertainty to Average
Uncertainty, where both the numerator and the denominator are adjusted by the contemporaneous level of the VIX. Pre-Earnings
Market Value
Book-to-Market
Analyst Following
Loss in Prior Quarter
Earnings Volatility
Analyst Dispersion
Pre-Earnings Uncertainty
Average Uncertainty
Relative Pre-Earnings Uncertainty
Pre-Earnings Expectations Gap
|Pre-Earnings Expectations Gap|
Earnings Surprise
|Earnings Surprise|
3-Day Earnings Period Return
|3-Day Earnings Period Return|
Table 2 Notes
Variable
Table 2 – Descriptive statistics
All variables are winsorized at the 1% and 99% levels.
32
Expectations Gap is the difference between quarter t+1 earnings per share and analyst estimates for quarter t+1 earnings, deflated by
stock price and measured prior to the quarter t earnings announcement. Earnings Surprise is quarter t actual earnings per share minus
analyst estimates for quarter t earnings, deflated by stock price. 3-Day Earnings Period Return is the cumulative 3-day stock return
around the earnings announcement.
(2)
Pre-Earnings
Uncertainty
(1)
Average
Uncertainty
1.00
0.81***
-0.25***
-0.50***
0.16***
0.83***
-0.08***
0.16***
0.31***
0.32***
-0.07***
0.39***
-0.16***
-0.07***
0.35***
0.01
0.32***
(3)
Relative PreEarnings
Uncertainty
33
This table shows correlations between our three measures of uncertainty and the variables described in Table 2. Pre-Earnings
Uncertainty is the implied volatility from a 30-day option measured two trading days prior to the earnings announcement. Average
Uncertainty is the median value of the implied volatility from 30-day options based on closing prices between the last quarter’s
earnings announcement and this quarter’s earnings announcement. Relative Pre-Earnings Uncertainty is the natural logarithm of the
ratio of Pre-Earnings Uncertainty to Average Uncertainty, where both the numerator and the denominator are adjusted by the
contemporaneous level of the VIX. See Table 2 for the definitions of all other variables.
(1) Average Uncertainty
(2) Pre-Earnings Uncertainty
1.00
(3) Relative Pre-Earnings Uncertainty
0.05***
1.00
(4) Market Value
-0.46***
0.20***
(5) Book-to-Market
0.15***
-0.06***
(6) Lagged Volatility
0.80***
-0.11***
(7) Analyst Following
-0.08***
0.04***
(8) Analyst Dispersion
0.15***
-0.04***
(9) Loss in Prior Quarter
0.27***
-0.10***
(10) Earnings Volatility
0.29***
-0.09***
(11) Earnings Non-commonality
-0.05***
0.04***
(12) |Prior EA 3-day Return|
0.38***
-0.02***
(13) Prior EA Management Forecast
-0.11***
0.12***
(14) Current EA Earnings Surprise
-0.07***
0.00
(15) |Current EA Earnings Surprise|
0.33***
-0.08***
(16) Current EA 3-day Return
0.00
0.01***
(17) |Current EA 3-day Return|
0.39***
-0.00
Table 3 Notes
***, **, * indicates a correlation significantly different from 0 at the 1%, 5%, and 10% level, respectively.
Table 3 – Correlations with uncertainty measures
Table 4 – Characteristics associated with abnormal pre-earnings uncertainty
Dependent variable: log(Relative Pre-Earnings Uncertainty)
Independent Variable
Log(Market Value)
0.061 ***
(23.30)
Book-to-Market
0.001
(0.26)
Stock Return Volatility
-1.021 ***
(-5.13)
Analyst Following
-0.003 ***
(-5.82)
Analyst Dispersion
0.022
(0.65)
Loss in Prior Quarter
-0.037 ***
(-6.41)
Earnings Volatility
-0.572 ***
(-5.87)
Earnings Non-Commonality
0.011 ***
(6.98)
|Prior EA 3-day Return|
0.306 ***
(8.61)
|Prior Earnings Surprise|
-2.240 ***
(-7.27)
Forecast at Last EA
0.077 ***
(13.20)
N
R2
60,474
0.056
Table 4 Notes:
***, **, * indicates a correlation significantly different from 0 at the 1%, 5%, and 10% level,
respectively.
34
This table shows the results of an OLS regression where the dependent variable is the natural
logarithm of Relative Pre-Earnings Uncertainty, equal to the ratio of Pre-Earnings Uncertainty
to Average Uncertainty, where both the numerator and the denominator are adjusted by the
contemporaneous level of the VIX.
The independent variables are defined as follows:
Log(Market Value) is the natural logarithm of the firm’s market value two trading days prior to
the earnings announcement. Book-to-Market is the ratio of the prior quarter’s shareholders’
equity value divided by the market value of equity two measured two trading days prior to the
current earnings announcement. Stock Return Volatility is the standard deviation of daily logged
stock returns between the prior and current quarter’s earnings announcement. Analyst Following
is the number of analyst issuing an earnings forecast for the current quarterly period. Analyst
Dispersion is the standard deviation of analysts’ earnings estimates for the current quarterly
period. Loss in Prior Quarter is an indicator equal to 1 if the prior quarters’ earnings before
extraordinary items was negative, and 0 otherwise. Earnings Volatility is the standard deviation
of the firm’s prior 12 quarters of earnings deflated by average total assets. Earnings NonCommonality is based Brown and Kimbrough (2011) and starts with rolling regressions of 20
quarters of the firm’s quarterly ROA on both the market and industry-level ROA for the same
periods. Earnings Non-Commonality is the log of [unexplained variance (1-R2) divided by 1
minus unexplained variance]. |Prior EA 3-day Return| is the absolute value of the 3-day stock
return around the firm’s prior quarterly earnings announcement. |Prior Earnings Surprise| is the
absolute value of the prior quarter’s earnings surprise, deflated by pre-earnings stock price.
Forecast at Prior EA is an indicator variable equal to 1 if I/B/E/S records a forecast issued in the
3-day period around the prior quarter’s earnings announcement, and 0 otherwise.
All continuous variables are winsorized at the 1% and 99% levels. Standard errors are clustered
by firm.
35
(see notes following Panel B)
Levels of the 4 Variables Interacted with
earnings?
N
R2
Year-Quarter Fixed Effects
Earnings Surprise*Analyst Dispersion
Earnings Surprise*Book-to-Market
Earnings Surprise*Earnings Volatility
130,002
0.067
Yes
36
130,002
0.067
Yes
Dependent variable: 3-day stock return around quarterly earnings announcements
Independent Variable
(1)
(2)
Earnings Surprise
3.764 ***
3.784 ***
(36.29)
(36.41)
Negative Earnings Surprise
-1.557 ***
-1.587 ***
(-12.41)
(-12.61)
Earnings Surprise*Relative PreEarnings Uncertainty
0.594 ***
0.581 ***
(5.26)
(5.15)
Relative Pre-Earnings Uncertainty
0.002 ***
(5.46)
Earnings Surprise*Log(Market Value)
Table 5 – Relation between uncertainty and investor response to unexpected earnings
Panel A: Using announcement-specific uncertainty (Relative Pre-Earnings IV)
Included
91,312
0.084
Yes
-0.002
(-0.03)
-6.690 ***
(-2.62)
-0.421 ***
(-6.09)
-8.158 ***
(-18.52)
0.572 ***
(4.09)
(3)
5.926 ***
(13.93)
-1.987 ***
(-11.14)
Included
91,312
0.084
Yes
0.556
(3.97)
0.002
(4.63)
-0.002
(-0.03)
-6.716
(-2.63)
-0.419
(-6.06)
-8.156
(-18.51)
***
***
***
***
***
(4)
5.935 ***
(13.96)
-1.997 ***
(-11.19)
Table 5 – Relation between uncertainty and investor response to unexpected earnings
Panel B: Using alternative measures of uncertainty
Dependent variable: 3-day stock return around quarterly earnings announcements
Independent Variable
(1)
(2)
(3)
Earnings Surprise
5.895 ***
5.955 ***
5.860 ***
(14.88)
(15.11)
(13.74)
Negative Earnings
Surprise
Earnings Surprise* PreEarnings Uncertainty
Pre-Earnings Uncertainty
-1.833 ***
(-12.09)
-1.916 ***
(-12.72)
-0.172
(-1.07)
0.003 ***
(3.60)
Earnings Surprise *
Average Uncertainty
-0.618 ***
(-3.84)
Average Uncertainty
-0.003 ***
(-3.42)
Earnings
Surprise*Analyst
Dispersion
-8.146 ***
(-18.48)
Analyst Dispersion
N
R2
Year-Quarter Fixed
Effects
-1.957 ***
(-10.93)
-0.051 ***
(-10.99)
106,793
0.074
Yes
106,793
0.075
Yes
91,312
0.083
Yes
Table 5 Notes:
***, **, * indicates coefficients statistically different from 0 at the 1%, 5%, and 10% levels,
respectively.
37
This table shows the results of OLS regressions with the same dependent variable: 3-day
(signed) stock returns surrounding firms’ quarterly earnings announcements. Earnings Surprise
is the difference between reported earnings per share (from I/B/E/S) and the mean of all analyst
estimates subsequent to the prior earnings announcement, deflated by the pre-announcement
stock price. Negative Earnings Surprise is equal to Earnings Surprise if Earnings Surprise is
negative, and 0 otherwise. Relative Pre-Earnings Uncertainty is the natural logarithm of the
ratio of Pre-Earnings Uncertainty (the implied volatility of a 30-day option two trading days
prior to the earnings announcement) to Average Uncertainty (the median implied volatility from
30-day options between earnings announcement periods), where both the numerator and the
denominator are adjusted by the contemporaneous level of the VIX.
The regressions shown in Panel B also include the Market Value, Book-to-Market, and Earnings
Volatility variables (both levels and interactions with the earnings surprise) from Panel A as
dependent variables, but those coefficient estimates are not presented.
All continuous variables are winsorized at the 1% and 99% levels. Standard errors are clustered
by firm.
38
0.236
0.173
0.135
0.102
0.079
1 (low)
2
3
4
5 (high)
1.340
1.364
1.245
1.356
1.096
1st Quarter
0.953
1.168
1.393
1.264
1.464
2nd Quarter
1.050
1.251
1.170
1.370
1.346
3rd Quarter
0.970
0.873
0.913
0.983
1.040
4th Quarter
90
0.139
N
R2
Table 6 Notes:
This table shows estimates from an annual regression of the form:
4.16 **
(2.13)
39
2.219 ***
(3.77)
Constant
Independent Variable
Quintile of Relative Pre-Earnings Uncertainty
Panel B: Regression of Ball and Shivakumar (2008) R2 on quintile of Relative Pre-Earnings Uncertainty
Intercept
Relative PreEarnings
Uncertainty
Quintile
Panel A: Quintiles of Relative Pre-Earnings Uncertainty
5.6
8.9
11.6
13.5
14.4
Abnormal R2
Table 6 – Relation between announcement-specific uncertainty and the informativeness of quarterly earnings announcements
40
Panel B shows the results from an OLS regression of abnormal adjusted R2 on the quintile of Relative Pre-Earnings Uncertainty.
where annual is firm i’s calendar year stock return and window1, window2, window3, and window4 are the 3-day stock returns around
firm i’s four quarterly earnings announcements during the same calendar year. Regressions are performed by year and quintile of
Relative Pre-Earnings Uncertainty, with the coefficients (averaged by quintile over all years) presented in Panel A. The right-most
column of Panel A shows the average abnormal adjusted R2 value from the annual regressions, where abnormal adjusted R2 is
calculated each year (and within each quintile) as the adjusted R2 from the regression minus its expectation assuming i.i.d. daily
returns.
Ri(annual) = α0 + α1Ri(window1) + α2Ri(window2)+ α3Ri(window3) + α4Ri(window4) + εi
0.133
0.136
0.144
0.161
0.199
1 (low)
2
3
4
5 (high)
Intercept
0.122
0.128
0.141
0.162
0.194
Average
Uncertainty
Quintile
1 (low)
2
3
4
5 (high)
1.370
1.202
1.090
1.143
1.030
1st Quarter
1.414
1.172
1.116
1.143
0.921
1st Quarter
Panel B: Quintiles of Average Uncertainty
Intercept
Pre-Earnings
Uncertainty
Quintile
Panel A: Quintiles of Pre-Earnings Uncertainty
41
1.167
1.268
1.186
1.014
0.738
2nd Quarter
1.257
1.261
1.158
0.935
0.757
2nd Quarter
1.209
1.343
1.062
1.095
0.994
3rd Quarter
1.435
1.275
1.044
1.111
0.967
3rd Quarter
1.024
0.985
1.012
0.946
0.798
4th Quarter
1.088
1.021
0.922
1.025
0.862
4th Quarter
6.5
11.0
11.5
11.3
8.2
Abnormal R2
7.3
10.5
10.5
11.3
6.4
Abnormal R2
Table 7 – Relation between alternative measures of uncertainty and the informativeness of quarterly earnings announcements
0.219
0.166
0.135
0.110
0.083
1 (low)
2
3
4
5 (high)
1.282
1.033
1.344
1.162
1.466
1st Quarter
1.205
1.031
1.302
1.330
1.386
2nd Quarter
1.144
1.205
1.130
1.167
1.305
3rd Quarter
0.832
1.021
1.082
1.045
1.182
4th Quarter
90.000
0.000
N
r2
Table 7 Notes:
8.887 ***
(5.20)
Constant
Independent Variable
Uncertainty Quintile
42
90.000
0.001
10.133 ***
(5.64)
Uncertainty quintiles formed based on:
Pre-Earnings
Average
Uncertainty
Uncertainty
0.102
-0.190
(0.20)
(-0.35)
90.000
0.046
12.758 ***
(7.21)
7.6
8.1
9.5
10.0
12.2
Abnormal R2
Analyst
Dispersion
-1.098 **
(-2.06)
Panel D: Regression of Ball and Shivakumar (2008) R2 on Quintile of Alternative Uncertainty Measures
Intercept
Analyst Dispersion
Quintile
Panel C: Quintiles of Analyst Dispersion
Table 7 (continued) – Relation between alternative measures of uncertainty and the informativeness of quarterly earnings
announcements
43
Panel D shows the results from separate OLS regressions of abnormal adjusted R2 on the quintile of each uncertainty measure for the
three panels using the three different uncertainty measures as the sorting variable.
where annual is firm i’s calendar year stock return and window1, window2, window3, and window4 are the 3-day stock returns around
firm i’s four quarterly earnings announcements during the same calendar year. Regressions are performed by year and quintile of
uncertainty measures, where uncertainty measures are Pre-Earnings Uncertainty (Panel A), Average Uncertainty (Panel B), and
Analyst Dispersion (Panel C). The coefficients (averaged by quintile over all years) are presented in Panels A, B, and C. The rightmost column of each panel shows the average abnormal adjusted R2 value from the annual regressions, where abnormal adjusted R2 is
calculated each year (and within each quintile) as the adjusted R2 from the regression minus its expectation assuming i.i.d. daily
returns.
Ri(annual) = α0 + α1Ri(window1) + α2Ri(window2)+ α3Ri(window3) + α4Ri(window4) + εi
This table shows estimates from an annual regression of the form: